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+All:Schedule
+============
+
+
+
+
+
+
+Current Schedules
+-----------------
+
+
+
+
+|  |  |  |  |  |  |  |
+| --- | --- | --- | --- | --- | --- | --- |
+| BSc (Full The full schedule is available: [at the link](https://docs.google.com/spreadsheets/d/1wJtbTxo-ZPmBIt27BKQizwxtVM4_1sKA9vDyxGBAq-w/edit#gid=398810915))
+ | [BS1](https://docs.google.com/spreadsheets/d/1wJtbTxo-ZPmBIt27BKQizwxtVM4_1sKA9vDyxGBAq-w/edit#gid=833790814) | [BS2](https://docs.google.com/spreadsheets/d/1wJtbTxo-ZPmBIt27BKQizwxtVM4_1sKA9vDyxGBAq-w/edit#gid=853942015) | [BS2 block 1](https://docs.google.com/spreadsheets/d/1wJtbTxo-ZPmBIt27BKQizwxtVM4_1sKA9vDyxGBAq-w/edit#gid=853942015) | [BS3 part 1](https://docs.google.com/spreadsheets/d/1wJtbTxo-ZPmBIt27BKQizwxtVM4_1sKA9vDyxGBAq-w/edit#gid=1309470909) | [BS3 part 2](https://docs.google.com/spreadsheets/d/1wJtbTxo-ZPmBIt27BKQizwxtVM4_1sKA9vDyxGBAq-w/edit#gid=50260034) | [BS4 part 1](https://docs.google.com/spreadsheets/d/1wJtbTxo-ZPmBIt27BKQizwxtVM4_1sKA9vDyxGBAq-w/edit#gid=1003503927) |
+| MSc
+ | [MS1&MS2 Part 1](https://docs.google.com/spreadsheets/d/1wJtbTxo-ZPmBIt27BKQizwxtVM4_1sKA9vDyxGBAq-w/edit#gid=734382502) | [MS1&MS2 Part 2](https://docs.google.com/spreadsheets/d/1wJtbTxo-ZPmBIt27BKQizwxtVM4_1sKA9vDyxGBAq-w/edit#gid=962774196) |
+| PhD
+ | [PhD](https://docs.google.com/spreadsheets/d/1lMFQzarNJyoX6jU8PT1-qGHO_qUM2BRBgkucQ1ZQq6U/edit?usp=sharing) |
+
+
+
+|  |  |  |
+| --- | --- | --- |
+| Electives
+ | [BS Tech](https://docs.google.com/spreadsheets/d/1bm0TudJCdISN05ZlmZrGa3hHolGdCgHc/edit#gid=2046289412) | [MS Hum & Tech](https://docs.google.com/spreadsheets/d/1bm0TudJCdISN05ZlmZrGa3hHolGdCgHc/edit#gid=1002832296) |
+| [BS Hum](https://docs.google.com/spreadsheets/d/1bm0TudJCdISN05ZlmZrGa3hHolGdCgHc/edit#gid=995125866) |
+
+
+
+
+
+
+
+
+
+

raw/raw_all_studyplan.md

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+
+
+
+ALL:StudyPlan
+=============
+
+
+
+
+
+
+Current Study Plans
+-------------------
+
+
+
+
+|  |  |
+| --- | --- |
+| Year
+ | Computer science
+ |
+| 2019-2023
+ | [BS4](https://docs.google.com/spreadsheets/d/1dBNs2wYwQdlpgxnQf3QqNM61IHWIFmt_/edit#gid=76894847) |
+| 2020-2024
+ | [BS4](https://docs.google.com/spreadsheets/d/1VuTSzvSEmxads4dtPqiYODO-vcBpxcFt/edit?usp=drive_link&ouid=112969423608769094940&rtpof=true&sd=true) |
+| 2021-2025
+ | [BS3](https://docs.google.com/spreadsheets/d/1Ow5WO2oxikJunim6ygiWAW6Z0BmX4oXr/edit?usp=drive_link&ouid=112969423608769094940&rtpof=true&sd=true) |
+| 2022-2026 DSAI
+ | [BS2](https://docs.google.com/spreadsheets/d/1fsc_bBRn-33MUClli14QcV048Dx2iOI3/edit?usp=drive_link&ouid=112969423608769094940&rtpof=true&sd=true) |
+| 2022-2026 ИИиВТ
+ | [BS2](https://docs.google.com/spreadsheets/d/1gzmcHTg-9i2NxKxAEBoV8V9jjLhHfVLL/edit?usp=drive_link&ouid=112969423608769094940&rtpof=true&sd=true) |
+| 2023-2027 DSAI
+ | [BS1](https://docs.google.com/spreadsheets/d/1J1jKZv7z1PMMJGDPkz71ow-L9Y-Rbs6M/edit?usp=drive_link&ouid=112969423608769094940&rtpof=true&sd=true) |
+| 2023-2027 CS
+ | [BS1](https://docs.google.com/spreadsheets/d/1fjE74URIBwza_-uWHDkusd1p96rjQUAd/edit?usp=drive_link&ouid=112969423608769094940&rtpof=true&sd=true) |
+
+
+
+|  |  |  |  |  |  |  |
+| --- | --- | --- | --- | --- | --- | --- |
+| Year
+ | DAAI
+ | ROCV
+ | SE
+ | SNE
+ | ITE
+ | AIDE
+ |
+| 2021-2023
+ | [MS2](https://docs.google.com/spreadsheets/d/1ylz5-21u9P2MVFb2VuNulsb2z-C3Lq9m/edit?rtpof=true) | [MS2](https://docs.google.com/spreadsheets/d/1i3GZRMwL5-_1AbbMJouDNztOeWoKpqkm/edit?rtpof=true) | [MS2](https://docs.google.com/spreadsheets/d/1vS3-qyO2VL8Q160x7Uysvc9idm5ltfoA/edit#gid=197434888) | [MS2](https://docs.google.com/spreadsheets/d/1hXgfNcwBhfjH8k1eTl5lygw_jD3XuTJu/edit#gid=1371183148) | []
+ |
+| 2022-2024
+ | [MS1](https://docs.google.com/spreadsheets/d/1slACHKr_Itg7imj31ZNYliCxaW1F-w1m/edit?usp=drive_link&ouid=117501431082377618383&rtpof=true&sd=true) | [MS1](https://docs.google.com/spreadsheets/d/10s0blbgnsTi94wLnl-Olmew44QD0K7-d/edit?usp=drive_link&ouid=117501431082377618383&rtpof=true&sd=true) | [MS1 SE](https://docs.google.com/spreadsheets/d/1LYBgL2eDBBCr3qkxg7-eRj7EnIukcHgx/edit?usp=drive_link&ouid=117501431082377618383&rtpof=true&sd=true) | [MS1 SNE](https://docs.google.com/spreadsheets/d/1gkg8xXpwxJY40EIEWePjGaL__5UYILNE/edit?usp=drive_link&ouid=117501431082377618383&rtpof=true&sd=true) | [MS1 ITE](https://docs.google.com/spreadsheets/d/17oNfIyZVTckSoXr4ZJ3oJ2jf6Yg3qOun/edit?usp=drive_link&ouid=117501431082377618383&rtpof=true&sd=true) | []
+ |
+| 2023-2025
+ |  | [MS1](https://docs.google.com/spreadsheets/d/1nniLTeyHQYcfD_ReCAQhGsz7UUAtBVBh/edit?usp=drive_link&ouid=117501431082377618383&rtpof=true&sd=true) | [MS1 SE](https://docs.google.com/spreadsheets/d/1jgcyiwApgvU5pJz2vTfilY8QyrP7819j/edit?usp=drive_link&ouid=117501431082377618383&rtpof=true&sd=true) | [MS1 SNE](https://docs.google.com/spreadsheets/d/1w5afVZgLbUQIBJWWFGTxO8ek0Mx8JD2g/edit?usp=drive_link&ouid=117501431082377618383&rtpof=true&sd=true) | [MS1 ITE](https://docs.google.com/spreadsheets/d/1KxyO41EYAblMttYCnA7KqY8XFQMoXhmr/edit?usp=drive_link&ouid=117501431082377618383&rtpof=true&sd=true) | [MS1 AIDE](https://docs.google.com/spreadsheets/d/1joX3k-cnQIN6akcqfbb0CmQgGGO2vuno/edit?usp=drive_link&ouid=117501431082377618383&rtpof=true&sd=true) |
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc_.md

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+
+
+
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+BSc:
+====
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Secure Systems Development](#Secure_Systems_Development)
+	+ [1.1 Course Characteristics](#Course_Characteristics)
+		- [1.1.1 Key concepts of the class](#Key_concepts_of_the_class)
+		- [1.1.2 What is the purpose of this course?](#What_is_the_purpose_of_this_course.3F)
+		- [1.1.3 Course objectives based on Bloom’s taxonomy](#Course_objectives_based_on_Bloom.E2.80.99s_taxonomy)
+		- [1.1.4 - What should a student remember at the end of the course?](#-_What_should_a_student_remember_at_the_end_of_the_course.3F)
+		- [1.1.5 - What should a student be able to understand at the end of the course?](#-_What_should_a_student_be_able_to_understand_at_the_end_of_the_course.3F)
+		- [1.1.6 - What should a student be able to apply at the end of the course?](#-_What_should_a_student_be_able_to_apply_at_the_end_of_the_course.3F)
+		- [1.1.7 Course evaluation](#Course_evaluation)
+		- [1.1.8 Grades range](#Grades_range)
+		- [1.1.9 Resources and reference material](#Resources_and_reference_material)
+	+ [1.2 Course Sections](#Course_Sections)
+		- [1.2.1 Section 1](#Section_1)
+			* [1.2.1.1 Section title:](#Section_title:)
+		- [1.2.2 Topics covered in this section:](#Topics_covered_in_this_section:)
+		- [1.2.3 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F)
+		- [1.2.4 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section)
+		- [1.2.5 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section)
+		- [1.2.6 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section)
+		- [1.2.7 Section 2](#Section_2)
+			* [1.2.7.1 Section title:](#Section_title:_2)
+		- [1.2.8 Topics covered in this section:](#Topics_covered_in_this_section:_2)
+		- [1.2.9 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_2)
+		- [1.2.10 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_2)
+		- [1.2.11 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_2)
+		- [1.2.12 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_2)
+		- [1.2.13 Section 3](#Section_3)
+			* [1.2.13.1 Section title:](#Section_title:_3)
+			* [1.2.13.2 Topics covered in this section:](#Topics_covered_in_this_section:_3)
+		- [1.2.14 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_3)
+		- [1.2.15 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_3)
+			* [1.2.15.1 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_3)
+			* [1.2.15.2 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_3)
+		- [1.2.16 Section 4](#Section_4)
+			* [1.2.16.1 Section title:](#Section_title:_4)
+			* [1.2.16.2 Topics covered in this section:](#Topics_covered_in_this_section:_4)
+		- [1.2.17 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_4)
+		- [1.2.18 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_4)
+			* [1.2.18.1 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_4)
+			* [1.2.18.2 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_4)
+
+
+
+Secure Systems Development
+==========================
+
+
+* **Course name:** Secure Systems Development
+* **Course number:** xyz
+
+
+Course Characteristics
+----------------------
+
+
+### Key concepts of the class
+
+
+* Identification of security risk, system requirements, and processes
+* Design and development of secure systems
+* Principles of secure programming
+* Secure software development
+* Security assurance and evaluation
+* Vulnerability and system security analysis
+
+
+### What is the purpose of this course?
+
+
+After the fundamentals of computer security are taught to the students, it is essential for cybersecurity students to understand the principles of secure systems development. In a broader term, secure systems development include security aspects in software development, secure programming, threat intelligence, security requirements, risks, and vulnerability analysis. Therefore, this course is aimed at equipping the students with required skills to design and develop secure systems and exercise secure programming practices during development. In essence, this course is at the crossroads of the software engineering and cybersecurity and complements both the fields.
+
+
+
+### Course objectives based on Bloom’s taxonomy
+
+
+### - What should a student remember at the end of the course?
+
+
+By the end of the course, the students should be able to remember the followings:
+
+
+
+* How to identify security risk
+* How to exercise secure design and coding
+* Understand and demonstrate the steps involved in secure software development
+* Perform vulnerability analysis
+* Manage and implement security assurance
+
+
+### - What should a student be able to understand at the end of the course?
+
+
+By the end of the course, the students should be able to understand the design and basic principles of secure systems development. Furthermore, the student will be able to:
+
+
+
+* Understand how to identify security risk
+* Demonstrate how to exercise secure design and coding
+* Understand and demonstrate the steps involved in secure software development
+* Perform vulnerability analysis
+* Manage and implement security assurance
+* Identify the research and development challenges for a security project and propose/develop relevant solutions
+* Use existing frameworks for analysing network traffic, identifying adversaries, and deploy attacks
+* Include security, cryptography and access control elements in mobile and web-based applications
+
+
+### - What should a student be able to apply at the end of the course?
+
+
+By the end of the course, the students should be able to develop, manage and implement different secure system development techniques that will include:
+
+
+
+* Secure software development life-cycle
+* Secure coding
+* Security and vulnerability analysis and testing
+* Risk assessment and management
+* Assess the existing products for security and risk
+* Develop and design secure systems including software
+
+
+### Course evaluation
+
+
+
+
+Course grade breakdown
+|  |  | **Proposed points** |
+| --- | --- | --- |
+| Labs/seminar classes
+ | 20
+ | 35
+ |
+| Interim performance assessment
+ | 30
+ | 35
+ |
+| Exams
+ | 50
+ | 30
+ |
+
+
+### Grades range
+
+
+
+
+Course grading range
+|  |  | **Proposed range** |
+| --- | --- | --- |
+| A. Excellent
+ | 90-100
+ | 90-100
+ |
+| B. Good
+ | 75-89
+ | 75-89
+ |
+| C. Satisfactory
+ | 60-74
+ | 60-74
+ |
+| D. Poor
+ | 0-59
+ | 0-59
+ |
+
+
+### Resources and reference material
+
+
+Since the course is multi-dimensional, therefore, there is no single source that will cover all the topics. For reference, the following sources (and their updated versions) might be considered.
+
+
+
+* Bishop, M. (2018). Computer Security: Art and Science. Addison-Wesley Professional
+* Secure Coding in C and C++, Robert C. Seacord, Addition-wesley
+* Software Security - Building Security In, Gary McGraw, Addition-Wesley Software Security Series
+* Secure Systems Development with UML – Jan Jurjens
+
+
+Course Sections
+---------------
+
+
+The main sections of the course and approximate hour distribution between them is as follows:
+
+
+
+
+
+Course Sections
+| **Section** | **Section Title** | **Teaching Hours** |
+| --- | --- | --- |
+| 1
+ | Security assessment and Vulnerability analysis
+ | 16
+ |
+| 2
+ | Software Security and secure coding
+ | 16
+ |
+| 3
+ | Secure software development techniques and frameworks
+ | 16
+ |
+| 4
+ | Best practices in secure systems development
+ | 16
+ |
+
+
+### Section 1
+
+
+#### Section title:
+
+
+Security assessment and Vulnerability analysis
+
+
+
+### Topics covered in this section:
+
+
+* Security requirements and rationale
+* Security assessment
+* Penetration testing
+* Vulnerability analysis
+* Tools and methods
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+|a|c| & **Yes/No**  
+
+Development of individual parts of software product code & 1  
+
+Homework and group projects & 1  
+
+Midterm evaluation & 1  
+
+Testing (written or computer based) & 1  
+
+Reports & 0  
+
+Essays & 0  
+
+Oral polls & 0  
+
+Discussions & 1  
+
+
+
+  
+
+
+
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. How to perform security assessment and which method is used in a particular environment?
+2. Why security assessment is essential?
+3. What is the role of penetration testing in security assessment and what methods are currently used in the industry?
+4. What is the difference between vulnerability and exploit and how a vulnerability can be converted into an exploit?
+5. What are the pros and cons of the existing security assessment tools?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Perform security assessment of an example application and/or service.
+2. Use a particular penetration testing method to find vulnerability in an application.
+3. Select at least 3 existing industry-grade tools and perform vulnerability assessment of an example application.
+4. After using particular tools and methods, document their pros and cons.
+
+
+### Test questions for final assessment in this section
+
+
+1. How to perform port scanning and when it is dangerous to do that?
+2. Choose any of the security assessment method to use and justify your choice.
+3. Can we skip the vulnerability assessment? Yes or No? Justify your answer in detail. What would be the downside of either skipping or not skipping it?
+4. How would you covert a vulnerability to an exploit and what are the essential methods to contain an exploit?
+5. What are the drawbacks of the existing security assessment tools?
+
+
+### Section 2
+
+
+#### Section title:
+
+
+Software Security and secure coding
+
+
+
+### Topics covered in this section:
+
+
+* Software security
+* Security in software development life-cycle
+* Software security requirements and testing
+* Secure programming
+* Best practices in secure coding
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+|a|c| & **Yes/No**  
+
+Development of individual parts of software product code & 1  
+
+Homework and group projects & 1  
+
+Midterm evaluation & 1  
+
+Testing (written or computer based) & 1  
+
+Reports & 0  
+
+Essays & 0  
+
+Oral polls & 0  
+
+Discussions & 1  
+
+
+
+  
+
+
+
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. At which step of software development, security must be considered?
+2. What are the principle of software security?
+3. What frameworks are proven to be the best for software security and why?
+4. What are the principles of secure coding?
+5. Explain the pitfalls of secure programming?
+6. How the requirements gathering for software can affect software security?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Given the scenario, document the requirements (both traditional and security)?
+2. Explain a scenario where the software development will pose a security risk?
+3. Demonstrate non-standard practices in software development that will lead to security issues?
+4. What assessment techniques can be used to detect software security issues in earlier stages of the software development?
+5. What are the best practices in software development from a security perspective?
+
+
+### Test questions for final assessment in this section
+
+
+1. same as above.
+
+
+### Section 3
+
+
+#### Section title:
+
+
+Secure software development techniques and frameworks
+
+
+
+#### Topics covered in this section:
+
+
+* Software security development frameworks
+* System security development frameworks
+* Security development and design techniques
+* Integration of security solutions
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+|a|c| & **Yes/No**  
+
+Development of individual parts of software product code & 1  
+
+Homework and group projects & 1  
+
+Midterm evaluation & 1  
+
+Testing (written or computer based) & 1  
+
+Reports & 0  
+
+Essays & 0  
+
+Oral polls & 0  
+
+Discussions & 1  
+
+
+
+  
+
+
+
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. Explain the existing software security and development frameworks?
+2. Given a software development scenario, how to select a particular framework?
+3. Does software development method affect the software security? Justify your answer.
+4. At which stage of a particular software development method, security is considered?
+5. Describe the rationale for security at every step of software development process?
+6. What is the difference between software and system security?
+7. Can software security techniques be used in system security? Justify your answer.
+
+
+#### Typical questions for seminar classes (labs) within this section
+
+
+1. Through secure programming and security frameworks of software, demonstrate the software resilience.
+2. Demonstrate the software security (with respect to requirements) at each step of the development process?
+3. What are the vulnerabilities and attacks associated with insecure programming practices? Demonstrate.
+4. Demonstrate if different programming paradigms have any effect on the software security?
+5. Through a proof-of-concept, demonstrate the difference between software and system security.
+
+
+#### Test questions for final assessment in this section
+
+
+1. same as above.
+
+
+### Section 4
+
+
+#### Section title:
+
+
+Best practices in secure systems development
+
+
+
+#### Topics covered in this section:
+
+
+* Industrial view on the systems security
+* Usage of best practices in software and system security
+* Secure development standards
+* Role of emerging technologies in secure systems development
+* Ongoing secure system development standardization activities
+* Existing projects considering secure system development
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+|a|c| & **Yes/No**  
+
+Development of individual parts of software product code & 1  
+
+Homework and group projects & 1  
+
+Midterm evaluation & 1  
+
+Testing (written or computer based) & 1  
+
+Reports & 0  
+
+Essays & 0  
+
+Oral polls & 0  
+
+Discussions & 1  
+
+
+
+  
+
+
+
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. What are the best practices in the industry for secure system development?
+2. What are the current issues with the best practices in the industry and what are their limitations?
+3. Cross-platform system development might affect the security of the system. Do you agree or not?
+4. Briefly explain the standardization efforts in the industry and academia regarding the secure system development?
+5. Can we apply the best practices of secure software development in secure system development? Justify your answer.
+
+
+#### Typical questions for seminar classes (labs) within this section
+
+
+1. Demonstrate the effectiveness of secure system development best practices.
+2. Demonstrate the analysis of using different development platforms on the secure system and software development.
+3. What is the role of traditional security mechanisms such as cryptography on the secure system development?
+4. With toy examples, demonstrate the attacker perspective and behavior on the (in)secure system development.
+5. Analyze the security of a given system by choosing any of the secure development framework?
+
+
+#### Test questions for final assessment in this section
+
+
+1. same as above.
+
+
+
+
+
+
+
+
+
+

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+
+
+
+
+
+
+
+BSc: Academic Research and Writing Culture
+==========================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Academic Writing and Research Culture I (AWRC I)](#Academic_Writing_and_Research_Culture_I_.28AWRC_I.29)
+	+ [1.1 Course Characteristics](#Course_Characteristics)
+		- [1.1.1 What subject area does your course (discipline) belong to?](#What_subject_area_does_your_course_.28discipline.29_belong_to.3F)
+		- [1.1.2 Key concepts of the class](#Key_concepts_of_the_class)
+		- [1.1.3 What is the purpose of this course?](#What_is_the_purpose_of_this_course.3F)
+	+ [1.2 Course Objectives Based on Bloom’s Taxonomy](#Course_Objectives_Based_on_Bloom.E2.80.99s_Taxonomy)
+		- [1.2.1 What should a student remember at the end of the course?](#What_should_a_student_remember_at_the_end_of_the_course.3F)
+		- [1.2.2 What should a student be able to understand at the end of the course?](#What_should_a_student_be_able_to_understand_at_the_end_of_the_course.3F)
+		- [1.2.3 What should a student be able to apply at the end of the course?](#What_should_a_student_be_able_to_apply_at_the_end_of_the_course.3F)
+		- [1.2.4 Course evaluation](#Course_evaluation)
+		- [1.2.5 Resources and reference material](#Resources_and_reference_material)
+			* [1.2.5.1 Textbook(s)](#Textbook.28s.29)
+			* [1.2.5.2 Reference Materials](#Reference_Materials)
+			* [1.2.5.3 Computer Resources](#Computer_Resources)
+			* [1.2.5.4 Laboratory Exercises](#Laboratory_Exercises)
+			* [1.2.5.5 Laboratory Resources](#Laboratory_Resources)
+		- [1.2.6 Late Submission Policy](#Late_Submission_Policy)
+		- [1.2.7 Cooperation Policy and Quotations](#Cooperation_Policy_and_Quotations)
+		- [1.2.8 Written assignments (Literature Review and Related Works chapter; Structured Abstract)](#Written_assignments_.28Literature_Review_and_Related_Works_chapter.3B_Structured_Abstract.29)
+		- [1.2.9 Course Sections](#Course_Sections)
+			* [1.2.9.1 Section 1](#Section_1)
+			* [1.2.9.2 Section 2](#Section_2)
+			* [1.2.9.3 Section 3](#Section_3)
+
+
+
+Academic Writing and Research Culture I (AWRC I)
+================================================
+
+
+* **Course name:** Academic Writing and Research Culture I
+* **Course number:** N/A
+* **Subject area:**
+
+
+Course Characteristics
+----------------------
+
+
+### What subject area does your course (discipline) belong to?
+
+
+### Key concepts of the class
+
+
+### What is the purpose of this course?
+
+
+Course Objectives Based on Bloom’s Taxonomy
+-------------------------------------------
+
+
+### What should a student remember at the end of the course?
+
+
+By the end of the course, the students should be able to remember and recognize
+
+
+• the key features of research papers and theses as genres of academic writing;
+
+
+• the key features of a good research question;
+
+
+• how to search related literature and how to write up literature review;
+
+
+• how to structure a research paper or a thesis;
+
+
+• how to organize their own writing process;
+
+
+• how to write effective sentences, paragraphs and arguments for research papers and theses.
+
+
+
+### What should a student be able to understand at the end of the course?
+
+
+### What should a student be able to apply at the end of the course?
+
+
+By the end of the course, the students should be able to
+
+
+
+### Course evaluation
+
+
+
+
+
+Course grade breakdown
+| **Task** | **Weight (%)** | **Task Details** |
+| --- | --- | --- |
+| Home assignments
+ | 30
+ | Weekly revision and practice tasks
+ |
+| Assignment (1)
+ | 50
+ | Literature Review and Related Works, thesis chapter draft submission
+ |
+| Assignment (2)
+ | 20
+ | Structured Abstract, submission
+ |
+| Total
+ | 100
+ |  |
+
+
+### Resources and reference material
+
+
+#### Textbook(s)
+
+
+There is no single text book which covers the course content. Some useful resources for this course are:
+
+
+1. Day, R. & Gastel, B., 2011, How to Write and Publish a Scientific Paper, Greenwood, Oxford.
+
+
+2. Zobel, J., 2014, Writing for Computer Science, Springer.
+
+
+3. Hofmann, A.H., 2014, Scientific Writing and Communication: Papers, Proposals and Presentations, Second edition, OUP.
+
+
+4. Glasman-Deal, H., 2010, Science Research Writing for Non-native Speakers of English, Imperial College Press.
+
+
+5. Bolkner, J., 1998, Writing Your Dissertation in Fifteen Minutes a Day, Henry Holt and Company.
+
+
+6. Wallwork, A., English for Academic Research: Writing Exercises, Springer.
+
+
+7. Wallwork, A., English for Academic Research: Grammar Exercises, Springer.
+
+
+8. Wallwork, A., English for Academic Research: Vocabulary Exercises, Springer.
+
+
+9. Wallwork, A., English for Academic Research: Grammar, Usage and Style, Springer.
+
+
+
+#### Reference Materials
+
+
+1. Elsevier Researcher Academy <https://researcheracademy.elsevier.com>
+
+
+2. IEEE Editorial Style Manual <https://journals.ieeeauthorcenter.ieee.org/your-role-in-articleproduction/ieee-editorial-style-manual/>
+
+
+3. Purdue University Online Writing Lab <https://owl.purdue.edu/owl/purdue_owl.html>
+
+
+4. Mark Davies’ text analysis tool based on Corpus of Contemporary American English (COCA)
+<https://www.wordandphrase.info>
+
+
+5. Texts analysis tool <https://writefull.com/researchers.html>
+
+
+6. Manchester University phrase bank <http://www.phrasebank.manchester.ac.uk/introducing-work/>
+
+
+7. Scopus Content Coverage Guide <https://www.elsevier.com/?a=69451>
+
+
+8. Google Scholar, top publication venues
+<https://scholar.google.com/citations?view_op=top_venues&hl=en>
+
+
+9. Some search tools: <https://www.sciencedirect.com>; <https://figshare.com>;
+<https://www.dimensions.ai/products/free/>
+
+
+10. Cambridge Dictionary Online <https://dictionary.cambridge.org>
+
+
+11. Previous years Innopolis University students’ theses <https://e.lanbook.com/vkrs?publisher=42>
+
+
+
+#### Computer Resources
+
+
+Students should have laptops with a word processor, camera, microphone and presentation software and wireless internet access. Each student needs access to the LMS.
+
+
+
+#### Laboratory Exercises
+
+
+Students are expected to be engaged in writing and texts revising 
+activities.
+
+
+
+#### Laboratory Resources
+
+
+Internet access, including access to Zoom and IU Moodle. 
+
+
+
+### Late Submission Policy
+
+
+The late submission policy will be strictly applied in this course. If a personal emergency should arise that affects your ability to turn in an assignment in a timely fashion, you must contact the course instructor BEFORE the deadline to get a “Special Late Submission Approval” from the course instructor. Without the “Special Late Submission Approval”, the submissions will be still accepted up to 48 hours late, but with a 50% penalty. No “Special Late Submission Approval” will be granted after the deadline.
+
+
+
+### Cooperation Policy and Quotations
+
+
+We encourage vigorous discussion and cooperation in this class. You should feel free to discuss any aspects of the class with any classmates. However, we insist that any written material that is not specifically designated as a Team Deliverable to be done by you alone. This includes answers to reading questions, individual reports associated with assignments, and labs. We also insist that if you include verbatim text from any source, you clearly indicate it using standard conventions of quotation or indentation and a note to indicate the source.
+
+
+
+### Written assignments (Literature Review and Related Works chapter; Structured Abstract)
+
+
+
+
+
+| **Band** | **Task fulfilment and content (30%)** | **Organization, cohesion and balance (20%)** | **Grammar and vocabulary (20%)** | **Communication and clarity (20%)** | **Style and register (10%)** |
+| --- | --- | --- | --- | --- | --- |
+| A
+ | Has responded to the task fully, using a wide range of ideas and developing them at least in part. Has concluded logically.
+ | Sophisticated progression of ideas. Purpose of each paragraph clear. Good cohesion within paragraphs. Good balance of ideas.
+ | Uses a wide range of language with some quite complex structures, if appropriate, and a wide range of appropriate vocabulary. Any errors will be non-impeding.
+ | The reader has practically no difficulty understanding the writer’s ideas and any time. Extremely fluent.
+ | The style is appropriate throughout.
+ |
+| B
+ | Has responded to the task appropriately and included a good range of ideas, which are well supported.
+ | Logical organization of ideas. Within the paragraphs reasonable cohesion. Use of signposts does not result in confusion. Reasonable balance of ideas.
+ | Uses a good range of language. There will be errors, but they are nonimpeding. Uses pre-learnt phrases appropriately.
+ | Communicates ideas with a good degree of fluency. No strain to the reader.
+ | Only very occasional use of style that may not be considered entirely appropriate.
+ |
+| C
+ | Has responded to the task, but there may be some repetition of the same ideas, or the ideas may be somewhat limited or irrelevant.
+ | There may be a division of paragraphs, but ideas are muddled within the paragraphs. Confusing discourse markers.
+ | Either has a rather poor level of accuracy in attempting to produce complex language or uses extremely simple language.
+ | Struggles to communicate meaning successfully. A certain amount of strain to the reader.
+ | Somewhat inappropriate style with personal pronouns, questions or inappropriate vocabulary.
+ |
+| D
+ | Has either written something completely irrelevant or has extremely limited ideas.
+ | Ideas follow no logical pattern. The arguments may be completely onesided.
+ | Many inaccuracies, even very basic errors. Poor range of structures.
+ | Considerable strain to the reader to understand the meaning.
+ | Inappropriate style throughout.
+ |
+
+
+### Course Sections
+
+
+#### Section 1
+
+
+#### Section 2
+
+
+#### Section 3
+
+
+
+
+
+
+
+
+
+
+

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+
+
+
+
+
+
+
+BSc: Academic Research and Writing Culture II
+=============================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Academic Research and Writing Culture 2](#Academic_Research_and_Writing_Culture_2)
+	+ [1.1 Course characteristics](#Course_characteristics)
+		- [1.1.1 Key concepts of the class](#Key_concepts_of_the_class)
+		- [1.1.2 What is the purpose of this course?](#What_is_the_purpose_of_this_course.3F)
+	+ [1.2 Course Objectives Based on Bloom’s Taxonomy](#Course_Objectives_Based_on_Bloom.E2.80.99s_Taxonomy)
+		- [1.2.1 What should a student remember at the end of the course?](#What_should_a_student_remember_at_the_end_of_the_course.3F)
+		- [1.2.2 What should a student be able to understand at the end of the course?](#What_should_a_student_be_able_to_understand_at_the_end_of_the_course.3F)
+		- [1.2.3 What should a student be able to apply at the end of the course?](#What_should_a_student_be_able_to_apply_at_the_end_of_the_course.3F)
+		- [1.2.4 Course evaluation](#Course_evaluation)
+		- [1.2.5 Grades range](#Grades_range)
+		- [1.2.6 Resources and reference material](#Resources_and_reference_material)
+	+ [1.3 Course Sections](#Course_Sections)
+		- [1.3.1 Section 1:](#Section_1:)
+			* [1.3.1.1 Section title](#Section_title)
+			* [1.3.1.2 Topics covered in this section](#Topics_covered_in_this_section)
+			* [1.3.1.3 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F)
+			* [1.3.1.4 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section)
+			* [1.3.1.5 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section)
+			* [1.3.1.6 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section)
+		- [1.3.2 Section 2:](#Section_2:)
+			* [1.3.2.1 Section title](#Section_title_2)
+			* [1.3.2.2 Topics covered in this section](#Topics_covered_in_this_section_2)
+			* [1.3.2.3 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_2)
+			* [1.3.2.4 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_2)
+			* [1.3.2.5 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_2)
+			* [1.3.2.6 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_2)
+		- [1.3.3 Section 3: Coordination, consistency, and replication in distributed systems](#Section_3:_Coordination.2C_consistency.2C_and_replication_in_distributed_systems)
+			* [1.3.3.1 Section title](#Section_title_3)
+			* [1.3.3.2 Topics covered in this section](#Topics_covered_in_this_section_3)
+			* [1.3.3.3 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_3)
+			* [1.3.3.4 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_3)
+			* [1.3.3.5 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_3)
+			* [1.3.3.6 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_3)
+		- [1.3.4 Section 4: Fault tolerance and security in distributed systems](#Section_4:_Fault_tolerance_and_security_in_distributed_systems)
+			* [1.3.4.1 Section title](#Section_title_4)
+			* [1.3.4.2 Topics covered in this section](#Topics_covered_in_this_section_4)
+			* [1.3.4.3 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_4)
+			* [1.3.4.4 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_4)
+			* [1.3.4.5 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_4)
+			* [1.3.4.6 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_4)
+
+
+
+Academic Research and Writing Culture 2
+=======================================
+
+
+* **Course name:** Academic Research and Writing Culture 2
+* **Course number:** XYZ
+* **Knowledge area:** xxx
+
+
+Course characteristics
+----------------------
+
+
+### Key concepts of the class
+
+
+* Academic Research and Writing Culture 2 concepts:
+
+
+### What is the purpose of this course?
+
+
+Academic Research and Writing Culture 2 have become 
+
+
+
+Course Objectives Based on Bloom’s Taxonomy
+-------------------------------------------
+
+
+#### What should a student remember at the end of the course?
+
+
+By the end of the course, the students should be able to recognize and define
+
+
+
+* 
+* 
+* 
+* 
+* 
+
+
+#### What should a student be able to understand at the end of the course?
+
+
+By the end of the course, the students should be able to describe and explain (with examples)
+
+
+
+* 
+* 
+* 
+* 
+* 
+* 
+
+
+#### What should a student be able to apply at the end of the course?
+
+
+By the end of the course, the students should be able to apply
+
+
+
+* 
+* 
+* 
+* 
+* 
+
+
+### Course evaluation
+
+
+
+
+
+Course grade breakdown
+| **Component** | **Points** |
+| --- | --- |
+| Laboratory assignments
+ | 55%
+ |
+| Final exam
+ | 35%
+ |
+| Attendance
+ | 10%
+ |
+
+
+**Important:** In order to successfully finish the course, the student is required to score at least 50% in final exam.
+
+
+  
+
+
+
+
+
+### Grades range
+
+
+
+
+
+Course grading range
+| A. Excellent
+ | 90-100
+ |
+| B. Good
+ | 75-89
+ |
+| C. Satisfactory
+ | 60-74
+ |
+| D. Poor
+ | 0-59
+ |
+
+
+
+  
+
+
+
+
+### Resources and reference material
+
+
+* **Textbook:**. Available online:
+* **Reference:**. Available online:
+* **Reference:**. Available online:
+
+
+Course Sections
+---------------
+
+
+The course is organized in 8 weeks, with every weeks 4 academics hours of lectures and 4 academic hours of tutorials/labs. The main sections of the course and approximate hour distribution between them is as follows:
+
+
+
+
+
+
+Course Sections
+| **Section** | **Section Title** | **Teaching Hours** |
+| --- | --- | --- |
+| 1
+ | Introduction to subject, computer networks basics, transport layer protocols, and socket programming
+ | 12
+ |
+| 2
+ | Multithreaded socket programming, remote procedure calls, and distributed system architecture
+ | 24
+ |
+| 3
+ | Coordination, consistency, and replication in distributed systems
+ | 24
+ |
+| 4
+ | Fault tolerance and security in distributed systems
+ | 30
+ |
+
+
+
+### Section 1:
+
+
+#### Section title
+
+
+Introduction to subject, computer networks basics, transport layer protocols, and socket programming
+
+
+
+#### Topics covered in this section
+
+
+* General introduction to the course
+* Computer networks basic
+* Socket programming
+* UDP socket programming
+* TCP socket programming
+
+
+#### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+
+|  |  |
+| --- | --- |
+|  **Form**  | **Yes/No** |
+| Development of individual parts of software product code
+ | 1
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 0
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 1
+ |
+| Discussions
+ | 1
+ |
+
+
+  
+
+
+
+
+
+#### Typical questions for ongoing performance evaluation within this section
+
+
+1. ?
+2. .
+3. ?
+4. ?
+5. ?
+6. ?
+7. ?
+
+
+#### Typical questions for seminar classes (labs) within this section
+
+
+1. 
+2. 
+3. 
+4. 
+5. 
+
+
+#### Test questions for final assessment in this section
+
+
+1. ?
+2. ?
+3. ?
+4. ?
+
+
+### Section 2:
+
+
+#### Section title
+
+
+#### Topics covered in this section
+
+
+* 
+* 
+* 
+
+
+#### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+
+|  |  |
+| --- | --- |
+|  **Form**  | **Yes/No** |
+| Development of individual parts of software product code
+ | 1
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 0
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 1
+ |
+| Discussions
+ | 1
+ |
+
+
+  
+
+
+
+
+
+  
+
+
+
+
+#### Typical questions for ongoing performance evaluation within this section
+
+
+1. ?
+2. ?
+3. ?
+4. ?
+5. ?
+
+
+  
+
+
+
+
+#### Typical questions for seminar classes (labs) within this section
+
+
+1. You have a list of large numbers, and you need to find if they are prime or not. Would you use multithreading, multiprocessing, or sequential programming in order to complete the task asap? Prove it in practice.
+2. You need to send multiple requests to a server and receive responses. Assume there is a few msecs of delay before you receive the response from the server. Would you use multithreading, multiprocessing, or sequential programming in order to complete the task asap? Prove it in practice. (Order of the requests/responses doesn't matter)
+3. Discuss two ways of creating the threads using threading module in Python: 1) passing the worker function as a target, 2) subclassing the Thread class
+4. Given the function implemented locally, make it available to be called through RPC from remote process? Use xmlRPC.
+
+
+#### Test questions for final assessment in this section
+
+
+1. .
+2. ?
+3. ?
+4. ?
+5. ?
+6. 
+
+
+  
+
+
+
+  
+
+
+
+
+### Section 3: Coordination, consistency, and replication in distributed systems
+
+
+#### Section title
+
+
+Coordination, consistency, and replication in distributed systems
+
+
+
+#### Topics covered in this section
+
+
+* 
+* 
+* 
+* 
+
+
+#### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+
+|  |  |
+| --- | --- |
+|  **Form**  | **Yes/No** |
+| Development of individual parts of software product code
+ | 1
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 0
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 1
+ |
+| Discussions
+ | 1
+ |
+
+
+  
+
+
+
+
+
+#### Typical questions for ongoing performance evaluation within this section
+
+
+1. ?
+2. ?
+3. ?
+4. ?
+5. ?
+
+
+#### Typical questions for seminar classes (labs) within this section
+
+
+1. 
+2. 
+3. 
+4. 
+
+
+#### Test questions for final assessment in this section
+
+
+1. 
+2. 
+3. 
+4. 
+
+
+### Section 4: Fault tolerance and security in distributed systems
+
+
+#### Section title
+
+
+Fault tolerance and security in distributed systems
+
+
+
+#### Topics covered in this section
+
+
+* 
+* 
+
+
+#### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+
+|  |  |
+| --- | --- |
+|  **Form**  | **Yes/No** |
+| Development of individual parts of software product code
+ | 1
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 0
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 1
+ |
+| Discussions
+ | 1
+ |
+
+
+  
+
+
+
+
+
+#### Typical questions for ongoing performance evaluation within this section
+
+
+1. 
+2. 
+3. 
+
+
+#### Typical questions for seminar classes (labs) within this section
+
+
+1. Same as above
+
+
+#### Test questions for final assessment in this section
+
+
+1. Same as above
+
+
+
+
+
+
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raw/raw_bsc__advanced_compilers_construction_and_program_analysis.md

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+BSc: Advanced Compilers Construction and Program Analysis
+=========================================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Advanced Compilers Construction and Program Analysis](#Advanced_Compilers_Construction_and_Program_Analysis)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+* [2 Course Objectives Based on Bloom’s Taxonomy](#Course_Objectives_Based_on_Bloom.E2.80.99s_Taxonomy)
+	+ [2.1 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+		- [2.1.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+		- [2.1.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+		- [2.1.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [2.2 Grading](#Grading)
+		- [2.2.1 Course grading range](#Course_grading_range)
+		- [2.2.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [2.2.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [2.3 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [2.3.1 Open access resources](#Open_access_resources)
+		- [2.3.2 Closed access resources](#Closed_access_resources)
+		- [2.3.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+		- [2.3.4 Resources and reference material](#Resources_and_reference_material)
+* [3 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [3.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [3.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [3.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [3.2.1.1 Section 1](#Section_1)
+			* [3.2.1.2 Section 2](#Section_2)
+			* [3.2.1.3 Section 3](#Section_3)
+			* [3.2.1.4 Section 4](#Section_4)
+		- [3.2.2 Final assessment](#Final_assessment)
+		- [3.2.3 The retake exam](#The_retake_exam)
+
+
+
+Advanced Compilers Construction and Program Analysis
+====================================================
+
+
+* **Course name**: Advanced Compilers Construction and Program Analysis
+* **Code discipline**: XYZ
+* **Subject area**: Programming Languages and Software Engineering
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: Advanced Compilers Construction and Program Analysis concepts:
+
+
+  
+
+Key concepts of the class
+
+
+
+* Type Systems
+* Lambda calculi as the core representation
+* Type checking and type inference
+* Simple types and derived forms
+* Subtyping
+* Imperative objects
+* Recursive types
+* Universal polymorphism
+* Compiling lazy functional languages
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Introduction to subject, computer networks basics, transport layer protocols, and socket programming | 1. General introduction to the course
+2. Computer networks basic
+3. Socket programming
+4. UDP socket programming
+5. TCP socket programming
+ |
+|  |  |
+| Coordination, consistency, and replication in distributed systems |  |
+| Fault tolerance and security in distributed systems |  |
+
+
+Course Sections
+
+
+
+
+
+The main sections of the course and approximate hour distribution between
+them is as follows:
+| Section Title | Lecture Hours | Seminars (labs) | Selfstudy | Knowledge evaluation
+ |
+| --- | --- | --- | --- | --- |
+| Lambda Calculus and Simple Types | 10 | 10 | 10 | 2
+ |
+| References, Exceptions, Imperative Objects, Featheweight Java | 8 | 8 | 8 | 1
+ |
+| Recursive Types, Type Reconstruction, Universal Polymorphism | 6 | 6 | 6 | 1
+ |
+| Compiling Lazy Functional Languages | 8 | 8 | 8 | 1
+ |
+| Project Presentation |  |  |  | 2
+ |
+
+
+  
+
+
+
+Section 1
+Section title: Lambda calculus and simple types
+
+
+Topics covered in this section:
+
+
+
+* The history of typed languages. Type systems and language design.
+* Basic notions: untyped lambda calculus, nameless representation, simple types.
+
+
+
+
+
+| Form of evaluation | Usage |  |
+| --- | --- | --- |
+| Development of individual parts of software product code | 1 |  |
+| Homework and group projects | 1 |  |
+| Midterm evaluation | 0 |  |
+| Testing (written or computer based) | 0 |  |
+| Reports | 1 |  |
+| Essays | 0 |  |
+| Oral polls | 1 |  |
+| Discussions | 1 |  |
+
+
+  
+
+Typical questions for ongoing performance evaluation within this section
+
+
+
+* What is the role of the type system in language design?
+* How to evaluate lambda terms using call-by-name/call-by-value strategies?
+* What is the typing relation?
+* What is type safety?
+* What is erasure of types?
+* What is general recursion?
+
+
+Typical questions for seminar classes (labs) within this section
+
+
+
+* Evaluate a given lambda expression using call-by-name strategy.
+* Convert a given lambda expression to/from a nameless representation.
+* Draw a type derivation tree for a given lambda term in simply typed lambda calculus.
+* Provide a type for a given lambda term in a given simple type system.
+
+
+Test questions for final assessment in this section
+
+
+
+* Present an implementation of an interpreter for untyped lambda calculus.
+* Present an implementation of a type checker for simply typed lambda
+
+
+calculus.
+
+
+  
+
+Section 2
+Section title: References, exceptions, imperative objects, Featherweight Java
+
+
+  
+
+Topics covered in this section:
+
+
+
+* References, store typings, raising and handling exceptions
+* Subsumption and the subtyping relation, coercion semantics, the Bottom Type
+* Object-oriented programming and lambda calculus with imperative objects
+* Featherweight Java
+
+
+  
+
+
+
+
+
+
+
+| Form of evaluation | Usage |  |
+| --- | --- | --- |
+| Development of individual parts of software product code | 1 |  |
+| Homework and group projects | 1 |  |
+| Midterm evaluation | 1 |  |
+| Testing (written or computer based) | 0 |  |
+| Reports | 1 |  |
+| Essays | 0 |  |
+| Oral polls | 1 |  |
+| Discussions | 1 |  |
+
+
+  
+
+Typical questions for ongoing performance evaluation within this section
+
+
+
+* How operational semantic changes when introducing references?
+* How operational semantic changes when introducing exceptions?
+* What is the concept of imperative objects?
+* What are the features of Featherweight Java?
+* Explain effects of call-by-name and call-by-value evaluation strategies on terms with references.
+
+
+Typical questions for seminar classes (labs) within this section
+
+
+
+* Evaluate given expression with references.
+* Evaluate given expression with exceptions.
+* Draw a type derivation tree for a given lambda term in simply typed
+
+
+lambda calculus with references and exceptions.
+
+
+
+* Provide a type for a given lambda term in a given simple type system with references and exceptions.
+
+
+Test questions for final assessment in this section
+
+
+
+* Present and/or explain an implementation of an interpreter for lambda calculus with references and exceptions.
+* Present and/or explain an implementation of a type checker for simply typed lambda calculus with references and exceptions.
+
+
+  
+
+Section 3
+Section title: Recursive types, type reconstruction, universal polymorphism
+
+
+What forms of evaluation were used to test students’ performance in
+this section?
+
+
+
+
+
+Form of evaluation
+| Form of evaluation | Usage |  |
+| --- | --- | --- |
+| Development of individual parts of software product code | 1 |  |
+| Homework and group projects | 1 |  |
+| Midterm evaluation | 0 |  |
+| Testing (written or computer based) | 0 |  |
+| Reports | 1 |  |
+| Essays | 0 |  |
+| Oral polls | 1 |  |
+| Form of evaluation | Usage |  |
+| Discussions | 1 |  |
+
+
+  
+
+
+
+Topics covered in this section:
+
+
+
+* Recursive types, induction and coinduction, finite and infinite types
+* Polymorphism, type reconstruction, universal types
+* System F and Hindley-Milner type system
+
+
+Typical questions for ongoing performance evaluation within this section
+
+
+
+* What is the concept of recursive types?
+* What is the motivation for universal types?
+* Explain the differences between System F and Hindley-Milner type system.
+
+
+Typical questions for seminar classes (labs) within this section
+
+
+
+* Evaluate given expression in System F with recursive types.
+* Draw a type derivation tree for a given term in System F.
+* Provide a type for a given term in System F.
+
+
+Test questions for final assessment in this section
+
+
+
+* Present and/or explain an implementation of an interpreter for lambda calculus with references and exceptions.
+* Present and/or explain an implementation of a type checker for simply typed lambda calculus with references and exceptions.
+* Present and/or explain the Hindley-Milner type inference algorithm.
+
+
+Section 4
+Section title: Compiling lazy functional languages
+
+
+Topics covered in this section:
+
+
+
+* Challenges of compiling lazy functional languages
+* Representing functional closures at run-time
+* Representing lazy data structures at run-time
+* The syntax and semantics of the STG language
+
+
+What forms of evaluation were used to test students’ performance in
+this section?
+
+
+
+
+
+Form of evaluation
+| Form of evaluation | Usage |  |
+| --- | --- | --- |
+| Development of individual parts of software product code | 1 |  |
+| Homework and group projects | 1 |  |
+| Midterm evaluation | 0 |  |
+| Testing (written or computer based) | 0 |  |
+| Reports | 1 |  |
+| Essays | 0 |  |
+| Oral polls | 1 |  |
+| Form of evaluation | Usage |  |
+| Discussions | 1 |  |
+
+
+  
+
+
+
+Typical questions for ongoing performance evaluation within this section
+
+
+
+* How are closures represented during run-time?
+* How are lazy data structures represented during run-time?
+* Describe the main constructions of the STG Language?
+
+
+Typical questions for seminar classes (labs) within this section
+
+
+
+* Explain how a given term in STG language evaluates.
+* Translate a given lambda term into STG language
+
+
+Test questions for final assessment in this section
+
+
+
+* Present and/or explain the STG machine.
+* Present an implementation of a type checker for simply typed lambda
+
+
+calculus.
+
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+This course partially covers two major topics:
+1. Theory and Implementation of Typed Programming Languages and
+2. Compilation of Lazy Functional Languages.
+We will study different type system features in detail, starting from an untyped language of lambda calculus and gradually adding new types and variations along the way. The course assumes familiarity with basics of compiler construction, basics of functional programming and familiarity with some static type systems (C++ and Java would suffice, but knowing type systems of Haskell or Scala will help). 
+Even though the most obvious benefit of static type systems is that it allows programmers to detect some errors early, it is by far not the only application. Types are used also as a tool for abstraction, documentation, language safety, efficiency and more. In this course we will look at features of type systems occurring in many programming languages, like C++, Java, Scala and Haskell. 
+After we have reached System F, a type system at the core of languages like Haskell, we will look into how lazy functional languages are implemented. We will in particular look in detail at Spineless Tagless Graph reduction machine (also known as STG machine) that is used to compile Haskell code. 
+
+
+Evaluation of the course consists of Lecture Quizzes, Lab Participation and the Final Project (split into several stages). The Final Project is a team project where students build a complete interpreter or compiler for a statically typed programming language, incorporating some of the features covered in this course.
+
+
+
+Course Objectives Based on Bloom’s Taxonomy
+===========================================
+
+
+What should a student remember at the end of the course?
+
+
+
+* Remember syntax and computation rules of untyped lambda calculus.
+* Remember nameless representation of lambda terms.
+* Remember definition of normal form, weak head normal form.
+* Remember syntax, typing and computation rules of simply typed lambda calculus.
+* Remember definition of imperative objects.
+* Remember syntax and semantics of Featherweight Java.
+* Remember typing rules for subtyping.
+* Remember typing rules for pairs, tuples, records, sums, variants, and lists.
+* Remember typing rules for let-bindings and type ascription.
+* Remember typing rules for recursive types.
+* Remember definition and typing rules for universal polymorphism.
+* Remember syntax, typing and computation rules for System F.
+* Remember representation of closures when compiling functional languages.
+* Remember representation of lazy data structures when compiling.
+* Remember the syntax and semantics of the STG language.
+
+
+What should a student be able to understand at the end of the course?
+
+
+
+* Understand how type systems relate to language design
+* Understand differences between call-by-name, call-by-need, and call-byvalue evaluation strategies.
+* Understand the tradeoffs introduced by various type system features.
+* Understand the idea of nameless representation of terms.
+* Understand the tradeoffs of mutable references and exceptions introduced in a language.
+* Understand how imperative objects model objects in modern objectoriented langauges.
+* Understand the difficulties of compiling lazy expressions.
+* Understand the differences between Hindley–Milner type system and System F.
+
+
+What should a student be able to apply at the end of the course?
+
+
+
+* Implement an interpreter for a programming language with untyped lambda calculus as its core representation.
+* Implement an interpreter for a programming language with simply typed lambda calculus as its core representation.
+* Implement type checking algorithm for a language with simple types, recursive types, imperative objects, and universal polymorphism.
+* Implement Damas–Hindley–Milner type inference algorithm for a programming language with a Hindley-Milner style type system.
+
+
+Course evaluation:
+
+
+
+* Labs/seminar classes (proposed points: 20)
+* Interim performance assessment (proposed points: 10)
+* Exams (proposed points: 70)
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+  
+
+
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+  
+
+
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 85-100 | -
+ |
+| B. Good | 75-84 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Laboratory assignments | 55%
+ |
+| Final exam | 35%
+ |
+| Attendance | 10%
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Textbook:. Available online:
+* Reference:. Available online:
+* Reference:. Available online:
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+### Resources and reference material
+
+
+* Benjamin C. Pierce. ’‘Types and Programming Languages. The MIT Press 2002”
+* Simon Peyton Jones. ’‘Implementing functional languages: a tutorial. Prentice Hall 1992”
+* Simon Peyton Jones. ’‘Implementing Lazy Functional Languages on Stock Hardware: The Spineless Tagless G-machine. Journal of Functional Programming 1992”
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4
+ |
+| --- | --- | --- | --- | --- |
+| Development of individual parts of software product code | 1 | 1 | 1 | 1
+ |
+| Homework and group projects | 1 | 1 | 1 | 1
+ |
+| Testing (written or computer based) | 1 | 1 | 1 | 1
+ |
+| Oral polls | 1 | 1 | 1 | 1
+ |
+| Discussions | 1 | 1 | 1 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | ? | 1
+ |
+| Question | . | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | You have a list of large numbers, and you need to find if they are prime or not. Would you use multithreading, multiprocessing, or sequential programming in order to complete the task asap? Prove it in practice. | 0
+ |
+| Question | You need to send multiple requests to a server and receive responses. Assume there is a few msecs of delay before you receive the response from the server. Would you use multithreading, multiprocessing, or sequential programming in order to complete the task asap? Prove it in practice. (Order of the requests/responses doesn't matter) | 0
+ |
+| Question | Discuss two ways of creating the threads using threading module in Python: 1) passing the worker function as a target, 2) subclassing the Thread class | 0
+ |
+| Question | Given the function implemented locally, make it available to be called through RPC from remote process? Use xmlRPC. | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+
+
+#### Section 4
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Same as above | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. ?
+2. ?
+3. ?
+4. ?
+
+
+**Section 2**
+
+
+
+1. 
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+
+1. Same as above
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__advanced_databases.md

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+
+
+
+
+
+
+
+BSc: Advanced Databases
+=======================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Advanced Databases](#Advanced_Databases)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+			* [2.2.1.4 Section 4](#Section_4)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Advanced Databases
+==================
+
+
+* **Course name**: Advanced Databases
+* **Code discipline**: XYZ
+* **Subject area**: xxx
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: DevOps Engineering concepts:.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Introduction to subject, computer networks basics, transport layer protocols, and socket programming | 1. General introduction to the course
+2. Computer networks basic
+3. Socket programming
+4. UDP socket programming
+5. TCP socket programming
+ |
+|  |  |
+| Coordination, consistency, and replication in distributed systems |  |
+| Fault tolerance and security in distributed systems |  |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+Advanced Databases have become
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+  
+
+
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+  
+
+
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Laboratory assignments | 55%
+ |
+| Final exam | 35%
+ |
+| Attendance | 10%
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Textbook:. Available online:
+* Reference:. Available online:
+* Reference:. Available online: h
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4
+ |
+| --- | --- | --- | --- | --- |
+| Development of individual parts of software product code | 1 | 1 | 1 | 1
+ |
+| Homework and group projects | 1 | 1 | 1 | 1
+ |
+| Testing (written or computer based) | 1 | 1 | 1 | 1
+ |
+| Oral polls | 1 | 1 | 1 | 1
+ |
+| Discussions | 1 | 1 | 1 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | ? | 1
+ |
+| Question | . | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | You have a list of large numbers, and you need to find if they are prime or not. Would you use multithreading, multiprocessing, or sequential programming in order to complete the task asap? Prove it in practice. | 0
+ |
+| Question | You need to send multiple requests to a server and receive responses. Assume there is a few msecs of delay before you receive the response from the server. Would you use multithreading, multiprocessing, or sequential programming in order to complete the task asap? Prove it in practice. (Order of the requests/responses doesn't matter) | 0
+ |
+| Question | Discuss two ways of creating the threads using threading module in Python: 1) passing the worker function as a target, 2) subclassing the Thread class | 0
+ |
+| Question | Given the function implemented locally, make it available to be called through RPC from remote process? Use xmlRPC. | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+
+
+#### Section 4
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Same as above | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. ?
+2. ?
+3. ?
+4. ?
+
+
+**Section 2**
+
+
+
+1. 
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+
+1. Same as above
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__advanced_linux.md

@@ -0,0 +1,777 @@
+
+
+
+
+
+
+
+BSc: Advanced Linux
+===================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Advanced Linux](#Advanced_Linux)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+			* [2.2.1.4 Section 4](#Section_4)
+			* [2.2.1.5 Section 5](#Section_5)
+			* [2.2.1.6 Section 6](#Section_6)
+			* [2.2.1.7 Section 7](#Section_7)
+			* [2.2.1.8 Section 8](#Section_8)
+			* [2.2.1.9 Section 9](#Section_9)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Advanced Linux
+==============
+
+
+* **Course name**: Advanced Linux
+* **Code discipline**: xxxxx
+* **Subject area**:
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: The fundamental principles for `booting`; Linux Kernel: understanding, programming, debugging, contributing; Device drivers; Power management; Graphical stack overview; Userspace: understating and interaction with Kernel, debugging userspace application and libraries.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| X86/Arm assembler introduction | 1. Basic assembler: registers, operations
+2. x86 ABI reference
+3. Context switching
+4. CPU security rings
+ |
+| Userspace | 1. Executable files overview
+2. ELF format
+3. SO format
+4. POSIX API
+ |
+| Userspace debugging (GDB) | 1. Debugging techniques overview
+2. GDB (Gnu debugger) usage
+3. Stack trace
+4. Watchpoints/breakpoints
+ |
+| Linux Kernel introduction | 1. Kernel usage
+2. Supported HW
+3. Building the kernel
+ |
+| Booting the Kernel | 1. Boot Sequence
+2. Device Tree
+3. U-boot
+4. initrd/initramfs
+ |
+| Kernel Modules | 1. Linux device and driver m​odel
+2. Virtual Filesystems
+ |
+| Memory management | 1. Physical Memory
+2. Virtual Memory
+3. Memory Allocation
+ |
+| Threads, processes and scheduling | 1. Thread
+2. Processes
+3. Timers
+ |
+| Concurrent access to resources | 1. Mutexes
+2. Spin locks
+3. RW-locks
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+The main purpose of this course is to give the students advanced knowledge of how Linux operation system boots, works and what parts it is consists of.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Principles of Operating Systems.
+* Principles of bootloaders (first- /second- stage).
+* Linux booting principles.
+* Linux Kernel and apps debugging principles.
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Memory management in Kernel and userspace.
+* Linux kernel subsustems.
+* Concurrent access to resources.
+* HW devices interaction in Linux.
+* Interrupt and multithreading execution.
+* Real- and virtual- filesystems interaction.
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Kernel drivers design skills.
+* Linux Kernel contribution and advanced GIT knowledge.
+* C language low-level Kernel programming.
+* C/C++ language system programming.
+* POSIX API usage.
+* Kernel and userspace debugging (including KGDB/GDB).
+* x86/ARM assembly programming.
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 100-150 | -
+ |
+| B. Good | 80-100 | -
+ |
+| C. Satisfactory | 60-79 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Labs/seminar classes | 100
+ |
+| Interim performance assessment | 0
+ |
+| Exams | 50
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Writing Kernel Module: i2c -
+* Fundamental Linux Kernel programming by Krishenko V.A., Rayzanova N.U. - /
+* Linux Operating System by Kuryachiy G.V., Malinskiy K.A. -
+* Systemd after 10 years, historical and techical review, -
+* Evolution of Linux Kernel by Novikov E.M., -
+* Online resources shared by instructor
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4 | Section 5 | Section 6 | Section 7 | Section 8 | Section 9
+ |
+| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
+| Development of individual parts of software product code | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
+ |
+| Homework and group projects | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0
+ |
+| Midterm evaluation | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0
+ |
+| Testing (written or computer based) | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
+ |
+| Discussions | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | ARM architecture is faster than x86, itn’s it? | 1
+ |
+| Question | Why does antivirus software works in RING0? | 1
+ |
+| Question | What is the main purpose of having interrupts? | 1
+ |
+| Question | How-to debug anything inside interrupt context? | 1
+ |
+| Question | Show the difference in x86 and ARM CPU registers. | 0
+ |
+| Question | Create `basic` atomic operations for ARM in x86 (and vice versa). | 0
+ |
+| Question | Implement simple context switching without threads. | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Why can’t we just use .EXE and .DLL files on Linux? | 1
+ |
+| Question | Do .SO files actually share same memory physical addresses? | 1
+ |
+| Question | POSIX vs WinAPI? Which is better from portability point of view? | 1
+ |
+| Question | What is the most secure method for interprocess communication? | 1
+ |
+| Question | What is the fastest method for interprocess communication? | 1
+ |
+| Question | Create simple app for ELF format parsing. | 0
+ |
+| Question | Create app that shows dependencies between .so and executable file. | 0
+ |
+| Question | Create two apps communicating with each other. At least 2 methods. Compare the speed. | 0
+ |
+| Question | Create app with joinable and detachable threads. Check the difference. | 0
+ |
+| Question | Create app that uses fork() and execve() with controlling child process. | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is GDB? What platforms can be debugged using GDB? | 1
+ |
+| Question | Do we have any alternatives for GDB? | 1
+ |
+| Question | What should we have related to the app to debug it in GDB? | 1
+ |
+| Question | Name popular GDB front-ends. Check what front-ends for GDB you already use. | 1
+ |
+| Question | What alternatives to GHIDRA do we have for different platforms? | 1
+ |
+| Question | Debug simple app using GDB with symbols in runtime. Use breakpoints and watchpoints and step by step debugging. | 0
+ |
+| Question | Load coredump and debug it in GDB. | 0
+ |
+| Question | Fix few variables in binary file using GHIDRA without source code. | 0
+ |
+
+
+#### Section 4
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Monolithic kernel vs Micro-kernel. What is faster and why? | 1
+ |
+| Question | How Linux works on HW without IOMMU? | 1
+ |
+| Question | Tools required for building Linux Kernel. | 1
+ |
+| Question | Name few operations systems bases on Linux and name the difference. | 1
+ |
+| Question | Contributing to Open Source software and Kernel. What is the difference? | 0
+ |
+| Question | Git usage: commits, email-patches. | 0
+ |
+| Question | Git usage: rewriting history. | 0
+ |
+| Question | Building Linux Kernel for your own PC. | 0
+ |
+| Question | Running new Kernel on your machine. | 0
+ |
+| Question | Kernel config file location and editing. | 0
+ |
+
+
+#### Section 5
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is the difference between BIOS and UEFI? What we prefer in nowadays? | 1
+ |
+| Question | What is the usage for secure boot? What requirements should be met for this? | 1
+ |
+| Question | Why in x86 we do not have device tree? And why is it required for ARM platforms? | 1
+ |
+| Question | What is the purpose of having initramfs? Can we skip that stage? | 1
+ |
+| Question | Build U-boot | 0
+ |
+| Question | Rebuilding initramfs | 0
+ |
+| Question | Changing boot order of your PC. Creating simple systemd service. | 0
+ |
+
+
+#### Section 6
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | How kernel module can be compiled and used inside or outside Linux Kernel Image? | 1
+ |
+| Question | What is the purpose of System.map file for correct Linux Kernel functionality? | 1
+ |
+| Question | What is the real requirement to have virtual filesystems in Linux Kernel? | 1
+ |
+| Question | Name few real and virtual filesystems. Briefly describe usage in real life. | 1
+ |
+| Question | Develop and deploy simple Kernel Module outside kernel image. Dynamic Loading. | 0
+ |
+| Question | Develop and deploy simple Kernel Module inside kernel image. | 0
+ |
+| Question | SysFS/ DebugFS / ProcFS/ TmpFS usage | 0
+ |
+
+
+#### Section 7
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Why do we need virtual memory? | 1
+ |
+| Question | Why does Linux Kernel maps itself to every process address space? | 1
+ |
+| Question | How does page fault handler work? | 1
+ |
+| Question | What is segmentation fault and how it handles in Linux Kernel? | 1
+ |
+| Question | Create simple allocator (myalloc/myfree). | 0
+ |
+| Question | Create benchmark for simple allocator. | 0
+ |
+
+
+#### Section 8
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is the difference between thread and process? | 1
+ |
+| Question | Can process exist without any threads? | 1
+ |
+| Question | What scheduling methods does Linux Kernel has? | 1
+ |
+| Question | What make `realtime` OS really realtime? | 1
+ |
+| Question | What is the difference between cooperative and preemptive multitasking? | 1
+ |
+| Question | Implement your own threads inside app. | 0
+ |
+| Question | Implement simple scheduler for your threading app. | 0
+ |
+| Question | Implement timer for your app without using `real` timers. | 0
+ |
+
+
+#### Section 9
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Why do we need locking structures? | 1
+ |
+| Question | Where is mutex preferred on spinlock? | 1
+ |
+| Question | Where is spinlock preferred on mutex? | 1
+ |
+| Question | Can we just write locking-free code? | 1
+ |
+| Question | What is deadlock and how it could be handled? | 1
+ |
+| Question | Implement simple locking structures. | 0
+ |
+| Question | Implement Wait-die lock. | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. Describe basic CPU registers and their purpose.
+2. Describe x86 ABI.
+3. What is context switching and how does it work?
+4. Name all CPU security rings and describe security levels.
+5. Interrupts. Interrupt handler.
+
+
+**Section 2**
+
+
+
+1. Describe ELF executable format.
+2. Describe how Linux processes could be load from ELF file.
+3. Describe .SO library loading and their layout in memory.
+4. Describe methods of interprocess communication (at least 2).
+5. POSIX. Describe network operations.
+6. POSIX. Describe pthread library.
+7. POSIX. Describe time operations.
+8. Describe select(), poll() methods. Name the difference.
+9. POSIX. Describe filesystem operations.
+
+
+**Section 3**
+
+
+
+1. GDB. Why do we need to have symbols? Can we debug without them?
+2. GDB. Describe debugging techniques only using coredump.
+3. GDB. Describe usage or breakpoints and watchpoints.
+4. GDB/GDB Server. Remote debugging. Describe how to do that.
+5. GDB. Describe multiarch debugging.
+6. GDB. Describe how to debug multithreaded application.
+7. GDB. Stack trace. Describe usage and how-to.
+8. GHIDRA. Describe usage flow.
+
+
+**Section 4**
+
+
+
+1. Briefly describe modern OS architecture. (for ex. Linux)
+2. Describe supported HW by Linux Kernel.
+3. Describe contribution process to Linux Kernel.
+
+
+**Section 5**
+
+
+
+1. Name popular bootloaders and briefly describe the difference.
+2. Describe all boot sequence starting from pushing START button.
+3. Describe in details the role of initrd/initramfs in booting process.
+4. First userspace process. Describe how it works and why do we need SystemV/system?
+
+
+**Section 6**
+
+
+
+1. Describe Linux device and driver model
+2. Real- and Virtual- filesystems. Describe in details.
+3. Name other Linux Kernel subsystems and their usage.
+
+
+**Section 7**
+
+
+
+1. Describe how virtual memory maps on physical memory.
+2. Describe in details how TLB works. How TLB increases memory operations?
+3. Describe structure of page table, its location and management from OS.
+4. Describe memory allocation techniques. Describe one of them in details.
+
+
+**Section 8**
+
+
+
+1. Describe how threading works.
+2. Describe pthread API usage.
+3. Describe difference between monotomic and realtime clocks.
+4. Describe scheduling strategies. Make a suggestion, which one is preferred for different situations.
+5. Describe difference in memory management between threads and processes.
+
+
+**Section 9**
+
+
+
+1. Describe mutex internals.
+2. Describe spin lock internals.
+3. Describe deadlock problem and how it could be handled.
+4. Compare different locking methods and make conclusion of which is faster and why.
+5. Deeply describe wait-die locks.
+6. P.1.2.10 Section 10
+7. Section title: Kernel debugging
+8. Topics covered in this section:
+9. Debugging techniques
+10. DebugFS
+11. Other methods overview (J-Tag etc).
+12. KGDB
+13. What forms of evaluation were used to test students’ performance in this section?
+14. Typical questions for ongoing performance evaluation within this section
+15. Name and briefly describe kernel-debugging techniques.
+16. What debug levels for printk do you know and what is their usage?
+17. What other methods of Kernel debugging techniques do you know?
+18. Why can’t we use regular GDB to debug Linux Kernel?
+19. Typical questions for seminar classes (labs) within this section
+20. Usage of DebugFS for basic debugging
+21. Usage of printk and debug levels.
+22. KGDB usage for Kernel debugging.
+23. Test questions for final assessment in this section
+24. Explain usage of debugFS in modern kernels.
+25. Describe main kernel debugging techniques.
+26. P.1.2.11 Section 11
+27. Section title: HW busses
+28. Topics covered in this section:
+29. GPIO
+30. UART
+31. i2c
+32. spi
+33. pin muxing
+34. DMA
+35. What forms of evaluation were used to test students’ performance in this section?
+36. Typical questions for ongoing performance evaluation within this section
+37. What HW bus type should we prefer for flash memory?
+38. What bus is the fastest?
+39. What should we do if we don’t have enough available pins for our needs?
+40. Can spi devices be connected in parallel? How can we do that?
+41. DMA – overkill technique or our current basic needs? Briefly review advantages and disadvantages of DMA.
+42. Typical questions for seminar classes (labs) within this section
+43. Implement connection to other device using UART. Exchange data.
+44. Note: additional tasks will be given depends on current HW availability.
+45. Test questions for final assessment in this section
+46. Describe i2c bus. Usage of i2c bus.
+47. Describe spi bus. Usage of spi bus.
+48. Describe GPIO subsystem. Usage of GPIO.
+49. Describe pin muxing.
+50. Describe usage of DMA and consider exchange speed with and without DMA.
+51. P.1.2.12 Section 12
+52. Section title: PCI
+53. Topics covered in this section:
+54. PCI Physical parameters
+55. PCI Electrical parameters
+56. PCI Logical model
+57. PCI Configuration
+58. What forms of evaluation were used to test students’ performance in this section?
+59. Typical questions for ongoing performance evaluation within this section
+60. Briefly describe PCI specification.
+61. What is difference between PCI and PCIe?
+62. Name devices that could be connected to PC using PCI bus.
+63. Device tree and PCI. Briefly describe how we can configure them.
+64. Typical questions for seminar classes (labs) within this section
+65. Measure PCI Ex bus speed with different connection types: x1, x2, x4 and x16.
+66. Test questions for final assessment in this section
+67. Describe parameters of PCI bus interface.
+68. Describe usage of PCI bus in modern PC/laptop.
+69. Describe configuration and enumeration of devices on PCI bus.
+70. P.1.2.13 Section 13
+71. Section title: USB
+72. Topics covered in this section:
+73. USB Physical parameters
+74. USB Electrical parameters
+75. USB Logical model
+76. USB Configuration and enumeration
+77. What forms of evaluation were used to test students’ performance in this section?
+78. Typical questions for ongoing performance evaluation within this section
+79. Briefly describe USB specification.
+80. USB/A/B – type C. Describe difference.
+81. What devices could be connected using USB bus?
+82. Why we do not reboot after USB device connection to discover it?
+83. Can we add USB devices to device tree for faster enumeration?
+84. Typical questions for seminar classes (labs) within this section
+85. Implement simple USB device driver for keyboard/flash card/mouse etc.
+86. Test questions for final assessment in this section
+87. Describe parameters of USB interface.
+88. Describe usage of USB in modern PC/laptop.
+89. Describe configuration and enumeration of devices on USB.
+90. P.1.2.14 Section 14
+91. Section title: Graphical Stack overview
+92. Topics covered in this section:
+93. Framebuffer
+94. X11
+95. Wayland
+96. UI interfaces: GTK/Qt
+97. What forms of evaluation were used to test students’ performance in this section?
+98. Typical questions for ongoing performance evaluation within this section
+99. Linux- and Windows- comparison of graphical stack.
+100. Can we access framebuffer when it is double- or triple- buffered?
+101. What part of OS owns framebuffer?
+102. How X11 knows when to redraw on screen info?
+103. Can we use X11 and Wayland together?
+104. Typical questions for seminar classes (labs) within this section
+105. Create app with direct access to framebuffer.
+106. Use X11 forwarding using SSH tunnel.
+107. Create simple GTK/Qt application.
+108. Test questions for final assessment in this section
+109. Describe the usage of framebuffer.
+110. Describe the purpose of X11 system.
+111. Describe the purpose and advantages of Wayland framework.
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+**Section 5**
+
+
+**Section 6**
+
+
+**Section 7**
+
+
+**Section 8**
+
+
+**Section 9**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__analytic_geometry_and_linear_algebra_i.f21.md

@@ -0,0 +1,2759 @@
+
+
+
+
+
+
+
+BSc: Analytic Geometry And Linear Algebra I.F21
+===============================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Analytical Geometry & Linear Algebra – I](#Analytical_Geometry_.26_Linear_Algebra_.E2.80.93_I)
+	+ [1.1 Course characteristics](#Course_characteristics)
+		- [1.1.1 Key concepts of the class](#Key_concepts_of_the_class)
+		- [1.1.2 What is the purpose of this course?](#What_is_the_purpose_of_this_course.3F)
+		- [1.1.3 Course Objectives Based on Bloom’s Taxonomy](#Course_Objectives_Based_on_Bloom.E2.80.99s_Taxonomy)
+		- [1.1.4 - What should a student remember at the end of the course?](#-_What_should_a_student_remember_at_the_end_of_the_course.3F)
+		- [1.1.5 - What should a student be able to understand at the end of the course?](#-_What_should_a_student_be_able_to_understand_at_the_end_of_the_course.3F)
+		- [1.1.6 - What should a student be able to apply at the end of the course?](#-_What_should_a_student_be_able_to_apply_at_the_end_of_the_course.3F)
+		- [1.1.7 Course evaluation](#Course_evaluation)
+		- [1.1.8 Grades range](#Grades_range)
+		- [1.1.9 Resources and reference material](#Resources_and_reference_material)
+			* [1.1.9.1 Textbooks:](#Textbooks:)
+			* [1.1.9.2 Reference material:](#Reference_material:)
+	+ [1.2 Course Sections](#Course_Sections)
+		- [1.2.1 Section 1](#Section_1)
+			* [1.2.1.1 Section title:](#Section_title:)
+		- [1.2.2 Topics covered in this section:](#Topics_covered_in_this_section:)
+		- [1.2.3 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F)
+		- [1.2.4 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section)
+		- [1.2.5 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section)
+		- [1.2.6 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section)
+		- [1.2.7 Section 2](#Section_2)
+			* [1.2.7.1 Section title:](#Section_title:_2)
+		- [1.2.8 Topics covered in this section:](#Topics_covered_in_this_section:_2)
+		- [1.2.9 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_2)
+		- [1.2.10 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_2)
+		- [1.2.11 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_2)
+		- [1.2.12 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_2)
+		- [1.2.13 Section 3](#Section_3)
+			* [1.2.13.1 Section title:](#Section_title:_3)
+		- [1.2.14 Topics covered in this section:](#Topics_covered_in_this_section:_3)
+		- [1.2.15 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_3)
+		- [1.2.16 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_3)
+		- [1.2.17 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_3)
+		- [1.2.18 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_3)
+		- [1.2.19 Section 4](#Section_4)
+			* [1.2.19.1 Section title:](#Section_title:_4)
+		- [1.2.20 Topics covered in this section:](#Topics_covered_in_this_section:_4)
+		- [1.2.21 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_4)
+		- [1.2.22 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_4)
+		- [1.2.23 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_4)
+		- [1.2.24 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_4)
+		- [1.2.25 Section 5](#Section_5)
+			* [1.2.25.1 Section title:](#Section_title:_5)
+		- [1.2.26 Topics covered in this section:](#Topics_covered_in_this_section:_5)
+		- [1.2.27 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_5)
+		- [1.2.28 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_5)
+		- [1.2.29 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_5)
+		- [1.2.30 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_5)
+		- [1.2.31 Section 6](#Section_6)
+			* [1.2.31.1 Section title:](#Section_title:_6)
+		- [1.2.32 Topics covered in this section:](#Topics_covered_in_this_section:_6)
+		- [1.2.33 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_6)
+		- [1.2.34 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_6)
+		- [1.2.35 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_6)
+		- [1.2.36 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_6)
+
+
+
+Analytical Geometry & Linear Algebra – I
+========================================
+
+
+* **Course name:** Analytical Geometry & Linear Algebra – I
+* **Course number:** XYZ
+* **Subject area:** Math
+
+
+Course characteristics
+----------------------
+
+
+### Key concepts of the class
+
+
+* fundamental principles of vector algebra,
+* concepts of basic geometry objects and their transformations in the plane and in the space
+
+
+### What is the purpose of this course?
+
+
+This is an introductory course in analytical geometry and linear algebra. After having studied the course, students get to know fundamental principles of vector algebra and its applications in solving various geometry problems, different types of equations of lines and planes, conics and quadric surfaces, transformations in the plane and in the space. An introduction on matrices and determinants as a fundamental knowledge of linear algebra is also provided.
+
+
+
+### Course Objectives Based on Bloom’s Taxonomy
+
+
+### - What should a student remember at the end of the course?
+
+
+* List basic notions of vector algebra,
+* recite the base form of the equations of transformations in planes and spaces,
+* recall equations of lines and planes,
+* identify the type of conic section,
+* recognize the kind of quadric surfaces.
+
+
+### - What should a student be able to understand at the end of the course?
+
+
+* explain the geometrical interpretation of the basic operations of vector algebra,
+* restate equations of lines and planes in different forms,
+* interpret the geometrical meaning of the conic sections in the mathematical expression,
+* give the examples of the surfaces of revolution,
+* understand the value of geometry in various fields of science and techniques.
+
+
+### - What should a student be able to apply at the end of the course?
+
+
+* Perform the basic operations of vector algebra,
+* use different types of equations of lines and planes to solve the plane and space problems,
+* represent the conic section in canonical form,
+* compose the equation of quadric surface.
+
+
+### Course evaluation
+
+
+
+
+Course grade breakdown
+|  |  | **Proposed points** |
+| --- | --- | --- |
+| Labs/seminar classes
+ | 20
+ | 10
+ |
+| Interim performance assessment
+ | 30
+ | 20
+ |
+| Exams
+ | 50
+ | 70
+ |
+
+
+### Grades range
+
+
+
+
+Course grading range
+|  |  | **Proposed range** |
+| --- | --- | --- |
+| A. Excellent
+ | 90-100
+ | 80-100
+ |
+| B. Good
+ | 75-89
+ | 60-79
+ |
+| C. Satisfactory
+ | 60-74
+ | 40-59
+ |
+| D. Poor
+ | 0-59
+ | 0-39
+ |
+
+
+### Resources and reference material
+
+
+#### Textbooks:
+
+
+* 
+
+
+#### Reference material:
+
+
+* 
+* 
+
+
+Course Sections
+---------------
+
+
+The main sections of the course and approximate hour distribution between them is as follows:
+
+
+
+
+
+Course Sections
+| **Section** | **Section Title** | **Lectures** | **Seminars** | **Self-study** | **Knowledge** |
+| **Number** |  | **(hours)** | **(labs)** |  | **evaluation** |
+| 1
+ | Vector algebra
+ | 8
+ | 4
+ | 10
+ | 2
+ |
+| 2
+ | Introduction to matrices and determinants
+ | 8
+ | 4
+ | 10
+ | 1
+ |
+| 3
+ | Lines in the plane and in the space
+ | 8
+ | 4
+ | 10
+ | 2
+ |
+| 4
+ | Planes in the space
+ | 8
+ | 4
+ | 10
+ | 1
+ |
+| 5
+ | Quadratic curves
+ | 8
+ | 4
+ | 10
+ | 2
+ |
+| 6
+ | Quadric surfaces
+ | 8
+ | 4
+ | 10
+ | 2
+ |
+| Final examination
+ |  |  |  |  | 2
+ |
+
+
+### Section 1
+
+
+#### Section title:
+
+
+Vector algebra
+
+
+
+### Topics covered in this section:
+
+
+* Vector spaces
+* Basic operations on vectors (summation, multiplication by scalar, dot product)
+* Linear dependency and in-dependency of the vectors
+* Basis in vector spaces
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. How to perform the shift of the vector?
+2. What is the geometrical interpretation of the dot product?
+3. How to determine whether the vectors are linearly dependent?
+4. What is a vector basis?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Evaluate 
+
+
+
+
+|
+
+
+
+a
+
+
+
+
+|
+
+
+2
+
+
+−
+2
+
+
+3
+
+
+
+
+a
+
+
+⋅
+
+
+b
+
+
+−
+7
+
+|
+
+
+
+b
+
+
+
+
+|
+
+
+2
+
+
+
+
+{\textstyle |{\textbf {a}}|^{2}-2{\sqrt {3}}{\textbf {a}}\cdot {\textbf {b}}-7|{\textbf {b}}|^{2}}
+
+![{\textstyle |{\textbf {a}}|^{2}-2{\sqrt {3}}{\textbf {a}}\cdot {\textbf {b}}-7|{\textbf {b}}|^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b39de16745ae08f1e071202ed4c68a7439df361b) given that 
+
+
+
+
+|
+
+
+
+a
+
+
+
+|
+
+=
+4
+
+
+{\textstyle |{\textbf {a}}|=4}
+
+![{\textstyle |{\textbf {a}}|=4}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dad653ed7b4f53967e38f14dc254a0b4ed40f4ac), 
+
+
+
+
+|
+
+
+
+b
+
+
+
+|
+
+=
+1
+
+
+{\textstyle |{\textbf {b}}|=1}
+
+![{\textstyle |{\textbf {b}}|=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2147d16bdc4fd215671610f46300d16ea8f1963d), 
+
+
+
+∠
+(
+
+
+a
+
+
+,
+
+
+
+b
+
+
+)
+=
+
+150
+
+∘
+
+
+
+
+{\textstyle \angle ({\textbf {a}},\,{\textbf {b}})=150^{\circ }}
+
+![{\textstyle \angle ({\textbf {a}},\,{\textbf {b}})=150^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/34c0c47f4b2dbe58c362811be01e2a9658ffd65e).
+2. Prove that vectors 
+
+
+
+
+
+b
+
+
+(
+
+
+a
+
+
+⋅
+
+
+c
+
+
+)
+−
+
+
+c
+
+
+(
+
+
+a
+
+
+⋅
+
+
+b
+
+
+)
+
+
+{\textstyle {\textbf {b}}({\textbf {a}}\cdot {\textbf {c}})-{\textbf {c}}({\textbf {a}}\cdot {\textbf {b}})}
+
+![{\textstyle {\textbf {b}}({\textbf {a}}\cdot {\textbf {c}})-{\textbf {c}}({\textbf {a}}\cdot {\textbf {b}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91d497e3670b2e628a97f0ccb57ca80a925ef32c) and 
+
+
+
+
+
+a
+
+
+
+
+{\textstyle {\textbf {a}}}
+
+![{\textstyle {\textbf {a}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0a7a4f8c41fd49715b57c7891e867192892aaf8b) are perpendicular to each other.
+3. Bases 
+
+
+
+A
+D
+
+
+{\textstyle AD}
+
+![{\textstyle AD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b67c9a22c95905ef6b81962b11b31e1c0ef52225) and 
+
+
+
+B
+C
+
+
+{\textstyle BC}
+
+![{\textstyle BC}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9357a907256f2d11e87040067a6ce9dd1976f725) of trapezoid 
+
+
+
+A
+B
+C
+D
+
+
+{\textstyle ABCD}
+
+![{\textstyle ABCD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/56e9dd14b4fcb989c106f3679aa2699f07eee6d4) are in the ratio of 
+
+
+
+4
+:
+1
+
+
+{\textstyle 4:1}
+
+![{\textstyle 4:1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/44785771746a94fd2cf3d26ff7cd5653f816763d). The diagonals of the trapezoid intersect at point 
+
+
+
+M
+
+
+{\textstyle M}
+
+![{\textstyle M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/913ace920108f7552777e36ac0b7ee3f5093a088) and the extensions of sides 
+
+
+
+A
+B
+
+
+{\textstyle AB}
+
+![{\textstyle AB}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac121a3e6c5dff2ebb2ff8340e4a7f1b35992e44) and 
+
+
+
+C
+D
+
+
+{\textstyle CD}
+
+![{\textstyle CD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/523217c283f1b3f72fe4f317b8ff09e22365f1e5) intersect at point 
+
+
+
+P
+
+
+{\textstyle P}
+
+![{\textstyle P}](https://wikimedia.org/api/rest_v1/media/math/render/svg/038590207af1024a629c1a08c855e9ac46bf5610). Let us consider the basis with 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) as the origin, 
+
+
+
+
+
+
+A
+D
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AD}}}
+
+![{\textstyle {\overrightarrow {AD}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a09091c3ae3ae05dbb915b79e411ee15a84401f1) and 
+
+
+
+
+
+
+A
+B
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AB}}}
+
+![{\textstyle {\overrightarrow {AB}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a6f9e6559e7cd7c16144340887587c73e294b4ba) as basis vectors. Find the coordinates of points 
+
+
+
+M
+
+
+{\textstyle M}
+
+![{\textstyle M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/913ace920108f7552777e36ac0b7ee3f5093a088) and 
+
+
+
+P
+
+
+{\textstyle P}
+
+![{\textstyle P}](https://wikimedia.org/api/rest_v1/media/math/render/svg/038590207af1024a629c1a08c855e9ac46bf5610) in this basis.
+4. A line segment joining a vertex of a tetrahedron with the centroid of the opposite face (the centroid of a triangle is an intersection point of all its medians) is called a median of this tetrahedron. Using vector algebra prove that all the four medians of any tetrahedron concur in a point that divides these medians in the ratio of 
+
+
+
+3
+:
+1
+
+
+{\textstyle 3:1}
+
+![{\textstyle 3:1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1bdfd3570b8991fb33d61e324c67dd54f08a0eef), the longer segments being on the side of the vertex of the tetrahedron.
+
+
+### Test questions for final assessment in this section
+
+
+1. Vector spaces. General concepts.
+2. Dot product as an operation on vectors.
+3. Basis in vector spaces. Its properties.
+
+
+### Section 2
+
+
+#### Section title:
+
+
+Introduction to matrices and determinants
+
+
+
+### Topics covered in this section:
+
+
+* Relationship between Linear Algebra and Analytical Geometry
+* Matrices 2x2, 3x3
+* Determinants 2x2, 3x3
+* Operations om matrices and determinants
+* The rank of a matrix
+* Inverse matrix
+* Systems of linear equations
+* Changing basis and coordinates
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. What is the difference between matrices and determinants?
+2. Matrices 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) and 
+
+
+
+C
+
+
+{\textstyle C}
+
+![{\textstyle C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6dca76d9ff4b48256b6a4a99bcb234b64b2fa72b) have dimensions of 
+
+
+
+m
+×
+n
+
+
+{\textstyle m\times n}
+
+![{\textstyle m\times n}](https://wikimedia.org/api/rest_v1/media/math/render/svg/37dc29fae3b1932f1b311a052ecc6ecb8692dc48) and 
+
+
+
+p
+×
+q
+
+
+{\textstyle p\times q}
+
+![{\textstyle p\times q}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cdbd208094b241eb647c2e3b515a05197f9e0fdc) respectively, and it is known that the product 
+
+
+
+A
+B
+C
+
+
+{\textstyle ABC}
+
+![{\textstyle ABC}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1516a55703463b2e378eb0b2eda76f08f6919636) exists. What are possible dimensions of 
+
+
+
+B
+
+
+{\textstyle B}
+
+![{\textstyle B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/de0b47ffc21636dc2df68f6c793177a268f10e9b) and 
+
+
+
+A
+B
+C
+
+
+{\textstyle ABC}
+
+![{\textstyle ABC}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1516a55703463b2e378eb0b2eda76f08f6919636)?
+3. How to determine the rank of a matrix?
+4. What is the meaning of the inverse matrix?
+5. How to restate a system of linear equations in the matrix form?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+Let 
+
+
+
+A
+=
+
+(
+
+
+
+
+3
+
+
+1
+
+
+
+
+5
+
+
+−
+2
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cc}3&1\\5&-2\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cc}3&1\\5&-2\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2239fc87faa1789417dbc59e4d88349c4ab50b1d), 
+
+
+
+B
+=
+
+(
+
+
+
+
+−
+2
+
+
+1
+
+
+
+
+3
+
+
+4
+
+
+
+
+)
+
+
+
+{\textstyle B=\left({\begin{array}{cc}-2&1\\3&4\\\end{array}}\right)}
+
+![{\textstyle B=\left({\begin{array}{cc}-2&1\\3&4\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cda45263ccde2633fc2b326112c4580c7d96c6d7), and 
+
+
+
+I
+=
+
+(
+
+
+
+
+1
+
+
+0
+
+
+
+
+0
+
+
+1
+
+
+
+
+)
+
+
+
+{\textstyle I=\left({\begin{array}{cc}1&0\\0&1\\\end{array}}\right)}
+
+![{\textstyle I=\left({\begin{array}{cc}1&0\\0&1\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1a8ec455e7245033a95fe9502af2fbae28f2f143).
+
+
+
+1. Find 
+
+
+
+A
++
+B
+
+
+{\textstyle A+B}
+
+![{\textstyle A+B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bdd957a1f1d7f480fb51c33b1e5ab3b8259cb37f) and 
+
+
+
+2
+A
+−
+3
+B
++
+I
+
+
+{\textstyle 2A-3B+I}
+
+![{\textstyle 2A-3B+I}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bf9f21726daa3bc4c5b46cdebf17900d2384c4bc).
+2. Find the products 
+
+
+
+A
+B
+
+
+{\textstyle AB}
+
+![{\textstyle AB}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac121a3e6c5dff2ebb2ff8340e4a7f1b35992e44) and 
+
+
+
+B
+A
+
+
+{\textstyle BA}
+
+![{\textstyle BA}](https://wikimedia.org/api/rest_v1/media/math/render/svg/30d370a5b049f1bf605e0849e5011dab921a3e80) (and so make sure that, in general, 
+
+
+
+A
+B
+≠
+B
+A
+
+
+{\textstyle AB\neq BA}
+
+![{\textstyle AB\neq BA}](https://wikimedia.org/api/rest_v1/media/math/render/svg/547dca1516d9c8402fe6b52671054d5412e39d7a) for matrices).
+3. Find the inverse matrices for the given ones.
+4. Find the determinants of the given matrices.
+5. Point 
+
+
+
+M
+
+
+{\textstyle M}
+
+![{\textstyle M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/913ace920108f7552777e36ac0b7ee3f5093a088) is the centroid of face 
+
+
+
+B
+C
+D
+
+
+{\textstyle BCD}
+
+![{\textstyle BCD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dbf276d48bdd841bc17d7b41806b4fefd4d93aec) of tetrahedron 
+
+
+
+A
+B
+C
+D
+
+
+{\textstyle ABCD}
+
+![{\textstyle ABCD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/56e9dd14b4fcb989c106f3679aa2699f07eee6d4). The old coordinate system is given by 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31), 
+
+
+
+
+
+
+A
+B
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AB}}}
+
+![{\textstyle {\overrightarrow {AB}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a6f9e6559e7cd7c16144340887587c73e294b4ba), 
+
+
+
+
+
+
+A
+C
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AC}}}
+
+![{\textstyle {\overrightarrow {AC}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cec90ca60916095907088cdf9c6807e322940609), 
+
+
+
+
+
+
+A
+D
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AD}}}
+
+![{\textstyle {\overrightarrow {AD}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a09091c3ae3ae05dbb915b79e411ee15a84401f1), and the new coordinate system is given by 
+
+
+
+M
+
+
+{\textstyle M}
+
+![{\textstyle M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/913ace920108f7552777e36ac0b7ee3f5093a088), 
+
+
+
+
+
+
+M
+B
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {MB}}}
+
+![{\textstyle {\overrightarrow {MB}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fc628c7e66ee539b78d720ffb8b08c68cda528bc), 
+
+
+
+
+
+
+M
+C
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {MC}}}
+
+![{\textstyle {\overrightarrow {MC}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e7b29574c4ba08f6b03fc30de162aa30153d3ab0), 
+
+
+
+
+
+
+M
+A
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {MA}}}
+
+![{\textstyle {\overrightarrow {MA}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef8be9dd7ec0faa12b4f2f9f335d65b1cab904c5). Find the coordinates of a point in the old coordinate system given its coordinates 
+
+
+
+
+x
+′
+
+
+
+{\textstyle x'}
+
+![{\textstyle x'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bdd4bbf7bc3c37c71d0a1f9e4ef6c504c8f9d5de), 
+
+
+
+
+y
+′
+
+
+
+{\textstyle y'}
+
+![{\textstyle y'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e40eea4dc71b01e5ddff1d14b9b89853fde81d), 
+
+
+
+
+z
+′
+
+
+
+{\textstyle z'}
+
+![{\textstyle z'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/80546fbdafc04d89612c5491bc04d509709aeb17) in the new one.
+
+
+### Test questions for final assessment in this section
+
+
+1. Operations om matrices and determinants.
+2. Inverse matrix.
+3. Systems of linear equations and their solution in matrix form.
+4. Changing basis and coordinates.
+
+
+### Section 3
+
+
+#### Section title:
+
+
+Lines in the plane and in the space
+
+
+
+### Topics covered in this section:
+
+
+* General equation of a line in the plane
+* General parametric equation of a line in the space
+* Line as intersection between planes
+* Vector equation of a line
+* Distance from a point to a line
+* Distance between lines
+* Inter-positioning of lines
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. How to represent a line in the vector form?
+2. What is the result of intersection of two planes in vector form?
+3. How to derive the formula for the distance from a point to a line?
+4. How to interpret geometrically the distance between lines?
+5. List all possible inter-positions of lines in the space.
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Two lines are given by the equations 
+
+
+
+
+
+r
+
+
+⋅
+
+
+n
+
+
+=
+A
+
+
+{\textstyle {\textbf {r}}\cdot {\textbf {n}}=A}
+
+![{\textstyle {\textbf {r}}\cdot {\textbf {n}}=A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d0bdfb3c03f3478452862b246cd0bec466eb624d) and 
+
+
+
+
+
+r
+
+
+=
+
+
+
+r
+
+
+
+0
+
+
++
+
+
+a
+
+
+t
+
+
+{\textstyle {\textbf {r}}={\textbf {r}}\_{0}+{\textbf {a}}t}
+
+![{\textstyle {\textbf {r}}={\textbf {r}}_{0}+{\textbf {a}}t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca83af73cef59fe73380c9737197485304b371ec), and at that 
+
+
+
+
+
+a
+
+
+⋅
+
+
+n
+
+
+≠
+0
+
+
+{\textstyle {\textbf {a}}\cdot {\textbf {n}}\neq 0}
+
+![{\textstyle {\textbf {a}}\cdot {\textbf {n}}\neq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/33673ddea1dea180b68cac92d5065f32f85016b1). Find the position vector of the intersection point of these lines.
+2. Find the distance from point 
+
+
+
+
+M
+
+0
+
+
+
+
+{\textstyle M\_{0}}
+
+![{\textstyle M_{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/feb4ebe89e459609fa9e97bf72ee561acb3f7836) with the position vector 
+
+
+
+
+
+
+r
+
+
+
+0
+
+
+
+
+{\textstyle {\textbf {r}}\_{0}}
+
+![{\textstyle {\textbf {r}}_{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b0b1d2beb050ff53f1db5422ed3c6067091489d2) to the line defined by the equation (a) 
+
+
+
+
+
+r
+
+
+=
+
+
+
+r
+
+
+
+0
+
+
++
+
+
+a
+
+
+t
+
+
+{\textstyle {\textbf {r}}={\textbf {r}}\_{0}+{\textbf {a}}t}
+
+![{\textstyle {\textbf {r}}={\textbf {r}}_{0}+{\textbf {a}}t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca83af73cef59fe73380c9737197485304b371ec); (b) 
+
+
+
+
+
+r
+
+
+⋅
+
+
+n
+
+
+=
+A
+
+
+{\textstyle {\textbf {r}}\cdot {\textbf {n}}=A}
+
+![{\textstyle {\textbf {r}}\cdot {\textbf {n}}=A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d0bdfb3c03f3478452862b246cd0bec466eb624d).
+3. Diagonals of a rhombus intersect at point 
+
+
+
+M
+(
+1
+;
+
+2
+)
+
+
+{\textstyle M(1;\,2)}
+
+![{\textstyle M(1;\,2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1f5f919c98511e9602aff3b5c6fb6a44b3c5d75c), the longest of them being parallel to a horizontal axis. The side of the rhombus equals 2 and its obtuse angle is 
+
+
+
+
+120
+
+∘
+
+
+
+
+{\textstyle 120^{\circ }}
+
+![{\textstyle 120^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/db4bd85704493ea3595bcef6a92dbadcef085e51). Compose the equations of the sides of this rhombus.
+4. Compose the equations of lines passing through point 
+
+
+
+A
+(
+2
+;
+−
+4
+)
+
+
+{\textstyle A(2;-4)}
+
+![{\textstyle A(2;-4)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/adb02900c49b8277ff0d9994f3c262b42712fc10) and forming angles of 
+
+
+
+
+60
+
+∘
+
+
+
+
+{\textstyle 60^{\circ }}
+
+![{\textstyle 60^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/880b547c0017493563c28efdad95fdac91f97352) with the line 
+
+
+
+
+
+
+1
+−
+2
+x
+
+3
+
+
+=
+
+
+
+3
++
+2
+y
+
+
+−
+2
+
+
+
+
+
+{\textstyle {\frac {1-2x}{3}}={\frac {3+2y}{-2}}}
+
+![{\textstyle {\frac {1-2x}{3}}={\frac {3+2y}{-2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9d3793ed8ac9c5b2a740ee251edbe89f3a25c7d4).
+
+
+### Test questions for final assessment in this section
+
+
+1. Lines in the plane and in the space. Equations of lines.
+2. Distance from a point to a line.
+3. Distance between two parallel lines.
+4. Distance between two skew lines.
+
+
+### Section 4
+
+
+#### Section title:
+
+
+Planes in the space
+
+
+
+### Topics covered in this section:
+
+
+* General equation of a plane
+* Normalized linear equation of a plane
+* Vector equation of a plane
+* Parametric equation a plane
+* Distance from a point to a plane
+* Projection of a vector on the plane
+* Inter-positioning of lines and planes
+* Cross Product of two vectors
+* Triple Scalar Product
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. What is the difference between general and normalized forms of equations of a plane?
+2. How to rewrite the equation of a plane in a vector form?
+3. What is the normal to a plane?
+4. How to interpret the cross products of two vectors?
+5. What is the meaning of scalar triple product of three vectors?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Find the cross product of (a) vectors 
+
+
+
+
+
+a
+
+
+(
+3
+;
+−
+2
+;
+
+1
+)
+
+
+{\textstyle {\textbf {a}}(3;-2;\,1)}
+
+![{\textstyle {\textbf {a}}(3;-2;\,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/24aa2e3d81f5e733ac961fc54c00c6400ac7c554) and 
+
+
+
+
+
+b
+
+
+(
+2
+;
+−
+5
+;
+−
+3
+)
+
+
+{\textstyle {\textbf {b}}(2;-5;-3)}
+
+![{\textstyle {\textbf {b}}(2;-5;-3)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ed4f1d0f60888ec6d6e29a3ef51f7c26784b688e); (b) vectors 
+
+
+
+
+
+a
+
+
+(
+3
+;
+−
+2
+;
+
+1
+)
+
+
+{\textstyle {\textbf {a}}(3;-2;\,1)}
+
+![{\textstyle {\textbf {a}}(3;-2;\,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/24aa2e3d81f5e733ac961fc54c00c6400ac7c554) and 
+
+
+
+
+
+c
+
+
+(
+−
+18
+;
+
+12
+;
+−
+6
+)
+
+
+{\textstyle {\textbf {c}}(-18;\,12;-6)}
+
+![{\textstyle {\textbf {c}}(-18;\,12;-6)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/536804f73bf9994ca0ac6a28c7c18f9b7c025d00).
+2. A triangle is constructed on vectors 
+
+
+
+
+
+a
+
+
+(
+2
+;
+4
+;
+−
+1
+)
+
+
+{\textstyle {\textbf {a}}(2;4;-1)}
+
+![{\textstyle {\textbf {a}}(2;4;-1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8dcfef96a8fb429db141d89ad1a4a7d2b79796c7) and 
+
+
+
+
+
+b
+
+
+(
+−
+2
+;
+1
+;
+1
+)
+
+
+{\textstyle {\textbf {b}}(-2;1;1)}
+
+![{\textstyle {\textbf {b}}(-2;1;1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/33194e12e69d8cf8bef0e3a7a975b0bbc27e0d59). (a) Find the area of this triangle. (b) Find the altitudes of this triangle.
+3. Find the scalar triple product of 
+
+
+
+
+
+a
+
+
+(
+1
+;
+
+2
+;
+−
+1
+)
+
+
+{\textstyle {\textbf {a}}(1;\,2;-1)}
+
+![{\textstyle {\textbf {a}}(1;\,2;-1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f4ff4c4819f08216a9b289eee65fae9e2409cd89), 
+
+
+
+
+
+b
+
+
+(
+7
+;
+3
+;
+−
+5
+)
+
+
+{\textstyle {\textbf {b}}(7;3;-5)}
+
+![{\textstyle {\textbf {b}}(7;3;-5)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bad88c6efacea267911438883c60e91aa7e641d4), 
+
+
+
+
+
+c
+
+
+(
+3
+;
+
+4
+;
+−
+3
+)
+
+
+{\textstyle {\textbf {c}}(3;\,4;-3)}
+
+![{\textstyle {\textbf {c}}(3;\,4;-3)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3075cbf140d048ec7105863bf15ffbc46d4ea011).
+4. It is known that basis vectors 
+
+
+
+
+
+
+e
+
+
+
+1
+
+
+
+
+{\textstyle {\textbf {e}}\_{1}}
+
+![{\textstyle {\textbf {e}}_{1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/633f38e385b970d94316cec9a3f0f8d8b2952c78), 
+
+
+
+
+
+
+e
+
+
+
+2
+
+
+
+
+{\textstyle {\textbf {e}}\_{2}}
+
+![{\textstyle {\textbf {e}}_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1141e813036efabb49e22e26699abda03db9c238), 
+
+
+
+
+
+
+e
+
+
+
+3
+
+
+
+
+{\textstyle {\textbf {e}}\_{3}}
+
+![{\textstyle {\textbf {e}}_{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4136ef375267fae398133caf33d6309b3491fe75) have lengths of 
+
+
+
+1
+
+
+{\textstyle 1}
+
+![{\textstyle 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6706df9ed9f240d1a94545fb4e522bda168fe8fd), 
+
+
+
+2
+
+
+{\textstyle 2}
+
+![{\textstyle 2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/78ed0cd8140e5a15b6fcce83602df58458e0f3b0), 
+
+
+
+2
+
+
+2
+
+
+
+
+{\textstyle 2{\sqrt {2}}}
+
+![{\textstyle 2{\sqrt {2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f302ae86c5e346beaf1dc60ab28ce51583d3a10f) respectively, and 
+
+
+
+∠
+(
+
+
+
+e
+
+
+
+1
+
+
+,
+
+
+
+e
+
+
+
+2
+
+
+)
+=
+
+120
+
+∘
+
+
+
+
+{\textstyle \angle ({\textbf {e}}\_{1},{\textbf {e}}\_{2})=120^{\circ }}
+
+![{\textstyle \angle ({\textbf {e}}_{1},{\textbf {e}}_{2})=120^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5bc355fb33e21d27781b3c69f604dfa4ac8a2335), 
+
+
+
+∠
+(
+
+
+
+e
+
+
+
+1
+
+
+,
+
+
+
+e
+
+
+
+3
+
+
+)
+=
+
+135
+
+∘
+
+
+
+
+{\textstyle \angle ({\textbf {e}}\_{1},{\textbf {e}}\_{3})=135^{\circ }}
+
+![{\textstyle \angle ({\textbf {e}}_{1},{\textbf {e}}_{3})=135^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/077d554778a6237a758bdd3cd174fb71e56c5a59), 
+
+
+
+∠
+(
+
+
+
+e
+
+
+
+2
+
+
+,
+
+
+
+e
+
+
+
+3
+
+
+)
+=
+
+45
+
+∘
+
+
+
+
+{\textstyle \angle ({\textbf {e}}\_{2},{\textbf {e}}\_{3})=45^{\circ }}
+
+![{\textstyle \angle ({\textbf {e}}_{2},{\textbf {e}}_{3})=45^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2c625e201eaf56a5ab2f55c468fb74919eecf950). Find the volume of a parallelepiped constructed on vectors with coordinates 
+
+
+
+(
+−
+1
+;
+
+0
+;
+
+2
+)
+
+
+{\textstyle (-1;\,0;\,2)}
+
+![{\textstyle (-1;\,0;\,2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6f80a6dd17132920d07de233c927f5b35fe55342), 
+
+
+
+(
+1
+;
+
+1
+
+4
+)
+
+
+{\textstyle (1;\,1\,4)}
+
+![{\textstyle (1;\,1\,4)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/93f2f019128f43ccd8b9bf1ec5fae847335c9609) and 
+
+
+
+(
+−
+2
+;
+
+1
+;
+
+1
+)
+
+
+{\textstyle (-2;\,1;\,1)}
+
+![{\textstyle (-2;\,1;\,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c29df73c5099969e89def9536b89bed1f8b8300b) in this basis.
+
+
+### Test questions for final assessment in this section
+
+
+1. Planes in the space. Equations of planes.
+2. Distance from a point to a plane, from a line to a plane.
+3. Projection of a vector on the plane.
+4. Cross product, its properties and geometrical interpretation.
+5. Scalar triple product, its properties and geometrical interpretation.
+
+
+### Section 5
+
+
+#### Section title:
+
+
+Quadratic curves
+
+
+
+### Topics covered in this section:
+
+
+* Circle
+* Ellipse
+* Hyperbola
+* Parabola
+* Canonical equations
+* Shifting of coordinate system
+* Rotating of coordinate system
+* Parametrization
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. Formulate the canonical equation of the given quadratic curve.
+2. Which orthogonal transformations of coordinates do you know?
+3. How to perform a transformation of the coordinate system?
+4. How to represent a curve in the space?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Prove that a curve given by 
+
+
+
+34
+
+x
+
+2
+
+
++
+24
+x
+y
++
+41
+
+y
+
+2
+
+
+−
+44
+x
++
+58
+y
++
+1
+=
+0
+
+
+{\textstyle 34x^{2}+24xy+41y^{2}-44x+58y+1=0}
+
+![{\textstyle 34x^{2}+24xy+41y^{2}-44x+58y+1=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2081edc20b56611eb9f1897a625f3bc0bc3df3b5) is an ellipse. Find the major and minor axes of this ellipse, its eccentricity, coordinates of its center and foci. Find the equations of axes and directrices of this ellipse.
+2. Determine types of curves given by the following equations. For each of the curves, find its canonical coordinate system (i.e. indicate the coordinates of origin and new basis vectors in the initial coordinate system) and its canonical equation. (a) 
+
+
+
+9
+
+x
+
+2
+
+
+−
+16
+
+y
+
+2
+
+
+−
+6
+x
++
+8
+y
+−
+144
+=
+0
+
+
+{\textstyle 9x^{2}-16y^{2}-6x+8y-144=0}
+
+![{\textstyle 9x^{2}-16y^{2}-6x+8y-144=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e2307372c3cf01eef66761c99845dcbe394be29f); (b) 
+
+
+
+9
+
+x
+
+2
+
+
++
+4
+
+y
+
+2
+
+
++
+6
+x
+−
+4
+y
+−
+2
+=
+0
+
+
+{\textstyle 9x^{2}+4y^{2}+6x-4y-2=0}
+
+![{\textstyle 9x^{2}+4y^{2}+6x-4y-2=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73b831469fdf03eac9e9c9656ae7fef80096fb94); (c) 
+
+
+
+12
+
+x
+
+2
+
+
+−
+12
+x
+−
+32
+y
+−
+29
+=
+0
+
+
+{\textstyle 12x^{2}-12x-32y-29=0}
+
+![{\textstyle 12x^{2}-12x-32y-29=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8cde74f6df39c7d1f475a31c4f1add253f1a43eb); (d) 
+
+
+
+x
+y
++
+2
+x
++
+y
+=
+0
+
+
+{\textstyle xy+2x+y=0}
+
+![{\textstyle xy+2x+y=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ced2a1c13f7eb77948ffc6ba9c1789659873573);
+3. Find the equations of lines tangent to curve 
+
+
+
+6
+x
+y
++
+8
+
+y
+
+2
+
+
+−
+12
+x
+−
+26
+y
++
+11
+=
+0
+
+
+{\textstyle 6xy+8y^{2}-12x-26y+11=0}
+
+![{\textstyle 6xy+8y^{2}-12x-26y+11=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/38463f126baaf801dce5a01c4e5d2e4c9d5e5080) that are (a) parallel to line 
+
+
+
+6
+x
++
+17
+y
+−
+4
+=
+0
+
+
+{\textstyle 6x+17y-4=0}
+
+![{\textstyle 6x+17y-4=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fe1136341a1ea0ad8bbc7101dbceadb86b33e90e); (b) perpendicular to line 
+
+
+
+41
+x
+−
+24
+y
++
+3
+=
+0
+
+
+{\textstyle 41x-24y+3=0}
+
+![{\textstyle 41x-24y+3=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91928594589b3b61e71e2f6d60125360b48cd4fd); (c) parallel to line 
+
+
+
+y
+=
+2
+
+
+{\textstyle y=2}
+
+![{\textstyle y=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/887628e811c56cc94aaccb0f5e4c773f19231cf9).
+
+
+### Test questions for final assessment in this section
+
+
+1. Determine the type of a given curve with the use of the method of invariant.
+2. Compose the canonical equation of a given curve.
+3. Determine the canonical coordinate system for a given curve.
+
+
+### Section 6
+
+
+#### Section title:
+
+
+Quadric surfaces
+
+
+
+### Topics covered in this section:
+
+
+* General equation of the quadric surfaces
+* Canonical equation of a sphere and ellipsoid
+* Canonical equation of a hyperboloid and paraboloid
+* Surfaces of revolution
+* Canonical equation of a cone and cylinder
+* Vector equations of some quadric surfaces
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. What is the type of a quadric surface given by a certain equation?
+2. How to compose the equation of a surface of revolution?
+3. What is the difference between a directrix and generatrix?
+4. How to represent a quadric surface in the vector form?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. For each value of parameter 
+
+
+
+a
+
+
+{\textstyle a}
+
+![{\textstyle a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a503f107a7c104e40e484cee9e1f5993d28ffd8) determine types of surfaces given by the equations: (a) 
+
+
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+−
+
+z
+
+2
+
+
+=
+a
+
+
+{\textstyle x^{2}+y^{2}-z^{2}=a}
+
+![{\textstyle x^{2}+y^{2}-z^{2}=a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aedac9a12be3e2a8bb6549e080cecd007665a44c); (b) 
+
+
+
+
+x
+
+2
+
+
++
+a
+
+(
+
+
+y
+
+2
+
+
++
+
+z
+
+2
+
+
+
+)
+
+=
+1
+
+
+{\textstyle x^{2}+a\left(y^{2}+z^{2}\right)=1}
+
+![{\textstyle x^{2}+a\left(y^{2}+z^{2}\right)=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/04136582473b57e7f0525feeebccc4460ecf7ad8); (c) 
+
+
+
+
+x
+
+2
+
+
++
+a
+
+y
+
+2
+
+
+=
+a
+z
+
+
+{\textstyle x^{2}+ay^{2}=az}
+
+![{\textstyle x^{2}+ay^{2}=az}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d9326d877d128ad9d17a96c9765e1da5f7c91e6); (d) 
+
+
+
+
+x
+
+2
+
+
++
+a
+
+y
+
+2
+
+
+=
+a
+z
++
+1
+
+
+{\textstyle x^{2}+ay^{2}=az+1}
+
+![{\textstyle x^{2}+ay^{2}=az+1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d1cd37bf6d43b7adafdd4ec58f392dd620872e3).
+2. Find a vector equation of a right circular cone with apex 
+
+
+
+
+M
+
+0
+
+
+
+(
+
+
+
+r
+
+
+
+0
+
+
+)
+
+
+
+{\textstyle M\_{0}\left({\textbf {r}}\_{0}\right)}
+
+![{\textstyle M_{0}\left({\textbf {r}}_{0}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f1b67abdb7e98da13a4de428625f69d249276ae5) and axis 
+
+
+
+
+
+r
+
+
+=
+
+
+
+r
+
+
+
+0
+
+
++
+
+
+a
+
+
+t
+
+
+{\textstyle {\textbf {r}}={\textbf {r}}\_{0}+{\textbf {a}}t}
+
+![{\textstyle {\textbf {r}}={\textbf {r}}_{0}+{\textbf {a}}t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca83af73cef59fe73380c9737197485304b371ec) if it is known that generatrices of this cone form the angle of 
+
+
+
+α
+
+
+{\textstyle \alpha }
+
+![{\textstyle \alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d86dbd6183264b2f8569da1751380b173c7b185) with its axis.
+3. Find the equation of a cylinder with radius 
+
+
+
+
+
+2
+
+
+
+
+{\textstyle {\sqrt {2}}}
+
+![{\textstyle {\sqrt {2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5094a5b1e2f42490aa4de2c7a4b7235a27f1b73f) that has an axis 
+
+
+
+x
+=
+1
++
+t
+
+
+{\textstyle x=1+t}
+
+![{\textstyle x=1+t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eca54a99a9fdad0ee1a0bba54ac67014e83a51e2), 
+
+
+
+y
+=
+2
++
+t
+
+
+{\textstyle y=2+t}
+
+![{\textstyle y=2+t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/213ba8ad271ceb3b25aaaafcbe23edd7c885c7f0), 
+
+
+
+z
+=
+3
++
+t
+
+
+{\textstyle z=3+t}
+
+![{\textstyle z=3+t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/582781cac22a2c157f5b5b60da347600c9778a6f).
+4. An ellipsoid is symmetric with respect to coordinate planes, passes through point 
+
+
+
+M
+(
+3
+;
+
+1
+;
+
+1
+)
+
+
+{\textstyle M(3;\,1;\,1)}
+
+![{\textstyle M(3;\,1;\,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6192e6c5728edd5b9a22b9c19aa8be852e2f0599) and circle 
+
+
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
++
+
+z
+
+2
+
+
+=
+9
+
+
+{\textstyle x^{2}+y^{2}+z^{2}=9}
+
+![{\textstyle x^{2}+y^{2}+z^{2}=9}](https://wikimedia.org/api/rest_v1/media/math/render/svg/29376da667d60dba7e1f552a56d1ce98caea3a4d), 
+
+
+
+x
+−
+z
+=
+0
+
+
+{\textstyle x-z=0}
+
+![{\textstyle x-z=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/709115599ad054688b92e60cdb84a4f32fe944f1). Find the equation of this ellipsoid.
+
+
+### Test questions for final assessment in this section
+
+
+1. Determine the type of a quadric surface given by a certain equation.
+2. Compose the equation of a surface of revolution with the given directrix and generatrix.
+3. Represent a given equation of a quadric surface in the vector form.
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__analytic_geometry_and_linear_algebra_i.f22.md

@@ -0,0 +1,2288 @@
+
+
+
+
+
+
+
+BSc: Analytic Geometry And Linear Algebra I.f22
+===============================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Analytical Geometry & Linear Algebra – I](#Analytical_Geometry_.26_Linear_Algebra_.E2.80.93_I)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Course Topics](#Course_Topics)
+	+ [1.3 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.3.1 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.3.1.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.3.1.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.3.1.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.4 Grading](#Grading)
+		- [1.4.1 Course grading range](#Course_grading_range)
+		- [1.4.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.4.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.5 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.5.1 Open access resources](#Open_access_resources)
+	+ [1.6 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [1.7 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [1.7.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [1.7.1.1 Section 1](#Section_1)
+			* [1.7.1.2 Section 2](#Section_2)
+			* [1.7.1.3 Section 3](#Section_3)
+		- [1.7.2 Final assessment](#Final_assessment)
+			* [1.7.2.1 Section 1](#Section_1_2)
+			* [1.7.2.2 Section 2](#Section_2_2)
+			* [1.7.2.3 Section 3](#Section_3_2)
+		- [1.7.3 The retake exam](#The_retake_exam)
+
+
+
+Analytical Geometry & Linear Algebra – I
+========================================
+
+
+* **Course name**: Analytical Geometry & Linear Algebra – I
+* **Code discipline**: CSE202
+* **Subject area**: Math
+
+
+Short Description
+-----------------
+
+
+This is an introductory course in analytical geometry and linear algebra. After having studied the course, students get to know fundamental principles of vector algebra and its applications in solving various geometry problems, different types of equations of lines and planes, conics and quadric surfaces, transformations in the plane and in the space. An introduction on matrices and determinants as a fundamental knowledge of linear algebra is also provided. 
+
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Vector algebra | 1. Vector spaces
+2. Basic operations on vectors (summation, multiplication by scalar, dot product)
+3. Linear dependency and independency of the vectors. Basis in vector spaces.
+4. Introduction to matrices and determinants. The rank of a matrix. Inverse matrix.
+5. Systems of linear equations
+6. Changing basis and coordinates
+ |
+| Line and Plane | 1. General equation of a line in the plane
+2. General parametric equation of a line in the space
+3. Line as intersection between planes.
+4. Vector equation of a line.
+5. Distance from a point to a line. Distance between lines
+6. General equation of a plane.
+7. Normalized linear equation of a plane.
+8. Vector equation of a plane. Parametric equation of a plane
+9. Inter-positioning of lines and planes
+10. Cross Product of two vectors. Triple Scalar Product
+ |
+| Quadratic curves and surfaces | 1. Circle, Ellipse, Hyperbola, Parabola. Canonical equations
+2. Shift of coordinate system. Rotation of coordinate system. Parametrization
+3. General equation of the quadric surfaces.
+4. Canonical equations of a sphere, ellipsoid, hyperboloid and paraboloid
+5. Surfaces of revolution. Canonical equation of a cone and cylinder
+6. Vector equations of some quadric surfaces
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### ILOs defined at three levels
+
+
+We specify the intended learning outcomes at three levels: conceptual knowledge, practical skills, and comprehensive skills.
+
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* explain the geometrical interpretation of the basic operations of vector algebra,
+* restate equations of lines and planes in different forms,
+* interpret the geometrical meaning of the conic sections in the mathematical expression,
+* give the examples of the surfaces of revolution,
+* understand the value of geometry in various fields of science and techniques.
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* perform the basic operations of vector algebra,
+* use different types of equations of lines and planes to solve the plane and space problems,
+* represent the conic section in canonical form,
+* compose the equation of quadric surface.
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* list basic notions of vector algebra,
+* recite the base form of the equations of transformations in planes and spaces,
+* recall equations of lines and planes,
+* identify the type of conic section,
+* recognize the kind of quadric surfaces.
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 85-100 | -
+ |
+| B. Good | 70-84 | -
+ |
+| C. Satisfactory | 55-70 | -
+ |
+| D. Fail | 0-54 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Midterm | 35
+ |
+| Tests | 30 (15 for each)
+ |
+| Final exam | 35
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+* Participation is important. Attending lectures is the key to success in this course.
+* Review lecture materials before classes to do well.
+* Reading the recommended literature is obligatory, and will give you a deeper understanding of the material.
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* V.V. Konev. Linear Algebra, Vector Algebra and Analytical Geometry. Textbook. Tomsk: TPU Press, 2009, 114 pp [book1](https://portal.tpu.ru/SHARED/k/KONVAL/Textbooks/Tab1/Konev-Linear_Algebra_Vector_Algebra_and_Analytical_Geome.pdf)
+* R.A.Sharipov. Course of Analytical Geometry Textbook, Ufa, BSU, 2013. 227pp [book2](https://arxiv.org/pdf/1111.6521.pdf)
+* P.R. Vital. Analytical Geometry 2D and 3D Analytical Geometry 2D and 3D [book3](https://www.amazon.com/Analytical-Geometry-2D-3D-Vittal/dp/8131773604)
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Teaching and Learning Methods within each section
+| Teaching Techniques | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Problem-based learning (students learn by solving open-ended problems without a strictly-defined solution) | 1 | 1 | 1
+ |
+| Project-based learning (students work on a project) | 0 | 0 | 0
+ |
+| Modular learning (facilitated self-study) | 0 | 0 | 0
+ |
+| Differentiated learning (provide tasks and activities at several levels of difficulty to fit students needs and level) | 1 | 1 | 1
+ |
+| Contextual learning (activities and tasks are connected to the real world to make it easier for students to relate to them) | 0 | 0 | 0
+ |
+| Business game (learn by playing a game that incorporates the principles of the material covered within the course) | 0 | 0 | 0
+ |
+| Inquiry-based learning | 0 | 0 | 0
+ |
+| Just-in-time teaching | 0 | 0 | 0
+ |
+| Process oriented guided inquiry learning (POGIL) | 0 | 0 | 0
+ |
+| Studio-based learning | 0 | 0 | 0
+ |
+| Universal design for learning | 0 | 0 | 0
+ |
+| Task-based learning | 0 | 0 | 0
+ |
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Lectures | 1 | 1 | 1
+ |
+| Interactive Lectures | 1 | 1 | 1
+ |
+| Lab exercises | 1 | 1 | 1
+ |
+| Experiments | 0 | 0 | 0
+ |
+| Modeling | 0 | 0 | 0
+ |
+| Cases studies | 0 | 0 | 0
+ |
+| Development of individual parts of software product code | 0 | 0 | 0
+ |
+| Individual Projects | 0 | 0 | 0
+ |
+| Group projects | 0 | 0 | 0
+ |
+| Flipped classroom | 0 | 0 | 0
+ |
+| Quizzes (written or computer based) | 1 | 1 | 1
+ |
+| Peer Review | 0 | 0 | 0
+ |
+| Discussions | 1 | 1 | 1
+ |
+| Presentations by students | 0 | 0 | 0
+ |
+| Written reports | 0 | 0 | 0
+ |
+| Simulations and role-plays | 0 | 0 | 0
+ |
+| Essays | 0 | 0 | 0
+ |
+| Oral Reports | 0 | 0 | 0
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+1. How to perform the shift of the vector?
+2. What is the geometrical interpretation of the dot product?
+3. How to determine whether the vectors are linearly dependent?
+4. What is a vector basis?
+5. What is the difference between matrices and determinants?
+6. Matrices 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) and 
+
+
+
+C
+
+
+{\textstyle C}
+
+![{\textstyle C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6dca76d9ff4b48256b6a4a99bcb234b64b2fa72b) have dimensions of 
+
+
+
+m
+×
+n
+
+
+{\textstyle m\times n}
+
+![{\textstyle m\times n}](https://wikimedia.org/api/rest_v1/media/math/render/svg/37dc29fae3b1932f1b311a052ecc6ecb8692dc48) and 
+
+
+
+p
+×
+q
+
+
+{\textstyle p\times q}
+
+![{\textstyle p\times q}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cdbd208094b241eb647c2e3b515a05197f9e0fdc) respectively, and it is known that the product 
+
+
+
+A
+B
+C
+
+
+{\textstyle ABC}
+
+![{\textstyle ABC}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1516a55703463b2e378eb0b2eda76f08f6919636) exists. What are possible dimensions of 
+
+
+
+B
+
+
+{\textstyle B}
+
+![{\textstyle B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/de0b47ffc21636dc2df68f6c793177a268f10e9b) and 
+
+
+
+A
+B
+C
+
+
+{\textstyle ABC}
+
+![{\textstyle ABC}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1516a55703463b2e378eb0b2eda76f08f6919636)?
+7. How to determine the rank of a matrix?
+8. What is the meaning of the inverse matrix?
+9. How to restate a system of linear equations in the matrix form?
+
+
+#### Section 2
+
+
+1. How to represent a line in the vector form?
+2. What is the result of intersection of two planes in vector form?
+3. How to derive the formula for the distance from a point to a line?
+4. How to interpret geometrically the distance between lines?
+5. List all possible inter-positions of lines in the space.
+6. What is the difference between general and normalized forms of equations of a plane?
+7. How to rewrite the equation of a plane in a vector form?
+8. What is the normal to a plane?
+9. How to interpret the cross products of two vectors?
+10. What is the meaning of scalar triple product of three vectors?
+
+
+#### Section 3
+
+
+1. Formulate the canonical equation of the given quadratic curve.
+2. Which orthogonal transformations of coordinates do you know?
+3. How to perform a transformation of the coordinate system?
+4. How to represent a curve in the space?
+5. What is the type of a quadric surface given by a certain equation?
+6. How to compose the equation of a surface of revolution?
+7. What is the difference between a directrix and generatrix?
+8. How to represent a quadric surface in the vector form?
+
+
+### Final assessment
+
+
+#### Section 1
+
+
+1. Evaluate 
+
+
+
+
+|
+
+
+
+a
+
+
+
+
+|
+
+
+2
+
+
+−
+2
+
+
+3
+
+
+
+
+a
+
+
+⋅
+
+
+b
+
+
+−
+7
+
+|
+
+
+
+b
+
+
+
+
+|
+
+
+2
+
+
+
+
+{\textstyle |{\textbf {a}}|^{2}-2{\sqrt {3}}{\textbf {a}}\cdot {\textbf {b}}-7|{\textbf {b}}|^{2}}
+
+![{\textstyle |{\textbf {a}}|^{2}-2{\sqrt {3}}{\textbf {a}}\cdot {\textbf {b}}-7|{\textbf {b}}|^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b39de16745ae08f1e071202ed4c68a7439df361b) given that 
+
+
+
+
+|
+
+
+
+a
+
+
+
+|
+
+=
+4
+
+
+{\textstyle |{\textbf {a}}|=4}
+
+![{\textstyle |{\textbf {a}}|=4}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dad653ed7b4f53967e38f14dc254a0b4ed40f4ac), 
+
+
+
+
+|
+
+
+
+b
+
+
+
+|
+
+=
+1
+
+
+{\textstyle |{\textbf {b}}|=1}
+
+![{\textstyle |{\textbf {b}}|=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2147d16bdc4fd215671610f46300d16ea8f1963d), 
+
+
+
+∠
+(
+
+
+a
+
+
+,
+
+
+
+b
+
+
+)
+=
+
+150
+
+∘
+
+
+
+
+{\textstyle \angle ({\textbf {a}},\,{\textbf {b}})=150^{\circ }}
+
+![{\textstyle \angle ({\textbf {a}},\,{\textbf {b}})=150^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/34c0c47f4b2dbe58c362811be01e2a9658ffd65e).
+2. Prove that vectors 
+
+
+
+
+
+b
+
+
+(
+
+
+a
+
+
+⋅
+
+
+c
+
+
+)
+−
+
+
+c
+
+
+(
+
+
+a
+
+
+⋅
+
+
+b
+
+
+)
+
+
+{\textstyle {\textbf {b}}({\textbf {a}}\cdot {\textbf {c}})-{\textbf {c}}({\textbf {a}}\cdot {\textbf {b}})}
+
+![{\textstyle {\textbf {b}}({\textbf {a}}\cdot {\textbf {c}})-{\textbf {c}}({\textbf {a}}\cdot {\textbf {b}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91d497e3670b2e628a97f0ccb57ca80a925ef32c) and 
+
+
+
+
+
+a
+
+
+
+
+{\textstyle {\textbf {a}}}
+
+![{\textstyle {\textbf {a}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0a7a4f8c41fd49715b57c7891e867192892aaf8b) are perpendicular to each other.
+3. Bases 
+
+
+
+A
+D
+
+
+{\textstyle AD}
+
+![{\textstyle AD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b67c9a22c95905ef6b81962b11b31e1c0ef52225) and 
+
+
+
+B
+C
+
+
+{\textstyle BC}
+
+![{\textstyle BC}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9357a907256f2d11e87040067a6ce9dd1976f725) of trapezoid 
+
+
+
+A
+B
+C
+D
+
+
+{\textstyle ABCD}
+
+![{\textstyle ABCD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/56e9dd14b4fcb989c106f3679aa2699f07eee6d4) are in the ratio of 
+
+
+
+4
+:
+1
+
+
+{\textstyle 4:1}
+
+![{\textstyle 4:1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/44785771746a94fd2cf3d26ff7cd5653f816763d). The diagonals of the trapezoid intersect at point 
+
+
+
+M
+
+
+{\textstyle M}
+
+![{\textstyle M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/913ace920108f7552777e36ac0b7ee3f5093a088) and the extensions of sides 
+
+
+
+A
+B
+
+
+{\textstyle AB}
+
+![{\textstyle AB}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac121a3e6c5dff2ebb2ff8340e4a7f1b35992e44) and 
+
+
+
+C
+D
+
+
+{\textstyle CD}
+
+![{\textstyle CD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/523217c283f1b3f72fe4f317b8ff09e22365f1e5) intersect at point 
+
+
+
+P
+
+
+{\textstyle P}
+
+![{\textstyle P}](https://wikimedia.org/api/rest_v1/media/math/render/svg/038590207af1024a629c1a08c855e9ac46bf5610). Let us consider the basis with 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) as the origin, 
+
+
+
+
+
+
+A
+D
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AD}}}
+
+![{\textstyle {\overrightarrow {AD}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a09091c3ae3ae05dbb915b79e411ee15a84401f1) and 
+
+
+
+
+
+
+A
+B
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AB}}}
+
+![{\textstyle {\overrightarrow {AB}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a6f9e6559e7cd7c16144340887587c73e294b4ba) as basis vectors. Find the coordinates of points 
+
+
+
+M
+
+
+{\textstyle M}
+
+![{\textstyle M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/913ace920108f7552777e36ac0b7ee3f5093a088) and 
+
+
+
+P
+
+
+{\textstyle P}
+
+![{\textstyle P}](https://wikimedia.org/api/rest_v1/media/math/render/svg/038590207af1024a629c1a08c855e9ac46bf5610) in this basis.
+4. A line segment joining a vertex of a tetrahedron with the centroid of the opposite face (the centroid of a triangle is an intersection point of all its medians) is called a median of this tetrahedron. Using vector algebra prove that all the four medians of any tetrahedron concur in a point that divides these medians in the ratio of 
+
+
+
+3
+:
+1
+
+
+{\textstyle 3:1}
+
+![{\textstyle 3:1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1bdfd3570b8991fb33d61e324c67dd54f08a0eef), the longer segments being on the side of the vertex of the tetrahedron.
+5. Find 
+
+
+
+A
++
+B
+
+
+{\textstyle A+B}
+
+![{\textstyle A+B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bdd957a1f1d7f480fb51c33b1e5ab3b8259cb37f) and 
+
+
+
+2
+A
+−
+3
+B
++
+I
+
+
+{\textstyle 2A-3B+I}
+
+![{\textstyle 2A-3B+I}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bf9f21726daa3bc4c5b46cdebf17900d2384c4bc).
+6. Find the products 
+
+
+
+A
+B
+
+
+{\textstyle AB}
+
+![{\textstyle AB}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac121a3e6c5dff2ebb2ff8340e4a7f1b35992e44) and 
+
+
+
+B
+A
+
+
+{\textstyle BA}
+
+![{\textstyle BA}](https://wikimedia.org/api/rest_v1/media/math/render/svg/30d370a5b049f1bf605e0849e5011dab921a3e80) (and so make sure that, in general, 
+
+
+
+A
+B
+≠
+B
+A
+
+
+{\textstyle AB\neq BA}
+
+![{\textstyle AB\neq BA}](https://wikimedia.org/api/rest_v1/media/math/render/svg/547dca1516d9c8402fe6b52671054d5412e39d7a) for matrices).
+7. Find the inverse matrices for the given ones.
+8. Find the determinants of the given matrices.
+9. Point 
+
+
+
+M
+
+
+{\textstyle M}
+
+![{\textstyle M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/913ace920108f7552777e36ac0b7ee3f5093a088) is the centroid of face 
+
+
+
+B
+C
+D
+
+
+{\textstyle BCD}
+
+![{\textstyle BCD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dbf276d48bdd841bc17d7b41806b4fefd4d93aec) of tetrahedron 
+
+
+
+A
+B
+C
+D
+
+
+{\textstyle ABCD}
+
+![{\textstyle ABCD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/56e9dd14b4fcb989c106f3679aa2699f07eee6d4). The old coordinate system is given by 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31), 
+
+
+
+
+
+
+A
+B
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AB}}}
+
+![{\textstyle {\overrightarrow {AB}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a6f9e6559e7cd7c16144340887587c73e294b4ba), 
+
+
+
+
+
+
+A
+C
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AC}}}
+
+![{\textstyle {\overrightarrow {AC}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cec90ca60916095907088cdf9c6807e322940609), 
+
+
+
+
+
+
+A
+D
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AD}}}
+
+![{\textstyle {\overrightarrow {AD}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a09091c3ae3ae05dbb915b79e411ee15a84401f1), and the new coordinate system is given by 
+
+
+
+M
+
+
+{\textstyle M}
+
+![{\textstyle M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/913ace920108f7552777e36ac0b7ee3f5093a088), 
+
+
+
+
+
+
+M
+B
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {MB}}}
+
+![{\textstyle {\overrightarrow {MB}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fc628c7e66ee539b78d720ffb8b08c68cda528bc), 
+
+
+
+
+
+
+M
+C
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {MC}}}
+
+![{\textstyle {\overrightarrow {MC}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e7b29574c4ba08f6b03fc30de162aa30153d3ab0), 
+
+
+
+
+
+
+M
+A
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {MA}}}
+
+![{\textstyle {\overrightarrow {MA}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef8be9dd7ec0faa12b4f2f9f335d65b1cab904c5). Find the coordinates of a point in the old coordinate system given its coordinates 
+
+
+
+
+x
+′
+
+
+
+{\textstyle x'}
+
+![{\textstyle x'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bdd4bbf7bc3c37c71d0a1f9e4ef6c504c8f9d5de), 
+
+
+
+
+y
+′
+
+
+
+{\textstyle y'}
+
+![{\textstyle y'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e40eea4dc71b01e5ddff1d14b9b89853fde81d), 
+
+
+
+
+z
+′
+
+
+
+{\textstyle z'}
+
+![{\textstyle z'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/80546fbdafc04d89612c5491bc04d509709aeb17) in the new one.
+
+
+#### Section 2
+
+
+1. Two lines are given by the equations 
+
+
+
+
+
+r
+
+
+⋅
+
+
+n
+
+
+=
+A
+
+
+{\textstyle {\textbf {r}}\cdot {\textbf {n}}=A}
+
+![{\textstyle {\textbf {r}}\cdot {\textbf {n}}=A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d0bdfb3c03f3478452862b246cd0bec466eb624d) and 
+
+
+
+
+
+r
+
+
+=
+
+
+
+r
+
+
+
+0
+
+
++
+
+
+a
+
+
+t
+
+
+{\textstyle {\textbf {r}}={\textbf {r}}\_{0}+{\textbf {a}}t}
+
+![{\textstyle {\textbf {r}}={\textbf {r}}_{0}+{\textbf {a}}t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca83af73cef59fe73380c9737197485304b371ec), and at that 
+
+
+
+
+
+a
+
+
+⋅
+
+
+n
+
+
+≠
+0
+
+
+{\textstyle {\textbf {a}}\cdot {\textbf {n}}\neq 0}
+
+![{\textstyle {\textbf {a}}\cdot {\textbf {n}}\neq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/33673ddea1dea180b68cac92d5065f32f85016b1). Find the position vector of the intersection point of these lines.
+2. Find the distance from point 
+
+
+
+
+M
+
+0
+
+
+
+
+{\textstyle M\_{0}}
+
+![{\textstyle M_{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/feb4ebe89e459609fa9e97bf72ee561acb3f7836) with the position vector 
+
+
+
+
+
+
+r
+
+
+
+0
+
+
+
+
+{\textstyle {\textbf {r}}\_{0}}
+
+![{\textstyle {\textbf {r}}_{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b0b1d2beb050ff53f1db5422ed3c6067091489d2) to the line defined by the equation (a) 
+
+
+
+
+
+r
+
+
+=
+
+
+
+r
+
+
+
+0
+
+
++
+
+
+a
+
+
+t
+
+
+{\textstyle {\textbf {r}}={\textbf {r}}\_{0}+{\textbf {a}}t}
+
+![{\textstyle {\textbf {r}}={\textbf {r}}_{0}+{\textbf {a}}t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca83af73cef59fe73380c9737197485304b371ec); (b) 
+
+
+
+
+
+r
+
+
+⋅
+
+
+n
+
+
+=
+A
+
+
+{\textstyle {\textbf {r}}\cdot {\textbf {n}}=A}
+
+![{\textstyle {\textbf {r}}\cdot {\textbf {n}}=A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d0bdfb3c03f3478452862b246cd0bec466eb624d).
+3. Diagonals of a rhombus intersect at point 
+
+
+
+M
+(
+1
+;
+
+2
+)
+
+
+{\textstyle M(1;\,2)}
+
+![{\textstyle M(1;\,2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1f5f919c98511e9602aff3b5c6fb6a44b3c5d75c), the longest of them being parallel to a horizontal axis. The side of the rhombus equals 2 and its obtuse angle is 
+
+
+
+
+120
+
+∘
+
+
+
+
+{\textstyle 120^{\circ }}
+
+![{\textstyle 120^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/db4bd85704493ea3595bcef6a92dbadcef085e51). Compose the equations of the sides of this rhombus.
+4. Compose the equations of lines passing through point 
+
+
+
+A
+(
+2
+;
+−
+4
+)
+
+
+{\textstyle A(2;-4)}
+
+![{\textstyle A(2;-4)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/adb02900c49b8277ff0d9994f3c262b42712fc10) and forming angles of 
+
+
+
+
+60
+
+∘
+
+
+
+
+{\textstyle 60^{\circ }}
+
+![{\textstyle 60^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/880b547c0017493563c28efdad95fdac91f97352) with the line 
+
+
+
+
+
+
+1
+−
+2
+x
+
+3
+
+
+=
+
+
+
+3
++
+2
+y
+
+
+−
+2
+
+
+
+
+
+{\textstyle {\frac {1-2x}{3}}={\frac {3+2y}{-2}}}
+
+![{\textstyle {\frac {1-2x}{3}}={\frac {3+2y}{-2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9d3793ed8ac9c5b2a740ee251edbe89f3a25c7d4).
+5. Find the cross product of (a) vectors 
+
+
+
+
+
+a
+
+
+(
+3
+;
+−
+2
+;
+
+1
+)
+
+
+{\textstyle {\textbf {a}}(3;-2;\,1)}
+
+![{\textstyle {\textbf {a}}(3;-2;\,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/24aa2e3d81f5e733ac961fc54c00c6400ac7c554) and 
+
+
+
+
+
+b
+
+
+(
+2
+;
+−
+5
+;
+−
+3
+)
+
+
+{\textstyle {\textbf {b}}(2;-5;-3)}
+
+![{\textstyle {\textbf {b}}(2;-5;-3)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ed4f1d0f60888ec6d6e29a3ef51f7c26784b688e); (b) vectors 
+
+
+
+
+
+a
+
+
+(
+3
+;
+−
+2
+;
+
+1
+)
+
+
+{\textstyle {\textbf {a}}(3;-2;\,1)}
+
+![{\textstyle {\textbf {a}}(3;-2;\,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/24aa2e3d81f5e733ac961fc54c00c6400ac7c554) and 
+
+
+
+
+
+c
+
+
+(
+−
+18
+;
+
+12
+;
+−
+6
+)
+
+
+{\textstyle {\textbf {c}}(-18;\,12;-6)}
+
+![{\textstyle {\textbf {c}}(-18;\,12;-6)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/536804f73bf9994ca0ac6a28c7c18f9b7c025d00).
+6. A triangle is constructed on vectors 
+
+
+
+
+
+a
+
+
+(
+2
+;
+4
+;
+−
+1
+)
+
+
+{\textstyle {\textbf {a}}(2;4;-1)}
+
+![{\textstyle {\textbf {a}}(2;4;-1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8dcfef96a8fb429db141d89ad1a4a7d2b79796c7) and 
+
+
+
+
+
+b
+
+
+(
+−
+2
+;
+1
+;
+1
+)
+
+
+{\textstyle {\textbf {b}}(-2;1;1)}
+
+![{\textstyle {\textbf {b}}(-2;1;1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/33194e12e69d8cf8bef0e3a7a975b0bbc27e0d59). (a) Find the area of this triangle. (b) Find the altitudes of this triangle.
+7. Find the scalar triple product of 
+
+
+
+
+
+a
+
+
+(
+1
+;
+
+2
+;
+−
+1
+)
+
+
+{\textstyle {\textbf {a}}(1;\,2;-1)}
+
+![{\textstyle {\textbf {a}}(1;\,2;-1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f4ff4c4819f08216a9b289eee65fae9e2409cd89), 
+
+
+
+
+
+b
+
+
+(
+7
+;
+3
+;
+−
+5
+)
+
+
+{\textstyle {\textbf {b}}(7;3;-5)}
+
+![{\textstyle {\textbf {b}}(7;3;-5)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bad88c6efacea267911438883c60e91aa7e641d4), 
+
+
+
+
+
+c
+
+
+(
+3
+;
+
+4
+;
+−
+3
+)
+
+
+{\textstyle {\textbf {c}}(3;\,4;-3)}
+
+![{\textstyle {\textbf {c}}(3;\,4;-3)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3075cbf140d048ec7105863bf15ffbc46d4ea011).
+8. It is known that basis vectors 
+
+
+
+
+
+
+e
+
+
+
+1
+
+
+
+
+{\textstyle {\textbf {e}}\_{1}}
+
+![{\textstyle {\textbf {e}}_{1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/633f38e385b970d94316cec9a3f0f8d8b2952c78), 
+
+
+
+
+
+
+e
+
+
+
+2
+
+
+
+
+{\textstyle {\textbf {e}}\_{2}}
+
+![{\textstyle {\textbf {e}}_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1141e813036efabb49e22e26699abda03db9c238), 
+
+
+
+
+
+
+e
+
+
+
+3
+
+
+
+
+{\textstyle {\textbf {e}}\_{3}}
+
+![{\textstyle {\textbf {e}}_{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4136ef375267fae398133caf33d6309b3491fe75) have lengths of 
+
+
+
+1
+
+
+{\textstyle 1}
+
+![{\textstyle 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6706df9ed9f240d1a94545fb4e522bda168fe8fd), 
+
+
+
+2
+
+
+{\textstyle 2}
+
+![{\textstyle 2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/78ed0cd8140e5a15b6fcce83602df58458e0f3b0), 
+
+
+
+2
+
+
+2
+
+
+
+
+{\textstyle 2{\sqrt {2}}}
+
+![{\textstyle 2{\sqrt {2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f302ae86c5e346beaf1dc60ab28ce51583d3a10f) respectively, and 
+
+
+
+∠
+(
+
+
+
+e
+
+
+
+1
+
+
+,
+
+
+
+e
+
+
+
+2
+
+
+)
+=
+
+120
+
+∘
+
+
+
+
+{\textstyle \angle ({\textbf {e}}\_{1},{\textbf {e}}\_{2})=120^{\circ }}
+
+![{\textstyle \angle ({\textbf {e}}_{1},{\textbf {e}}_{2})=120^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5bc355fb33e21d27781b3c69f604dfa4ac8a2335), 
+
+
+
+∠
+(
+
+
+
+e
+
+
+
+1
+
+
+,
+
+
+
+e
+
+
+
+3
+
+
+)
+=
+
+135
+
+∘
+
+
+
+
+{\textstyle \angle ({\textbf {e}}\_{1},{\textbf {e}}\_{3})=135^{\circ }}
+
+![{\textstyle \angle ({\textbf {e}}_{1},{\textbf {e}}_{3})=135^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/077d554778a6237a758bdd3cd174fb71e56c5a59), 
+
+
+
+∠
+(
+
+
+
+e
+
+
+
+2
+
+
+,
+
+
+
+e
+
+
+
+3
+
+
+)
+=
+
+45
+
+∘
+
+
+
+
+{\textstyle \angle ({\textbf {e}}\_{2},{\textbf {e}}\_{3})=45^{\circ }}
+
+![{\textstyle \angle ({\textbf {e}}_{2},{\textbf {e}}_{3})=45^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2c625e201eaf56a5ab2f55c468fb74919eecf950). Find the volume of a parallelepiped constructed on vectors with coordinates 
+
+
+
+(
+−
+1
+;
+
+0
+;
+
+2
+)
+
+
+{\textstyle (-1;\,0;\,2)}
+
+![{\textstyle (-1;\,0;\,2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6f80a6dd17132920d07de233c927f5b35fe55342), 
+
+
+
+(
+1
+;
+
+1
+
+4
+)
+
+
+{\textstyle (1;\,1\,4)}
+
+![{\textstyle (1;\,1\,4)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/93f2f019128f43ccd8b9bf1ec5fae847335c9609) and 
+
+
+
+(
+−
+2
+;
+
+1
+;
+
+1
+)
+
+
+{\textstyle (-2;\,1;\,1)}
+
+![{\textstyle (-2;\,1;\,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c29df73c5099969e89def9536b89bed1f8b8300b) in this basis.
+
+
+#### Section 3
+
+
+1. Prove that a curve given by 
+
+
+
+34
+
+x
+
+2
+
+
++
+24
+x
+y
++
+41
+
+y
+
+2
+
+
+−
+44
+x
++
+58
+y
++
+1
+=
+0
+
+
+{\textstyle 34x^{2}+24xy+41y^{2}-44x+58y+1=0}
+
+![{\textstyle 34x^{2}+24xy+41y^{2}-44x+58y+1=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2081edc20b56611eb9f1897a625f3bc0bc3df3b5) is an ellipse. Find the major and minor axes of this ellipse, its eccentricity, coordinates of its center and foci. Find the equations of axes and directrices of this ellipse.
+2. Determine types of curves given by the following equations. For each of the curves, find its canonical coordinate system (i.e. indicate the coordinates of origin and new basis vectors in the initial coordinate system) and its canonical equation. (a) 
+
+
+
+9
+
+x
+
+2
+
+
+−
+16
+
+y
+
+2
+
+
+−
+6
+x
++
+8
+y
+−
+144
+=
+0
+
+
+{\textstyle 9x^{2}-16y^{2}-6x+8y-144=0}
+
+![{\textstyle 9x^{2}-16y^{2}-6x+8y-144=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e2307372c3cf01eef66761c99845dcbe394be29f); (b) 
+
+
+
+9
+
+x
+
+2
+
+
++
+4
+
+y
+
+2
+
+
++
+6
+x
+−
+4
+y
+−
+2
+=
+0
+
+
+{\textstyle 9x^{2}+4y^{2}+6x-4y-2=0}
+
+![{\textstyle 9x^{2}+4y^{2}+6x-4y-2=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73b831469fdf03eac9e9c9656ae7fef80096fb94); (c) 
+
+
+
+12
+
+x
+
+2
+
+
+−
+12
+x
+−
+32
+y
+−
+29
+=
+0
+
+
+{\textstyle 12x^{2}-12x-32y-29=0}
+
+![{\textstyle 12x^{2}-12x-32y-29=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8cde74f6df39c7d1f475a31c4f1add253f1a43eb); (d) 
+
+
+
+x
+y
++
+2
+x
++
+y
+=
+0
+
+
+{\textstyle xy+2x+y=0}
+
+![{\textstyle xy+2x+y=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ced2a1c13f7eb77948ffc6ba9c1789659873573);
+3. Find the equations of lines tangent to curve 
+
+
+
+6
+x
+y
++
+8
+
+y
+
+2
+
+
+−
+12
+x
+−
+26
+y
++
+11
+=
+0
+
+
+{\textstyle 6xy+8y^{2}-12x-26y+11=0}
+
+![{\textstyle 6xy+8y^{2}-12x-26y+11=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/38463f126baaf801dce5a01c4e5d2e4c9d5e5080) that are (a) parallel to line 
+
+
+
+6
+x
++
+17
+y
+−
+4
+=
+0
+
+
+{\textstyle 6x+17y-4=0}
+
+![{\textstyle 6x+17y-4=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fe1136341a1ea0ad8bbc7101dbceadb86b33e90e); (b) perpendicular to line 
+
+
+
+41
+x
+−
+24
+y
++
+3
+=
+0
+
+
+{\textstyle 41x-24y+3=0}
+
+![{\textstyle 41x-24y+3=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91928594589b3b61e71e2f6d60125360b48cd4fd); (c) parallel to line 
+
+
+
+y
+=
+2
+
+
+{\textstyle y=2}
+
+![{\textstyle y=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/887628e811c56cc94aaccb0f5e4c773f19231cf9).
+4. For each value of parameter 
+
+
+
+a
+
+
+{\textstyle a}
+
+![{\textstyle a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a503f107a7c104e40e484cee9e1f5993d28ffd8) determine types of surfaces given by the equations: (a) 
+
+
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+−
+
+z
+
+2
+
+
+=
+a
+
+
+{\textstyle x^{2}+y^{2}-z^{2}=a}
+
+![{\textstyle x^{2}+y^{2}-z^{2}=a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aedac9a12be3e2a8bb6549e080cecd007665a44c); (b) 
+
+
+
+
+x
+
+2
+
+
++
+a
+
+(
+
+
+y
+
+2
+
+
++
+
+z
+
+2
+
+
+
+)
+
+=
+1
+
+
+{\textstyle x^{2}+a\left(y^{2}+z^{2}\right)=1}
+
+![{\textstyle x^{2}+a\left(y^{2}+z^{2}\right)=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/04136582473b57e7f0525feeebccc4460ecf7ad8); (c) 
+
+
+
+
+x
+
+2
+
+
++
+a
+
+y
+
+2
+
+
+=
+a
+z
+
+
+{\textstyle x^{2}+ay^{2}=az}
+
+![{\textstyle x^{2}+ay^{2}=az}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d9326d877d128ad9d17a96c9765e1da5f7c91e6); (d) 
+
+
+
+
+x
+
+2
+
+
++
+a
+
+y
+
+2
+
+
+=
+a
+z
++
+1
+
+
+{\textstyle x^{2}+ay^{2}=az+1}
+
+![{\textstyle x^{2}+ay^{2}=az+1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d1cd37bf6d43b7adafdd4ec58f392dd620872e3).
+5. Find a vector equation of a right circular cone with apex 
+
+
+
+
+M
+
+0
+
+
+
+(
+
+
+
+r
+
+
+
+0
+
+
+)
+
+
+
+{\textstyle M\_{0}\left({\textbf {r}}\_{0}\right)}
+
+![{\textstyle M_{0}\left({\textbf {r}}_{0}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f1b67abdb7e98da13a4de428625f69d249276ae5) and axis 
+
+
+
+
+
+r
+
+
+=
+
+
+
+r
+
+
+
+0
+
+
++
+
+
+a
+
+
+t
+
+
+{\textstyle {\textbf {r}}={\textbf {r}}\_{0}+{\textbf {a}}t}
+
+![{\textstyle {\textbf {r}}={\textbf {r}}_{0}+{\textbf {a}}t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca83af73cef59fe73380c9737197485304b371ec) if it is known that generatrices of this cone form the angle of 
+
+
+
+α
+
+
+{\textstyle \alpha }
+
+![{\textstyle \alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d86dbd6183264b2f8569da1751380b173c7b185) with its axis.
+6. Find the equation of a cylinder with radius 
+
+
+
+
+
+2
+
+
+
+
+{\textstyle {\sqrt {2}}}
+
+![{\textstyle {\sqrt {2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5094a5b1e2f42490aa4de2c7a4b7235a27f1b73f) that has an axis 
+
+
+
+x
+=
+1
++
+t
+
+
+{\textstyle x=1+t}
+
+![{\textstyle x=1+t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eca54a99a9fdad0ee1a0bba54ac67014e83a51e2), 
+
+
+
+y
+=
+2
++
+t
+
+
+{\textstyle y=2+t}
+
+![{\textstyle y=2+t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/213ba8ad271ceb3b25aaaafcbe23edd7c885c7f0), 
+
+
+
+z
+=
+3
++
+t
+
+
+{\textstyle z=3+t}
+
+![{\textstyle z=3+t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/582781cac22a2c157f5b5b60da347600c9778a6f).
+7. An ellipsoid is symmetric with respect to coordinate planes, passes through point 
+
+
+
+M
+(
+3
+;
+
+1
+;
+
+1
+)
+
+
+{\textstyle M(3;\,1;\,1)}
+
+![{\textstyle M(3;\,1;\,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6192e6c5728edd5b9a22b9c19aa8be852e2f0599) and circle 
+
+
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
++
+
+z
+
+2
+
+
+=
+9
+
+
+{\textstyle x^{2}+y^{2}+z^{2}=9}
+
+![{\textstyle x^{2}+y^{2}+z^{2}=9}](https://wikimedia.org/api/rest_v1/media/math/render/svg/29376da667d60dba7e1f552a56d1ce98caea3a4d), 
+
+
+
+x
+−
+z
+=
+0
+
+
+{\textstyle x-z=0}
+
+![{\textstyle x-z=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/709115599ad054688b92e60cdb84a4f32fe944f1). Find the equation of this ellipsoid.
+
+
+### The retake exam
+
+
+Retakes will be run as a comprehensive exam, where the student will be assessed the acquired knowledge coming from the textbooks, the lectures, the labs, and the additional required reading material, as supplied by the instructor. During such comprehensive oral/written the student could be asked to solve exercises and to explain theoretical and practical aspects of the course.
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__analytic_geometry_and_linear_algebra_i.f23.md

@@ -0,0 +1,2288 @@
+
+
+
+
+
+
+
+BSc: Analytic Geometry And Linear Algebra I.f23
+===============================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Analytical Geometry & Linear Algebra – I](#Analytical_Geometry_.26_Linear_Algebra_.E2.80.93_I)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Course Topics](#Course_Topics)
+	+ [1.3 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.3.1 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.3.1.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.3.1.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.3.1.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.4 Grading](#Grading)
+		- [1.4.1 Course grading range](#Course_grading_range)
+		- [1.4.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.4.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.5 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.5.1 Open access resources](#Open_access_resources)
+	+ [1.6 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [1.7 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [1.7.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [1.7.1.1 Section 1](#Section_1)
+			* [1.7.1.2 Section 2](#Section_2)
+			* [1.7.1.3 Section 3](#Section_3)
+		- [1.7.2 Final assessment](#Final_assessment)
+			* [1.7.2.1 Section 1](#Section_1_2)
+			* [1.7.2.2 Section 2](#Section_2_2)
+			* [1.7.2.3 Section 3](#Section_3_2)
+		- [1.7.3 The retake exam](#The_retake_exam)
+
+
+
+Analytical Geometry & Linear Algebra – I
+========================================
+
+
+* **Course name**: Analytical Geometry & Linear Algebra – I
+* **Code discipline**: CSE202
+* **Subject area**: Math
+
+
+Short Description
+-----------------
+
+
+This is an introductory course in analytical geometry and linear algebra. After having studied the course, students get to know fundamental principles of vector algebra and its applications in solving various geometry problems, different types of equations of lines and planes, conics and quadric surfaces, transformations in the plane and in the space. An introduction on matrices and determinants as a fundamental knowledge of linear algebra is also provided. 
+
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Vector algebra | 1. Vector spaces
+2. Basic operations on vectors (summation, multiplication by scalar, dot product)
+3. Linear dependency and independency of the vectors. Basis in vector spaces.
+4. Introduction to matrices and determinants. The rank of a matrix. Inverse matrix.
+5. Systems of linear equations
+6. Changing basis and coordinates
+ |
+| Line and Plane | 1. General equation of a line in the plane
+2. General parametric equation of a line in the space
+3. Line as intersection between planes.
+4. Vector equation of a line.
+5. Distance from a point to a line. Distance between lines
+6. General equation of a plane.
+7. Normalized linear equation of a plane.
+8. Vector equation of a plane. Parametric equation of a plane
+9. Inter-positioning of lines and planes
+10. Cross Product of two vectors. Triple Scalar Product
+ |
+| Quadratic curves and surfaces | 1. Circle, Ellipse, Hyperbola, Parabola. Canonical equations
+2. Shift of coordinate system. Rotation of coordinate system. Parametrization
+3. General equation of the quadric surfaces.
+4. Canonical equations of a sphere, ellipsoid, hyperboloid and paraboloid
+5. Surfaces of revolution. Canonical equation of a cone and cylinder
+6. Vector equations of some quadric surfaces
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### ILOs defined at three levels
+
+
+We specify the intended learning outcomes at three levels: conceptual knowledge, practical skills, and comprehensive skills.
+
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* explain the geometrical interpretation of the basic operations of vector algebra,
+* restate equations of lines and planes in different forms,
+* interpret the geometrical meaning of the conic sections in the mathematical expression,
+* give the examples of the surfaces of revolution,
+* understand the value of geometry in various fields of science and techniques.
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* perform the basic operations of vector algebra,
+* use different types of equations of lines and planes to solve the plane and space problems,
+* represent the conic section in canonical form,
+* compose the equation of quadric surface.
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* list basic notions of vector algebra,
+* recite the base form of the equations of transformations in planes and spaces,
+* recall equations of lines and planes,
+* identify the type of conic section,
+* recognize the kind of quadric surfaces.
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 85-100 | -
+ |
+| B. Good | 70-84 | -
+ |
+| C. Satisfactory | 55-70 | -
+ |
+| D. Fail | 0-54 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Midterm | 35
+ |
+| Tests | 30 (15 for each)
+ |
+| Final exam | 35
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+* Participation is important. Attending lectures is the key to success in this course.
+* Review lecture materials before classes to do well.
+* Reading the recommended literature is obligatory, and will give you a deeper understanding of the material.
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* V.V. Konev. Linear Algebra, Vector Algebra and Analytical Geometry. Textbook. Tomsk: TPU Press, 2009, 114 pp [book1](https://portal.tpu.ru/SHARED/k/KONVAL/Textbooks/Tab1/Konev-Linear_Algebra_Vector_Algebra_and_Analytical_Geome.pdf)
+* R.A.Sharipov. Course of Analytical Geometry Textbook, Ufa, BSU, 2013. 227pp [book2](https://arxiv.org/pdf/1111.6521.pdf)
+* P.R. Vital. Analytical Geometry 2D and 3D Analytical Geometry 2D and 3D [book3](https://www.amazon.com/Analytical-Geometry-2D-3D-Vittal/dp/8131773604)
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Teaching and Learning Methods within each section
+| Teaching Techniques | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Problem-based learning (students learn by solving open-ended problems without a strictly-defined solution) | 1 | 1 | 1
+ |
+| Project-based learning (students work on a project) | 0 | 0 | 0
+ |
+| Modular learning (facilitated self-study) | 0 | 0 | 0
+ |
+| Differentiated learning (provide tasks and activities at several levels of difficulty to fit students needs and level) | 1 | 1 | 1
+ |
+| Contextual learning (activities and tasks are connected to the real world to make it easier for students to relate to them) | 0 | 0 | 0
+ |
+| Business game (learn by playing a game that incorporates the principles of the material covered within the course) | 0 | 0 | 0
+ |
+| Inquiry-based learning | 0 | 0 | 0
+ |
+| Just-in-time teaching | 0 | 0 | 0
+ |
+| Process oriented guided inquiry learning (POGIL) | 0 | 0 | 0
+ |
+| Studio-based learning | 0 | 0 | 0
+ |
+| Universal design for learning | 0 | 0 | 0
+ |
+| Task-based learning | 0 | 0 | 0
+ |
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Lectures | 1 | 1 | 1
+ |
+| Interactive Lectures | 1 | 1 | 1
+ |
+| Lab exercises | 1 | 1 | 1
+ |
+| Experiments | 0 | 0 | 0
+ |
+| Modeling | 0 | 0 | 0
+ |
+| Cases studies | 0 | 0 | 0
+ |
+| Development of individual parts of software product code | 0 | 0 | 0
+ |
+| Individual Projects | 0 | 0 | 0
+ |
+| Group projects | 0 | 0 | 0
+ |
+| Flipped classroom | 0 | 0 | 0
+ |
+| Quizzes (written or computer based) | 1 | 1 | 1
+ |
+| Peer Review | 0 | 0 | 0
+ |
+| Discussions | 1 | 1 | 1
+ |
+| Presentations by students | 0 | 0 | 0
+ |
+| Written reports | 0 | 0 | 0
+ |
+| Simulations and role-plays | 0 | 0 | 0
+ |
+| Essays | 0 | 0 | 0
+ |
+| Oral Reports | 0 | 0 | 0
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+1. How to perform the shift of the vector?
+2. What is the geometrical interpretation of the dot product?
+3. How to determine whether the vectors are linearly dependent?
+4. What is a vector basis?
+5. What is the difference between matrices and determinants?
+6. Matrices 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) and 
+
+
+
+C
+
+
+{\textstyle C}
+
+![{\textstyle C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6dca76d9ff4b48256b6a4a99bcb234b64b2fa72b) have dimensions of 
+
+
+
+m
+×
+n
+
+
+{\textstyle m\times n}
+
+![{\textstyle m\times n}](https://wikimedia.org/api/rest_v1/media/math/render/svg/37dc29fae3b1932f1b311a052ecc6ecb8692dc48) and 
+
+
+
+p
+×
+q
+
+
+{\textstyle p\times q}
+
+![{\textstyle p\times q}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cdbd208094b241eb647c2e3b515a05197f9e0fdc) respectively, and it is known that the product 
+
+
+
+A
+B
+C
+
+
+{\textstyle ABC}
+
+![{\textstyle ABC}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1516a55703463b2e378eb0b2eda76f08f6919636) exists. What are possible dimensions of 
+
+
+
+B
+
+
+{\textstyle B}
+
+![{\textstyle B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/de0b47ffc21636dc2df68f6c793177a268f10e9b) and 
+
+
+
+A
+B
+C
+
+
+{\textstyle ABC}
+
+![{\textstyle ABC}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1516a55703463b2e378eb0b2eda76f08f6919636)?
+7. How to determine the rank of a matrix?
+8. What is the meaning of the inverse matrix?
+9. How to restate a system of linear equations in the matrix form?
+
+
+#### Section 2
+
+
+1. How to represent a line in the vector form?
+2. What is the result of intersection of two planes in vector form?
+3. How to derive the formula for the distance from a point to a line?
+4. How to interpret geometrically the distance between lines?
+5. List all possible inter-positions of lines in the space.
+6. What is the difference between general and normalized forms of equations of a plane?
+7. How to rewrite the equation of a plane in a vector form?
+8. What is the normal to a plane?
+9. How to interpret the cross products of two vectors?
+10. What is the meaning of scalar triple product of three vectors?
+
+
+#### Section 3
+
+
+1. Formulate the canonical equation of the given quadratic curve.
+2. Which orthogonal transformations of coordinates do you know?
+3. How to perform a transformation of the coordinate system?
+4. How to represent a curve in the space?
+5. What is the type of a quadric surface given by a certain equation?
+6. How to compose the equation of a surface of revolution?
+7. What is the difference between a directrix and generatrix?
+8. How to represent a quadric surface in the vector form?
+
+
+### Final assessment
+
+
+#### Section 1
+
+
+1. Evaluate 
+
+
+
+
+|
+
+
+
+a
+
+
+
+
+|
+
+
+2
+
+
+−
+2
+
+
+3
+
+
+
+
+a
+
+
+⋅
+
+
+b
+
+
+−
+7
+
+|
+
+
+
+b
+
+
+
+
+|
+
+
+2
+
+
+
+
+{\textstyle |{\textbf {a}}|^{2}-2{\sqrt {3}}{\textbf {a}}\cdot {\textbf {b}}-7|{\textbf {b}}|^{2}}
+
+![{\textstyle |{\textbf {a}}|^{2}-2{\sqrt {3}}{\textbf {a}}\cdot {\textbf {b}}-7|{\textbf {b}}|^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b39de16745ae08f1e071202ed4c68a7439df361b) given that 
+
+
+
+
+|
+
+
+
+a
+
+
+
+|
+
+=
+4
+
+
+{\textstyle |{\textbf {a}}|=4}
+
+![{\textstyle |{\textbf {a}}|=4}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dad653ed7b4f53967e38f14dc254a0b4ed40f4ac), 
+
+
+
+
+|
+
+
+
+b
+
+
+
+|
+
+=
+1
+
+
+{\textstyle |{\textbf {b}}|=1}
+
+![{\textstyle |{\textbf {b}}|=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2147d16bdc4fd215671610f46300d16ea8f1963d), 
+
+
+
+∠
+(
+
+
+a
+
+
+,
+
+
+
+b
+
+
+)
+=
+
+150
+
+∘
+
+
+
+
+{\textstyle \angle ({\textbf {a}},\,{\textbf {b}})=150^{\circ }}
+
+![{\textstyle \angle ({\textbf {a}},\,{\textbf {b}})=150^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/34c0c47f4b2dbe58c362811be01e2a9658ffd65e).
+2. Prove that vectors 
+
+
+
+
+
+b
+
+
+(
+
+
+a
+
+
+⋅
+
+
+c
+
+
+)
+−
+
+
+c
+
+
+(
+
+
+a
+
+
+⋅
+
+
+b
+
+
+)
+
+
+{\textstyle {\textbf {b}}({\textbf {a}}\cdot {\textbf {c}})-{\textbf {c}}({\textbf {a}}\cdot {\textbf {b}})}
+
+![{\textstyle {\textbf {b}}({\textbf {a}}\cdot {\textbf {c}})-{\textbf {c}}({\textbf {a}}\cdot {\textbf {b}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91d497e3670b2e628a97f0ccb57ca80a925ef32c) and 
+
+
+
+
+
+a
+
+
+
+
+{\textstyle {\textbf {a}}}
+
+![{\textstyle {\textbf {a}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0a7a4f8c41fd49715b57c7891e867192892aaf8b) are perpendicular to each other.
+3. Bases 
+
+
+
+A
+D
+
+
+{\textstyle AD}
+
+![{\textstyle AD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b67c9a22c95905ef6b81962b11b31e1c0ef52225) and 
+
+
+
+B
+C
+
+
+{\textstyle BC}
+
+![{\textstyle BC}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9357a907256f2d11e87040067a6ce9dd1976f725) of trapezoid 
+
+
+
+A
+B
+C
+D
+
+
+{\textstyle ABCD}
+
+![{\textstyle ABCD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/56e9dd14b4fcb989c106f3679aa2699f07eee6d4) are in the ratio of 
+
+
+
+4
+:
+1
+
+
+{\textstyle 4:1}
+
+![{\textstyle 4:1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/44785771746a94fd2cf3d26ff7cd5653f816763d). The diagonals of the trapezoid intersect at point 
+
+
+
+M
+
+
+{\textstyle M}
+
+![{\textstyle M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/913ace920108f7552777e36ac0b7ee3f5093a088) and the extensions of sides 
+
+
+
+A
+B
+
+
+{\textstyle AB}
+
+![{\textstyle AB}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac121a3e6c5dff2ebb2ff8340e4a7f1b35992e44) and 
+
+
+
+C
+D
+
+
+{\textstyle CD}
+
+![{\textstyle CD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/523217c283f1b3f72fe4f317b8ff09e22365f1e5) intersect at point 
+
+
+
+P
+
+
+{\textstyle P}
+
+![{\textstyle P}](https://wikimedia.org/api/rest_v1/media/math/render/svg/038590207af1024a629c1a08c855e9ac46bf5610). Let us consider the basis with 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) as the origin, 
+
+
+
+
+
+
+A
+D
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AD}}}
+
+![{\textstyle {\overrightarrow {AD}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a09091c3ae3ae05dbb915b79e411ee15a84401f1) and 
+
+
+
+
+
+
+A
+B
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AB}}}
+
+![{\textstyle {\overrightarrow {AB}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a6f9e6559e7cd7c16144340887587c73e294b4ba) as basis vectors. Find the coordinates of points 
+
+
+
+M
+
+
+{\textstyle M}
+
+![{\textstyle M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/913ace920108f7552777e36ac0b7ee3f5093a088) and 
+
+
+
+P
+
+
+{\textstyle P}
+
+![{\textstyle P}](https://wikimedia.org/api/rest_v1/media/math/render/svg/038590207af1024a629c1a08c855e9ac46bf5610) in this basis.
+4. A line segment joining a vertex of a tetrahedron with the centroid of the opposite face (the centroid of a triangle is an intersection point of all its medians) is called a median of this tetrahedron. Using vector algebra prove that all the four medians of any tetrahedron concur in a point that divides these medians in the ratio of 
+
+
+
+3
+:
+1
+
+
+{\textstyle 3:1}
+
+![{\textstyle 3:1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1bdfd3570b8991fb33d61e324c67dd54f08a0eef), the longer segments being on the side of the vertex of the tetrahedron.
+5. Find 
+
+
+
+A
++
+B
+
+
+{\textstyle A+B}
+
+![{\textstyle A+B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bdd957a1f1d7f480fb51c33b1e5ab3b8259cb37f) and 
+
+
+
+2
+A
+−
+3
+B
++
+I
+
+
+{\textstyle 2A-3B+I}
+
+![{\textstyle 2A-3B+I}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bf9f21726daa3bc4c5b46cdebf17900d2384c4bc).
+6. Find the products 
+
+
+
+A
+B
+
+
+{\textstyle AB}
+
+![{\textstyle AB}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac121a3e6c5dff2ebb2ff8340e4a7f1b35992e44) and 
+
+
+
+B
+A
+
+
+{\textstyle BA}
+
+![{\textstyle BA}](https://wikimedia.org/api/rest_v1/media/math/render/svg/30d370a5b049f1bf605e0849e5011dab921a3e80) (and so make sure that, in general, 
+
+
+
+A
+B
+≠
+B
+A
+
+
+{\textstyle AB\neq BA}
+
+![{\textstyle AB\neq BA}](https://wikimedia.org/api/rest_v1/media/math/render/svg/547dca1516d9c8402fe6b52671054d5412e39d7a) for matrices).
+7. Find the inverse matrices for the given ones.
+8. Find the determinants of the given matrices.
+9. Point 
+
+
+
+M
+
+
+{\textstyle M}
+
+![{\textstyle M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/913ace920108f7552777e36ac0b7ee3f5093a088) is the centroid of face 
+
+
+
+B
+C
+D
+
+
+{\textstyle BCD}
+
+![{\textstyle BCD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dbf276d48bdd841bc17d7b41806b4fefd4d93aec) of tetrahedron 
+
+
+
+A
+B
+C
+D
+
+
+{\textstyle ABCD}
+
+![{\textstyle ABCD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/56e9dd14b4fcb989c106f3679aa2699f07eee6d4). The old coordinate system is given by 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31), 
+
+
+
+
+
+
+A
+B
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AB}}}
+
+![{\textstyle {\overrightarrow {AB}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a6f9e6559e7cd7c16144340887587c73e294b4ba), 
+
+
+
+
+
+
+A
+C
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AC}}}
+
+![{\textstyle {\overrightarrow {AC}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cec90ca60916095907088cdf9c6807e322940609), 
+
+
+
+
+
+
+A
+D
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AD}}}
+
+![{\textstyle {\overrightarrow {AD}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a09091c3ae3ae05dbb915b79e411ee15a84401f1), and the new coordinate system is given by 
+
+
+
+M
+
+
+{\textstyle M}
+
+![{\textstyle M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/913ace920108f7552777e36ac0b7ee3f5093a088), 
+
+
+
+
+
+
+M
+B
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {MB}}}
+
+![{\textstyle {\overrightarrow {MB}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fc628c7e66ee539b78d720ffb8b08c68cda528bc), 
+
+
+
+
+
+
+M
+C
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {MC}}}
+
+![{\textstyle {\overrightarrow {MC}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e7b29574c4ba08f6b03fc30de162aa30153d3ab0), 
+
+
+
+
+
+
+M
+A
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {MA}}}
+
+![{\textstyle {\overrightarrow {MA}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef8be9dd7ec0faa12b4f2f9f335d65b1cab904c5). Find the coordinates of a point in the old coordinate system given its coordinates 
+
+
+
+
+x
+′
+
+
+
+{\textstyle x'}
+
+![{\textstyle x'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bdd4bbf7bc3c37c71d0a1f9e4ef6c504c8f9d5de), 
+
+
+
+
+y
+′
+
+
+
+{\textstyle y'}
+
+![{\textstyle y'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e40eea4dc71b01e5ddff1d14b9b89853fde81d), 
+
+
+
+
+z
+′
+
+
+
+{\textstyle z'}
+
+![{\textstyle z'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/80546fbdafc04d89612c5491bc04d509709aeb17) in the new one.
+
+
+#### Section 2
+
+
+1. Two lines are given by the equations 
+
+
+
+
+
+r
+
+
+⋅
+
+
+n
+
+
+=
+A
+
+
+{\textstyle {\textbf {r}}\cdot {\textbf {n}}=A}
+
+![{\textstyle {\textbf {r}}\cdot {\textbf {n}}=A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d0bdfb3c03f3478452862b246cd0bec466eb624d) and 
+
+
+
+
+
+r
+
+
+=
+
+
+
+r
+
+
+
+0
+
+
++
+
+
+a
+
+
+t
+
+
+{\textstyle {\textbf {r}}={\textbf {r}}\_{0}+{\textbf {a}}t}
+
+![{\textstyle {\textbf {r}}={\textbf {r}}_{0}+{\textbf {a}}t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca83af73cef59fe73380c9737197485304b371ec), and at that 
+
+
+
+
+
+a
+
+
+⋅
+
+
+n
+
+
+≠
+0
+
+
+{\textstyle {\textbf {a}}\cdot {\textbf {n}}\neq 0}
+
+![{\textstyle {\textbf {a}}\cdot {\textbf {n}}\neq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/33673ddea1dea180b68cac92d5065f32f85016b1). Find the position vector of the intersection point of these lines.
+2. Find the distance from point 
+
+
+
+
+M
+
+0
+
+
+
+
+{\textstyle M\_{0}}
+
+![{\textstyle M_{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/feb4ebe89e459609fa9e97bf72ee561acb3f7836) with the position vector 
+
+
+
+
+
+
+r
+
+
+
+0
+
+
+
+
+{\textstyle {\textbf {r}}\_{0}}
+
+![{\textstyle {\textbf {r}}_{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b0b1d2beb050ff53f1db5422ed3c6067091489d2) to the line defined by the equation (a) 
+
+
+
+
+
+r
+
+
+=
+
+
+
+r
+
+
+
+0
+
+
++
+
+
+a
+
+
+t
+
+
+{\textstyle {\textbf {r}}={\textbf {r}}\_{0}+{\textbf {a}}t}
+
+![{\textstyle {\textbf {r}}={\textbf {r}}_{0}+{\textbf {a}}t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca83af73cef59fe73380c9737197485304b371ec); (b) 
+
+
+
+
+
+r
+
+
+⋅
+
+
+n
+
+
+=
+A
+
+
+{\textstyle {\textbf {r}}\cdot {\textbf {n}}=A}
+
+![{\textstyle {\textbf {r}}\cdot {\textbf {n}}=A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d0bdfb3c03f3478452862b246cd0bec466eb624d).
+3. Diagonals of a rhombus intersect at point 
+
+
+
+M
+(
+1
+;
+
+2
+)
+
+
+{\textstyle M(1;\,2)}
+
+![{\textstyle M(1;\,2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1f5f919c98511e9602aff3b5c6fb6a44b3c5d75c), the longest of them being parallel to a horizontal axis. The side of the rhombus equals 2 and its obtuse angle is 
+
+
+
+
+120
+
+∘
+
+
+
+
+{\textstyle 120^{\circ }}
+
+![{\textstyle 120^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/db4bd85704493ea3595bcef6a92dbadcef085e51). Compose the equations of the sides of this rhombus.
+4. Compose the equations of lines passing through point 
+
+
+
+A
+(
+2
+;
+−
+4
+)
+
+
+{\textstyle A(2;-4)}
+
+![{\textstyle A(2;-4)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/adb02900c49b8277ff0d9994f3c262b42712fc10) and forming angles of 
+
+
+
+
+60
+
+∘
+
+
+
+
+{\textstyle 60^{\circ }}
+
+![{\textstyle 60^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/880b547c0017493563c28efdad95fdac91f97352) with the line 
+
+
+
+
+
+
+1
+−
+2
+x
+
+3
+
+
+=
+
+
+
+3
++
+2
+y
+
+
+−
+2
+
+
+
+
+
+{\textstyle {\frac {1-2x}{3}}={\frac {3+2y}{-2}}}
+
+![{\textstyle {\frac {1-2x}{3}}={\frac {3+2y}{-2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9d3793ed8ac9c5b2a740ee251edbe89f3a25c7d4).
+5. Find the cross product of (a) vectors 
+
+
+
+
+
+a
+
+
+(
+3
+;
+−
+2
+;
+
+1
+)
+
+
+{\textstyle {\textbf {a}}(3;-2;\,1)}
+
+![{\textstyle {\textbf {a}}(3;-2;\,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/24aa2e3d81f5e733ac961fc54c00c6400ac7c554) and 
+
+
+
+
+
+b
+
+
+(
+2
+;
+−
+5
+;
+−
+3
+)
+
+
+{\textstyle {\textbf {b}}(2;-5;-3)}
+
+![{\textstyle {\textbf {b}}(2;-5;-3)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ed4f1d0f60888ec6d6e29a3ef51f7c26784b688e); (b) vectors 
+
+
+
+
+
+a
+
+
+(
+3
+;
+−
+2
+;
+
+1
+)
+
+
+{\textstyle {\textbf {a}}(3;-2;\,1)}
+
+![{\textstyle {\textbf {a}}(3;-2;\,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/24aa2e3d81f5e733ac961fc54c00c6400ac7c554) and 
+
+
+
+
+
+c
+
+
+(
+−
+18
+;
+
+12
+;
+−
+6
+)
+
+
+{\textstyle {\textbf {c}}(-18;\,12;-6)}
+
+![{\textstyle {\textbf {c}}(-18;\,12;-6)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/536804f73bf9994ca0ac6a28c7c18f9b7c025d00).
+6. A triangle is constructed on vectors 
+
+
+
+
+
+a
+
+
+(
+2
+;
+4
+;
+−
+1
+)
+
+
+{\textstyle {\textbf {a}}(2;4;-1)}
+
+![{\textstyle {\textbf {a}}(2;4;-1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8dcfef96a8fb429db141d89ad1a4a7d2b79796c7) and 
+
+
+
+
+
+b
+
+
+(
+−
+2
+;
+1
+;
+1
+)
+
+
+{\textstyle {\textbf {b}}(-2;1;1)}
+
+![{\textstyle {\textbf {b}}(-2;1;1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/33194e12e69d8cf8bef0e3a7a975b0bbc27e0d59). (a) Find the area of this triangle. (b) Find the altitudes of this triangle.
+7. Find the scalar triple product of 
+
+
+
+
+
+a
+
+
+(
+1
+;
+
+2
+;
+−
+1
+)
+
+
+{\textstyle {\textbf {a}}(1;\,2;-1)}
+
+![{\textstyle {\textbf {a}}(1;\,2;-1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f4ff4c4819f08216a9b289eee65fae9e2409cd89), 
+
+
+
+
+
+b
+
+
+(
+7
+;
+3
+;
+−
+5
+)
+
+
+{\textstyle {\textbf {b}}(7;3;-5)}
+
+![{\textstyle {\textbf {b}}(7;3;-5)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bad88c6efacea267911438883c60e91aa7e641d4), 
+
+
+
+
+
+c
+
+
+(
+3
+;
+
+4
+;
+−
+3
+)
+
+
+{\textstyle {\textbf {c}}(3;\,4;-3)}
+
+![{\textstyle {\textbf {c}}(3;\,4;-3)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3075cbf140d048ec7105863bf15ffbc46d4ea011).
+8. It is known that basis vectors 
+
+
+
+
+
+
+e
+
+
+
+1
+
+
+
+
+{\textstyle {\textbf {e}}\_{1}}
+
+![{\textstyle {\textbf {e}}_{1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/633f38e385b970d94316cec9a3f0f8d8b2952c78), 
+
+
+
+
+
+
+e
+
+
+
+2
+
+
+
+
+{\textstyle {\textbf {e}}\_{2}}
+
+![{\textstyle {\textbf {e}}_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1141e813036efabb49e22e26699abda03db9c238), 
+
+
+
+
+
+
+e
+
+
+
+3
+
+
+
+
+{\textstyle {\textbf {e}}\_{3}}
+
+![{\textstyle {\textbf {e}}_{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4136ef375267fae398133caf33d6309b3491fe75) have lengths of 
+
+
+
+1
+
+
+{\textstyle 1}
+
+![{\textstyle 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6706df9ed9f240d1a94545fb4e522bda168fe8fd), 
+
+
+
+2
+
+
+{\textstyle 2}
+
+![{\textstyle 2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/78ed0cd8140e5a15b6fcce83602df58458e0f3b0), 
+
+
+
+2
+
+
+2
+
+
+
+
+{\textstyle 2{\sqrt {2}}}
+
+![{\textstyle 2{\sqrt {2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f302ae86c5e346beaf1dc60ab28ce51583d3a10f) respectively, and 
+
+
+
+∠
+(
+
+
+
+e
+
+
+
+1
+
+
+,
+
+
+
+e
+
+
+
+2
+
+
+)
+=
+
+120
+
+∘
+
+
+
+
+{\textstyle \angle ({\textbf {e}}\_{1},{\textbf {e}}\_{2})=120^{\circ }}
+
+![{\textstyle \angle ({\textbf {e}}_{1},{\textbf {e}}_{2})=120^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5bc355fb33e21d27781b3c69f604dfa4ac8a2335), 
+
+
+
+∠
+(
+
+
+
+e
+
+
+
+1
+
+
+,
+
+
+
+e
+
+
+
+3
+
+
+)
+=
+
+135
+
+∘
+
+
+
+
+{\textstyle \angle ({\textbf {e}}\_{1},{\textbf {e}}\_{3})=135^{\circ }}
+
+![{\textstyle \angle ({\textbf {e}}_{1},{\textbf {e}}_{3})=135^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/077d554778a6237a758bdd3cd174fb71e56c5a59), 
+
+
+
+∠
+(
+
+
+
+e
+
+
+
+2
+
+
+,
+
+
+
+e
+
+
+
+3
+
+
+)
+=
+
+45
+
+∘
+
+
+
+
+{\textstyle \angle ({\textbf {e}}\_{2},{\textbf {e}}\_{3})=45^{\circ }}
+
+![{\textstyle \angle ({\textbf {e}}_{2},{\textbf {e}}_{3})=45^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2c625e201eaf56a5ab2f55c468fb74919eecf950). Find the volume of a parallelepiped constructed on vectors with coordinates 
+
+
+
+(
+−
+1
+;
+
+0
+;
+
+2
+)
+
+
+{\textstyle (-1;\,0;\,2)}
+
+![{\textstyle (-1;\,0;\,2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6f80a6dd17132920d07de233c927f5b35fe55342), 
+
+
+
+(
+1
+;
+
+1
+
+4
+)
+
+
+{\textstyle (1;\,1\,4)}
+
+![{\textstyle (1;\,1\,4)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/93f2f019128f43ccd8b9bf1ec5fae847335c9609) and 
+
+
+
+(
+−
+2
+;
+
+1
+;
+
+1
+)
+
+
+{\textstyle (-2;\,1;\,1)}
+
+![{\textstyle (-2;\,1;\,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c29df73c5099969e89def9536b89bed1f8b8300b) in this basis.
+
+
+#### Section 3
+
+
+1. Prove that a curve given by 
+
+
+
+34
+
+x
+
+2
+
+
++
+24
+x
+y
++
+41
+
+y
+
+2
+
+
+−
+44
+x
++
+58
+y
++
+1
+=
+0
+
+
+{\textstyle 34x^{2}+24xy+41y^{2}-44x+58y+1=0}
+
+![{\textstyle 34x^{2}+24xy+41y^{2}-44x+58y+1=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2081edc20b56611eb9f1897a625f3bc0bc3df3b5) is an ellipse. Find the major and minor axes of this ellipse, its eccentricity, coordinates of its center and foci. Find the equations of axes and directrices of this ellipse.
+2. Determine types of curves given by the following equations. For each of the curves, find its canonical coordinate system (i.e. indicate the coordinates of origin and new basis vectors in the initial coordinate system) and its canonical equation. (a) 
+
+
+
+9
+
+x
+
+2
+
+
+−
+16
+
+y
+
+2
+
+
+−
+6
+x
++
+8
+y
+−
+144
+=
+0
+
+
+{\textstyle 9x^{2}-16y^{2}-6x+8y-144=0}
+
+![{\textstyle 9x^{2}-16y^{2}-6x+8y-144=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e2307372c3cf01eef66761c99845dcbe394be29f); (b) 
+
+
+
+9
+
+x
+
+2
+
+
++
+4
+
+y
+
+2
+
+
++
+6
+x
+−
+4
+y
+−
+2
+=
+0
+
+
+{\textstyle 9x^{2}+4y^{2}+6x-4y-2=0}
+
+![{\textstyle 9x^{2}+4y^{2}+6x-4y-2=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73b831469fdf03eac9e9c9656ae7fef80096fb94); (c) 
+
+
+
+12
+
+x
+
+2
+
+
+−
+12
+x
+−
+32
+y
+−
+29
+=
+0
+
+
+{\textstyle 12x^{2}-12x-32y-29=0}
+
+![{\textstyle 12x^{2}-12x-32y-29=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8cde74f6df39c7d1f475a31c4f1add253f1a43eb); (d) 
+
+
+
+x
+y
++
+2
+x
++
+y
+=
+0
+
+
+{\textstyle xy+2x+y=0}
+
+![{\textstyle xy+2x+y=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ced2a1c13f7eb77948ffc6ba9c1789659873573);
+3. Find the equations of lines tangent to curve 
+
+
+
+6
+x
+y
++
+8
+
+y
+
+2
+
+
+−
+12
+x
+−
+26
+y
++
+11
+=
+0
+
+
+{\textstyle 6xy+8y^{2}-12x-26y+11=0}
+
+![{\textstyle 6xy+8y^{2}-12x-26y+11=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/38463f126baaf801dce5a01c4e5d2e4c9d5e5080) that are (a) parallel to line 
+
+
+
+6
+x
++
+17
+y
+−
+4
+=
+0
+
+
+{\textstyle 6x+17y-4=0}
+
+![{\textstyle 6x+17y-4=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fe1136341a1ea0ad8bbc7101dbceadb86b33e90e); (b) perpendicular to line 
+
+
+
+41
+x
+−
+24
+y
++
+3
+=
+0
+
+
+{\textstyle 41x-24y+3=0}
+
+![{\textstyle 41x-24y+3=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91928594589b3b61e71e2f6d60125360b48cd4fd); (c) parallel to line 
+
+
+
+y
+=
+2
+
+
+{\textstyle y=2}
+
+![{\textstyle y=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/887628e811c56cc94aaccb0f5e4c773f19231cf9).
+4. For each value of parameter 
+
+
+
+a
+
+
+{\textstyle a}
+
+![{\textstyle a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a503f107a7c104e40e484cee9e1f5993d28ffd8) determine types of surfaces given by the equations: (a) 
+
+
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+−
+
+z
+
+2
+
+
+=
+a
+
+
+{\textstyle x^{2}+y^{2}-z^{2}=a}
+
+![{\textstyle x^{2}+y^{2}-z^{2}=a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aedac9a12be3e2a8bb6549e080cecd007665a44c); (b) 
+
+
+
+
+x
+
+2
+
+
++
+a
+
+(
+
+
+y
+
+2
+
+
++
+
+z
+
+2
+
+
+
+)
+
+=
+1
+
+
+{\textstyle x^{2}+a\left(y^{2}+z^{2}\right)=1}
+
+![{\textstyle x^{2}+a\left(y^{2}+z^{2}\right)=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/04136582473b57e7f0525feeebccc4460ecf7ad8); (c) 
+
+
+
+
+x
+
+2
+
+
++
+a
+
+y
+
+2
+
+
+=
+a
+z
+
+
+{\textstyle x^{2}+ay^{2}=az}
+
+![{\textstyle x^{2}+ay^{2}=az}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d9326d877d128ad9d17a96c9765e1da5f7c91e6); (d) 
+
+
+
+
+x
+
+2
+
+
++
+a
+
+y
+
+2
+
+
+=
+a
+z
++
+1
+
+
+{\textstyle x^{2}+ay^{2}=az+1}
+
+![{\textstyle x^{2}+ay^{2}=az+1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d1cd37bf6d43b7adafdd4ec58f392dd620872e3).
+5. Find a vector equation of a right circular cone with apex 
+
+
+
+
+M
+
+0
+
+
+
+(
+
+
+
+r
+
+
+
+0
+
+
+)
+
+
+
+{\textstyle M\_{0}\left({\textbf {r}}\_{0}\right)}
+
+![{\textstyle M_{0}\left({\textbf {r}}_{0}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f1b67abdb7e98da13a4de428625f69d249276ae5) and axis 
+
+
+
+
+
+r
+
+
+=
+
+
+
+r
+
+
+
+0
+
+
++
+
+
+a
+
+
+t
+
+
+{\textstyle {\textbf {r}}={\textbf {r}}\_{0}+{\textbf {a}}t}
+
+![{\textstyle {\textbf {r}}={\textbf {r}}_{0}+{\textbf {a}}t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca83af73cef59fe73380c9737197485304b371ec) if it is known that generatrices of this cone form the angle of 
+
+
+
+α
+
+
+{\textstyle \alpha }
+
+![{\textstyle \alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d86dbd6183264b2f8569da1751380b173c7b185) with its axis.
+6. Find the equation of a cylinder with radius 
+
+
+
+
+
+2
+
+
+
+
+{\textstyle {\sqrt {2}}}
+
+![{\textstyle {\sqrt {2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5094a5b1e2f42490aa4de2c7a4b7235a27f1b73f) that has an axis 
+
+
+
+x
+=
+1
++
+t
+
+
+{\textstyle x=1+t}
+
+![{\textstyle x=1+t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eca54a99a9fdad0ee1a0bba54ac67014e83a51e2), 
+
+
+
+y
+=
+2
++
+t
+
+
+{\textstyle y=2+t}
+
+![{\textstyle y=2+t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/213ba8ad271ceb3b25aaaafcbe23edd7c885c7f0), 
+
+
+
+z
+=
+3
++
+t
+
+
+{\textstyle z=3+t}
+
+![{\textstyle z=3+t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/582781cac22a2c157f5b5b60da347600c9778a6f).
+7. An ellipsoid is symmetric with respect to coordinate planes, passes through point 
+
+
+
+M
+(
+3
+;
+
+1
+;
+
+1
+)
+
+
+{\textstyle M(3;\,1;\,1)}
+
+![{\textstyle M(3;\,1;\,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6192e6c5728edd5b9a22b9c19aa8be852e2f0599) and circle 
+
+
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
++
+
+z
+
+2
+
+
+=
+9
+
+
+{\textstyle x^{2}+y^{2}+z^{2}=9}
+
+![{\textstyle x^{2}+y^{2}+z^{2}=9}](https://wikimedia.org/api/rest_v1/media/math/render/svg/29376da667d60dba7e1f552a56d1ce98caea3a4d), 
+
+
+
+x
+−
+z
+=
+0
+
+
+{\textstyle x-z=0}
+
+![{\textstyle x-z=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/709115599ad054688b92e60cdb84a4f32fe944f1). Find the equation of this ellipsoid.
+
+
+### The retake exam
+
+
+Retakes will be run as a comprehensive exam, where the student will be assessed the acquired knowledge coming from the textbooks, the lectures, the labs, and the additional required reading material, as supplied by the instructor. During such comprehensive oral/written the student could be asked to solve exercises and to explain theoretical and practical aspects of the course.
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__analytic_geometry_and_linear_algebra_i.md

@@ -0,0 +1,2759 @@
+
+
+
+
+
+
+
+BSc: Analytic Geometry And Linear Algebra I
+===========================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Analytical Geometry & Linear Algebra – I](#Analytical_Geometry_.26_Linear_Algebra_.E2.80.93_I)
+	+ [1.1 Course characteristics](#Course_characteristics)
+		- [1.1.1 Key concepts of the class](#Key_concepts_of_the_class)
+		- [1.1.2 What is the purpose of this course?](#What_is_the_purpose_of_this_course.3F)
+		- [1.1.3 Course Objectives Based on Bloom’s Taxonomy](#Course_Objectives_Based_on_Bloom.E2.80.99s_Taxonomy)
+		- [1.1.4 - What should a student remember at the end of the course?](#-_What_should_a_student_remember_at_the_end_of_the_course.3F)
+		- [1.1.5 - What should a student be able to understand at the end of the course?](#-_What_should_a_student_be_able_to_understand_at_the_end_of_the_course.3F)
+		- [1.1.6 - What should a student be able to apply at the end of the course?](#-_What_should_a_student_be_able_to_apply_at_the_end_of_the_course.3F)
+		- [1.1.7 Course evaluation](#Course_evaluation)
+		- [1.1.8 Grades range](#Grades_range)
+		- [1.1.9 Resources and reference material](#Resources_and_reference_material)
+			* [1.1.9.1 Textbooks:](#Textbooks:)
+			* [1.1.9.2 Reference material:](#Reference_material:)
+	+ [1.2 Course Sections](#Course_Sections)
+		- [1.2.1 Section 1](#Section_1)
+			* [1.2.1.1 Section title:](#Section_title:)
+		- [1.2.2 Topics covered in this section:](#Topics_covered_in_this_section:)
+		- [1.2.3 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F)
+		- [1.2.4 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section)
+		- [1.2.5 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section)
+		- [1.2.6 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section)
+		- [1.2.7 Section 2](#Section_2)
+			* [1.2.7.1 Section title:](#Section_title:_2)
+		- [1.2.8 Topics covered in this section:](#Topics_covered_in_this_section:_2)
+		- [1.2.9 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_2)
+		- [1.2.10 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_2)
+		- [1.2.11 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_2)
+		- [1.2.12 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_2)
+		- [1.2.13 Section 3](#Section_3)
+			* [1.2.13.1 Section title:](#Section_title:_3)
+		- [1.2.14 Topics covered in this section:](#Topics_covered_in_this_section:_3)
+		- [1.2.15 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_3)
+		- [1.2.16 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_3)
+		- [1.2.17 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_3)
+		- [1.2.18 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_3)
+		- [1.2.19 Section 4](#Section_4)
+			* [1.2.19.1 Section title:](#Section_title:_4)
+		- [1.2.20 Topics covered in this section:](#Topics_covered_in_this_section:_4)
+		- [1.2.21 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_4)
+		- [1.2.22 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_4)
+		- [1.2.23 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_4)
+		- [1.2.24 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_4)
+		- [1.2.25 Section 5](#Section_5)
+			* [1.2.25.1 Section title:](#Section_title:_5)
+		- [1.2.26 Topics covered in this section:](#Topics_covered_in_this_section:_5)
+		- [1.2.27 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_5)
+		- [1.2.28 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_5)
+		- [1.2.29 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_5)
+		- [1.2.30 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_5)
+		- [1.2.31 Section 6](#Section_6)
+			* [1.2.31.1 Section title:](#Section_title:_6)
+		- [1.2.32 Topics covered in this section:](#Topics_covered_in_this_section:_6)
+		- [1.2.33 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_6)
+		- [1.2.34 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_6)
+		- [1.2.35 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_6)
+		- [1.2.36 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_6)
+
+
+
+Analytical Geometry & Linear Algebra – I
+========================================
+
+
+* **Course name:** Analytical Geometry & Linear Algebra – I
+* **Course number:** XYZ
+* **Subject area:** Math
+
+
+Course characteristics
+----------------------
+
+
+### Key concepts of the class
+
+
+* fundamental principles of vector algebra,
+* concepts of basic geometry objects and their transformations in the plane and in the space
+
+
+### What is the purpose of this course?
+
+
+This is an introductory course in analytical geometry and linear algebra. After having studied the course, students get to know fundamental principles of vector algebra and its applications in solving various geometry problems, different types of equations of lines and planes, conics and quadric surfaces, transformations in the plane and in the space. An introduction on matrices and determinants as a fundamental knowledge of linear algebra is also provided.
+
+
+
+### Course Objectives Based on Bloom’s Taxonomy
+
+
+### - What should a student remember at the end of the course?
+
+
+* List basic notions of vector algebra,
+* recite the base form of the equations of transformations in planes and spaces,
+* recall equations of lines and planes,
+* identify the type of conic section,
+* recognize the kind of quadric surfaces.
+
+
+### - What should a student be able to understand at the end of the course?
+
+
+* explain the geometrical interpretation of the basic operations of vector algebra,
+* restate equations of lines and planes in different forms,
+* interpret the geometrical meaning of the conic sections in the mathematical expression,
+* give the examples of the surfaces of revolution,
+* understand the value of geometry in various fields of science and techniques.
+
+
+### - What should a student be able to apply at the end of the course?
+
+
+* Perform the basic operations of vector algebra,
+* use different types of equations of lines and planes to solve the plane and space problems,
+* represent the conic section in canonical form,
+* compose the equation of quadric surface.
+
+
+### Course evaluation
+
+
+
+
+Course grade breakdown
+|  |  | **Proposed points** |
+| --- | --- | --- |
+| Labs/seminar classes
+ | 20
+ | 10
+ |
+| Interim performance assessment
+ | 30
+ | 20
+ |
+| Exams
+ | 50
+ | 70
+ |
+
+
+### Grades range
+
+
+
+
+Course grading range
+|  |  | **Proposed range** |
+| --- | --- | --- |
+| A. Excellent
+ | 90-100
+ | 80-100
+ |
+| B. Good
+ | 75-89
+ | 60-79
+ |
+| C. Satisfactory
+ | 60-74
+ | 40-59
+ |
+| D. Poor
+ | 0-59
+ | 0-39
+ |
+
+
+### Resources and reference material
+
+
+#### Textbooks:
+
+
+* 
+
+
+#### Reference material:
+
+
+* 
+* 
+
+
+Course Sections
+---------------
+
+
+The main sections of the course and approximate hour distribution between them is as follows:
+
+
+
+
+
+Course Sections
+| **Section** | **Section Title** | **Lectures** | **Seminars** | **Self-study** | **Knowledge** |
+| **Number** |  | **(hours)** | **(labs)** |  | **evaluation** |
+| 1
+ | Vector algebra
+ | 8
+ | 4
+ | 10
+ | 2
+ |
+| 2
+ | Introduction to matrices and determinants
+ | 8
+ | 4
+ | 10
+ | 1
+ |
+| 3
+ | Lines in the plane and in the space
+ | 8
+ | 4
+ | 10
+ | 2
+ |
+| 4
+ | Planes in the space
+ | 8
+ | 4
+ | 10
+ | 1
+ |
+| 5
+ | Quadratic curves
+ | 8
+ | 4
+ | 10
+ | 2
+ |
+| 6
+ | Quadric surfaces
+ | 8
+ | 4
+ | 10
+ | 2
+ |
+| Final examination
+ |  |  |  |  | 2
+ |
+
+
+### Section 1
+
+
+#### Section title:
+
+
+Vector algebra
+
+
+
+### Topics covered in this section:
+
+
+* Vector spaces
+* Basic operations on vectors (summation, multiplication by scalar, dot product)
+* Linear dependency and in-dependency of the vectors
+* Basis in vector spaces
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. How to perform the shift of the vector?
+2. What is the geometrical interpretation of the dot product?
+3. How to determine whether the vectors are linearly dependent?
+4. What is a vector basis?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Evaluate 
+
+
+
+
+|
+
+
+
+a
+
+
+
+
+|
+
+
+2
+
+
+−
+2
+
+
+3
+
+
+
+
+a
+
+
+⋅
+
+
+b
+
+
+−
+7
+
+|
+
+
+
+b
+
+
+
+
+|
+
+
+2
+
+
+
+
+{\textstyle |{\textbf {a}}|^{2}-2{\sqrt {3}}{\textbf {a}}\cdot {\textbf {b}}-7|{\textbf {b}}|^{2}}
+
+![{\textstyle |{\textbf {a}}|^{2}-2{\sqrt {3}}{\textbf {a}}\cdot {\textbf {b}}-7|{\textbf {b}}|^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b39de16745ae08f1e071202ed4c68a7439df361b) given that 
+
+
+
+
+|
+
+
+
+a
+
+
+
+|
+
+=
+4
+
+
+{\textstyle |{\textbf {a}}|=4}
+
+![{\textstyle |{\textbf {a}}|=4}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dad653ed7b4f53967e38f14dc254a0b4ed40f4ac), 
+
+
+
+
+|
+
+
+
+b
+
+
+
+|
+
+=
+1
+
+
+{\textstyle |{\textbf {b}}|=1}
+
+![{\textstyle |{\textbf {b}}|=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2147d16bdc4fd215671610f46300d16ea8f1963d), 
+
+
+
+∠
+(
+
+
+a
+
+
+,
+
+
+
+b
+
+
+)
+=
+
+150
+
+∘
+
+
+
+
+{\textstyle \angle ({\textbf {a}},\,{\textbf {b}})=150^{\circ }}
+
+![{\textstyle \angle ({\textbf {a}},\,{\textbf {b}})=150^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/34c0c47f4b2dbe58c362811be01e2a9658ffd65e).
+2. Prove that vectors 
+
+
+
+
+
+b
+
+
+(
+
+
+a
+
+
+⋅
+
+
+c
+
+
+)
+−
+
+
+c
+
+
+(
+
+
+a
+
+
+⋅
+
+
+b
+
+
+)
+
+
+{\textstyle {\textbf {b}}({\textbf {a}}\cdot {\textbf {c}})-{\textbf {c}}({\textbf {a}}\cdot {\textbf {b}})}
+
+![{\textstyle {\textbf {b}}({\textbf {a}}\cdot {\textbf {c}})-{\textbf {c}}({\textbf {a}}\cdot {\textbf {b}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91d497e3670b2e628a97f0ccb57ca80a925ef32c) and 
+
+
+
+
+
+a
+
+
+
+
+{\textstyle {\textbf {a}}}
+
+![{\textstyle {\textbf {a}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0a7a4f8c41fd49715b57c7891e867192892aaf8b) are perpendicular to each other.
+3. Bases 
+
+
+
+A
+D
+
+
+{\textstyle AD}
+
+![{\textstyle AD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b67c9a22c95905ef6b81962b11b31e1c0ef52225) and 
+
+
+
+B
+C
+
+
+{\textstyle BC}
+
+![{\textstyle BC}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9357a907256f2d11e87040067a6ce9dd1976f725) of trapezoid 
+
+
+
+A
+B
+C
+D
+
+
+{\textstyle ABCD}
+
+![{\textstyle ABCD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/56e9dd14b4fcb989c106f3679aa2699f07eee6d4) are in the ratio of 
+
+
+
+4
+:
+1
+
+
+{\textstyle 4:1}
+
+![{\textstyle 4:1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/44785771746a94fd2cf3d26ff7cd5653f816763d). The diagonals of the trapezoid intersect at point 
+
+
+
+M
+
+
+{\textstyle M}
+
+![{\textstyle M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/913ace920108f7552777e36ac0b7ee3f5093a088) and the extensions of sides 
+
+
+
+A
+B
+
+
+{\textstyle AB}
+
+![{\textstyle AB}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac121a3e6c5dff2ebb2ff8340e4a7f1b35992e44) and 
+
+
+
+C
+D
+
+
+{\textstyle CD}
+
+![{\textstyle CD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/523217c283f1b3f72fe4f317b8ff09e22365f1e5) intersect at point 
+
+
+
+P
+
+
+{\textstyle P}
+
+![{\textstyle P}](https://wikimedia.org/api/rest_v1/media/math/render/svg/038590207af1024a629c1a08c855e9ac46bf5610). Let us consider the basis with 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) as the origin, 
+
+
+
+
+
+
+A
+D
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AD}}}
+
+![{\textstyle {\overrightarrow {AD}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a09091c3ae3ae05dbb915b79e411ee15a84401f1) and 
+
+
+
+
+
+
+A
+B
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AB}}}
+
+![{\textstyle {\overrightarrow {AB}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a6f9e6559e7cd7c16144340887587c73e294b4ba) as basis vectors. Find the coordinates of points 
+
+
+
+M
+
+
+{\textstyle M}
+
+![{\textstyle M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/913ace920108f7552777e36ac0b7ee3f5093a088) and 
+
+
+
+P
+
+
+{\textstyle P}
+
+![{\textstyle P}](https://wikimedia.org/api/rest_v1/media/math/render/svg/038590207af1024a629c1a08c855e9ac46bf5610) in this basis.
+4. A line segment joining a vertex of a tetrahedron with the centroid of the opposite face (the centroid of a triangle is an intersection point of all its medians) is called a median of this tetrahedron. Using vector algebra prove that all the four medians of any tetrahedron concur in a point that divides these medians in the ratio of 
+
+
+
+3
+:
+1
+
+
+{\textstyle 3:1}
+
+![{\textstyle 3:1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1bdfd3570b8991fb33d61e324c67dd54f08a0eef), the longer segments being on the side of the vertex of the tetrahedron.
+
+
+### Test questions for final assessment in this section
+
+
+1. Vector spaces. General concepts.
+2. Dot product as an operation on vectors.
+3. Basis in vector spaces. Its properties.
+
+
+### Section 2
+
+
+#### Section title:
+
+
+Introduction to matrices and determinants
+
+
+
+### Topics covered in this section:
+
+
+* Relationship between Linear Algebra and Analytical Geometry
+* Matrices 2x2, 3x3
+* Determinants 2x2, 3x3
+* Operations om matrices and determinants
+* The rank of a matrix
+* Inverse matrix
+* Systems of linear equations
+* Changing basis and coordinates
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. What is the difference between matrices and determinants?
+2. Matrices 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) and 
+
+
+
+C
+
+
+{\textstyle C}
+
+![{\textstyle C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6dca76d9ff4b48256b6a4a99bcb234b64b2fa72b) have dimensions of 
+
+
+
+m
+×
+n
+
+
+{\textstyle m\times n}
+
+![{\textstyle m\times n}](https://wikimedia.org/api/rest_v1/media/math/render/svg/37dc29fae3b1932f1b311a052ecc6ecb8692dc48) and 
+
+
+
+p
+×
+q
+
+
+{\textstyle p\times q}
+
+![{\textstyle p\times q}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cdbd208094b241eb647c2e3b515a05197f9e0fdc) respectively, and it is known that the product 
+
+
+
+A
+B
+C
+
+
+{\textstyle ABC}
+
+![{\textstyle ABC}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1516a55703463b2e378eb0b2eda76f08f6919636) exists. What are possible dimensions of 
+
+
+
+B
+
+
+{\textstyle B}
+
+![{\textstyle B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/de0b47ffc21636dc2df68f6c793177a268f10e9b) and 
+
+
+
+A
+B
+C
+
+
+{\textstyle ABC}
+
+![{\textstyle ABC}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1516a55703463b2e378eb0b2eda76f08f6919636)?
+3. How to determine the rank of a matrix?
+4. What is the meaning of the inverse matrix?
+5. How to restate a system of linear equations in the matrix form?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+Let 
+
+
+
+A
+=
+
+(
+
+
+
+
+3
+
+
+1
+
+
+
+
+5
+
+
+−
+2
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cc}3&1\\5&-2\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cc}3&1\\5&-2\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2239fc87faa1789417dbc59e4d88349c4ab50b1d), 
+
+
+
+B
+=
+
+(
+
+
+
+
+−
+2
+
+
+1
+
+
+
+
+3
+
+
+4
+
+
+
+
+)
+
+
+
+{\textstyle B=\left({\begin{array}{cc}-2&1\\3&4\\\end{array}}\right)}
+
+![{\textstyle B=\left({\begin{array}{cc}-2&1\\3&4\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cda45263ccde2633fc2b326112c4580c7d96c6d7), and 
+
+
+
+I
+=
+
+(
+
+
+
+
+1
+
+
+0
+
+
+
+
+0
+
+
+1
+
+
+
+
+)
+
+
+
+{\textstyle I=\left({\begin{array}{cc}1&0\\0&1\\\end{array}}\right)}
+
+![{\textstyle I=\left({\begin{array}{cc}1&0\\0&1\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1a8ec455e7245033a95fe9502af2fbae28f2f143).
+
+
+
+1. Find 
+
+
+
+A
++
+B
+
+
+{\textstyle A+B}
+
+![{\textstyle A+B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bdd957a1f1d7f480fb51c33b1e5ab3b8259cb37f) and 
+
+
+
+2
+A
+−
+3
+B
++
+I
+
+
+{\textstyle 2A-3B+I}
+
+![{\textstyle 2A-3B+I}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bf9f21726daa3bc4c5b46cdebf17900d2384c4bc).
+2. Find the products 
+
+
+
+A
+B
+
+
+{\textstyle AB}
+
+![{\textstyle AB}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac121a3e6c5dff2ebb2ff8340e4a7f1b35992e44) and 
+
+
+
+B
+A
+
+
+{\textstyle BA}
+
+![{\textstyle BA}](https://wikimedia.org/api/rest_v1/media/math/render/svg/30d370a5b049f1bf605e0849e5011dab921a3e80) (and so make sure that, in general, 
+
+
+
+A
+B
+≠
+B
+A
+
+
+{\textstyle AB\neq BA}
+
+![{\textstyle AB\neq BA}](https://wikimedia.org/api/rest_v1/media/math/render/svg/547dca1516d9c8402fe6b52671054d5412e39d7a) for matrices).
+3. Find the inverse matrices for the given ones.
+4. Find the determinants of the given matrices.
+5. Point 
+
+
+
+M
+
+
+{\textstyle M}
+
+![{\textstyle M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/913ace920108f7552777e36ac0b7ee3f5093a088) is the centroid of face 
+
+
+
+B
+C
+D
+
+
+{\textstyle BCD}
+
+![{\textstyle BCD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dbf276d48bdd841bc17d7b41806b4fefd4d93aec) of tetrahedron 
+
+
+
+A
+B
+C
+D
+
+
+{\textstyle ABCD}
+
+![{\textstyle ABCD}](https://wikimedia.org/api/rest_v1/media/math/render/svg/56e9dd14b4fcb989c106f3679aa2699f07eee6d4). The old coordinate system is given by 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31), 
+
+
+
+
+
+
+A
+B
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AB}}}
+
+![{\textstyle {\overrightarrow {AB}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a6f9e6559e7cd7c16144340887587c73e294b4ba), 
+
+
+
+
+
+
+A
+C
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AC}}}
+
+![{\textstyle {\overrightarrow {AC}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cec90ca60916095907088cdf9c6807e322940609), 
+
+
+
+
+
+
+A
+D
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {AD}}}
+
+![{\textstyle {\overrightarrow {AD}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a09091c3ae3ae05dbb915b79e411ee15a84401f1), and the new coordinate system is given by 
+
+
+
+M
+
+
+{\textstyle M}
+
+![{\textstyle M}](https://wikimedia.org/api/rest_v1/media/math/render/svg/913ace920108f7552777e36ac0b7ee3f5093a088), 
+
+
+
+
+
+
+M
+B
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {MB}}}
+
+![{\textstyle {\overrightarrow {MB}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fc628c7e66ee539b78d720ffb8b08c68cda528bc), 
+
+
+
+
+
+
+M
+C
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {MC}}}
+
+![{\textstyle {\overrightarrow {MC}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e7b29574c4ba08f6b03fc30de162aa30153d3ab0), 
+
+
+
+
+
+
+M
+A
+
+→
+
+
+
+
+{\textstyle {\overrightarrow {MA}}}
+
+![{\textstyle {\overrightarrow {MA}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef8be9dd7ec0faa12b4f2f9f335d65b1cab904c5). Find the coordinates of a point in the old coordinate system given its coordinates 
+
+
+
+
+x
+′
+
+
+
+{\textstyle x'}
+
+![{\textstyle x'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bdd4bbf7bc3c37c71d0a1f9e4ef6c504c8f9d5de), 
+
+
+
+
+y
+′
+
+
+
+{\textstyle y'}
+
+![{\textstyle y'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e40eea4dc71b01e5ddff1d14b9b89853fde81d), 
+
+
+
+
+z
+′
+
+
+
+{\textstyle z'}
+
+![{\textstyle z'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/80546fbdafc04d89612c5491bc04d509709aeb17) in the new one.
+
+
+### Test questions for final assessment in this section
+
+
+1. Operations om matrices and determinants.
+2. Inverse matrix.
+3. Systems of linear equations and their solution in matrix form.
+4. Changing basis and coordinates.
+
+
+### Section 3
+
+
+#### Section title:
+
+
+Lines in the plane and in the space
+
+
+
+### Topics covered in this section:
+
+
+* General equation of a line in the plane
+* General parametric equation of a line in the space
+* Line as intersection between planes
+* Vector equation of a line
+* Distance from a point to a line
+* Distance between lines
+* Inter-positioning of lines
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. How to represent a line in the vector form?
+2. What is the result of intersection of two planes in vector form?
+3. How to derive the formula for the distance from a point to a line?
+4. How to interpret geometrically the distance between lines?
+5. List all possible inter-positions of lines in the space.
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Two lines are given by the equations 
+
+
+
+
+
+r
+
+
+⋅
+
+
+n
+
+
+=
+A
+
+
+{\textstyle {\textbf {r}}\cdot {\textbf {n}}=A}
+
+![{\textstyle {\textbf {r}}\cdot {\textbf {n}}=A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d0bdfb3c03f3478452862b246cd0bec466eb624d) and 
+
+
+
+
+
+r
+
+
+=
+
+
+
+r
+
+
+
+0
+
+
++
+
+
+a
+
+
+t
+
+
+{\textstyle {\textbf {r}}={\textbf {r}}\_{0}+{\textbf {a}}t}
+
+![{\textstyle {\textbf {r}}={\textbf {r}}_{0}+{\textbf {a}}t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca83af73cef59fe73380c9737197485304b371ec), and at that 
+
+
+
+
+
+a
+
+
+⋅
+
+
+n
+
+
+≠
+0
+
+
+{\textstyle {\textbf {a}}\cdot {\textbf {n}}\neq 0}
+
+![{\textstyle {\textbf {a}}\cdot {\textbf {n}}\neq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/33673ddea1dea180b68cac92d5065f32f85016b1). Find the position vector of the intersection point of these lines.
+2. Find the distance from point 
+
+
+
+
+M
+
+0
+
+
+
+
+{\textstyle M\_{0}}
+
+![{\textstyle M_{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/feb4ebe89e459609fa9e97bf72ee561acb3f7836) with the position vector 
+
+
+
+
+
+
+r
+
+
+
+0
+
+
+
+
+{\textstyle {\textbf {r}}\_{0}}
+
+![{\textstyle {\textbf {r}}_{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b0b1d2beb050ff53f1db5422ed3c6067091489d2) to the line defined by the equation (a) 
+
+
+
+
+
+r
+
+
+=
+
+
+
+r
+
+
+
+0
+
+
++
+
+
+a
+
+
+t
+
+
+{\textstyle {\textbf {r}}={\textbf {r}}\_{0}+{\textbf {a}}t}
+
+![{\textstyle {\textbf {r}}={\textbf {r}}_{0}+{\textbf {a}}t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca83af73cef59fe73380c9737197485304b371ec); (b) 
+
+
+
+
+
+r
+
+
+⋅
+
+
+n
+
+
+=
+A
+
+
+{\textstyle {\textbf {r}}\cdot {\textbf {n}}=A}
+
+![{\textstyle {\textbf {r}}\cdot {\textbf {n}}=A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d0bdfb3c03f3478452862b246cd0bec466eb624d).
+3. Diagonals of a rhombus intersect at point 
+
+
+
+M
+(
+1
+;
+
+2
+)
+
+
+{\textstyle M(1;\,2)}
+
+![{\textstyle M(1;\,2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1f5f919c98511e9602aff3b5c6fb6a44b3c5d75c), the longest of them being parallel to a horizontal axis. The side of the rhombus equals 2 and its obtuse angle is 
+
+
+
+
+120
+
+∘
+
+
+
+
+{\textstyle 120^{\circ }}
+
+![{\textstyle 120^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/db4bd85704493ea3595bcef6a92dbadcef085e51). Compose the equations of the sides of this rhombus.
+4. Compose the equations of lines passing through point 
+
+
+
+A
+(
+2
+;
+−
+4
+)
+
+
+{\textstyle A(2;-4)}
+
+![{\textstyle A(2;-4)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/adb02900c49b8277ff0d9994f3c262b42712fc10) and forming angles of 
+
+
+
+
+60
+
+∘
+
+
+
+
+{\textstyle 60^{\circ }}
+
+![{\textstyle 60^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/880b547c0017493563c28efdad95fdac91f97352) with the line 
+
+
+
+
+
+
+1
+−
+2
+x
+
+3
+
+
+=
+
+
+
+3
++
+2
+y
+
+
+−
+2
+
+
+
+
+
+{\textstyle {\frac {1-2x}{3}}={\frac {3+2y}{-2}}}
+
+![{\textstyle {\frac {1-2x}{3}}={\frac {3+2y}{-2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9d3793ed8ac9c5b2a740ee251edbe89f3a25c7d4).
+
+
+### Test questions for final assessment in this section
+
+
+1. Lines in the plane and in the space. Equations of lines.
+2. Distance from a point to a line.
+3. Distance between two parallel lines.
+4. Distance between two skew lines.
+
+
+### Section 4
+
+
+#### Section title:
+
+
+Planes in the space
+
+
+
+### Topics covered in this section:
+
+
+* General equation of a plane
+* Normalized linear equation of a plane
+* Vector equation of a plane
+* Parametric equation a plane
+* Distance from a point to a plane
+* Projection of a vector on the plane
+* Inter-positioning of lines and planes
+* Cross Product of two vectors
+* Triple Scalar Product
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. What is the difference between general and normalized forms of equations of a plane?
+2. How to rewrite the equation of a plane in a vector form?
+3. What is the normal to a plane?
+4. How to interpret the cross products of two vectors?
+5. What is the meaning of scalar triple product of three vectors?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Find the cross product of (a) vectors 
+
+
+
+
+
+a
+
+
+(
+3
+;
+−
+2
+;
+
+1
+)
+
+
+{\textstyle {\textbf {a}}(3;-2;\,1)}
+
+![{\textstyle {\textbf {a}}(3;-2;\,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/24aa2e3d81f5e733ac961fc54c00c6400ac7c554) and 
+
+
+
+
+
+b
+
+
+(
+2
+;
+−
+5
+;
+−
+3
+)
+
+
+{\textstyle {\textbf {b}}(2;-5;-3)}
+
+![{\textstyle {\textbf {b}}(2;-5;-3)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ed4f1d0f60888ec6d6e29a3ef51f7c26784b688e); (b) vectors 
+
+
+
+
+
+a
+
+
+(
+3
+;
+−
+2
+;
+
+1
+)
+
+
+{\textstyle {\textbf {a}}(3;-2;\,1)}
+
+![{\textstyle {\textbf {a}}(3;-2;\,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/24aa2e3d81f5e733ac961fc54c00c6400ac7c554) and 
+
+
+
+
+
+c
+
+
+(
+−
+18
+;
+
+12
+;
+−
+6
+)
+
+
+{\textstyle {\textbf {c}}(-18;\,12;-6)}
+
+![{\textstyle {\textbf {c}}(-18;\,12;-6)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/536804f73bf9994ca0ac6a28c7c18f9b7c025d00).
+2. A triangle is constructed on vectors 
+
+
+
+
+
+a
+
+
+(
+2
+;
+4
+;
+−
+1
+)
+
+
+{\textstyle {\textbf {a}}(2;4;-1)}
+
+![{\textstyle {\textbf {a}}(2;4;-1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8dcfef96a8fb429db141d89ad1a4a7d2b79796c7) and 
+
+
+
+
+
+b
+
+
+(
+−
+2
+;
+1
+;
+1
+)
+
+
+{\textstyle {\textbf {b}}(-2;1;1)}
+
+![{\textstyle {\textbf {b}}(-2;1;1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/33194e12e69d8cf8bef0e3a7a975b0bbc27e0d59). (a) Find the area of this triangle. (b) Find the altitudes of this triangle.
+3. Find the scalar triple product of 
+
+
+
+
+
+a
+
+
+(
+1
+;
+
+2
+;
+−
+1
+)
+
+
+{\textstyle {\textbf {a}}(1;\,2;-1)}
+
+![{\textstyle {\textbf {a}}(1;\,2;-1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f4ff4c4819f08216a9b289eee65fae9e2409cd89), 
+
+
+
+
+
+b
+
+
+(
+7
+;
+3
+;
+−
+5
+)
+
+
+{\textstyle {\textbf {b}}(7;3;-5)}
+
+![{\textstyle {\textbf {b}}(7;3;-5)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bad88c6efacea267911438883c60e91aa7e641d4), 
+
+
+
+
+
+c
+
+
+(
+3
+;
+
+4
+;
+−
+3
+)
+
+
+{\textstyle {\textbf {c}}(3;\,4;-3)}
+
+![{\textstyle {\textbf {c}}(3;\,4;-3)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3075cbf140d048ec7105863bf15ffbc46d4ea011).
+4. It is known that basis vectors 
+
+
+
+
+
+
+e
+
+
+
+1
+
+
+
+
+{\textstyle {\textbf {e}}\_{1}}
+
+![{\textstyle {\textbf {e}}_{1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/633f38e385b970d94316cec9a3f0f8d8b2952c78), 
+
+
+
+
+
+
+e
+
+
+
+2
+
+
+
+
+{\textstyle {\textbf {e}}\_{2}}
+
+![{\textstyle {\textbf {e}}_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1141e813036efabb49e22e26699abda03db9c238), 
+
+
+
+
+
+
+e
+
+
+
+3
+
+
+
+
+{\textstyle {\textbf {e}}\_{3}}
+
+![{\textstyle {\textbf {e}}_{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4136ef375267fae398133caf33d6309b3491fe75) have lengths of 
+
+
+
+1
+
+
+{\textstyle 1}
+
+![{\textstyle 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6706df9ed9f240d1a94545fb4e522bda168fe8fd), 
+
+
+
+2
+
+
+{\textstyle 2}
+
+![{\textstyle 2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/78ed0cd8140e5a15b6fcce83602df58458e0f3b0), 
+
+
+
+2
+
+
+2
+
+
+
+
+{\textstyle 2{\sqrt {2}}}
+
+![{\textstyle 2{\sqrt {2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f302ae86c5e346beaf1dc60ab28ce51583d3a10f) respectively, and 
+
+
+
+∠
+(
+
+
+
+e
+
+
+
+1
+
+
+,
+
+
+
+e
+
+
+
+2
+
+
+)
+=
+
+120
+
+∘
+
+
+
+
+{\textstyle \angle ({\textbf {e}}\_{1},{\textbf {e}}\_{2})=120^{\circ }}
+
+![{\textstyle \angle ({\textbf {e}}_{1},{\textbf {e}}_{2})=120^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5bc355fb33e21d27781b3c69f604dfa4ac8a2335), 
+
+
+
+∠
+(
+
+
+
+e
+
+
+
+1
+
+
+,
+
+
+
+e
+
+
+
+3
+
+
+)
+=
+
+135
+
+∘
+
+
+
+
+{\textstyle \angle ({\textbf {e}}\_{1},{\textbf {e}}\_{3})=135^{\circ }}
+
+![{\textstyle \angle ({\textbf {e}}_{1},{\textbf {e}}_{3})=135^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/077d554778a6237a758bdd3cd174fb71e56c5a59), 
+
+
+
+∠
+(
+
+
+
+e
+
+
+
+2
+
+
+,
+
+
+
+e
+
+
+
+3
+
+
+)
+=
+
+45
+
+∘
+
+
+
+
+{\textstyle \angle ({\textbf {e}}\_{2},{\textbf {e}}\_{3})=45^{\circ }}
+
+![{\textstyle \angle ({\textbf {e}}_{2},{\textbf {e}}_{3})=45^{\circ }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2c625e201eaf56a5ab2f55c468fb74919eecf950). Find the volume of a parallelepiped constructed on vectors with coordinates 
+
+
+
+(
+−
+1
+;
+
+0
+;
+
+2
+)
+
+
+{\textstyle (-1;\,0;\,2)}
+
+![{\textstyle (-1;\,0;\,2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6f80a6dd17132920d07de233c927f5b35fe55342), 
+
+
+
+(
+1
+;
+
+1
+
+4
+)
+
+
+{\textstyle (1;\,1\,4)}
+
+![{\textstyle (1;\,1\,4)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/93f2f019128f43ccd8b9bf1ec5fae847335c9609) and 
+
+
+
+(
+−
+2
+;
+
+1
+;
+
+1
+)
+
+
+{\textstyle (-2;\,1;\,1)}
+
+![{\textstyle (-2;\,1;\,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c29df73c5099969e89def9536b89bed1f8b8300b) in this basis.
+
+
+### Test questions for final assessment in this section
+
+
+1. Planes in the space. Equations of planes.
+2. Distance from a point to a plane, from a line to a plane.
+3. Projection of a vector on the plane.
+4. Cross product, its properties and geometrical interpretation.
+5. Scalar triple product, its properties and geometrical interpretation.
+
+
+### Section 5
+
+
+#### Section title:
+
+
+Quadratic curves
+
+
+
+### Topics covered in this section:
+
+
+* Circle
+* Ellipse
+* Hyperbola
+* Parabola
+* Canonical equations
+* Shifting of coordinate system
+* Rotating of coordinate system
+* Parametrization
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. Formulate the canonical equation of the given quadratic curve.
+2. Which orthogonal transformations of coordinates do you know?
+3. How to perform a transformation of the coordinate system?
+4. How to represent a curve in the space?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Prove that a curve given by 
+
+
+
+34
+
+x
+
+2
+
+
++
+24
+x
+y
++
+41
+
+y
+
+2
+
+
+−
+44
+x
++
+58
+y
++
+1
+=
+0
+
+
+{\textstyle 34x^{2}+24xy+41y^{2}-44x+58y+1=0}
+
+![{\textstyle 34x^{2}+24xy+41y^{2}-44x+58y+1=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2081edc20b56611eb9f1897a625f3bc0bc3df3b5) is an ellipse. Find the major and minor axes of this ellipse, its eccentricity, coordinates of its center and foci. Find the equations of axes and directrices of this ellipse.
+2. Determine types of curves given by the following equations. For each of the curves, find its canonical coordinate system (i.e. indicate the coordinates of origin and new basis vectors in the initial coordinate system) and its canonical equation. (a) 
+
+
+
+9
+
+x
+
+2
+
+
+−
+16
+
+y
+
+2
+
+
+−
+6
+x
++
+8
+y
+−
+144
+=
+0
+
+
+{\textstyle 9x^{2}-16y^{2}-6x+8y-144=0}
+
+![{\textstyle 9x^{2}-16y^{2}-6x+8y-144=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e2307372c3cf01eef66761c99845dcbe394be29f); (b) 
+
+
+
+9
+
+x
+
+2
+
+
++
+4
+
+y
+
+2
+
+
++
+6
+x
+−
+4
+y
+−
+2
+=
+0
+
+
+{\textstyle 9x^{2}+4y^{2}+6x-4y-2=0}
+
+![{\textstyle 9x^{2}+4y^{2}+6x-4y-2=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73b831469fdf03eac9e9c9656ae7fef80096fb94); (c) 
+
+
+
+12
+
+x
+
+2
+
+
+−
+12
+x
+−
+32
+y
+−
+29
+=
+0
+
+
+{\textstyle 12x^{2}-12x-32y-29=0}
+
+![{\textstyle 12x^{2}-12x-32y-29=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8cde74f6df39c7d1f475a31c4f1add253f1a43eb); (d) 
+
+
+
+x
+y
++
+2
+x
++
+y
+=
+0
+
+
+{\textstyle xy+2x+y=0}
+
+![{\textstyle xy+2x+y=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ced2a1c13f7eb77948ffc6ba9c1789659873573);
+3. Find the equations of lines tangent to curve 
+
+
+
+6
+x
+y
++
+8
+
+y
+
+2
+
+
+−
+12
+x
+−
+26
+y
++
+11
+=
+0
+
+
+{\textstyle 6xy+8y^{2}-12x-26y+11=0}
+
+![{\textstyle 6xy+8y^{2}-12x-26y+11=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/38463f126baaf801dce5a01c4e5d2e4c9d5e5080) that are (a) parallel to line 
+
+
+
+6
+x
++
+17
+y
+−
+4
+=
+0
+
+
+{\textstyle 6x+17y-4=0}
+
+![{\textstyle 6x+17y-4=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fe1136341a1ea0ad8bbc7101dbceadb86b33e90e); (b) perpendicular to line 
+
+
+
+41
+x
+−
+24
+y
++
+3
+=
+0
+
+
+{\textstyle 41x-24y+3=0}
+
+![{\textstyle 41x-24y+3=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91928594589b3b61e71e2f6d60125360b48cd4fd); (c) parallel to line 
+
+
+
+y
+=
+2
+
+
+{\textstyle y=2}
+
+![{\textstyle y=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/887628e811c56cc94aaccb0f5e4c773f19231cf9).
+
+
+### Test questions for final assessment in this section
+
+
+1. Determine the type of a given curve with the use of the method of invariant.
+2. Compose the canonical equation of a given curve.
+3. Determine the canonical coordinate system for a given curve.
+
+
+### Section 6
+
+
+#### Section title:
+
+
+Quadric surfaces
+
+
+
+### Topics covered in this section:
+
+
+* General equation of the quadric surfaces
+* Canonical equation of a sphere and ellipsoid
+* Canonical equation of a hyperboloid and paraboloid
+* Surfaces of revolution
+* Canonical equation of a cone and cylinder
+* Vector equations of some quadric surfaces
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. What is the type of a quadric surface given by a certain equation?
+2. How to compose the equation of a surface of revolution?
+3. What is the difference between a directrix and generatrix?
+4. How to represent a quadric surface in the vector form?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. For each value of parameter 
+
+
+
+a
+
+
+{\textstyle a}
+
+![{\textstyle a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a503f107a7c104e40e484cee9e1f5993d28ffd8) determine types of surfaces given by the equations: (a) 
+
+
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+−
+
+z
+
+2
+
+
+=
+a
+
+
+{\textstyle x^{2}+y^{2}-z^{2}=a}
+
+![{\textstyle x^{2}+y^{2}-z^{2}=a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aedac9a12be3e2a8bb6549e080cecd007665a44c); (b) 
+
+
+
+
+x
+
+2
+
+
++
+a
+
+(
+
+
+y
+
+2
+
+
++
+
+z
+
+2
+
+
+
+)
+
+=
+1
+
+
+{\textstyle x^{2}+a\left(y^{2}+z^{2}\right)=1}
+
+![{\textstyle x^{2}+a\left(y^{2}+z^{2}\right)=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/04136582473b57e7f0525feeebccc4460ecf7ad8); (c) 
+
+
+
+
+x
+
+2
+
+
++
+a
+
+y
+
+2
+
+
+=
+a
+z
+
+
+{\textstyle x^{2}+ay^{2}=az}
+
+![{\textstyle x^{2}+ay^{2}=az}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d9326d877d128ad9d17a96c9765e1da5f7c91e6); (d) 
+
+
+
+
+x
+
+2
+
+
++
+a
+
+y
+
+2
+
+
+=
+a
+z
++
+1
+
+
+{\textstyle x^{2}+ay^{2}=az+1}
+
+![{\textstyle x^{2}+ay^{2}=az+1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d1cd37bf6d43b7adafdd4ec58f392dd620872e3).
+2. Find a vector equation of a right circular cone with apex 
+
+
+
+
+M
+
+0
+
+
+
+(
+
+
+
+r
+
+
+
+0
+
+
+)
+
+
+
+{\textstyle M\_{0}\left({\textbf {r}}\_{0}\right)}
+
+![{\textstyle M_{0}\left({\textbf {r}}_{0}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f1b67abdb7e98da13a4de428625f69d249276ae5) and axis 
+
+
+
+
+
+r
+
+
+=
+
+
+
+r
+
+
+
+0
+
+
++
+
+
+a
+
+
+t
+
+
+{\textstyle {\textbf {r}}={\textbf {r}}\_{0}+{\textbf {a}}t}
+
+![{\textstyle {\textbf {r}}={\textbf {r}}_{0}+{\textbf {a}}t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca83af73cef59fe73380c9737197485304b371ec) if it is known that generatrices of this cone form the angle of 
+
+
+
+α
+
+
+{\textstyle \alpha }
+
+![{\textstyle \alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d86dbd6183264b2f8569da1751380b173c7b185) with its axis.
+3. Find the equation of a cylinder with radius 
+
+
+
+
+
+2
+
+
+
+
+{\textstyle {\sqrt {2}}}
+
+![{\textstyle {\sqrt {2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5094a5b1e2f42490aa4de2c7a4b7235a27f1b73f) that has an axis 
+
+
+
+x
+=
+1
++
+t
+
+
+{\textstyle x=1+t}
+
+![{\textstyle x=1+t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eca54a99a9fdad0ee1a0bba54ac67014e83a51e2), 
+
+
+
+y
+=
+2
++
+t
+
+
+{\textstyle y=2+t}
+
+![{\textstyle y=2+t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/213ba8ad271ceb3b25aaaafcbe23edd7c885c7f0), 
+
+
+
+z
+=
+3
++
+t
+
+
+{\textstyle z=3+t}
+
+![{\textstyle z=3+t}](https://wikimedia.org/api/rest_v1/media/math/render/svg/582781cac22a2c157f5b5b60da347600c9778a6f).
+4. An ellipsoid is symmetric with respect to coordinate planes, passes through point 
+
+
+
+M
+(
+3
+;
+
+1
+;
+
+1
+)
+
+
+{\textstyle M(3;\,1;\,1)}
+
+![{\textstyle M(3;\,1;\,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6192e6c5728edd5b9a22b9c19aa8be852e2f0599) and circle 
+
+
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
++
+
+z
+
+2
+
+
+=
+9
+
+
+{\textstyle x^{2}+y^{2}+z^{2}=9}
+
+![{\textstyle x^{2}+y^{2}+z^{2}=9}](https://wikimedia.org/api/rest_v1/media/math/render/svg/29376da667d60dba7e1f552a56d1ce98caea3a4d), 
+
+
+
+x
+−
+z
+=
+0
+
+
+{\textstyle x-z=0}
+
+![{\textstyle x-z=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/709115599ad054688b92e60cdb84a4f32fe944f1). Find the equation of this ellipsoid.
+
+
+### Test questions for final assessment in this section
+
+
+1. Determine the type of a quadric surface given by a certain equation.
+2. Compose the equation of a surface of revolution with the given directrix and generatrix.
+3. Represent a given equation of a quadric surface in the vector form.
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__analytic_geometry_and_linear_algebra_ii.md

@@ -0,0 +1,2313 @@
+
+
+
+
+
+
+
+BSc: Analytic Geometry And Linear Algebra II
+============================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Analytical Geometry & Linear Algebra – II](#Analytical_Geometry_.26_Linear_Algebra_.E2.80.93_II)
+	+ [1.1 Course characteristics](#Course_characteristics)
+		- [1.1.1 Key concepts of the class](#Key_concepts_of_the_class)
+		- [1.1.2 What is the purpose of this course?](#What_is_the_purpose_of_this_course.3F)
+	+ [1.2 Course Objectives Based on Bloom’s Taxonomy](#Course_Objectives_Based_on_Bloom.E2.80.99s_Taxonomy)
+		- [1.2.1 What should a student remember at the end of the course?](#What_should_a_student_remember_at_the_end_of_the_course.3F)
+		- [1.2.2 What should a student be able to understand at the end of the course?](#What_should_a_student_be_able_to_understand_at_the_end_of_the_course.3F)
+		- [1.2.3 What should a student be able to apply at the end of the course?](#What_should_a_student_be_able_to_apply_at_the_end_of_the_course.3F)
+		- [1.2.4 Course evaluation](#Course_evaluation)
+		- [1.2.5 Grades range](#Grades_range)
+		- [1.2.6 Resources and reference material](#Resources_and_reference_material)
+			* [1.2.6.1 Textbooks:](#Textbooks:)
+			* [1.2.6.2 Reference material:](#Reference_material:)
+	+ [1.3 Course Sections](#Course_Sections)
+		- [1.3.1 Section 1](#Section_1)
+			* [1.3.1.1 Section title:](#Section_title:)
+		- [1.3.2 Topics covered in this section:](#Topics_covered_in_this_section:)
+		- [1.3.3 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F)
+		- [1.3.4 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section)
+		- [1.3.5 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section)
+		- [1.3.6 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section)
+		- [1.3.7 Section 2](#Section_2)
+			* [1.3.7.1 Section title:](#Section_title:_2)
+		- [1.3.8 Topics covered in this section:](#Topics_covered_in_this_section:_2)
+		- [1.3.9 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_2)
+		- [1.3.10 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_2)
+		- [1.3.11 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_2)
+		- [1.3.12 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_2)
+		- [1.3.13 Section 3](#Section_3)
+			* [1.3.13.1 Section title:](#Section_title:_3)
+		- [1.3.14 Topics covered in this section:](#Topics_covered_in_this_section:_3)
+		- [1.3.15 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_3)
+		- [1.3.16 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_3)
+		- [1.3.17 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_3)
+		- [1.3.18 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_3)
+		- [1.3.19 Section 4](#Section_4)
+			* [1.3.19.1 Section title:](#Section_title:_4)
+		- [1.3.20 Topics covered in this section:](#Topics_covered_in_this_section:_4)
+		- [1.3.21 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_4)
+		- [1.3.22 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_4)
+		- [1.3.23 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_4)
+		- [1.3.24 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_4)
+	+ [1.4 Exams and retake planning](#Exams_and_retake_planning)
+		- [1.4.1 Exam](#Exam)
+		- [1.4.2 Retake 1](#Retake_1)
+		- [1.4.3 Retake 2](#Retake_2)
+
+
+
+Analytical Geometry & Linear Algebra – II
+=========================================
+
+
+* **Course name:** Analytical Geometry & Linear Algebra – II
+* **Course number:** XYZ
+* **Subject area:** Math
+
+
+Course characteristics
+----------------------
+
+
+### Key concepts of the class
+
+
+* fundamental principles of linear algebra,
+* concepts of linear algebra objects and their representation in vector-matrix form
+
+
+### What is the purpose of this course?
+
+
+This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines. Linear algebra is a branch of mathematics that studies systems of linear equations and the properties of matrices. The concepts of linear algebra are extremely useful in physics, data sciences, and robotics. Due to its broad range of applications, linear algebra is one of the most widely used subjects in mathematics.
+
+
+
+Course Objectives Based on Bloom’s Taxonomy
+-------------------------------------------
+
+
+### What should a student remember at the end of the course?
+
+
+* List basic notions of linear algebra
+* Understand key principles involved in solution of linear equation systems and the properties of matrices
+* Linear regression analysis
+* Fast Fourier Transform
+* How to find eigenvalues and eigenvectors for matrix diagonalization and single value decomposition
+
+
+### What should a student be able to understand at the end of the course?
+
+
+* Key principles involved in solution of linear equation systems and the properties of matrices
+* Become familiar with the four fundamental subspaces
+* Linear regression analysis
+* Fast Fourier Transform
+* How to find eigenvalues and eigenvectors for matrix diagonalization and single value decomposition
+
+
+### What should a student be able to apply at the end of the course?
+
+
+* Linear equation system solving by using the vector-matrix approach
+* Make linear regression analysis
+* Fast Fourier Transform
+* To find eigenvalues and eigenvectors for matrix diagonalization and single value decomposition
+
+
+### Course evaluation
+
+
+
+
+Course grade breakdown
+|  |  | **Proposed points** |
+| --- | --- | --- |
+| Labs/seminar classes
+ | 20
+ | 20
+ |
+| Interim performance assessment
+ | 30
+ | 30
+ |
+| Exams
+ | 50
+ | 50
+ |
+
+
+### Grades range
+
+
+
+
+Course grading range
+|  |  | **Proposed range** |
+| --- | --- | --- |
+| A. Excellent
+ | 90-100
+ | 85-100
+ |
+| B. Good
+ | 75-89
+ | 65-84
+ |
+| C. Satisfactory
+ | 60-74
+ | 50-64
+ |
+| D. Poor
+ | 0-59
+ | 0-49
+ |
+
+
+### Resources and reference material
+
+
+#### Textbooks:
+
+
+* Gilbert Strang. Linear Algebra and Its Applications, 4th Edition, Brooks Cole, 2006. ISBN: 9780030105678
+* Gilbert Strang. Introduction to Linear Algebra, 4th Edition, Wellesley, MA: Wellesley-Cambridge Press, 2009. ISBN: 9780980232714
+
+
+#### Reference material:
+
+
+* Gilbert Strang, Brett Coonley, Andrew Bulman-Fleming. Student Solutions Manual for Strang’s Linear Algebra and Its Applications, 4th Edition, Thomson Brooks, 2005. ISBN-13: 9780495013259
+
+
+Course Sections
+---------------
+
+
+The main sections of the course and approximate hour distribution between them is as follows:
+
+
+
+
+
+Course Sections
+| **Section** | **Section Title** | **Lectures** | **Seminars** | **Self-study** | **Knowledge** |
+| **Number** |  | **(hours)** | **(labs)** |  | **evaluation** |
+| 1
+ | Linear equation system solving by using the vector-matrix approach.
+ | 16
+ | 8
+ | 24
+ | 2
+ |
+| 2
+ | Linear regression analysis and decomposition A=QR.
+ | 12
+ | 6
+ | 18
+ | 2
+ |
+| 3
+ | Fast Fourier Transform. Matrix Diagonalization.
+ | 12
+ | 6
+ | 18
+ | 2
+ |
+| 4
+ | Symmetric, positive definite and similar matrices. Singular value decomposition.
+ | 12
+ | 6
+ | 18
+ | 2
+ |
+| Final examination
+ |  |  |  |  | 2
+ |
+
+
+### Section 1
+
+
+#### Section title:
+
+
+Linear equation system solving by using the vector-matrix approach
+
+
+
+### Topics covered in this section:
+
+
+* The geometry of linear equations. Elimination with matrices.
+* Matrix operations, including inverses. 
+
+
+
+L
+U
+
+
+{\textstyle LU}
+
+![{\textstyle LU}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8becb581eaf8755b3963ff74d22e595dbab347be) and 
+
+
+
+L
+D
+U
+
+
+{\textstyle LDU}
+
+![{\textstyle LDU}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d50e39c40f892f559d3e04ad1e7ad429023e26c7) factorization.
+* Transposes and permutations. Vector spaces and subspaces.
+* The null space: Solving 
+
+
+
+A
+x
+=
+0
+
+
+{\textstyle Ax=0}
+
+![{\textstyle Ax=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d79c4f8ca184c0e1fd6f960bd23efda90fec26a) and 
+
+
+
+A
+x
+=
+b
+
+
+{\textstyle Ax=b}
+
+![{\textstyle Ax=b}](https://wikimedia.org/api/rest_v1/media/math/render/svg/18892a5ddb5ea2e30e8a4a9488b35d67a3fdbf6d). Row reduced echelon form. Matrix rank.
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 1
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. How to perform Gauss elimination?
+2. How to perform matrices multiplication?
+3. How to perform LU factorization?
+4. How to find complete solution for any linear equation system Ax=b?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Find the solution for the given linear equation system 
+
+
+
+A
+x
+=
+b
+
+
+{\textstyle Ax=b}
+
+![{\textstyle Ax=b}](https://wikimedia.org/api/rest_v1/media/math/render/svg/18892a5ddb5ea2e30e8a4a9488b35d67a3fdbf6d) by using Gauss elimination.
+2. Perform 
+
+
+
+A
+=
+L
+U
+
+
+{\textstyle A=LU}
+
+![{\textstyle A=LU}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0e9cc8c928452cd1beaf333bb649af9853b5d12) factorization for the given matrix 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31).
+3. Factor the given symmetric matrix 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) into 
+
+
+
+A
+=
+L
+D
+
+L
+
+T
+
+
+
+
+{\textstyle A=LDL^{T}}
+
+![{\textstyle A=LDL^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/625b5b21d4aa4c805a55b29d0d03380a17343a90) with the diagonal pivot matrix 
+
+
+
+D
+
+
+{\textstyle D}
+
+![{\textstyle D}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4e5200f518cb5afe304ec42ffdd4f6c63c702f77).
+4. Find inverse matrix 
+
+
+
+
+A
+
+−
+
+
+1
+
+
+{\textstyle A^{-}1}
+
+![{\textstyle A^{-}1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8051e1bf4ce05cdb5fdf4cc58f3564bf843c3f96) for the given matrix 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31).
+
+
+### Test questions for final assessment in this section
+
+
+1. Find linear independent vectors (exclude dependent): 
+
+
+
+
+
+a
+→
+
+
+=
+[
+4
+,
+0
+,
+3
+,
+2
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {a}}=[4,0,3,2]^{T}}
+
+![{\textstyle {\overrightarrow {a}}=[4,0,3,2]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b573acd686425e4bb95dcc7342a0c8cdff33e546), 
+
+
+
+
+
+b
+→
+
+
+=
+[
+1
+,
+−
+7
+,
+4
+,
+5
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {b}}=[1,-7,4,5]^{T}}
+
+![{\textstyle {\overrightarrow {b}}=[1,-7,4,5]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8f97f34707d7d042d0080df772a5cc5bf030c784), 
+
+
+
+
+
+c
+→
+
+
+=
+[
+7
+,
+1
+,
+5
+,
+3
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {c}}=[7,1,5,3]^{T}}
+
+![{\textstyle {\overrightarrow {c}}=[7,1,5,3]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/77c5a21e300ddbdd0f7fecdd617b910827046006), 
+
+
+
+
+
+d
+→
+
+
+=
+[
+−
+5
+,
+−
+3
+,
+−
+3
+,
+−
+1
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {d}}=[-5,-3,-3,-1]^{T}}
+
+![{\textstyle {\overrightarrow {d}}=[-5,-3,-3,-1]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/424ab1d843887cea7abfa3dca20106545d8a8a0b), 
+
+
+
+
+
+e
+→
+
+
+=
+[
+1
+,
+−
+5
+,
+2
+,
+3
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {e}}=[1,-5,2,3]^{T}}
+
+![{\textstyle {\overrightarrow {e}}=[1,-5,2,3]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d6b9b7357251158c6b1954e17b912f77a1e38c4b). Find 
+
+
+
+r
+a
+n
+k
+(
+A
+)
+
+
+{\textstyle rank(A)}
+
+![{\textstyle rank(A)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/af25f6717bd9130cfded69f3333e47486b7d71cc) if 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) is a composition of this vectors. Find 
+
+
+
+r
+a
+n
+k
+(
+
+A
+
+T
+
+
+)
+
+
+{\textstyle rank(A^{T})}
+
+![{\textstyle rank(A^{T})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/671f71d97f14e03b5a9b0e0fb5724ef62720a731).
+2. Find 
+
+
+
+E
+
+
+{\textstyle E}
+
+![{\textstyle E}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6d934f67126f64e9c061b598b8941b8767a8d343): 
+
+
+
+E
+A
+=
+U
+
+
+{\textstyle EA=U}
+
+![{\textstyle EA=U}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ab6a98a37022c82117c658535da16aecb68ac071) (
+
+
+
+U
+
+
+{\textstyle U}
+
+![{\textstyle U}](https://wikimedia.org/api/rest_v1/media/math/render/svg/087a7d8a39fe35012cbf2f561879f9e975cb4555) – upper-triangular matrix). Find 
+
+
+
+L
+=
+
+E
+
+−
+
+
+1
+
+
+{\textstyle L=E^{-}1}
+
+![{\textstyle L=E^{-}1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e415e968cd0834b022ca5585654bf2ba668c5954), if 
+
+
+
+A
+=
+
+(
+
+
+
+
+2
+
+
+5
+
+
+7
+
+
+
+
+6
+
+
+4
+
+
+9
+
+
+
+
+4
+
+
+1
+
+
+8
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{ccc}2&5&7\\6&4&9\\4&1&8\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{ccc}2&5&7\\6&4&9\\4&1&8\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/270385e97a68b305e3c25e81e8ef90cc0b8dc9cc).
+3. Find complete solution for the system 
+
+
+
+A
+x
+=
+b
+
+
+{\textstyle Ax=b}
+
+![{\textstyle Ax=b}](https://wikimedia.org/api/rest_v1/media/math/render/svg/18892a5ddb5ea2e30e8a4a9488b35d67a3fdbf6d), if 
+
+
+
+b
+=
+[
+7
+,
+18
+,
+5
+
+]
+
+T
+
+
+
+
+{\textstyle b=[7,18,5]^{T}}
+
+![{\textstyle b=[7,18,5]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4faa204bdd0b26fb09cd8abebf3124e7a6b8ca1e) and 
+
+
+
+A
+=
+
+(
+
+
+
+
+6
+
+
+−
+2
+
+
+1
+
+
+−
+4
+
+
+
+
+4
+
+
+2
+
+
+14
+
+
+−
+31
+
+
+
+
+2
+
+
+−
+1
+
+
+3
+
+
+−
+7
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cccc}6&-2&1&-4\\4&2&14&-31\\2&-1&3&-7\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cccc}6&-2&1&-4\\4&2&14&-31\\2&-1&3&-7\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5a27c93084b6e998864553331b01fc5eb2339f12). Provide an example of vector b that makes this system unsolvable.
+
+
+### Section 2
+
+
+#### Section title:
+
+
+Linear regression analysis and decomposition 
+
+
+
+A
+=
+Q
+R
+
+
+{\textstyle A=QR}
+
+![{\textstyle A=QR}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f7960350ee376840d36b9f7d47d761d8112fbfe).
+
+
+
+### Topics covered in this section:
+
+
+* Independence, basis and dimension. The four fundamental subspaces.
+* Orthogonal vectors and subspaces. Projections onto subspaces
+* Projection matrices. Least squares approximations. Gram-Schmidt and A = QR.
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 1
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. What is linear independence of vectors?
+2. Define the four fundamental subspaces of a matrix?
+3. How to define orthogonal vectors and subspaces?
+4. How to define orthogonal complements of the space?
+5. How to find vector projection on a subspace?
+6. How to perform linear regression for the given measurements?
+7. How to find an orthonormal basis for the subspace spanned by the given vectors?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Check out linear independence of the given vectors
+2. Find four fundamental subspaces of the given matrix.
+3. Check out orthogonality of the given subspaces.
+4. Find orthogonal complement for the given subspace.
+5. Find vector projection on the given subspace.
+6. Perform linear regression for the given measurements.
+7. Find an orthonormal basis for the subspace spanned by the given vectors.
+
+
+### Test questions for final assessment in this section
+
+
+1. Find the dimensions of the four fundamental subspaces associated with 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31), depending on the parameters 
+
+
+
+a
+
+
+{\textstyle a}
+
+![{\textstyle a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a503f107a7c104e40e484cee9e1f5993d28ffd8) and 
+
+
+
+b
+
+
+{\textstyle b}
+
+![{\textstyle b}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73a780b69dfc55238880ef18a134dc65260877e2): 
+
+
+
+A
+=
+
+(
+
+
+
+
+7
+
+
+8
+
+
+5
+
+
+3
+
+
+
+
+4
+
+
+a
+
+
+3
+
+
+2
+
+
+
+
+6
+
+
+8
+
+
+4
+
+
+b
+
+
+
+
+3
+
+
+4
+
+
+2
+
+
+1
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cccc}7&8&5&3\\4&a&3&2\\6&8&4&b\\3&4&2&1\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cccc}7&8&5&3\\4&a&3&2\\6&8&4&b\\3&4&2&1\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fc803202bc5e0460954845a195e4b92208ac2a54).
+2. Find a vector 
+
+
+
+x
+
+
+{\textstyle x}
+
+![{\textstyle x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d951e0f3b54b6a3d73bb9a0a005749046cbce781) orthogonal to the Row space of matrix 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31), and a vector 
+
+
+
+y
+
+
+{\textstyle y}
+
+![{\textstyle y}](https://wikimedia.org/api/rest_v1/media/math/render/svg/db9936ddb2761b76fa640fb275cb5d1fa4d6fa23) orthogonal to the 
+
+
+
+C
+(
+A
+)
+
+
+{\textstyle C(A)}
+
+![{\textstyle C(A)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/50e890f8d67ec1b4b4fd8b7a6fbbfb8172f20866), and a vector 
+
+
+
+z
+
+
+{\textstyle z}
+
+![{\textstyle z}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a33e37010e3acdeeb80fdb95df9bfe411fd79e6) orthogonal to the 
+
+
+
+N
+(
+A
+)
+
+
+{\textstyle N(A)}
+
+![{\textstyle N(A)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/766235dfa8f2a0cbce4df704eb334785c7094ca4): 
+
+
+
+A
+=
+
+(
+
+
+
+
+1
+
+
+2
+
+
+2
+
+
+
+
+3
+
+
+4
+
+
+2
+
+
+
+
+4
+
+
+6
+
+
+4
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{ccc}1&2&2\\3&4&2\\4&6&4\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{ccc}1&2&2\\3&4&2\\4&6&4\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c65bde22a0e3936c85821df45484f3216a7dd74e).
+3. Find the best straight-line 
+
+
+
+y
+(
+x
+)
+
+
+{\textstyle y(x)}
+
+![{\textstyle y(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4639e7d86a9d2274f64a48570e7fe4ef17f7efa) fit to the measurements: 
+
+
+
+y
+(
+−
+2
+)
+=
+4
+
+
+{\textstyle y(-2)=4}
+
+![{\textstyle y(-2)=4}](https://wikimedia.org/api/rest_v1/media/math/render/svg/75edda9fdb1aa1cab6ac772869d7441bdf5539ef), 
+
+
+
+y
+(
+−
+1
+)
+=
+3
+
+
+{\textstyle y(-1)=3}
+
+![{\textstyle y(-1)=3}](https://wikimedia.org/api/rest_v1/media/math/render/svg/39365fc4327d63e6b3f4568f085c953942a32bcc), 
+
+
+
+y
+(
+0
+)
+=
+2
+
+
+{\textstyle y(0)=2}
+
+![{\textstyle y(0)=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4321858864c6ee38bc8ea6a44b43c1fb7b1b7bdb), 
+
+
+
+y
+(
+1
+)
+−
+0
+
+
+{\textstyle y(1)-0}
+
+![{\textstyle y(1)-0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f3ac0d6451cf2f604f303ed26f3e1b26941b680a).
+4. Find the projection matrix 
+
+
+
+P
+
+
+{\textstyle P}
+
+![{\textstyle P}](https://wikimedia.org/api/rest_v1/media/math/render/svg/038590207af1024a629c1a08c855e9ac46bf5610) of vector 
+
+
+
+[
+4
+,
+3
+,
+2
+,
+0
+
+]
+
+T
+
+
+
+
+{\textstyle [4,3,2,0]^{T}}
+
+![{\textstyle [4,3,2,0]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a1407743b577f1595b88b73ce535c1b1c6810d14) onto the 
+
+
+
+C
+(
+A
+)
+
+
+{\textstyle C(A)}
+
+![{\textstyle C(A)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/50e890f8d67ec1b4b4fd8b7a6fbbfb8172f20866): 
+
+
+
+A
+=
+
+(
+
+
+
+
+1
+
+
+−
+2
+
+
+
+
+1
+
+
+−
+1
+
+
+
+
+1
+
+
+0
+
+
+
+
+1
+
+
+1
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cc}1&-2\\1&-1\\1&0\\1&1\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cc}1&-2\\1&-1\\1&0\\1&1\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/42f35bb9ce7dd23b55e504ef145789134642fd56).
+5. Find an orthonormal basis for the subspace spanned by the vectors: 
+
+
+
+
+
+a
+→
+
+
+=
+[
+−
+2
+,
+2
+,
+0
+,
+0
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {a}}=[-2,2,0,0]^{T}}
+
+![{\textstyle {\overrightarrow {a}}=[-2,2,0,0]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d10ddb57c762601e62967544737ea022841f1c7e), 
+
+
+
+
+
+b
+→
+
+
+=
+[
+0
+,
+1
+,
+−
+1
+,
+0
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {b}}=[0,1,-1,0]^{T}}
+
+![{\textstyle {\overrightarrow {b}}=[0,1,-1,0]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a91f7a5cfe5477b27b926bf40a2ab8579777b444), 
+
+
+
+
+
+c
+→
+
+
+=
+[
+0
+,
+1
+,
+0
+,
+−
+1
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {c}}=[0,1,0,-1]^{T}}
+
+![{\textstyle {\overrightarrow {c}}=[0,1,0,-1]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6018717796286d4e371639685094a4653c67237b). Then express 
+
+
+
+A
+=
+[
+a
+,
+b
+,
+c
+]
+
+
+{\textstyle A=[a,b,c]}
+
+![{\textstyle A=[a,b,c]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/473b98961e85b063ef9a834f6f8a2caeeeb8b199) in the form of 
+
+
+
+A
+=
+Q
+R
+
+
+{\textstyle A=QR}
+
+![{\textstyle A=QR}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f7960350ee376840d36b9f7d47d761d8112fbfe)
+
+
+### Section 3
+
+
+#### Section title:
+
+
+Fast Fourier Transform. Matrix Diagonalization.
+
+
+
+### Topics covered in this section:
+
+
+* Complex Numbers. Hermitian and Unitary Matrices.
+* Fourier Series. The Fast Fourier Transform
+* Eigenvalues and eigenvectors. Matrix diagonalization.
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 1
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. Make the definition of Hermitian Matrix.
+2. Make the definition of Unitary Matrix.
+3. How to find matrix for the Fourier transform?
+4. When we can make fast Fourier transform?
+5. How to find eigenvalues and eigenvectors of a matrix?
+6. How to diagonalize a square matrix?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Check out is the given matrix Hermitian.
+2. Check out is the given matrix Unitary.
+3. Find the matrix for the given Fourier transform.
+4. Find eigenvalues and eigenvectors for the given matrix.
+5. Find diagonalize form for the given matrix.
+
+
+### Test questions for final assessment in this section
+
+
+1. Find eigenvector of the circulant matrix 
+
+
+
+C
+
+
+{\textstyle C}
+
+![{\textstyle C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6dca76d9ff4b48256b6a4a99bcb234b64b2fa72b) for the eigenvalue = 
+
+
+
+
+
+c
+
+
+1
+
+
+
+
+{\textstyle {c}\_{1}}
+
+![{\textstyle {c}_{1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0405b69bc9082831ceeeb8fa7936239466318b4e)+
+
+
+
+
+
+c
+
+
+2
+
+
+
+
+{\textstyle {c}\_{2}}
+
+![{\textstyle {c}_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a63a7c192e428b5b247dedd7a2dc5d9d2bc4ade)+
+
+
+
+
+
+c
+
+
+3
+
+
+
+
+{\textstyle {c}\_{3}}
+
+![{\textstyle {c}_{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7bd3760c114db3e5fbe4f814e7755ce35617c2b2)+
+
+
+
+
+
+c
+
+
+4
+
+
+
+
+{\textstyle {c}\_{4}}
+
+![{\textstyle {c}_{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/54dd52f52cb3ef9c6a5591247f6625340fd561ef): 
+
+
+
+C
+=
+
+(
+
+
+
+
+
+
+c
+
+
+1
+
+
+
+
+
+
+c
+
+
+2
+
+
+
+
+
+
+c
+
+
+3
+
+
+
+
+
+
+c
+
+
+4
+
+
+
+
+
+
+
+
+c
+
+
+4
+
+
+
+
+
+
+c
+
+
+1
+
+
+
+
+
+
+c
+
+
+2
+
+
+
+
+
+
+c
+
+
+3
+
+
+
+
+
+
+
+
+c
+
+
+3
+
+
+
+
+
+
+c
+
+
+4
+
+
+
+
+
+
+c
+
+
+1
+
+
+
+
+
+
+c
+
+
+2
+
+
+
+
+
+
+
+
+c
+
+
+2
+
+
+
+
+
+
+c
+
+
+3
+
+
+
+
+
+
+c
+
+
+4
+
+
+
+
+
+
+c
+
+
+1
+
+
+
+
+
+
+)
+
+
+
+{\textstyle C=\left({\begin{array}{cccc}{c}\_{1}&{c}\_{2}&{c}\_{3}&{c}\_{4}\\{c}\_{4}&{c}\_{1}&{c}\_{2}&{c}\_{3}\\{c}\_{3}&{c}\_{4}&{c}\_{1}&{c}\_{2}\\{c}\_{2}&{c}\_{3}&{c}\_{4}&{c}\_{1}\\\end{array}}\right)}
+
+![{\textstyle C=\left({\begin{array}{cccc}{c}_{1}&{c}_{2}&{c}_{3}&{c}_{4}\\{c}_{4}&{c}_{1}&{c}_{2}&{c}_{3}\\{c}_{3}&{c}_{4}&{c}_{1}&{c}_{2}\\{c}_{2}&{c}_{3}&{c}_{4}&{c}_{1}\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/69efe5a0d7045da18110c47c68ba00309abb5323).
+2. Diagonalize this matrix: 
+
+
+
+A
+=
+
+(
+
+
+
+
+2
+
+
+1
+−
+i
+
+
+
+
+1
++
+i
+
+
+3
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cc}2&1-i\\1+i&3\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cc}2&1-i\\1+i&3\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/de9882c4748ca263e22135e69cccce208a645a47).
+3. A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) is the matrix with full set of orthonormal eigenvectors. Prove that 
+
+
+
+A
+A
+=
+
+A
+
+H
+
+
+
+A
+
+H
+
+
+
+
+{\textstyle AA=A^{H}A^{H}}
+
+![{\textstyle AA=A^{H}A^{H}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/79272abd7682c09ed733b7808f9b5a49b522957d).
+4. Find all eigenvalues and eigenvectors of the cyclic permutation matrix 
+
+
+
+P
+=
+
+(
+
+
+
+
+0
+
+
+1
+
+
+0
+
+
+0
+
+
+
+
+0
+
+
+0
+
+
+1
+
+
+0
+
+
+
+
+0
+
+
+0
+
+
+0
+
+
+1
+
+
+
+
+1
+
+
+0
+
+
+0
+
+
+0
+
+
+
+
+)
+
+
+
+{\textstyle P=\left({\begin{array}{cccc}0&1&0&0\\0&0&1&0\\0&0&0&1\\1&0&0&0\\\end{array}}\right)}
+
+![{\textstyle P=\left({\begin{array}{cccc}0&1&0&0\\0&0&1&0\\0&0&0&1\\1&0&0&0\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cdf3bc0ef61513dc72ccbe9d43301d8f22ac731f).
+
+
+### Section 4
+
+
+#### Section title:
+
+
+Symmetric, positive definite and similar matrices. Singular value decomposition.
+
+
+
+### Topics covered in this section:
+
+
+* Linear differential equations.
+* Symmetric matrices. Positive definite matrices.
+* Similar matrices. Left and right inverses, pseudoinverse. Singular value decomposition (SVD).
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 1
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. How to solve linear differential equations?
+2. Make the definition of symmetric matrix?
+3. Make the definition of positive definite matrix?
+4. Make the definition of similar matrices?
+5. How to find left and right inverses matrices, pseudoinverse matrix?
+6. How to make singular value decomposition of the matrix?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Find solution of the linear differential equation.
+2. Make the definition of symmetric matrix.
+3. Check out the given matrix on positive definess
+4. Check out the given matrices on similarity.
+5. For the given matrix find left and right inverse matrices, pseudoinverse matrix.
+6. Make the singular value decomposition of the given matrix.
+
+
+### Test questions for final assessment in this section
+
+
+1. Find 
+
+
+
+d
+e
+t
+(
+
+e
+
+A
+
+
+)
+
+
+{\textstyle det(e^{A})}
+
+![{\textstyle det(e^{A})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2fe0bc4f6b8861e3358b76828c70affbe91b5546) for 
+
+
+
+A
+=
+
+(
+
+
+
+
+2
+
+
+1
+
+
+
+
+2
+
+
+3
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cc}2&1\\2&3\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cc}2&1\\2&3\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d8b79dfa2ad1a2c18b276ba62242becf7749a0b4).
+2. Write down the first order equation system for the following differential equation and solve it:
+
+
+
+
+
+
+
+d
+
+3
+
+
+y
+
+/
+
+d
+x
++
+
+d
+
+2
+
+
+y
+
+/
+
+d
+x
+−
+2
+d
+y
+
+/
+
+d
+x
+=
+0
+
+
+{\textstyle d^{3}y/dx+d^{2}y/dx-2dy/dx=0}
+
+![{\textstyle d^{3}y/dx+d^{2}y/dx-2dy/dx=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b8e608e72541239be7801b94dd8fed3e355050fc)
+
+
+
+
+
+
+
+y
+″
+
+(
+0
+)
+=
+6
+
+
+{\textstyle y''(0)=6}
+
+![{\textstyle y''(0)=6}](https://wikimedia.org/api/rest_v1/media/math/render/svg/92039ff6d21382f32158e6eef4642cb55688b549), 
+
+
+
+
+y
+′
+
+(
+0
+)
+=
+0
+
+
+{\textstyle y'(0)=0}
+
+![{\textstyle y'(0)=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6d8839484b7380ec6af6ed1f232536ae98cf093a), 
+
+
+
+y
+(
+0
+)
+=
+3
+
+
+{\textstyle y(0)=3}
+
+![{\textstyle y(0)=3}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7459acffb9257b7b7f64ba0c5d24c4ca651280f5).
+
+
+Is the solution of this system will be stable?
+3. For which 
+
+
+
+a
+
+
+{\textstyle a}
+
+![{\textstyle a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a503f107a7c104e40e484cee9e1f5993d28ffd8) and 
+
+
+
+b
+
+
+{\textstyle b}
+
+![{\textstyle b}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73a780b69dfc55238880ef18a134dc65260877e2) quadratic form 
+
+
+
+Q
+(
+x
+,
+y
+,
+z
+)
+
+
+{\textstyle Q(x,y,z)}
+
+![{\textstyle Q(x,y,z)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/723d35bcca34d49404fcc5d0e7cca10bbaf9ec8c) is positive definite:
+
+
+
+
+
+
+Q
+(
+x
+,
+y
+,
+z
+)
+=
+a
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
++
+2
+
+z
+
+2
+
+
++
+2
+b
+x
+y
++
+4
+x
+z
+
+
+{\textstyle Q(x,y,z)=ax^{2}+y^{2}+2z^{2}+2bxy+4xz}
+
+![{\textstyle Q(x,y,z)=ax^{2}+y^{2}+2z^{2}+2bxy+4xz}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f831bc4412b380c9a2c2940d4cd3dd6f46d7f3dc)
+4. Find the SVD and the pseudoinverse of the matrix 
+
+
+
+A
+=
+
+(
+
+
+
+
+1
+
+
+0
+
+
+0
+
+
+
+
+0
+
+
+1
+
+
+1
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{ccc}1&0&0\\0&1&1\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{ccc}1&0&0\\0&1&1\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/152a05619788dda3e990b8af6b737277189c507d).
+
+
+Exams and retake planning
+-------------------------
+
+
+### Exam
+
+
+Exams will be paper-based and will be conducted in a form of problem solving, where the problems will be similar to those mentioned above. Students will be given 1-2 hours to complete the exam.
+
+
+
+### Retake 1
+
+
+First retake will be conducted in the same form as the midterm and final exams. The weight of the retake exam will be the same as the all course.
+
+
+
+### Retake 2
+
+
+Second retake will be conducted in the same form as the midterm and final exams. The weight of the retake exam will be the same as the all course.
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__analytic_geometry_and_linear_algebra_ii.s22.md

@@ -0,0 +1,2313 @@
+
+
+
+
+
+
+
+BSc: Analytic Geometry And Linear Algebra II.s22
+================================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Analytical Geometry & Linear Algebra – II](#Analytical_Geometry_.26_Linear_Algebra_.E2.80.93_II)
+	+ [1.1 Course characteristics](#Course_characteristics)
+		- [1.1.1 Key concepts of the class](#Key_concepts_of_the_class)
+		- [1.1.2 What is the purpose of this course?](#What_is_the_purpose_of_this_course.3F)
+	+ [1.2 Course Objectives Based on Bloom’s Taxonomy](#Course_Objectives_Based_on_Bloom.E2.80.99s_Taxonomy)
+		- [1.2.1 What should a student remember at the end of the course?](#What_should_a_student_remember_at_the_end_of_the_course.3F)
+		- [1.2.2 What should a student be able to understand at the end of the course?](#What_should_a_student_be_able_to_understand_at_the_end_of_the_course.3F)
+		- [1.2.3 What should a student be able to apply at the end of the course?](#What_should_a_student_be_able_to_apply_at_the_end_of_the_course.3F)
+		- [1.2.4 Course evaluation](#Course_evaluation)
+		- [1.2.5 Grades range](#Grades_range)
+		- [1.2.6 Resources and reference material](#Resources_and_reference_material)
+			* [1.2.6.1 Textbooks:](#Textbooks:)
+			* [1.2.6.2 Reference material:](#Reference_material:)
+	+ [1.3 Course Sections](#Course_Sections)
+		- [1.3.1 Section 1](#Section_1)
+			* [1.3.1.1 Section title:](#Section_title:)
+		- [1.3.2 Topics covered in this section:](#Topics_covered_in_this_section:)
+		- [1.3.3 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F)
+		- [1.3.4 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section)
+		- [1.3.5 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section)
+		- [1.3.6 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section)
+		- [1.3.7 Section 2](#Section_2)
+			* [1.3.7.1 Section title:](#Section_title:_2)
+		- [1.3.8 Topics covered in this section:](#Topics_covered_in_this_section:_2)
+		- [1.3.9 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_2)
+		- [1.3.10 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_2)
+		- [1.3.11 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_2)
+		- [1.3.12 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_2)
+		- [1.3.13 Section 3](#Section_3)
+			* [1.3.13.1 Section title:](#Section_title:_3)
+		- [1.3.14 Topics covered in this section:](#Topics_covered_in_this_section:_3)
+		- [1.3.15 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_3)
+		- [1.3.16 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_3)
+		- [1.3.17 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_3)
+		- [1.3.18 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_3)
+		- [1.3.19 Section 4](#Section_4)
+			* [1.3.19.1 Section title:](#Section_title:_4)
+		- [1.3.20 Topics covered in this section:](#Topics_covered_in_this_section:_4)
+		- [1.3.21 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_4)
+		- [1.3.22 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_4)
+		- [1.3.23 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_4)
+		- [1.3.24 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_4)
+	+ [1.4 Exams and retake planning](#Exams_and_retake_planning)
+		- [1.4.1 Exam](#Exam)
+		- [1.4.2 Retake 1](#Retake_1)
+		- [1.4.3 Retake 2](#Retake_2)
+
+
+
+Analytical Geometry & Linear Algebra – II
+=========================================
+
+
+* **Course name:** Analytical Geometry & Linear Algebra – II
+* **Course number:** XYZ
+* **Subject area:** Math
+
+
+Course characteristics
+----------------------
+
+
+### Key concepts of the class
+
+
+* fundamental principles of linear algebra,
+* concepts of linear algebra objects and their representation in vector-matrix form
+
+
+### What is the purpose of this course?
+
+
+This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines. Linear algebra is a branch of mathematics that studies systems of linear equations and the properties of matrices. The concepts of linear algebra are extremely useful in physics, data sciences, and robotics. Due to its broad range of applications, linear algebra is one of the most widely used subjects in mathematics.
+
+
+
+Course Objectives Based on Bloom’s Taxonomy
+-------------------------------------------
+
+
+### What should a student remember at the end of the course?
+
+
+* List basic notions of linear algebra
+* Understand key principles involved in solution of linear equation systems and the properties of matrices
+* Linear regression analysis
+* Fast Fourier Transform
+* How to find eigenvalues and eigenvectors for matrix diagonalization and single value decomposition
+
+
+### What should a student be able to understand at the end of the course?
+
+
+* Key principles involved in solution of linear equation systems and the properties of matrices
+* Become familiar with the four fundamental subspaces
+* Linear regression analysis
+* Fast Fourier Transform
+* How to find eigenvalues and eigenvectors for matrix diagonalization and single value decomposition
+
+
+### What should a student be able to apply at the end of the course?
+
+
+* Linear equation system solving by using the vector-matrix approach
+* Make linear regression analysis
+* Fast Fourier Transform
+* To find eigenvalues and eigenvectors for matrix diagonalization and single value decomposition
+
+
+### Course evaluation
+
+
+
+
+Course grade breakdown
+|  |  | **Proposed points** |
+| --- | --- | --- |
+| Labs/seminar classes
+ | 20
+ | 20
+ |
+| Interim performance assessment
+ | 30
+ | 30
+ |
+| Exams
+ | 50
+ | 50
+ |
+
+
+### Grades range
+
+
+
+
+Course grading range
+|  |  | **Proposed range** |
+| --- | --- | --- |
+| A. Excellent
+ | 90-100
+ | 85-100
+ |
+| B. Good
+ | 75-89
+ | 65-84
+ |
+| C. Satisfactory
+ | 60-74
+ | 50-64
+ |
+| D. Poor
+ | 0-59
+ | 0-49
+ |
+
+
+### Resources and reference material
+
+
+#### Textbooks:
+
+
+* Gilbert Strang. Linear Algebra and Its Applications, 4th Edition, Brooks Cole, 2006. ISBN: 9780030105678
+* Gilbert Strang. Introduction to Linear Algebra, 4th Edition, Wellesley, MA: Wellesley-Cambridge Press, 2009. ISBN: 9780980232714
+
+
+#### Reference material:
+
+
+* Gilbert Strang, Brett Coonley, Andrew Bulman-Fleming. Student Solutions Manual for Strang’s Linear Algebra and Its Applications, 4th Edition, Thomson Brooks, 2005. ISBN-13: 9780495013259
+
+
+Course Sections
+---------------
+
+
+The main sections of the course and approximate hour distribution between them is as follows:
+
+
+
+
+
+Course Sections
+| **Section** | **Section Title** | **Lectures** | **Seminars** | **Self-study** | **Knowledge** |
+| **Number** |  | **(hours)** | **(labs)** |  | **evaluation** |
+| 1
+ | Linear equation system solving by using the vector-matrix approach.
+ | 16
+ | 8
+ | 24
+ | 2
+ |
+| 2
+ | Linear regression analysis and decomposition A=QR.
+ | 12
+ | 6
+ | 18
+ | 2
+ |
+| 3
+ | Fast Fourier Transform. Matrix Diagonalization.
+ | 12
+ | 6
+ | 18
+ | 2
+ |
+| 4
+ | Symmetric, positive definite and similar matrices. Singular value decomposition.
+ | 12
+ | 6
+ | 18
+ | 2
+ |
+| Final examination
+ |  |  |  |  | 2
+ |
+
+
+### Section 1
+
+
+#### Section title:
+
+
+Linear equation system solving by using the vector-matrix approach
+
+
+
+### Topics covered in this section:
+
+
+* The geometry of linear equations. Elimination with matrices.
+* Matrix operations, including inverses. 
+
+
+
+L
+U
+
+
+{\textstyle LU}
+
+![{\textstyle LU}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8becb581eaf8755b3963ff74d22e595dbab347be) and 
+
+
+
+L
+D
+U
+
+
+{\textstyle LDU}
+
+![{\textstyle LDU}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d50e39c40f892f559d3e04ad1e7ad429023e26c7) factorization.
+* Transposes and permutations. Vector spaces and subspaces.
+* The null space: Solving 
+
+
+
+A
+x
+=
+0
+
+
+{\textstyle Ax=0}
+
+![{\textstyle Ax=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d79c4f8ca184c0e1fd6f960bd23efda90fec26a) and 
+
+
+
+A
+x
+=
+b
+
+
+{\textstyle Ax=b}
+
+![{\textstyle Ax=b}](https://wikimedia.org/api/rest_v1/media/math/render/svg/18892a5ddb5ea2e30e8a4a9488b35d67a3fdbf6d). Row reduced echelon form. Matrix rank.
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 1
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. How to perform Gauss elimination?
+2. How to perform matrices multiplication?
+3. How to perform LU factorization?
+4. How to find complete solution for any linear equation system Ax=b?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Find the solution for the given linear equation system 
+
+
+
+A
+x
+=
+b
+
+
+{\textstyle Ax=b}
+
+![{\textstyle Ax=b}](https://wikimedia.org/api/rest_v1/media/math/render/svg/18892a5ddb5ea2e30e8a4a9488b35d67a3fdbf6d) by using Gauss elimination.
+2. Perform 
+
+
+
+A
+=
+L
+U
+
+
+{\textstyle A=LU}
+
+![{\textstyle A=LU}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0e9cc8c928452cd1beaf333bb649af9853b5d12) factorization for the given matrix 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31).
+3. Factor the given symmetric matrix 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) into 
+
+
+
+A
+=
+L
+D
+
+L
+
+T
+
+
+
+
+{\textstyle A=LDL^{T}}
+
+![{\textstyle A=LDL^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/625b5b21d4aa4c805a55b29d0d03380a17343a90) with the diagonal pivot matrix 
+
+
+
+D
+
+
+{\textstyle D}
+
+![{\textstyle D}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4e5200f518cb5afe304ec42ffdd4f6c63c702f77).
+4. Find inverse matrix 
+
+
+
+
+A
+
+−
+
+
+1
+
+
+{\textstyle A^{-}1}
+
+![{\textstyle A^{-}1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8051e1bf4ce05cdb5fdf4cc58f3564bf843c3f96) for the given matrix 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31).
+
+
+### Test questions for final assessment in this section
+
+
+1. Find linear independent vectors (exclude dependent): 
+
+
+
+
+
+a
+→
+
+
+=
+[
+4
+,
+0
+,
+3
+,
+2
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {a}}=[4,0,3,2]^{T}}
+
+![{\textstyle {\overrightarrow {a}}=[4,0,3,2]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b573acd686425e4bb95dcc7342a0c8cdff33e546), 
+
+
+
+
+
+b
+→
+
+
+=
+[
+1
+,
+−
+7
+,
+4
+,
+5
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {b}}=[1,-7,4,5]^{T}}
+
+![{\textstyle {\overrightarrow {b}}=[1,-7,4,5]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8f97f34707d7d042d0080df772a5cc5bf030c784), 
+
+
+
+
+
+c
+→
+
+
+=
+[
+7
+,
+1
+,
+5
+,
+3
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {c}}=[7,1,5,3]^{T}}
+
+![{\textstyle {\overrightarrow {c}}=[7,1,5,3]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/77c5a21e300ddbdd0f7fecdd617b910827046006), 
+
+
+
+
+
+d
+→
+
+
+=
+[
+−
+5
+,
+−
+3
+,
+−
+3
+,
+−
+1
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {d}}=[-5,-3,-3,-1]^{T}}
+
+![{\textstyle {\overrightarrow {d}}=[-5,-3,-3,-1]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/424ab1d843887cea7abfa3dca20106545d8a8a0b), 
+
+
+
+
+
+e
+→
+
+
+=
+[
+1
+,
+−
+5
+,
+2
+,
+3
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {e}}=[1,-5,2,3]^{T}}
+
+![{\textstyle {\overrightarrow {e}}=[1,-5,2,3]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d6b9b7357251158c6b1954e17b912f77a1e38c4b). Find 
+
+
+
+r
+a
+n
+k
+(
+A
+)
+
+
+{\textstyle rank(A)}
+
+![{\textstyle rank(A)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/af25f6717bd9130cfded69f3333e47486b7d71cc) if 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) is a composition of this vectors. Find 
+
+
+
+r
+a
+n
+k
+(
+
+A
+
+T
+
+
+)
+
+
+{\textstyle rank(A^{T})}
+
+![{\textstyle rank(A^{T})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/671f71d97f14e03b5a9b0e0fb5724ef62720a731).
+2. Find 
+
+
+
+E
+
+
+{\textstyle E}
+
+![{\textstyle E}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6d934f67126f64e9c061b598b8941b8767a8d343): 
+
+
+
+E
+A
+=
+U
+
+
+{\textstyle EA=U}
+
+![{\textstyle EA=U}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ab6a98a37022c82117c658535da16aecb68ac071) (
+
+
+
+U
+
+
+{\textstyle U}
+
+![{\textstyle U}](https://wikimedia.org/api/rest_v1/media/math/render/svg/087a7d8a39fe35012cbf2f561879f9e975cb4555) – upper-triangular matrix). Find 
+
+
+
+L
+=
+
+E
+
+−
+
+
+1
+
+
+{\textstyle L=E^{-}1}
+
+![{\textstyle L=E^{-}1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e415e968cd0834b022ca5585654bf2ba668c5954), if 
+
+
+
+A
+=
+
+(
+
+
+
+
+2
+
+
+5
+
+
+7
+
+
+
+
+6
+
+
+4
+
+
+9
+
+
+
+
+4
+
+
+1
+
+
+8
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{ccc}2&5&7\\6&4&9\\4&1&8\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{ccc}2&5&7\\6&4&9\\4&1&8\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/270385e97a68b305e3c25e81e8ef90cc0b8dc9cc).
+3. Find complete solution for the system 
+
+
+
+A
+x
+=
+b
+
+
+{\textstyle Ax=b}
+
+![{\textstyle Ax=b}](https://wikimedia.org/api/rest_v1/media/math/render/svg/18892a5ddb5ea2e30e8a4a9488b35d67a3fdbf6d), if 
+
+
+
+b
+=
+[
+7
+,
+18
+,
+5
+
+]
+
+T
+
+
+
+
+{\textstyle b=[7,18,5]^{T}}
+
+![{\textstyle b=[7,18,5]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4faa204bdd0b26fb09cd8abebf3124e7a6b8ca1e) and 
+
+
+
+A
+=
+
+(
+
+
+
+
+6
+
+
+−
+2
+
+
+1
+
+
+−
+4
+
+
+
+
+4
+
+
+2
+
+
+14
+
+
+−
+31
+
+
+
+
+2
+
+
+−
+1
+
+
+3
+
+
+−
+7
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cccc}6&-2&1&-4\\4&2&14&-31\\2&-1&3&-7\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cccc}6&-2&1&-4\\4&2&14&-31\\2&-1&3&-7\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5a27c93084b6e998864553331b01fc5eb2339f12). Provide an example of vector b that makes this system unsolvable.
+
+
+### Section 2
+
+
+#### Section title:
+
+
+Linear regression analysis and decomposition 
+
+
+
+A
+=
+Q
+R
+
+
+{\textstyle A=QR}
+
+![{\textstyle A=QR}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f7960350ee376840d36b9f7d47d761d8112fbfe).
+
+
+
+### Topics covered in this section:
+
+
+* Independence, basis and dimension. The four fundamental subspaces.
+* Orthogonal vectors and subspaces. Projections onto subspaces
+* Projection matrices. Least squares approximations. Gram-Schmidt and A = QR.
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 1
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. What is linear independence of vectors?
+2. Define the four fundamental subspaces of a matrix?
+3. How to define orthogonal vectors and subspaces?
+4. How to define orthogonal complements of the space?
+5. How to find vector projection on a subspace?
+6. How to perform linear regression for the given measurements?
+7. How to find an orthonormal basis for the subspace spanned by the given vectors?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Check out linear independence of the given vectors
+2. Find four fundamental subspaces of the given matrix.
+3. Check out orthogonality of the given subspaces.
+4. Find orthogonal complement for the given subspace.
+5. Find vector projection on the given subspace.
+6. Perform linear regression for the given measurements.
+7. Find an orthonormal basis for the subspace spanned by the given vectors.
+
+
+### Test questions for final assessment in this section
+
+
+1. Find the dimensions of the four fundamental subspaces associated with 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31), depending on the parameters 
+
+
+
+a
+
+
+{\textstyle a}
+
+![{\textstyle a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a503f107a7c104e40e484cee9e1f5993d28ffd8) and 
+
+
+
+b
+
+
+{\textstyle b}
+
+![{\textstyle b}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73a780b69dfc55238880ef18a134dc65260877e2): 
+
+
+
+A
+=
+
+(
+
+
+
+
+7
+
+
+8
+
+
+5
+
+
+3
+
+
+
+
+4
+
+
+a
+
+
+3
+
+
+2
+
+
+
+
+6
+
+
+8
+
+
+4
+
+
+b
+
+
+
+
+3
+
+
+4
+
+
+2
+
+
+1
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cccc}7&8&5&3\\4&a&3&2\\6&8&4&b\\3&4&2&1\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cccc}7&8&5&3\\4&a&3&2\\6&8&4&b\\3&4&2&1\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fc803202bc5e0460954845a195e4b92208ac2a54).
+2. Find a vector 
+
+
+
+x
+
+
+{\textstyle x}
+
+![{\textstyle x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d951e0f3b54b6a3d73bb9a0a005749046cbce781) orthogonal to the Row space of matrix 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31), and a vector 
+
+
+
+y
+
+
+{\textstyle y}
+
+![{\textstyle y}](https://wikimedia.org/api/rest_v1/media/math/render/svg/db9936ddb2761b76fa640fb275cb5d1fa4d6fa23) orthogonal to the 
+
+
+
+C
+(
+A
+)
+
+
+{\textstyle C(A)}
+
+![{\textstyle C(A)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/50e890f8d67ec1b4b4fd8b7a6fbbfb8172f20866), and a vector 
+
+
+
+z
+
+
+{\textstyle z}
+
+![{\textstyle z}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a33e37010e3acdeeb80fdb95df9bfe411fd79e6) orthogonal to the 
+
+
+
+N
+(
+A
+)
+
+
+{\textstyle N(A)}
+
+![{\textstyle N(A)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/766235dfa8f2a0cbce4df704eb334785c7094ca4): 
+
+
+
+A
+=
+
+(
+
+
+
+
+1
+
+
+2
+
+
+2
+
+
+
+
+3
+
+
+4
+
+
+2
+
+
+
+
+4
+
+
+6
+
+
+4
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{ccc}1&2&2\\3&4&2\\4&6&4\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{ccc}1&2&2\\3&4&2\\4&6&4\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c65bde22a0e3936c85821df45484f3216a7dd74e).
+3. Find the best straight-line 
+
+
+
+y
+(
+x
+)
+
+
+{\textstyle y(x)}
+
+![{\textstyle y(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4639e7d86a9d2274f64a48570e7fe4ef17f7efa) fit to the measurements: 
+
+
+
+y
+(
+−
+2
+)
+=
+4
+
+
+{\textstyle y(-2)=4}
+
+![{\textstyle y(-2)=4}](https://wikimedia.org/api/rest_v1/media/math/render/svg/75edda9fdb1aa1cab6ac772869d7441bdf5539ef), 
+
+
+
+y
+(
+−
+1
+)
+=
+3
+
+
+{\textstyle y(-1)=3}
+
+![{\textstyle y(-1)=3}](https://wikimedia.org/api/rest_v1/media/math/render/svg/39365fc4327d63e6b3f4568f085c953942a32bcc), 
+
+
+
+y
+(
+0
+)
+=
+2
+
+
+{\textstyle y(0)=2}
+
+![{\textstyle y(0)=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4321858864c6ee38bc8ea6a44b43c1fb7b1b7bdb), 
+
+
+
+y
+(
+1
+)
+−
+0
+
+
+{\textstyle y(1)-0}
+
+![{\textstyle y(1)-0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f3ac0d6451cf2f604f303ed26f3e1b26941b680a).
+4. Find the projection matrix 
+
+
+
+P
+
+
+{\textstyle P}
+
+![{\textstyle P}](https://wikimedia.org/api/rest_v1/media/math/render/svg/038590207af1024a629c1a08c855e9ac46bf5610) of vector 
+
+
+
+[
+4
+,
+3
+,
+2
+,
+0
+
+]
+
+T
+
+
+
+
+{\textstyle [4,3,2,0]^{T}}
+
+![{\textstyle [4,3,2,0]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a1407743b577f1595b88b73ce535c1b1c6810d14) onto the 
+
+
+
+C
+(
+A
+)
+
+
+{\textstyle C(A)}
+
+![{\textstyle C(A)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/50e890f8d67ec1b4b4fd8b7a6fbbfb8172f20866): 
+
+
+
+A
+=
+
+(
+
+
+
+
+1
+
+
+−
+2
+
+
+
+
+1
+
+
+−
+1
+
+
+
+
+1
+
+
+0
+
+
+
+
+1
+
+
+1
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cc}1&-2\\1&-1\\1&0\\1&1\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cc}1&-2\\1&-1\\1&0\\1&1\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/42f35bb9ce7dd23b55e504ef145789134642fd56).
+5. Find an orthonormal basis for the subspace spanned by the vectors: 
+
+
+
+
+
+a
+→
+
+
+=
+[
+−
+2
+,
+2
+,
+0
+,
+0
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {a}}=[-2,2,0,0]^{T}}
+
+![{\textstyle {\overrightarrow {a}}=[-2,2,0,0]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d10ddb57c762601e62967544737ea022841f1c7e), 
+
+
+
+
+
+b
+→
+
+
+=
+[
+0
+,
+1
+,
+−
+1
+,
+0
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {b}}=[0,1,-1,0]^{T}}
+
+![{\textstyle {\overrightarrow {b}}=[0,1,-1,0]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a91f7a5cfe5477b27b926bf40a2ab8579777b444), 
+
+
+
+
+
+c
+→
+
+
+=
+[
+0
+,
+1
+,
+0
+,
+−
+1
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {c}}=[0,1,0,-1]^{T}}
+
+![{\textstyle {\overrightarrow {c}}=[0,1,0,-1]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6018717796286d4e371639685094a4653c67237b). Then express 
+
+
+
+A
+=
+[
+a
+,
+b
+,
+c
+]
+
+
+{\textstyle A=[a,b,c]}
+
+![{\textstyle A=[a,b,c]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/473b98961e85b063ef9a834f6f8a2caeeeb8b199) in the form of 
+
+
+
+A
+=
+Q
+R
+
+
+{\textstyle A=QR}
+
+![{\textstyle A=QR}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f7960350ee376840d36b9f7d47d761d8112fbfe)
+
+
+### Section 3
+
+
+#### Section title:
+
+
+Fast Fourier Transform. Matrix Diagonalization.
+
+
+
+### Topics covered in this section:
+
+
+* Complex Numbers. Hermitian and Unitary Matrices.
+* Fourier Series. The Fast Fourier Transform
+* Eigenvalues and eigenvectors. Matrix diagonalization.
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 1
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. Make the definition of Hermitian Matrix.
+2. Make the definition of Unitary Matrix.
+3. How to find matrix for the Fourier transform?
+4. When we can make fast Fourier transform?
+5. How to find eigenvalues and eigenvectors of a matrix?
+6. How to diagonalize a square matrix?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Check out is the given matrix Hermitian.
+2. Check out is the given matrix Unitary.
+3. Find the matrix for the given Fourier transform.
+4. Find eigenvalues and eigenvectors for the given matrix.
+5. Find diagonalize form for the given matrix.
+
+
+### Test questions for final assessment in this section
+
+
+1. Find eigenvector of the circulant matrix 
+
+
+
+C
+
+
+{\textstyle C}
+
+![{\textstyle C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6dca76d9ff4b48256b6a4a99bcb234b64b2fa72b) for the eigenvalue = 
+
+
+
+
+
+c
+
+
+1
+
+
+
+
+{\textstyle {c}\_{1}}
+
+![{\textstyle {c}_{1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0405b69bc9082831ceeeb8fa7936239466318b4e)+
+
+
+
+
+
+c
+
+
+2
+
+
+
+
+{\textstyle {c}\_{2}}
+
+![{\textstyle {c}_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a63a7c192e428b5b247dedd7a2dc5d9d2bc4ade)+
+
+
+
+
+
+c
+
+
+3
+
+
+
+
+{\textstyle {c}\_{3}}
+
+![{\textstyle {c}_{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7bd3760c114db3e5fbe4f814e7755ce35617c2b2)+
+
+
+
+
+
+c
+
+
+4
+
+
+
+
+{\textstyle {c}\_{4}}
+
+![{\textstyle {c}_{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/54dd52f52cb3ef9c6a5591247f6625340fd561ef): 
+
+
+
+C
+=
+
+(
+
+
+
+
+
+
+c
+
+
+1
+
+
+
+
+
+
+c
+
+
+2
+
+
+
+
+
+
+c
+
+
+3
+
+
+
+
+
+
+c
+
+
+4
+
+
+
+
+
+
+
+
+c
+
+
+4
+
+
+
+
+
+
+c
+
+
+1
+
+
+
+
+
+
+c
+
+
+2
+
+
+
+
+
+
+c
+
+
+3
+
+
+
+
+
+
+
+
+c
+
+
+3
+
+
+
+
+
+
+c
+
+
+4
+
+
+
+
+
+
+c
+
+
+1
+
+
+
+
+
+
+c
+
+
+2
+
+
+
+
+
+
+
+
+c
+
+
+2
+
+
+
+
+
+
+c
+
+
+3
+
+
+
+
+
+
+c
+
+
+4
+
+
+
+
+
+
+c
+
+
+1
+
+
+
+
+
+
+)
+
+
+
+{\textstyle C=\left({\begin{array}{cccc}{c}\_{1}&{c}\_{2}&{c}\_{3}&{c}\_{4}\\{c}\_{4}&{c}\_{1}&{c}\_{2}&{c}\_{3}\\{c}\_{3}&{c}\_{4}&{c}\_{1}&{c}\_{2}\\{c}\_{2}&{c}\_{3}&{c}\_{4}&{c}\_{1}\\\end{array}}\right)}
+
+![{\textstyle C=\left({\begin{array}{cccc}{c}_{1}&{c}_{2}&{c}_{3}&{c}_{4}\\{c}_{4}&{c}_{1}&{c}_{2}&{c}_{3}\\{c}_{3}&{c}_{4}&{c}_{1}&{c}_{2}\\{c}_{2}&{c}_{3}&{c}_{4}&{c}_{1}\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/69efe5a0d7045da18110c47c68ba00309abb5323).
+2. Diagonalize this matrix: 
+
+
+
+A
+=
+
+(
+
+
+
+
+2
+
+
+1
+−
+i
+
+
+
+
+1
++
+i
+
+
+3
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cc}2&1-i\\1+i&3\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cc}2&1-i\\1+i&3\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/de9882c4748ca263e22135e69cccce208a645a47).
+3. A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) is the matrix with full set of orthonormal eigenvectors. Prove that 
+
+
+
+A
+A
+=
+
+A
+
+H
+
+
+
+A
+
+H
+
+
+
+
+{\textstyle AA=A^{H}A^{H}}
+
+![{\textstyle AA=A^{H}A^{H}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/79272abd7682c09ed733b7808f9b5a49b522957d).
+4. Find all eigenvalues and eigenvectors of the cyclic permutation matrix 
+
+
+
+P
+=
+
+(
+
+
+
+
+0
+
+
+1
+
+
+0
+
+
+0
+
+
+
+
+0
+
+
+0
+
+
+1
+
+
+0
+
+
+
+
+0
+
+
+0
+
+
+0
+
+
+1
+
+
+
+
+1
+
+
+0
+
+
+0
+
+
+0
+
+
+
+
+)
+
+
+
+{\textstyle P=\left({\begin{array}{cccc}0&1&0&0\\0&0&1&0\\0&0&0&1\\1&0&0&0\\\end{array}}\right)}
+
+![{\textstyle P=\left({\begin{array}{cccc}0&1&0&0\\0&0&1&0\\0&0&0&1\\1&0&0&0\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cdf3bc0ef61513dc72ccbe9d43301d8f22ac731f).
+
+
+### Section 4
+
+
+#### Section title:
+
+
+Symmetric, positive definite and similar matrices. Singular value decomposition.
+
+
+
+### Topics covered in this section:
+
+
+* Linear differential equations.
+* Symmetric matrices. Positive definite matrices.
+* Similar matrices. Left and right inverses, pseudoinverse. Singular value decomposition (SVD).
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 1
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. How to solve linear differential equations?
+2. Make the definition of symmetric matrix?
+3. Make the definition of positive definite matrix?
+4. Make the definition of similar matrices?
+5. How to find left and right inverses matrices, pseudoinverse matrix?
+6. How to make singular value decomposition of the matrix?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Find solution of the linear differential equation.
+2. Make the definition of symmetric matrix.
+3. Check out the given matrix on positive definess
+4. Check out the given matrices on similarity.
+5. For the given matrix find left and right inverse matrices, pseudoinverse matrix.
+6. Make the singular value decomposition of the given matrix.
+
+
+### Test questions for final assessment in this section
+
+
+1. Find 
+
+
+
+d
+e
+t
+(
+
+e
+
+A
+
+
+)
+
+
+{\textstyle det(e^{A})}
+
+![{\textstyle det(e^{A})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2fe0bc4f6b8861e3358b76828c70affbe91b5546) for 
+
+
+
+A
+=
+
+(
+
+
+
+
+2
+
+
+1
+
+
+
+
+2
+
+
+3
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cc}2&1\\2&3\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cc}2&1\\2&3\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d8b79dfa2ad1a2c18b276ba62242becf7749a0b4).
+2. Write down the first order equation system for the following differential equation and solve it:
+
+
+
+
+
+
+
+d
+
+3
+
+
+y
+
+/
+
+d
+x
++
+
+d
+
+2
+
+
+y
+
+/
+
+d
+x
+−
+2
+d
+y
+
+/
+
+d
+x
+=
+0
+
+
+{\textstyle d^{3}y/dx+d^{2}y/dx-2dy/dx=0}
+
+![{\textstyle d^{3}y/dx+d^{2}y/dx-2dy/dx=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b8e608e72541239be7801b94dd8fed3e355050fc)
+
+
+
+
+
+
+
+y
+″
+
+(
+0
+)
+=
+6
+
+
+{\textstyle y''(0)=6}
+
+![{\textstyle y''(0)=6}](https://wikimedia.org/api/rest_v1/media/math/render/svg/92039ff6d21382f32158e6eef4642cb55688b549), 
+
+
+
+
+y
+′
+
+(
+0
+)
+=
+0
+
+
+{\textstyle y'(0)=0}
+
+![{\textstyle y'(0)=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6d8839484b7380ec6af6ed1f232536ae98cf093a), 
+
+
+
+y
+(
+0
+)
+=
+3
+
+
+{\textstyle y(0)=3}
+
+![{\textstyle y(0)=3}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7459acffb9257b7b7f64ba0c5d24c4ca651280f5).
+
+
+Is the solution of this system will be stable?
+3. For which 
+
+
+
+a
+
+
+{\textstyle a}
+
+![{\textstyle a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a503f107a7c104e40e484cee9e1f5993d28ffd8) and 
+
+
+
+b
+
+
+{\textstyle b}
+
+![{\textstyle b}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73a780b69dfc55238880ef18a134dc65260877e2) quadratic form 
+
+
+
+Q
+(
+x
+,
+y
+,
+z
+)
+
+
+{\textstyle Q(x,y,z)}
+
+![{\textstyle Q(x,y,z)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/723d35bcca34d49404fcc5d0e7cca10bbaf9ec8c) is positive definite:
+
+
+
+
+
+
+Q
+(
+x
+,
+y
+,
+z
+)
+=
+a
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
++
+2
+
+z
+
+2
+
+
++
+2
+b
+x
+y
++
+4
+x
+z
+
+
+{\textstyle Q(x,y,z)=ax^{2}+y^{2}+2z^{2}+2bxy+4xz}
+
+![{\textstyle Q(x,y,z)=ax^{2}+y^{2}+2z^{2}+2bxy+4xz}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f831bc4412b380c9a2c2940d4cd3dd6f46d7f3dc)
+4. Find the SVD and the pseudoinverse of the matrix 
+
+
+
+A
+=
+
+(
+
+
+
+
+1
+
+
+0
+
+
+0
+
+
+
+
+0
+
+
+1
+
+
+1
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{ccc}1&0&0\\0&1&1\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{ccc}1&0&0\\0&1&1\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/152a05619788dda3e990b8af6b737277189c507d).
+
+
+Exams and retake planning
+-------------------------
+
+
+### Exam
+
+
+Exams will be paper-based and will be conducted in a form of problem solving, where the problems will be similar to those mentioned above. Students will be given 1-2 hours to complete the exam.
+
+
+
+### Retake 1
+
+
+First retake will be conducted in the same form as the midterm and final exams. The weight of the retake exam will be the same as the all course.
+
+
+
+### Retake 2
+
+
+Second retake will be conducted in the same form as the midterm and final exams. The weight of the retake exam will be the same as the all course.
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__analytic_geometry_and_linear_algebra_ii.s23.md

@@ -0,0 +1,1972 @@
+
+
+
+
+
+
+
+BSc: Analytic Geometry And Linear Algebra II.s23
+================================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Analytical Geometry & Linear Algebra – II](#Analytical_Geometry_.26_Linear_Algebra_.E2.80.93_II)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Course Topics](#Course_Topics)
+	+ [1.3 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.3.1 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.3.1.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.3.1.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.3.1.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.4 Grading](#Grading)
+		- [1.4.1 Course grading range](#Course_grading_range)
+		- [1.4.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.4.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.5 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.5.1 Open access resources](#Open_access_resources)
+	+ [1.6 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [1.7 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [1.7.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [1.7.1.1 Section 1](#Section_1)
+			* [1.7.1.2 Section 2](#Section_2)
+			* [1.7.1.3 Section 3](#Section_3)
+			* [1.7.1.4 Section 4](#Section_4)
+		- [1.7.2 Final assessment](#Final_assessment)
+			* [1.7.2.1 Section 1](#Section_1_2)
+			* [1.7.2.2 Section 2](#Section_2_2)
+			* [1.7.2.3 Section 3](#Section_3_2)
+			* [1.7.2.4 Section 4](#Section_4_2)
+		- [1.7.3 The retake exam](#The_retake_exam)
+
+
+
+Analytical Geometry & Linear Algebra – II
+=========================================
+
+
+* **Course name**: Analytical Geometry & Linear Algebra – II
+* **Code discipline**: CSE204
+* **Subject area**: Math
+
+
+Short Description
+-----------------
+
+
+This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines. Linear algebra is a branch of mathematics that studies systems of linear equations and the properties of matrices. The concepts of linear algebra are extremely useful in physics, data sciences, and robotics. Due to its broad range of applications, linear algebra is one of the most widely used subjects in mathematics.
+
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Linear equation system solving by using the vector-matrix approach | 1. The geometry of linear equations. Elimination with matrices
+2. Matrix operations, including inverses
+3. LU and LDU factorization
+4. Transposes and permutations
+5. Vector spaces and subspaces
+6. The null space: Solving Ax=0 and Ax=b
+7. Row reduced echelon form. Matrix rank
+8. Numerical methods for solving systems of linear algebraic equations
+ |
+| Linear regression analysis, QR-decomposition | 1. Independence, basis and dimension
+2. The four fundamental subspaces
+3. Orthogonal vectors and subspaces
+4. Projections onto subspaces Projection matrices
+5. Least squares approximations
+6. Gram-Schmidt orthogonalization and A = QR
+ |
+| Matrix Diagonalization | 1. Complex Numbers
+2. Hermitian and Unitary Matrices
+3. Eigenvalues and eigenvectors
+4. Matrix diagonalization
+ |
+| Symmetric, positive definite and similar matrices. Singular value decomposition | 1. Linear differential equations.
+2. Symmetric matrices.
+3. Positive definite matrices
+4. Similar matrices.
+5. Left and right inverses, pseudoinverse
+6. Singular value decomposition (SVD)
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### ILOs defined at three levels
+
+
+We specify the intended learning outcomes at three levels: conceptual knowledge, practical skills, and comprehensive skills.
+
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* explain the geometrical interpretation of the basic operations of vector algebra,
+* restate equations of lines and planes in different forms,
+* interpret the geometrical meaning of the conic sections in the mathematical expression,
+* give the examples of the surfaces of revolution,
+* understand the value of geometry in various fields of science and techniques.
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* perform the basic operations of vector algebra,
+* use different types of equations of lines and planes to solve the plane and space problems,
+* represent the conic section in canonical form,
+* compose the equation of quadric surface.
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* list basic notions of vector algebra,
+* recite the base form of the equations of transformations in planes and spaces,
+* recall equations of lines and planes,
+* identify the type of conic section,
+* recognize the kind of quadric surfaces.
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-110 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Fail | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Midterm | 30
+ |
+| Two intermediate tests | 30 (15 for each)
+ |
+| Final exam | 30
+ |
+| Five programming tasks | 20
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+* Participation is important. Attending lectures is the key to success in this course.
+* Review lecture materials before classes to do well.
+* Reading the recommended literature is obligatory, and will give you a deeper understanding of the material.
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Gilbert Strang. Linear Algebra and Its Applications, 4th Edition, Brooks Cole, 2006. ISBN: 9780030105678
+* Gilbert Strang. Introduction to Linear Algebra, 4th Edition, Wellesley, MA: Wellesley-Cambridge Press, 2009. ISBN: 9780980232714
+* Gilbert Strang, Brett Coonley, Andrew Bulman-Fleming. Student Solutions Manual for Strang’s Linear Algebra and Its Applications, 4th Edition, Thomson Brooks, 2005. ISBN-13: 9780495013259
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Teaching and Learning Methods within each section
+| Teaching Techniques | Section 1 | Section 2 | Section 3 | Section 4
+ |
+| --- | --- | --- | --- | --- |
+| Problem-based learning (students learn by solving open-ended problems without a strictly-defined solution) | 0 | 0 | 0 | 0
+ |
+| Project-based learning (students work on a project) | 0 | 0 | 0 | 0
+ |
+| Modular learning (facilitated self-study) | 0 | 0 | 0 | 0
+ |
+| Differentiated learning (provide tasks and activities at several levels of difficulty to fit students needs and level) | 1 | 1 | 1 | 1
+ |
+| Contextual learning (activities and tasks are connected to the real world to make it easier for students to relate to them) | 0 | 0 | 0 | 0
+ |
+| Business game (learn by playing a game that incorporates the principles of the material covered within the course) | 0 | 0 | 0 | 0
+ |
+| Inquiry-based learning | 0 | 0 | 0 | 0
+ |
+| Just-in-time teaching | 0 | 0 | 0 | 0
+ |
+| Process oriented guided inquiry learning (POGIL) | 0 | 0 | 0 | 0
+ |
+| Studio-based learning | 0 | 0 | 0 | 0
+ |
+| Universal design for learning | 0 | 0 | 0 | 0
+ |
+| Task-based learning | 0 | 0 | 0 | 0
+ |
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4
+ |
+| --- | --- | --- | --- | --- |
+| Lectures | 1 | 1 | 1 | 1
+ |
+| Interactive Lectures | 1 | 1 | 1 | 1
+ |
+| Lab exercises | 1 | 1 | 1 | 1
+ |
+| Experiments | 0 | 0 | 0 | 0
+ |
+| Modeling | 0 | 0 | 0 | 0
+ |
+| Cases studies | 0 | 0 | 0 | 0
+ |
+| Development of individual parts of software product code | 0 | 0 | 0 | 0
+ |
+| Individual Projects | 0 | 0 | 0 | 0
+ |
+| Group projects | 0 | 0 | 0 | 0
+ |
+| Flipped classroom | 0 | 0 | 0 | 0
+ |
+| Quizzes (written or computer based) | 1 | 1 | 1 | 1
+ |
+| Peer Review | 0 | 0 | 0 | 0
+ |
+| Discussions | 1 | 1 | 1 | 1
+ |
+| Presentations by students | 0 | 0 | 0 | 0
+ |
+| Written reports | 0 | 0 | 0 | 0
+ |
+| Simulations and role-plays | 0 | 0 | 0 | 0
+ |
+| Essays | 0 | 0 | 0 | 0
+ |
+| Oral Reports | 0 | 0 | 0 | 0
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+1. How to perform Gauss elimination?
+2. How to perform matrices multiplication?
+3. How to perform LU factorization?
+4. How to find complete solution for any linear equation system Ax=b?
+
+
+#### Section 2
+
+
+1. What is linear independence of vectors?
+2. Define the four fundamental subspaces of a matrix?
+3. How to define orthogonal vectors and subspaces?
+4. How to define orthogonal complements of the space?
+5. How to find vector projection on a subspace?
+6. How to perform linear regression for the given measurements?
+7. How to find an orthonormal basis for the subspace spanned by the given vectors?
+
+
+#### Section 3
+
+
+1. Give the definition of Hermitian Matrix.
+2. Give the definition of Unitary Matrix.
+3. How to find matrix for the Fourier transform?
+4. When we can make fast Fourier transform?
+5. How to find eigenvalues and eigenvectors of a matrix?
+6. How to diagonalize a square matrix?
+
+
+#### Section 4
+
+
+1. How to solve linear differential equations?
+2. Make the definition of symmetric matrix?
+3. Make the definition of positive definite matrix?
+4. Make the definition of similar matrices?
+5. How to find left and right inverses matrices, pseudoinverse matrix?
+6. How to make singular value decomposition of the matrix?
+
+
+### Final assessment
+
+
+#### Section 1
+
+
+1. Find linear independent vectors (exclude dependent): 
+
+
+
+
+
+a
+→
+
+
+=
+[
+4
+,
+0
+,
+3
+,
+2
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {a}}=[4,0,3,2]^{T}}
+
+![{\textstyle {\overrightarrow {a}}=[4,0,3,2]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b573acd686425e4bb95dcc7342a0c8cdff33e546), 
+
+
+
+
+
+b
+→
+
+
+=
+[
+1
+,
+−
+7
+,
+4
+,
+5
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {b}}=[1,-7,4,5]^{T}}
+
+![{\textstyle {\overrightarrow {b}}=[1,-7,4,5]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8f97f34707d7d042d0080df772a5cc5bf030c784), 
+
+
+
+
+
+c
+→
+
+
+=
+[
+7
+,
+1
+,
+5
+,
+3
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {c}}=[7,1,5,3]^{T}}
+
+![{\textstyle {\overrightarrow {c}}=[7,1,5,3]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/77c5a21e300ddbdd0f7fecdd617b910827046006), 
+
+
+
+
+
+d
+→
+
+
+=
+[
+−
+5
+,
+−
+3
+,
+−
+3
+,
+−
+1
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {d}}=[-5,-3,-3,-1]^{T}}
+
+![{\textstyle {\overrightarrow {d}}=[-5,-3,-3,-1]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/424ab1d843887cea7abfa3dca20106545d8a8a0b), 
+
+
+
+
+
+e
+→
+
+
+=
+[
+1
+,
+−
+5
+,
+2
+,
+3
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {e}}=[1,-5,2,3]^{T}}
+
+![{\textstyle {\overrightarrow {e}}=[1,-5,2,3]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d6b9b7357251158c6b1954e17b912f77a1e38c4b). Find 
+
+
+
+r
+a
+n
+k
+(
+A
+)
+
+
+{\textstyle rank(A)}
+
+![{\textstyle rank(A)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/af25f6717bd9130cfded69f3333e47486b7d71cc) if 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) is a composition of this vectors. Find 
+
+
+
+r
+a
+n
+k
+(
+
+A
+
+T
+
+
+)
+
+
+{\textstyle rank(A^{T})}
+
+![{\textstyle rank(A^{T})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/671f71d97f14e03b5a9b0e0fb5724ef62720a731).
+2. Find 
+
+
+
+E
+
+
+{\textstyle E}
+
+![{\textstyle E}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6d934f67126f64e9c061b598b8941b8767a8d343): 
+
+
+
+E
+A
+=
+U
+
+
+{\textstyle EA=U}
+
+![{\textstyle EA=U}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ab6a98a37022c82117c658535da16aecb68ac071) (
+
+
+
+U
+
+
+{\textstyle U}
+
+![{\textstyle U}](https://wikimedia.org/api/rest_v1/media/math/render/svg/087a7d8a39fe35012cbf2f561879f9e975cb4555) – upper-triangular matrix). Find 
+
+
+
+L
+=
+
+E
+
+−
+
+
+1
+
+
+{\textstyle L=E^{-}1}
+
+![{\textstyle L=E^{-}1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e415e968cd0834b022ca5585654bf2ba668c5954), if 
+
+
+
+A
+=
+
+(
+
+
+
+
+2
+
+
+5
+
+
+7
+
+
+
+
+6
+
+
+4
+
+
+9
+
+
+
+
+4
+
+
+1
+
+
+8
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{ccc}2&5&7\\6&4&9\\4&1&8\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{ccc}2&5&7\\6&4&9\\4&1&8\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/270385e97a68b305e3c25e81e8ef90cc0b8dc9cc).
+3. Find complete solution for the system 
+
+
+
+A
+x
+=
+b
+
+
+{\textstyle Ax=b}
+
+![{\textstyle Ax=b}](https://wikimedia.org/api/rest_v1/media/math/render/svg/18892a5ddb5ea2e30e8a4a9488b35d67a3fdbf6d), if 
+
+
+
+b
+=
+[
+7
+,
+18
+,
+5
+
+]
+
+T
+
+
+
+
+{\textstyle b=[7,18,5]^{T}}
+
+![{\textstyle b=[7,18,5]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4faa204bdd0b26fb09cd8abebf3124e7a6b8ca1e) and 
+
+
+
+A
+=
+
+(
+
+
+
+
+6
+
+
+−
+2
+
+
+1
+
+
+−
+4
+
+
+
+
+4
+
+
+2
+
+
+14
+
+
+−
+31
+
+
+
+
+2
+
+
+−
+1
+
+
+3
+
+
+−
+7
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cccc}6&-2&1&-4\\4&2&14&-31\\2&-1&3&-7\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cccc}6&-2&1&-4\\4&2&14&-31\\2&-1&3&-7\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5a27c93084b6e998864553331b01fc5eb2339f12). Provide an example of vector b that makes this system unsolvable.
+
+
+#### Section 2
+
+
+1. Find the dimensions of the four fundamental subspaces associated with 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31), depending on the parameters 
+
+
+
+a
+
+
+{\textstyle a}
+
+![{\textstyle a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a503f107a7c104e40e484cee9e1f5993d28ffd8) and 
+
+
+
+b
+
+
+{\textstyle b}
+
+![{\textstyle b}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73a780b69dfc55238880ef18a134dc65260877e2): 
+
+
+
+A
+=
+
+(
+
+
+
+
+7
+
+
+8
+
+
+5
+
+
+3
+
+
+
+
+4
+
+
+a
+
+
+3
+
+
+2
+
+
+
+
+6
+
+
+8
+
+
+4
+
+
+b
+
+
+
+
+3
+
+
+4
+
+
+2
+
+
+1
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cccc}7&8&5&3\\4&a&3&2\\6&8&4&b\\3&4&2&1\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cccc}7&8&5&3\\4&a&3&2\\6&8&4&b\\3&4&2&1\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fc803202bc5e0460954845a195e4b92208ac2a54).
+2. Find a vector 
+
+
+
+x
+
+
+{\textstyle x}
+
+![{\textstyle x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d951e0f3b54b6a3d73bb9a0a005749046cbce781) orthogonal to the Row space of matrix 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31), and a vector 
+
+
+
+y
+
+
+{\textstyle y}
+
+![{\textstyle y}](https://wikimedia.org/api/rest_v1/media/math/render/svg/db9936ddb2761b76fa640fb275cb5d1fa4d6fa23) orthogonal to the 
+
+
+
+C
+(
+A
+)
+
+
+{\textstyle C(A)}
+
+![{\textstyle C(A)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/50e890f8d67ec1b4b4fd8b7a6fbbfb8172f20866), and a vector 
+
+
+
+z
+
+
+{\textstyle z}
+
+![{\textstyle z}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a33e37010e3acdeeb80fdb95df9bfe411fd79e6) orthogonal to the 
+
+
+
+N
+(
+A
+)
+
+
+{\textstyle N(A)}
+
+![{\textstyle N(A)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/766235dfa8f2a0cbce4df704eb334785c7094ca4): 
+
+
+
+A
+=
+
+(
+
+
+
+
+1
+
+
+2
+
+
+2
+
+
+
+
+3
+
+
+4
+
+
+2
+
+
+
+
+4
+
+
+6
+
+
+4
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{ccc}1&2&2\\3&4&2\\4&6&4\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{ccc}1&2&2\\3&4&2\\4&6&4\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c65bde22a0e3936c85821df45484f3216a7dd74e).
+3. Find the best straight-line 
+
+
+
+y
+(
+x
+)
+
+
+{\textstyle y(x)}
+
+![{\textstyle y(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4639e7d86a9d2274f64a48570e7fe4ef17f7efa) fit to the measurements: 
+
+
+
+y
+(
+−
+2
+)
+=
+4
+
+
+{\textstyle y(-2)=4}
+
+![{\textstyle y(-2)=4}](https://wikimedia.org/api/rest_v1/media/math/render/svg/75edda9fdb1aa1cab6ac772869d7441bdf5539ef), 
+
+
+
+y
+(
+−
+1
+)
+=
+3
+
+
+{\textstyle y(-1)=3}
+
+![{\textstyle y(-1)=3}](https://wikimedia.org/api/rest_v1/media/math/render/svg/39365fc4327d63e6b3f4568f085c953942a32bcc), 
+
+
+
+y
+(
+0
+)
+=
+2
+
+
+{\textstyle y(0)=2}
+
+![{\textstyle y(0)=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4321858864c6ee38bc8ea6a44b43c1fb7b1b7bdb), 
+
+
+
+y
+(
+1
+)
+−
+0
+
+
+{\textstyle y(1)-0}
+
+![{\textstyle y(1)-0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f3ac0d6451cf2f604f303ed26f3e1b26941b680a).
+4. Find the projection matrix 
+
+
+
+P
+
+
+{\textstyle P}
+
+![{\textstyle P}](https://wikimedia.org/api/rest_v1/media/math/render/svg/038590207af1024a629c1a08c855e9ac46bf5610) of vector 
+
+
+
+[
+4
+,
+3
+,
+2
+,
+0
+
+]
+
+T
+
+
+
+
+{\textstyle [4,3,2,0]^{T}}
+
+![{\textstyle [4,3,2,0]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a1407743b577f1595b88b73ce535c1b1c6810d14) onto the 
+
+
+
+C
+(
+A
+)
+
+
+{\textstyle C(A)}
+
+![{\textstyle C(A)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/50e890f8d67ec1b4b4fd8b7a6fbbfb8172f20866): 
+
+
+
+A
+=
+
+(
+
+
+
+
+1
+
+
+−
+2
+
+
+
+
+1
+
+
+−
+1
+
+
+
+
+1
+
+
+0
+
+
+
+
+1
+
+
+1
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cc}1&-2\\1&-1\\1&0\\1&1\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cc}1&-2\\1&-1\\1&0\\1&1\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/42f35bb9ce7dd23b55e504ef145789134642fd56).
+5. Find an orthonormal basis for the subspace spanned by the vectors: 
+
+
+
+
+
+a
+→
+
+
+=
+[
+−
+2
+,
+2
+,
+0
+,
+0
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {a}}=[-2,2,0,0]^{T}}
+
+![{\textstyle {\overrightarrow {a}}=[-2,2,0,0]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d10ddb57c762601e62967544737ea022841f1c7e), 
+
+
+
+
+
+b
+→
+
+
+=
+[
+0
+,
+1
+,
+−
+1
+,
+0
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {b}}=[0,1,-1,0]^{T}}
+
+![{\textstyle {\overrightarrow {b}}=[0,1,-1,0]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a91f7a5cfe5477b27b926bf40a2ab8579777b444), 
+
+
+
+
+
+c
+→
+
+
+=
+[
+0
+,
+1
+,
+0
+,
+−
+1
+
+]
+
+T
+
+
+
+
+{\textstyle {\overrightarrow {c}}=[0,1,0,-1]^{T}}
+
+![{\textstyle {\overrightarrow {c}}=[0,1,0,-1]^{T}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6018717796286d4e371639685094a4653c67237b). Then express 
+
+
+
+A
+=
+[
+a
+,
+b
+,
+c
+]
+
+
+{\textstyle A=[a,b,c]}
+
+![{\textstyle A=[a,b,c]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/473b98961e85b063ef9a834f6f8a2caeeeb8b199) in the form of 
+
+
+
+A
+=
+Q
+R
+
+
+{\textstyle A=QR}
+
+![{\textstyle A=QR}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f7960350ee376840d36b9f7d47d761d8112fbfe)
+
+
+#### Section 3
+
+
+1. Find eigenvector of the circulant matrix 
+
+
+
+C
+
+
+{\textstyle C}
+
+![{\textstyle C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6dca76d9ff4b48256b6a4a99bcb234b64b2fa72b) for the eigenvalue = 
+
+
+
+
+
+c
+
+
+1
+
+
+
+
+{\textstyle {c}\_{1}}
+
+![{\textstyle {c}_{1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0405b69bc9082831ceeeb8fa7936239466318b4e)+
+
+
+
+
+
+c
+
+
+2
+
+
+
+
+{\textstyle {c}\_{2}}
+
+![{\textstyle {c}_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a63a7c192e428b5b247dedd7a2dc5d9d2bc4ade)+
+
+
+
+
+
+c
+
+
+3
+
+
+
+
+{\textstyle {c}\_{3}}
+
+![{\textstyle {c}_{3}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7bd3760c114db3e5fbe4f814e7755ce35617c2b2)+
+
+
+
+
+
+c
+
+
+4
+
+
+
+
+{\textstyle {c}\_{4}}
+
+![{\textstyle {c}_{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/54dd52f52cb3ef9c6a5591247f6625340fd561ef): 
+
+
+
+C
+=
+
+(
+
+
+
+
+
+
+c
+
+
+1
+
+
+
+
+
+
+c
+
+
+2
+
+
+
+
+
+
+c
+
+
+3
+
+
+
+
+
+
+c
+
+
+4
+
+
+
+
+
+
+
+
+c
+
+
+4
+
+
+
+
+
+
+c
+
+
+1
+
+
+
+
+
+
+c
+
+
+2
+
+
+
+
+
+
+c
+
+
+3
+
+
+
+
+
+
+
+
+c
+
+
+3
+
+
+
+
+
+
+c
+
+
+4
+
+
+
+
+
+
+c
+
+
+1
+
+
+
+
+
+
+c
+
+
+2
+
+
+
+
+
+
+
+
+c
+
+
+2
+
+
+
+
+
+
+c
+
+
+3
+
+
+
+
+
+
+c
+
+
+4
+
+
+
+
+
+
+c
+
+
+1
+
+
+
+
+
+
+)
+
+
+
+{\textstyle C=\left({\begin{array}{cccc}{c}\_{1}&{c}\_{2}&{c}\_{3}&{c}\_{4}\\{c}\_{4}&{c}\_{1}&{c}\_{2}&{c}\_{3}\\{c}\_{3}&{c}\_{4}&{c}\_{1}&{c}\_{2}\\{c}\_{2}&{c}\_{3}&{c}\_{4}&{c}\_{1}\\\end{array}}\right)}
+
+![{\textstyle C=\left({\begin{array}{cccc}{c}_{1}&{c}_{2}&{c}_{3}&{c}_{4}\\{c}_{4}&{c}_{1}&{c}_{2}&{c}_{3}\\{c}_{3}&{c}_{4}&{c}_{1}&{c}_{2}\\{c}_{2}&{c}_{3}&{c}_{4}&{c}_{1}\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/69efe5a0d7045da18110c47c68ba00309abb5323).
+2. Diagonalize this matrix: 
+
+
+
+A
+=
+
+(
+
+
+
+
+2
+
+
+1
+−
+i
+
+
+
+
+1
++
+i
+
+
+3
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cc}2&1-i\\1+i&3\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cc}2&1-i\\1+i&3\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/de9882c4748ca263e22135e69cccce208a645a47).
+3. A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) is the matrix with full set of orthonormal eigenvectors. Prove that 
+
+
+
+A
+A
+=
+
+A
+
+H
+
+
+
+A
+
+H
+
+
+
+
+{\textstyle AA=A^{H}A^{H}}
+
+![{\textstyle AA=A^{H}A^{H}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/79272abd7682c09ed733b7808f9b5a49b522957d).
+4. Find all eigenvalues and eigenvectors of the cyclic permutation matrix 
+
+
+
+P
+=
+
+(
+
+
+
+
+0
+
+
+1
+
+
+0
+
+
+0
+
+
+
+
+0
+
+
+0
+
+
+1
+
+
+0
+
+
+
+
+0
+
+
+0
+
+
+0
+
+
+1
+
+
+
+
+1
+
+
+0
+
+
+0
+
+
+0
+
+
+
+
+)
+
+
+
+{\textstyle P=\left({\begin{array}{cccc}0&1&0&0\\0&0&1&0\\0&0&0&1\\1&0&0&0\\\end{array}}\right)}
+
+![{\textstyle P=\left({\begin{array}{cccc}0&1&0&0\\0&0&1&0\\0&0&0&1\\1&0&0&0\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cdf3bc0ef61513dc72ccbe9d43301d8f22ac731f).
+
+
+#### Section 4
+
+
+1. Find 
+
+
+
+d
+e
+t
+(
+
+e
+
+A
+
+
+)
+
+
+{\textstyle det(e^{A})}
+
+![{\textstyle det(e^{A})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2fe0bc4f6b8861e3358b76828c70affbe91b5546) for 
+
+
+
+A
+=
+
+(
+
+
+
+
+2
+
+
+1
+
+
+
+
+2
+
+
+3
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{cc}2&1\\2&3\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{cc}2&1\\2&3\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d8b79dfa2ad1a2c18b276ba62242becf7749a0b4).
+2. Write down the first order equation system for the following differential equation and solve it:
+
+
+
+
+
+
+
+d
+
+3
+
+
+y
+
+/
+
+d
+x
++
+
+d
+
+2
+
+
+y
+
+/
+
+d
+x
+−
+2
+d
+y
+
+/
+
+d
+x
+=
+0
+
+
+{\textstyle d^{3}y/dx+d^{2}y/dx-2dy/dx=0}
+
+![{\textstyle d^{3}y/dx+d^{2}y/dx-2dy/dx=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b8e608e72541239be7801b94dd8fed3e355050fc)
+
+
+
+
+
+
+
+y
+″
+
+(
+0
+)
+=
+6
+
+
+{\textstyle y''(0)=6}
+
+![{\textstyle y''(0)=6}](https://wikimedia.org/api/rest_v1/media/math/render/svg/92039ff6d21382f32158e6eef4642cb55688b549), 
+
+
+
+
+y
+′
+
+(
+0
+)
+=
+0
+
+
+{\textstyle y'(0)=0}
+
+![{\textstyle y'(0)=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6d8839484b7380ec6af6ed1f232536ae98cf093a), 
+
+
+
+y
+(
+0
+)
+=
+3
+
+
+{\textstyle y(0)=3}
+
+![{\textstyle y(0)=3}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7459acffb9257b7b7f64ba0c5d24c4ca651280f5).
+
+
+Is the solution of this system will be stable?
+3. For which 
+
+
+
+a
+
+
+{\textstyle a}
+
+![{\textstyle a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a503f107a7c104e40e484cee9e1f5993d28ffd8) and 
+
+
+
+b
+
+
+{\textstyle b}
+
+![{\textstyle b}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73a780b69dfc55238880ef18a134dc65260877e2) quadratic form 
+
+
+
+Q
+(
+x
+,
+y
+,
+z
+)
+
+
+{\textstyle Q(x,y,z)}
+
+![{\textstyle Q(x,y,z)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/723d35bcca34d49404fcc5d0e7cca10bbaf9ec8c) is positive definite:
+
+
+
+
+
+
+Q
+(
+x
+,
+y
+,
+z
+)
+=
+a
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
++
+2
+
+z
+
+2
+
+
++
+2
+b
+x
+y
++
+4
+x
+z
+
+
+{\textstyle Q(x,y,z)=ax^{2}+y^{2}+2z^{2}+2bxy+4xz}
+
+![{\textstyle Q(x,y,z)=ax^{2}+y^{2}+2z^{2}+2bxy+4xz}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f831bc4412b380c9a2c2940d4cd3dd6f46d7f3dc)
+4. Find the SVD and the pseudoinverse of the matrix 
+
+
+
+A
+=
+
+(
+
+
+
+
+1
+
+
+0
+
+
+0
+
+
+
+
+0
+
+
+1
+
+
+1
+
+
+
+
+)
+
+
+
+{\textstyle A=\left({\begin{array}{ccc}1&0&0\\0&1&1\\\end{array}}\right)}
+
+![{\textstyle A=\left({\begin{array}{ccc}1&0&0\\0&1&1\\\end{array}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/152a05619788dda3e990b8af6b737277189c507d).
+
+
+### The retake exam
+
+
+Exams will be paper-based and will be conducted in a form of problem solving, where the problems will be similar to those mentioned above. Students will be given 1-2 hours to complete the exam.
+First retake will be conducted in the same form as the midterm and final exams. The weight of the retake exam will be the same as the all course.
+Second retake will be conducted in the same form as the midterm and final exams. The weight of the retake exam will be the same as the all course.
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__capstone_project.md

@@ -0,0 +1,400 @@
+
+
+
+
+
+
+
+BSc: Capstone Project
+=====================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Capstone Project](#Capstone_Project)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Capstone Project
+================
+
+
+* **Course name**: Capstone Project
+* **Code discipline**: -
+* **Subject area**: Subject Areas to choose from: -
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: People Management; Processes and Project Development, Planning and Controlling.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+* CSE113 - Logic & Discrete Maths
+* CSE201 - Mathematical Analysis I
+* CSE202 - Analytical Geometry and Linear Algebra I
+* CSE401 - Fundamentals of Computer Architecture
+* CSE101 - Introduction to Programming
+* CSE103 - Theoretical Computer Science
+* CSE203 - Mathematical Analysis II
+* CSE204 - Analytical Geometry and Linear Algebra II
+* CSE117 - Data Structures and Algorithms
+* CSE112 - Software System Analysis and Design
+* CSE801 - Software Project
+* CSE301 - Introduction to Artificial Intelligence
+* CSE206 - Probability and Statistics
+* CSE402 - Physics I (Mechanics)
+* CSE105 - Operating Systems
+* CSE205 - Differential Equations
+* CSE333 - Introduction to Optimization
+* CSE302 - Introduction to Machine Learning
+* (SD, CS, DS, AAI) CSE106 - Databases
+* (SD, CS, DS, AAI) CSE501 - Networks
+* (SD, CS) CSE502 - System and Network Administration
+* (SD, CS, AAI) CSE114 - Distributed and Network Programming
+* (AAI) CSE338 - Reinforcement Learning
+* (DS) CSE310 - Statistical Techniques
+* (DS) CSE340 - Nature Inspired Computing
+* (RO) CSE410 - Physics II (Electrical Engineering)
+* (RO) CSE403 - Control Theory
+* (RO) CSE408 - Theoretical Mechanics
+* (RO) CSE406 - Fundamental of Robotics
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| People Management, Leadership and Teamwork | 1. People Management Styles
+2. People management & Leadership skills
+3. Teamwork Tools: Trello, BitBucket, Miro, Github
+ |
+| Project development and realization | 1. Defining and measuring processes
+2. Project Life Cycle
+3. Project Development and Management methodology
+ |
+| Planning and controlling projects | 1. Introduction - Planning & Controlling Software Development Projects
+2. Work Breakdown Structures
+3. Estimation Methods
+4. Activity Planning
+5. Milestone Planning
+6. Release Planning
+7. Tracking Reporting & Controlling
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+What is the main goal of this course formulated in one sentence?
+The main goal of this course is to enable a student to understand the phases of project development; to manage both human and computational resources through control of the development process. The main task is to combine all the knowledge obtained during the study at the university and turn it into real projects.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* List existing tools for a teamwork
+* Describe the skills required for people manager
+* Describe the skills required for a good leader
+* Explain the steps of project Life Cycle
+* Know how to plan and control software/hardware projects
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Get ideas about the work in the main structural divisions
+* Formulate the idea as a project task
+* Set objectives and goals properly
+* Perform the given tasks in a certain limit of time
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Adapt to real working conditions in various institutions and organizations
+* Gain experience while working in teams
+* Organize and plan the projects
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| Pass | 60-100 | -
+ |
+| Fail | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Presentation | 45
+ |
+| Final Presentation | 55
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Participation is important. Showing up is the key to success in this course.  
+You will work in teams, so coordinating teamwork will be an important factor for success.
+
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Teaching and Learning Methods within each section
+| Teaching Techniques | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Problem-based learning (students learn by solving open-ended problems without a strictly-defined solution) | 1 | 1 | 1
+ |
+| Project-based learning (students work on a project) | 1 | 1 | 1
+ |
+| Contextual learning (activities and tasks are connected to the real world to make it easier for students to relate to them); | 1 | 1 | 1
+ |
+| inquiry-based learning | 1 | 1 | 1
+ |
+| Process oriented guided inquiry learning (POGIL) | 1 | 1 | 1
+ |
+| Task-based learning | 1 | 1 | 1
+ |
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Experiments | 1 | 1 | 1
+ |
+| Modeling | 1 | 1 | 1
+ |
+| Cases studies | 1 | 1 | 1
+ |
+| Development of individual parts of software product code | 1 | 1 | 1
+ |
+| Group projects | 1 | 1 | 1
+ |
+| Discussions | 1 | 1 | 1
+ |
+| Presentations by students | 1 | 1 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Presentation | Prepare a short 2-minutes pitch for your project idea (2-5 slides). Suggested structure:What problem you are solving:- State the problem clearly in 2-3 short sentences.What methodology are you going to apply:- Shortly describe the method(-s) that could solve the problem. | 1
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Presentation of Current Progress | Prepare a short pitch for your current project progress (5-7 slides). Suggested structure:What problem you are solving:- State the problem clearly in 2-3 short sentences.What methodology are you going to apply:- Shortly describe the method(-s) that could solve the problem.Which tasks are you performing:- Shortly describe the tasks that are being solved.- Describe the current problems in realization if any. | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Presentation (Project Defense) | Prepare a 5-minutes presentation on your project. During the presentation clearly define the role and contribution of each member of a team.Suggested structure:What problem you are solving:- State the problem clearly in 2-3 short sentences.What methodology is used:- Describe the method(-s) that were used to solve the problem.What are the results:- Describe what you achieved during the course. | 1
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. Grading criteria for the midterm project presentation:
+2. 1. Problem: short clear statement on what you are solving, and why it’s important.
+3. 2. Methodology: clear statement of the methods to be used.
+
+
+**Section 2**
+
+
+
+1. The activity in this section is not graded. The presentation is needed only to see the current state of the project realization.
+
+
+**Section 3**
+
+
+
+1. Grading criteria for the final project presentation:
+2. 1. Problem: short clear statement on what you are solving, and why it’s important.
+3. 2. Methodology: clear statement of the methods used.
+4. 3. Results: students provided the achieved results and can interpret them
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+
+1. For the retake, students have to follow the guidelines of the course and contribute to a new project. The complexity of the product can be reduced, if it is one person working on it. The grading criteria for each section are the same as for the final project presentation. There has to be a meeting before the retake itself to plan and agree on the project content, and to answer questions.
+2. P7. Activities and Teaching Methods by Sections
+3. Mark what techniques and methods are used in each section (1 is used, 0 is not used).
+4. Table A1: Teaching and Learning Methods within each section
+5. Table A2: Activities within each section
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__compilers_construction.md

@@ -0,0 +1,364 @@
+
+
+
+
+
+
+
+BSc: Compilers Construction
+===========================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Compiler Construction](#Compiler_Construction)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Compiler Construction
+=====================
+
+
+* **Course name**: Compiler Construction
+* **Code discipline**: n/a
+* **Subject area**: Programming Languages and Software Engineering
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: Overall compilation architecture; Lexical analysis; Syntax analysis; Semantic analysis; Code generation; Program optimization; Virtual machines and JIT technology.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Introduction to compilers and compiler construction | 1. Basic notions: source and target languages, target architecture, compilation phases.
+2. The history of languages and compiler development. Typical compiler examples.
+3. Compilation & interpretation. Virtual machines, JIT & AOT technologies. Hybrid modes.
+ |
+| Lexical, syntax and semantic analyses | 1. Compilation pipeline & compilation data structures
+2. Lexical analysis and deterministic state automata
+3. Bottom-up and top-down parsing
+4. Principles of semantic analysis
+ |
+| Code generation, optimization and virtual machines | 1. Low-level code generation: machine instructions, assembly language
+2. Virtual machines’ architecture and their byte codes.
+3. The notion of language projections.
+4. Introduction to optimization techniques.
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+The software development process and the depth of programming cannot be understood without a detailed analysis of the compilation process, from the lexical analysis to the syntactical and semantic analysis up to code generation and optimization, and without understanding both strength and limitation of this process. This course dig deeper into this topic building on the fundamental notions studied in theoretical computer science of which is the natural continuation. The typical compiler pipeline will be studied and a project will allow students to practice with the relevant tools.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Understanding in depth the compilation process
+* Realizing the limits of the process and of Semantic Analysis
+* Read and write grammars for programming language constructs
+* Perform lexical analysis and use lexical analyzer generators
+* Perform top-down parsing, bottom-up parsing and use parser generators
+* Perform semantic analysis
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* How to design and develop compilers and language-related tools.
+* The contents of each phase of the compilation process.
+* How integrate compilers into an IDE.
+* How to design a virtual machine for a language.
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* To be able to develop a language compiler.
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 85-100 | -
+ |
+| B. Good | 75-84 | -
+ |
+| C. Satisfactory | 60-75 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Labs/seminar classes | 40
+ |
+| Interim performance assessment | 40
+ |
+| Exams | 30
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Alfred V.Aho, Monica S.Lam, Ravi Sethi, Jeffrey D. Ullman. Compilers. Principles, Techniques, & Tools, Second Edition, Addison-Wesley, 2007, ISBN 0-321-48681-1.
+* N. Wirth, Compiler Construction, Addison-Wesley, 1996, ISBN 0-201-40353-6
+* <http://www.ethoberon.ethz.ch/WirthPubl/CBEAll.pdf>, 2005
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Development of individual parts of software product code | 1 | 1 | 1
+ |
+| Homework and group projects | 1 | 1 | 1
+ |
+| Oral polls | 1 | 0 | 0
+ |
+| Discussions | 1 | 1 | 0
+ |
+| Reports | 0 | 1 | 0
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is compilation process? | 1
+ |
+| Question | What’s the difference between compiler and interpreter? | 1
+ |
+| Question | How to compile a program? | 0
+ |
+| Question | How to run a program? | 0
+ |
+| Question | How to debug a program? | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Abstract syntax tree & symbol tables: what is it for and how create and manage them? | 1
+ |
+| Question | How to organize communication between compilation phases? | 1
+ |
+| Question | What are basic differences between bottom-up and top-down parsing? | 1
+ |
+| Question | How to implement a hash function for a symbol table? | 0
+ |
+| Question | How to write a grammar for an expression using YACC/Bison tool? | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What’s the difference between assembly and machine instructions? | 1
+ |
+| Question | What’s the similarities and differences between real target platforms and virtual machines? | 1
+ |
+| Question | Explain some of widely used approaches for optimizing program source code? How these approaches can be implemented in a compiler? | 1
+ |
+| Question | Explain the idea behind the notion of control flow graph. | 0
+ |
+| Question | What is “basic block” in CFG and what is it for? | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. What are significant phases of a compilation process?
+2. Why do we need optimization phase?
+3. What’s the difference between syntax and semantic analyses?
+
+
+**Section 2**
+
+
+
+1. Characterize the principles of top-down and bottom-up parsing.
+2. Explain how a symbol table can be implemented.
+3. AST: is it a tree or a graph? What’s about semantic attributes in an AST?
+
+
+**Section 3**
+
+
+
+1. Give some simple examples of language-code projections.
+2. How the object code for an expression can be optimized?
+3. How to avoid tail recursion while optimizing code?
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__computer_architecture.md

@@ -0,0 +1,821 @@
+
+
+
+
+
+
+
+BSc: Computer Architecture
+==========================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Fundamentals of Computer Architecture](#Fundamentals_of_Computer_Architecture)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+			* [2.2.1.4 Section 4](#Section_4)
+			* [2.2.1.5 Section 5](#Section_5)
+			* [2.2.1.6 Section 6](#Section_6)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Fundamentals of Computer Architecture
+=====================================
+
+
+* **Course name**: Fundamentals of Computer Architecture
+* **Code discipline**: XXX
+* **Subject area**: Computer Science Fundamentals
+
+
+Short Description
+-----------------
+
+
+This course covers the fundamental principles of modern computer systems and software/hardware interaction, the representation and execution of computer instructions, computer arithmetics.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+* Informatics
+* Basic programming skills
+* The basics of Boolean logic
+
+
+  
+
+
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Introduction to the Fundamental Concepts of Computer Architecture | 1. Key Components of a Computer System
+2. Fundamental Ideas of Computer Architecture
+3. Translation Hierarchy of a High-Level Program into Machine Code
+4. Performance Metrics of a Computer System
+ |
+| Computational Logic Implementation in a Computer System | 1. Logic Gates and Boolean Algebra
+2. Logic Circuits
+3. Combinational and Sequential Logic
+4. Number Systems
+5. The Basics of Verilog Hardware Description Language (HDL) Programming
+ |
+| Instruction Representation and Execution in a Computer System | 1. Instruction Set Architecture (ISA)
+2. The Overview of MIPS ISA
+3. Types of MIPS Instructions and Their Representation in a Binary Format
+4. Sample MIPS Assembly Programs
+ |
+| Computer Arithmetics | 1. Basic Arithmetic Operations (Bitwise, Shifts, Multiplication, Division, and Others)
+2. Overflow and Underflow Problems for Arithmetic Operations
+3. Arithmetic Operations with Floation Point Numbers
+4. Problems Related to Precision and Conversion for Floating Point Numbers
+ |
+| Processor Architecture | 1. Key Components of a Processor: Control and Arithmetic Logic Unit, Registers
+2. Processor Datapath and Control Signals
+3. The Notion of a Pipelined Execution, Pipeline Hazards, and Their Solutions
+4. A Simple and Pipelined Implementation Schemes of a Processor
+ |
+| Advanced Topics | 1. Computer Security and Vulnerabilities
+2. Graphics Processing Unit (GPU) and General-Purpose GPU Programming
+3. Modern Approaches for Memory Hierarchy Design
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+The main purpose of this course is to cover the fundamental theoretical principles of computer systems design. We first overview the key hardware components of a modern computer system, available performance metrics, and the general principles of computer architecture. We then discuss the representation and execution of computer instructions, instruction set architecture, the translation hierarchy of a high-level program into machine code. We also cover the elements of computer arithmetics, logic circuits, including combinational and sequential logic circuits. These theoretical principles are illustrated by using MIPS instruction set architecture, FPGA, and Verilog HDL programming language during the labs. We then study in details simple and pipelined implementation schemes of a processor, the idea of a pipelined execution, related hazards and their solutions. We complete the course by introducing several advanced topics, including computer security and vulnerabilities, GPU programming, and modern principles for memory hierarchy design.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Key components of a modern computer system
+* Available performance metrics for computer systems
+* Computer arithmetics operations, including floating point numbers
+* Number systems and conversion between them
+* Representation formats for computer instructions
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Fundamental principles of computer architecture (Moore’s law, memory hierarchy, multiprocessing, speculative execution, and others)
+* The design scheme of a modern processor
+* The interaction principles between software and hardware
+* Program representation and execution by a computer system
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* The design skills of logic circuits by using Verilog HDL programming language
+* FPGA programming by using Quartus Prime software
+* MIPS assembly programming (including MARS simulator)
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 70-89 | -
+ |
+| C. Satisfactory | 60-69 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Labs/seminar Classes | 15
+ |
+| Regular quizzes during tutorials (excluding 3 worst) | 5
+ |
+| Midterm Exam | 20
+ |
+| Final Exam | 60
+ |
+| Bonus points for optional FPGA projects | 5
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Handouts supplied by the instructor
+* Online resources shared by instructor
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4 | Section 5 | Section 6
+ |
+| --- | --- | --- | --- | --- | --- | --- |
+| Development of individual parts of software product code | 1 | 1 | 1 | 1 | 1 | 1
+ |
+| Homework and group projects | 1 | 1 | 1 | 1 | 1 | 1
+ |
+| Midterm evaluation | 1 | 1 | 1 | 0 | 0 | 0
+ |
+| Testing (written or computer based) | 1 | 1 | 1 | 1 | 1 | 1
+ |
+| Oral polls | 1 | 1 | 1 | 1 | 1 | 1
+ |
+| Discussions | 1 | 1 | 1 | 1 | 1 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Do you agree that main memory (RAM) is a non-volatile memory? | 1
+ |
+| Question | There are several types of memory available for computers, such as CPU cache, main memory (RAM), SSD, etc. What are the key differences between them? | 1
+ |
+| Question | What is the key principle behind the Von Neumann Architecture? | 1
+ |
+| Question | Specify a correct order for tools used during high-level program translation and execution: Compiler, Assebler, Linker, Loader; | 1
+ |
+| Question | Let a program run on a computer comprised of one processor only. Let us now increase the number of processors up to m>1, so that multiple instructions of that program can be executed in parallel. Assume that all processor speeds are the same. Do you agree that a program can never execute slower on m processors, as compared to the case of one processor? | 1
+ |
+| Question | Demonstration and description of key elements of an FPGA board (memory unit, PCI slot, clock generator, etc.); | 0
+ |
+| Question | Description of specific features of FPGA as compared to other integrated circuit devices; | 0
+ |
+| Question | Writing basic code for FPGA board; | 0
+ |
+| Question | Configuration and usage of the basic functionality in Quartus Prime software | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Convert decimal number 123 into base-5 format; | 1
+ |
+| Question | Do you agree that a S/R latch and a D flip-flop have different storage capacities? | 1
+ |
+| Question | Choose the key differences between SRAM and DRAM memory types: cost, power consumption, volatility, access speed, storage capacity, etc.; | 1
+ |
+| Question | Do you agree that one of the key differences between sequential and combinational logic circuits is the presence of memory elements? | 1
+ |
+| Question | Questions regarding the basic logic gates; | 0
+ |
+| Question | Assignments to design simple logic circuits with 2-3 logic gates on a white board; | 0
+ |
+| Question | Programming assignments in Quartus Prime software, to design and compile simple logic circuits; | 0
+ |
+| Question | Programming an FPGA board by using Verilog HDL in Quartus Prime environment, such as turning on or off leds based on a switch position; | 0
+ |
+| Question | Questions regarding the difference between combinational and sequential logic circuits; | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | How many bits are in one MIPS word? | 1
+ |
+| Question | Which MIPS directive would you use to create a string data? | 1
+ |
+| Question | For MIPS instruction set architecture (ISA), each register is reserved for a specific purpose. Describe the purpose of registers listed below: 
+
+
+
+v
+0
+,
+
+
+{\displaystyle v0,}
+
+{\displaystyle v0,}s0-
+
+
+
+s
+7
+,
+
+
+{\displaystyle s7,}
+
+{\displaystyle s7,}t0-$t7; | 1
+ |
+| Question | In MARS simulator for MIPS programming, all register values, that are displayed in the register viewer, start with prefix "0x". What is the meaning of this prefix? | 1
+ |
+| Question | Print a "Hello, World!" message in a console; | 0
+ |
+| Question | Computation of a simple arithmetic expression for integer parameters; | 0
+ |
+| Question | Computation of the first 10 Fibonacci numbers; | 0
+ |
+| Question | Implementation of more advanced program structures, such as conditional loops | 0
+ |
+
+
+#### Section 4
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Assume that two MIPS registers, 
+
+
+
+s
+0
+a
+n
+d
+
+
+{\displaystyle s0and}
+
+{\displaystyle s0and}s1, contain the following binary data: 
+
+
+
+s
+0
+:
+00100000
+;
+
+
+{\displaystyle s0:00100000;}
+
+{\displaystyle s0:00100000;}s1: 01010101 (For simplicity, we assume 8-bit registers, rather that 32) What is the value of 
+
+
+
+s
+1
+a
+f
+t
+e
+r
+t
+h
+e
+e
+x
+e
+c
+u
+t
+i
+o
+n
+o
+f
+t
+h
+e
+f
+o
+l
+l
+o
+w
+i
+n
+g
+i
+n
+s
+t
+r
+u
+c
+t
+i
+o
+n
+?
+:
+s
+l
+l
+
+
+{\displaystyle s1aftertheexecutionofthefollowinginstruction?:sll}
+
+{\displaystyle s1aftertheexecutionofthefollowinginstruction?:sll}s1, $s0, 4 | 1
+ |
+| Question | What is a "register spilling" in the context of MIPS instruction set architecture? | 1
+ |
+| Question | Do you agree with the following statement? In some cases, MIPS logical shift operations, sll and srl, can be used as an efficient alternative to multiplication and division operations, mul and div. | 1
+ |
+| Question | Do you agree that overflow and underflow exceptions correspond to cases, when the result of an arithmetic operation surpasses and subceeds, respectively, the maximum and the minimum value for an appropriate data type returned by that arithmetic operation? | 1
+ |
+| Question | Division of two floating-point numbers; | 0
+ |
+| Question | Conversion of Fahrenheit into Celsius temperature, and vice versa; | 0
+ |
+| Question | Computation of a sphere surphase area; | 0
+ |
+| Question | Questions regarding the execution of arithmetic operations with interger and floating-point values | 0
+ |
+
+
+#### Section 5
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Do you agree that the key motivation for the CPU pipelining is to speed-up the execution of a program by exploring multiple CPU cores? | 1
+ |
+| Question | Which CPU block(s) is/are accessed during the execution of the following instruction? lw 
+
+
+
+1
+,
+5
+(
+
+
+{\displaystyle 1,5(}
+
+{\displaystyle 1,5(}2) | 1
+ |
+| Question | What are 5 major stages of a pipelined instruction execution? | 1
+ |
+| Question | Do you agree that, for a processor with 5 pipelined stages, the number of concurrently executed instructions is up to 4? | 1
+ |
+| Question | There are several types of processors available, including single-cycle and multicycle.The major advantage of a single-cycle processor is the simplicity of its design. But what is its key drawback? | 1
+ |
+| Question | Design of a testbench in ModelSim for Quartus Prime programming environment; | 0
+ |
+| Question | The design of Half-Adder, Full-Adder, Ripple Carry Adder by using Verilog HDL in Quartus Prime | 0
+ |
+| Question | Testing the correctness of Verilog HDL design by using ModelSim | 0
+ |
+
+
+#### Section 6
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Cold boot attack explores vulnerabilities in a memory dump mechanism. What is a memory dump? | 1
+ |
+| Question | Below is a list of possible vulnerability attacks. Choose the one(s) that explore(s) vulnerabilities in a speculative execution of modern processors: Meltdown, Foreshadow, Cold boot attack, Spectre, No choice is correct; | 1
+ |
+| Question | Choose the most precise definition for a side-channel attack: An attack that explores vulnerabilities in the hardware implementation of a computer system, An attack that explores vulnerabilities in the software components of a computer system; | 1
+ |
+| Question | Do you agree that Meltdown and Spectre vulnerabilities both explore race conditions in existing memory circuits? | 1
+ |
+| Question | Programming assignment to implement Multiplexor using Verilog HDL in Quartus Prime; | 0
+ |
+| Question | Performance optimization of a Verilog HDL design; | 0
+ |
+| Question | The design of a simple Arithmetic-Logic Unit (ALU); | 0
+ |
+| Question | Revision questions | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. Briefly describe the principles of Von Neumann architecture. Illustrate with a diagram.
+2. Describe the steps that transform a program written in a high-level language such as C into a representation that is directly executed by a computer processor. Illustrate with a diagram; provide a brief description for each step.
+3. Consider three different processors P1, P2, and P3 executing the same instruction set. P1 has a 3 GHz clock rate and a CPI of 1.5. P2 has a 2.5 GHz clock rate and a CPI of 1.0. P3 has a 4.0 GHz clock rate and has a CPI of 2.2. Answer the following questions: a) Which processor has the highest performance expressed in instructions per second? b) If the processors each execute a program in 10 seconds, find the number of cycles and the number of instructions. c) We are trying to reduce the execution time by 30% but this leads to an increase of 20% in the CPI. What clock rate should we have to get this time reduction?
+
+
+**Section 2**
+
+
+
+1. Prove that the AND and NOT logic gates can be implemented by using only the NOR logic gate.
+2. What are the S/R latch and D latch? Draw the respective logic circuits. Describe the differences between them.
+3. Briefly describe the key difference(s) between combinational and sequential logic circuits.
+4. Define what a multiplexor logic circuit is (with an arbitrary number of inputs). Provide a truth table for a 2-to-1 multiplexor. Provide a logic circuit implementing a 2-to-1 multiplexor, that uses AND, NOT, and OR logic gates. Describe a Verilog module implementing such a logic circuit of a 2-to-1 multiplexor.
+
+
+**Section 3**
+
+
+
+1. Translate the following MIPS code to C (or pseudocode). Assume that variables f, g, h, and i are assigned to registers 
+
+
+
+s
+0
+,
+
+
+{\displaystyle s0,}
+
+![{\displaystyle s0,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0774f15776777fa7c649bb32f3eba630bc161064)s1, 
+
+
+
+s
+2
+,
+a
+n
+d
+
+
+{\displaystyle s2,and}
+
+![{\displaystyle s2,and}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ded29f0beb1166aed71401647dce9fee610707a3)s3, respectively. Code to translate: sub 
+
+
+
+t
+0
+,
+
+
+{\displaystyle t0,}
+
+![{\displaystyle t0,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0b436be8d28cf3be0c8fe3b2426b79e11e4951be)s1, 
+
+
+
+s
+2
+;
+a
+d
+d
+i
+<
+m
+a
+t
+h
+>
+t
+0
+,
+
+
+{\displaystyle s2;addi<math>t0,}
+
+![{\displaystyle s2;addi<math>t0,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9d69f57e93a67f1d52ce060133245188e74025a0)t0, 3; add 
+
+
+
+s
+0
+,
+
+
+{\displaystyle s0,}
+
+![{\displaystyle s0,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0774f15776777fa7c649bb32f3eba630bc161064)s3, </math>t0
+2. Assume that two MIPS registers, 
+
+
+
+
+
+s
+0
+a
+n
+d
+
+
+
+
+{\displaystyle {\textstyle s0and}}
+
+![{\displaystyle {\textstyle s0and}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2e614dfbf70d48cb55a9eab091117a7faf8c55c4) s1, contain the following binary data (for simplicity, we assume 8-bit registers, rather that 32): 
+
+
+
+s
+0
+:
+00100000
+;
+
+
+{\displaystyle s0:00100000;}
+
+![{\displaystyle s0:00100000;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c12f86ba6a51109fac819f46211a693a2379e54a)s1: 01010101. What is the value of register 
+
+
+
+s
+1
+a
+f
+t
+e
+r
+t
+h
+e
+e
+x
+e
+c
+u
+t
+i
+o
+n
+o
+f
+t
+h
+e
+f
+o
+l
+l
+o
+w
+i
+n
+g
+M
+I
+P
+S
+i
+n
+s
+t
+r
+u
+c
+t
+i
+o
+n
+?
+:
+s
+l
+l
+
+
+{\displaystyle s1aftertheexecutionofthefollowingMIPSinstruction?:sll}
+
+![{\displaystyle s1aftertheexecutionofthefollowingMIPSinstruction?:sll}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7201a3a236b16509cde095a65181365be09482c3)s1, $s0, 4.
+3. List and describe the purpose of general-purpose MIPS registers.
+
+
+**Section 4**
+
+
+
+1. Briefly describe the overflow and underflow problems for arithmetic operations.
+2. Describe the difference between executing arithmetic operations with integers and floating-point values for a MIPS processor.
+3. What is a precision problem for a floating-point operation?
+
+
+**Section 5**
+
+
+
+1. What is a Program Counter (PC) register of a processor?
+2. Describe the principle of a pipelined CPU execution. Provide a diagram illustrating the concept. Briefly describe the 5 key stages of a classical pipeline.
+3. What are the key differences between Control Unit (CU) and Arithmetic Logic Unit (ALU) of a processor? Which purposes do they serve?
+4. What is a CPU datapath?
+
+
+**Section 6**
+
+
+
+1. What is an out-of-order execution? What hardware features of CPU implementation, in addition to an out-of-order execution, are exploited by Meltdown vulnerability? How serious is Meltdown vulnerability?
+2. What is an instruction-level parallelism?
+3. Describe the idea of a general-purpose GPU programming.
+4. Briefly explain the working principles of a CPU cache.
+5. Discuss advantages and drawbacks of a hierarchical memory model for computer systems.
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+**Section 5**
+
+
+**Section 6**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__control_theory.md

@@ -0,0 +1,1433 @@
+
+
+
+
+
+
+
+BSc: Control Theory
+===================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Control Theory](#Control_Theory)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Control Theory
+==============
+
+
+* **Course name**: Control Theory
+* **Code discipline**: [S20]
+* **Subject area**: Sensors and actuators; Robotic control.
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: Introduction to Linear Control, Stability of linear dynamical systems; Controller design; Sensing, observers, Adaptive control.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+* [CSE204 - Geometry And Linear Algebra II](https://eduwiki.innopolis.university/index.php/BSc:AnalyticGeometryAndLinearAlgebraI): Semidefinite matrices, Eigenvalues, Eigendecomposition (weak prerequisite), matrix exponentials (weak prerequisite), SVD (weak prerequisite)
+* [CSE205 - Differential Equations](https://eduwiki.innopolis.university/index.php/BSc:DifferentialEquations)
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Introduction to Linear Control, Stability of linear dynamical systems | 1. Control, introduction. Examples.
+2. Single input single output (SISO) systems. Block diagrams.
+3. From linear differential equations to state space models.
+4. DC motor as a linear system.
+5. Spring-damper as a linear system.
+6. The concept of stability of the control system. Proof of stability for a linear system with negative real parts of eigenvalues.
+7. Multi input multi output (MIMO) systems.
+8. Linear Time Invariant (LTI) systems and their properties.
+9. Linear Time Varying (LTV) systems and their properties.
+10. Transfer function representation.
+ |
+| Controller design. | 1. Stabilizing control. Control error.
+2. Proportional control.
+3. PD control. Order of a system and order of the controller.
+4. PID control.
+5. P, PD and PID control for DC motor.
+6. Trajectory tracking. Control input types. Standard inputs (Heaviside step function, Dirac delta function, sine wave).
+7. Tuning PD and PID. Pole placement.
+8. Formal statements about stability. Lyapunov theory.
+9. Types of stability; Lyapunov stability, asymptotic stability, exponential stability.
+10. Eigenvalues in stability theory. Reasoning about solution of the autonomous linear system.
+11. Stability proof for PD control.
+12. Stability in stabilizing control and trajectory tracking.
+13. Frequency response. Phase response.
+14. Optimal control of linear systems. From Hamilton-Jacobi-Bellman to algebraic Riccati equation. LQR.
+15. Stability of LQR.
+16. Controllability.
+ |
+| Sensing, observers, Adaptive control | 1. Modelling digital sensors: quantization, discretization, lag.
+2. Modelling sensor noise. Gaussian noise. Additive models. Multiplicative models. Dynamic sensor models.
+3. Observability.
+4. Filters.
+5. State observers.
+6. Optimal state observer for linear systems.
+7. Linearization of nonlinear systems.
+8. Linearization along trajectory.
+9. Linearization of Inverted pendulum dynamics.
+10. Model errors. Differences between random disturbances and unmodeled dynamics/processes.
+11. Adaptive control.
+12. Control for sets of linear systems.
+13. Discretization, discretization error.
+14. Control for discrete linear systems.
+15. Stability of discrete linear systems.
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+Linear Control Theory is both an active tool for modern industrial engineering and a prerequisite for most of the state-of-the-art level control techniques and the corresponding courses. With this in mind, the Linear Control course is both building a foundation for the following development of the student as a learner in the fields of Robotics, Control, Nonlinear Dynamics and others, as well as it is one of the essential practical courses in the engineering curricula.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* methods for control synthesis (linear controller gain tuning)
+* methods for controller analysis
+* methods for sensory data processing for linear systems
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* State-space models
+* Eigenvalue analysis for linear systems
+* Proportional and PD controllers
+* How to stabilize a linear system
+* Lyapunov Stability
+* How to check if the system is controllable
+* Observer design
+* Sources of sensor noise
+* Filters
+* Adaptive Control
+* Optimal Control
+* Linear Quadratic Regulator
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Turn a system of linear differential equations into a state-space model.
+* Design a controller by solving Algebraic Riccati eq.
+* Find if a system is stable or not, using eigenvalue analysis.
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 85-100 | -
+ |
+| B. Good | 70-84 | -
+ |
+| C. Satisfactory | 50-69 | -
+ |
+| D. Poor | 0-49 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Labs/seminar classes | 30
+ |
+| Interim performance assessment | 20
+ |
+| Exams | 50
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Ogata, K., 1994. Solving control engineering problems with MATLAB. Englewood Cliffs, NJ: Prentice-Hall.
+* Williams, R.L. and Lawrence, D.A., 2007. Linear state-space control systems. John Wiley & Sons.
+* Ogata, K., 1995. Discrete-time control systems (Vol. 2, pp. 446-480). Englewood Cliffs, NJ: Prentice Hall.
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Homework and group projects | 1 | 1 | 1
+ |
+| Testing (written or computer based) | 1 | 0 | 0
+ |
+| Reports | 1 | 1 | 1
+ |
+| Midterm evaluation | 0 | 1 | 0
+ |
+| Discussions | 0 | 1 | 0
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is a linear dynamical system? | 1
+ |
+| Question | What is an LTI system? | 1
+ |
+| Question | What is an LTV system? | 1
+ |
+| Question | Provide examples of LTI systems. | 1
+ |
+| Question | What is a MIMO system? | 1
+ |
+| Question | Simulate a linear dynamic system as a higher order differential equation or in state-space form (Language is a free choice, Python and Google Colab are recommended. Use built-in solvers or implement Runge-Kutta or Euler method. | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is stability in the sense of Lyapunov? | 1
+ |
+| Question | What is stabilizing control? | 1
+ |
+| Question | What is trajectory tracking? | 1
+ |
+| Question | Why the control for a state-space system does not include the derivative of the state variable in the feedback law? | 1
+ |
+| Question | How can a PD controller for a second-order linear mechanical system can be re-written in the state-space form? | 1
+ |
+| Question | Write a closed-loop dynamics for an LTI system with a proportional controller. | 1
+ |
+| Question | Give stability conditions for an LTI system with a proportional controller. | 1
+ |
+| Question | Provide an example of a LTV system with negative eigenvalues that is not stable. | 1
+ |
+| Question | Write algebraic Riccati equation for a standard additive quadratic cost. | 1
+ |
+| Question | Derive algebraic Riccati equation for a given additive quadratic cost. | 1
+ |
+| Question | Derive differential Riccati equation for a standard additive quadratic cost. | 1
+ |
+| Question | What is the meaning of the unknown variable in the Riccati equation? What are its property in case of LTI dynamics. | 1
+ |
+| Question | What is a frequency response? | 1
+ |
+| Question | What is a phase response? | 1
+ |
+| Question | Design control for an LTI system using pole placement. | 0
+ |
+| Question | Design control for an LTI system using Riccati (LQR). | 0
+ |
+| Question | Simulate an LTI system with LQR controller. | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What are the sources of sensor noise? | 1
+ |
+| Question | How can we combat the lack of sensory information? | 1
+ |
+| Question | When it is possible to combat the lack of sensory information? | 1
+ |
+| Question | How can we combat the sensory noise? | 1
+ |
+| Question | What is an Observer? | 1
+ |
+| Question | What is a filter? | 1
+ |
+| Question | How is additive noise different from multiplicative noise? | 1
+ |
+| Question | Simulate an LTI system with proportional control and sensor noise. | 0
+ |
+| Question | Design an observer for an LTI system with proportional control and lack of sensory information. | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. Convert a linear differential equation into a state space form.
+2. Convert a transfer function into a state space form.
+3. Convert a linear differential equation into a transfer function.
+4. What does it mean for a linear differential equation to be stable?
+
+
+**Section 2**
+
+
+
+1. You have a linear system: 
+
+
+
+
+
+
+
+
+x
+˙
+
+
+
+=
+A
+x
++
+B
+u
+
+
+
+
+{\displaystyle {\displaystyle {\dot {x}}=Ax+Bu}}
+
+![{\displaystyle {\displaystyle {\dot {x}}=Ax+Bu}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e4bf3ada8bafed299cdfaacc34637b816d2b4477) and a cost function: a) 
+
+
+
+
+
+J
+=
+∫
+(
+
+x
+
+⊤
+
+
+Q
+x
++
+
+u
+
+⊤
+
+
+I
+u
+)
+d
+t
+
+
+
+
+{\displaystyle {\textstyle J=\int (x^{\top }Qx+u^{\top }Iu)dt}}
+
+![{\displaystyle {\textstyle J=\int (x^{\top }Qx+u^{\top }Iu)dt}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c274707dff116b2105e84a0125a9197b45760f83) b) 
+
+
+
+
+
+J
+=
+∫
+(
+
+x
+
+⊤
+
+
+I
+x
++
+
+u
+
+⊤
+
+
+R
+u
+)
+d
+t
+
+
+
+
+{\displaystyle {\textstyle J=\int (x^{\top }Ix+u^{\top }Ru)dt}}
+
+![{\displaystyle {\textstyle J=\int (x^{\top }Ix+u^{\top }Ru)dt}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2e39947b7aa2e15bcf70da52199efe8a4bd24514) Write Riccati eq. and find LQR gain analytically.
+2. You have a linear system a) 
+
+
+
+
+
+
+
+[
+
+
+
+
+
+
+
+x
+˙
+
+
+
+
+1
+
+
+
+
+
+
+
+
+
+
+x
+˙
+
+
+
+
+2
+
+
+
+
+
+]
+
+
+=
+
+
+[
+
+
+
+1
+
+
+10
+
+
+
+
+−
+3
+
+
+4
+
+
+
+]
+
+
+
+
+[
+
+
+
+
+x
+
+1
+
+
+
+
+
+
+
+x
+
+2
+
+
+
+
+
+]
+
+
+
+
+
+
+{\displaystyle {\textstyle {\begin{bmatrix}{\dot {x}}\_{1}\\{\dot {x}}\_{2}\end{bmatrix}}={\begin{bmatrix}1&10\\-3&4\end{bmatrix}}{\begin{bmatrix}x\_{1}\\x\_{2}\end{bmatrix}}}}
+
+![{\displaystyle {\textstyle {\begin{bmatrix}{\dot {x}}_{1}\\{\dot {x}}_{2}\end{bmatrix}}={\begin{bmatrix}1&10\\-3&4\end{bmatrix}}{\begin{bmatrix}x_{1}\\x_{2}\end{bmatrix}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d1bc5bdf4ddf06f4fa774d9346aca4a2728a0b50) b) 
+
+
+
+
+
+
+
+[
+
+
+
+
+
+
+
+x
+˙
+
+
+
+
+1
+
+
+
+
+
+
+
+
+
+
+x
+˙
+
+
+
+
+2
+
+
+
+
+
+]
+
+
+=
+
+
+[
+
+
+
+−
+2
+
+
+1
+
+
+
+
+2
+
+
+40
+
+
+
+]
+
+
+
+
+[
+
+
+
+
+x
+
+1
+
+
+
+
+
+
+
+x
+
+2
+
+
+
+
+
+]
+
+
+
+
+
+
+{\displaystyle {\textstyle {\begin{bmatrix}{\dot {x}}\_{1}\\{\dot {x}}\_{2}\end{bmatrix}}={\begin{bmatrix}-2&1\\2&40\end{bmatrix}}{\begin{bmatrix}x\_{1}\\x\_{2}\end{bmatrix}}}}
+
+![{\displaystyle {\textstyle {\begin{bmatrix}{\dot {x}}_{1}\\{\dot {x}}_{2}\end{bmatrix}}={\begin{bmatrix}-2&1\\2&40\end{bmatrix}}{\begin{bmatrix}x_{1}\\x_{2}\end{bmatrix}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eb9e56fd8715942dddcf766918860bea58b3ab17) Prove whether or not it is stable.
+3. You have a linear system a) 
+
+
+
+
+
+
+
+[
+
+
+
+
+
+
+
+x
+˙
+
+
+
+
+1
+
+
+
+
+
+
+
+
+
+
+x
+˙
+
+
+
+
+2
+
+
+
+
+
+]
+
+
+=
+
+
+[
+
+
+
+1
+
+
+10
+
+
+
+
+−
+3
+
+
+4
+
+
+
+]
+
+
+
+
+[
+
+
+
+
+x
+
+1
+
+
+
+
+
+
+
+x
+
+2
+
+
+
+
+
+]
+
+
++
+
+
+[
+
+
+
+
+u
+
+1
+
+
+
+
+
+
+
+u
+
+2
+
+
+
+
+
+]
+
+
+
+
+
+
+{\displaystyle {\displaystyle {\begin{bmatrix}{\dot {x}}\_{1}\\{\dot {x}}\_{2}\end{bmatrix}}={\begin{bmatrix}1&10\\-3&4\end{bmatrix}}{\begin{bmatrix}x\_{1}\\x\_{2}\end{bmatrix}}+{\begin{bmatrix}u\_{1}\\u\_{2}\end{bmatrix}}}}
+
+![{\displaystyle {\displaystyle {\begin{bmatrix}{\dot {x}}_{1}\\{\dot {x}}_{2}\end{bmatrix}}={\begin{bmatrix}1&10\\-3&4\end{bmatrix}}{\begin{bmatrix}x_{1}\\x_{2}\end{bmatrix}}+{\begin{bmatrix}u_{1}\\u_{2}\end{bmatrix}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/87faecb7b594fc89188ec0b29cc1549a60a38168) b) 
+
+
+
+
+
+
+
+[
+
+
+
+
+
+
+
+x
+˙
+
+
+
+
+1
+
+
+
+
+
+
+
+
+
+
+x
+˙
+
+
+
+
+2
+
+
+
+
+
+]
+
+
+=
+
+
+[
+
+
+
+−
+2
+
+
+1
+
+
+
+
+2
+
+
+40
+
+
+
+]
+
+
+
+
+[
+
+
+
+
+x
+
+1
+
+
+
+
+
+
+
+x
+
+2
+
+
+
+
+
+]
+
+
++
+
+
+[
+
+
+
+
+u
+
+1
+
+
+
+
+
+
+
+u
+
+2
+
+
+
+
+
+]
+
+
+
+
+
+
+{\displaystyle {\displaystyle {\begin{bmatrix}{\dot {x}}\_{1}\\{\dot {x}}\_{2}\end{bmatrix}}={\begin{bmatrix}-2&1\\2&40\end{bmatrix}}{\begin{bmatrix}x\_{1}\\x\_{2}\end{bmatrix}}+{\begin{bmatrix}u\_{1}\\u\_{2}\end{bmatrix}}}}
+
+![{\displaystyle {\displaystyle {\begin{bmatrix}{\dot {x}}_{1}\\{\dot {x}}_{2}\end{bmatrix}}={\begin{bmatrix}-2&1\\2&40\end{bmatrix}}{\begin{bmatrix}x_{1}\\x_{2}\end{bmatrix}}+{\begin{bmatrix}u_{1}\\u_{2}\end{bmatrix}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f501668baf1f22b9200a11c2465d2ef3d73d270f) Your controller is: a) 
+
+
+
+
+
+
+
+[
+
+
+
+
+u
+
+1
+
+
+
+
+
+
+
+u
+
+2
+
+
+
+
+
+]
+
+
+=
+
+
+[
+
+
+
+100
+
+
+1
+
+
+
+
+1
+
+
+20
+
+
+
+]
+
+
+
+
+[
+
+
+
+
+x
+
+1
+
+
+
+
+
+
+
+x
+
+2
+
+
+
+
+
+]
+
+
+
+
+
+
+{\displaystyle {\textstyle {\begin{bmatrix}u\_{1}\\u\_{2}\end{bmatrix}}={\begin{bmatrix}100&1\\1&20\end{bmatrix}}{\begin{bmatrix}x\_{1}\\x\_{2}\end{bmatrix}}}}
+
+![{\displaystyle {\textstyle {\begin{bmatrix}u_{1}\\u_{2}\end{bmatrix}}={\begin{bmatrix}100&1\\1&20\end{bmatrix}}{\begin{bmatrix}x_{1}\\x_{2}\end{bmatrix}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91b22a42571dee07244b61cd734f77245322356a) b) 
+
+
+
+
+
+
+
+[
+
+
+
+
+u
+
+1
+
+
+
+
+
+
+
+u
+
+2
+
+
+
+
+
+]
+
+
+=
+
+
+[
+
+
+
+7
+
+
+2
+
+
+
+
+2
+
+
+5
+
+
+
+]
+
+
+
+
+[
+
+
+
+
+x
+
+1
+
+
+
+
+
+
+
+x
+
+2
+
+
+
+
+
+]
+
+
+
+
+
+
+{\displaystyle {\textstyle {\begin{bmatrix}u\_{1}\\u\_{2}\end{bmatrix}}={\begin{bmatrix}7&2\\2&5\end{bmatrix}}{\begin{bmatrix}x\_{1}\\x\_{2}\end{bmatrix}}}}
+
+![{\displaystyle {\textstyle {\begin{bmatrix}u_{1}\\u_{2}\end{bmatrix}}={\begin{bmatrix}7&2\\2&5\end{bmatrix}}{\begin{bmatrix}x_{1}\\x_{2}\end{bmatrix}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4872fd9ba71d2c96d6a2fe5237bcdf4933f44566) Prove whether the control system is stable.
+4. You have linear dynamics:
+
+
+a) 
+
+
+
+
+
+2
+
+
+
+q
+¨
+
+
+
++
+3
+
+
+
+q
+˙
+
+
+
+−
+5
+q
+=
+u
+
+
+
+
+{\displaystyle {\textstyle 2{\ddot {q}}+3{\dot {q}}-5q=u}}
+
+![{\displaystyle {\textstyle 2{\ddot {q}}+3{\dot {q}}-5q=u}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bbd10b4b71db048873878c3a52d3a8e7cb3a3efc) 
+b) 
+
+
+
+
+
+10
+
+
+
+q
+¨
+
+
+
+−
+7
+
+
+
+q
+˙
+
+
+
++
+10
+q
+=
+u
+
+
+
+
+{\displaystyle {\textstyle 10{\ddot {q}}-7{\dot {q}}+10q=u}}
+
+![{\displaystyle {\textstyle 10{\ddot {q}}-7{\dot {q}}+10q=u}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cdf9789ac84e4d4747fe46f29e7a19293789d1aa) 
+c) 
+
+
+
+
+
+15
+
+
+
+q
+¨
+
+
+
++
+17
+
+
+
+q
+˙
+
+
+
++
+11
+q
+=
+2
+u
+
+
+
+
+{\displaystyle {\textstyle 15{\ddot {q}}+17{\dot {q}}+11q=2u}}
+
+![{\displaystyle {\textstyle 15{\ddot {q}}+17{\dot {q}}+11q=2u}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/22376da4802494e1e78b5b811b2dafa40ce3c981) 
+d) 
+
+
+
+
+
+20
+
+
+
+q
+¨
+
+
+
+−
+
+
+
+q
+˙
+
+
+
+−
+2
+q
+=
+−
+u
+
+
+
+
+{\displaystyle {\textstyle 20{\ddot {q}}-{\dot {q}}-2q=-u}}
+
+![{\displaystyle {\textstyle 20{\ddot {q}}-{\dot {q}}-2q=-u}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c7cac19e27fe1c85ac14a726fd2cb931c1a9858a) 
+If 
+
+
+
+
+
+u
+=
+0
+
+
+
+
+{\displaystyle {\textstyle u=0}}
+
+![{\displaystyle {\textstyle u=0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b9fd97947cd2d67a0459307e8fa3680b8872db21) , which are stable (a - d)?
+Find 
+
+
+
+
+
+u
+
+
+
+
+{\displaystyle {\textstyle u}}
+
+![{\displaystyle {\textstyle u}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5862c118ef85972552f0f1f2c3993b65b46a2714) that makes the dynamics stable.
+Write transfer functions for the cases 
+
+
+
+
+
+u
+=
+0
+
+
+
+
+{\displaystyle {\textstyle u=0}}
+
+![{\displaystyle {\textstyle u=0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b9fd97947cd2d67a0459307e8fa3680b8872db21) and 
+
+
+
+
+
+u
+=
+−
+100
+x
+
+
+
+
+{\displaystyle {\textstyle u=-100x}}
+
+![{\displaystyle {\textstyle u=-100x}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/912419475f3d35d59dc17db8af0df6724143568b) .
+
+
+
+1. What is the difference between exponential stability, asymptotic stability and optimality?
+
+
+**Section 3**
+
+
+
+1. Write a model of a linear system with additive Gaussian noise.
+2. Derive and implement an observer.
+3. Derive and implement a filter.
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__data_mining.md

@@ -0,0 +1,160 @@
+
+
+
+
+
+
+
+BSc: Data Mining
+================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Data Mining](#Data_Mining)
+	+ [1.1 Administrative details](#Administrative_details)
+	+ [1.2 Prerequisites](#Prerequisites)
+	+ [1.3 Course outline](#Course_outline)
+	+ [1.4 Expected learning outcomes](#Expected_learning_outcomes)
+	+ [1.5 Expected acquired core competences](#Expected_acquired_core_competences)
+	+ [1.6 Detailed topics covered in the course](#Detailed_topics_covered_in_the_course)
+	+ [1.7 Textbook](#Textbook)
+	+ [1.8 Reference material](#Reference_material)
+	+ [1.9 Required computer resources](#Required_computer_resources)
+	+ [1.10 Evaluation](#Evaluation)
+
+
+
+Data Mining
+===========
+
+
+* **Course name:** Data Mining
+* **Course number:** XYZ
+* **Knowledge area:** Data Science
+
+
+Administrative details
+----------------------
+
+
+* **Faculty:** Computer Science and Engineering
+* **Year of instruction:** 3rd year of BS
+* **Semester of instruction:** 2nd semester
+* **No. of Credits:** 4 ECTS
+* **Total workload on average:** 144 hours overall.
+* **Class lecture hours:** 2 per week.
+* **Class tutorial hours:** 0
+* **Lab hours:** 2 per week.
+* **Individual lab hours:** 2 per week
+* **Frequency:** weekly throughout the semester.
+* **Grading mode:** letters: A, B, C, D.
+
+
+Prerequisites
+-------------
+
+
+* [CSE201 — Mathematical Analysis I](https://eduwiki.innopolis.university/index.php/BSc:_Mathematical_Analysis_I)
+* [CSE201 — Mathematical Analysis II](https://eduwiki.innopolis.university/index.php/BSc:_Mathematical_Analysis_II)
+* [CSE202 — Analytical Geometry and Linear Algebra I](https://eduwiki.innopolis.university/index.php/BSc:_Analytic_Geometry_And_Linear_Algebra_I)
+* [CSE204 — Analytic Geometry And Linear Algebra II](https://eduwiki.innopolis.university/index.php/BSc:_Analytic_Geometry_And_Linear_Algebra_II)
+* [CSE206 — Probability And Statistics](https://eduwiki.innopolis.university/index.php/BSc:_Probability_And_Statistics)
+* [CSE117 — Data Structures and Algorithms](https://eduwiki.innopolis.university/index.php/BSc:_Data_Structures_Algorithms)
+* [CSE113 — Philosophy I - (Discrete Math and Logic)](https://eduwiki.innopolis.university/index.php/BSc:Logic_and_Discrete_Mathematics)
+
+
+Course outline
+--------------
+
+
+This course is designed for undergraduate students to provide core techniques of data processing and applications. Data Mining is an analytic process, which explores large data sets (also known as big data) to discover consistent patterns. This computational process involves a use of methods at the intersection of artificial intelligence, machine learning, statistics, and database systems. This course will discuss advanced algorithms for classification, clustering, association analysis, and mining social network analysis. The subjects are treated both theoretically and practically through lab sessions.
+
+
+
+Expected learning outcomes
+--------------------------
+
+
+* Understand the entire chain of data processing
+* Understand principle theories, models, tools and techniques
+* Analyze and apply adequate models for new problems
+* Understand new data mining tasks and provide solutions in different domains
+* Design an appropriate model to cope with new requirements
+
+
+Expected acquired core competences
+----------------------------------
+
+
+* Latest trends, algorithms, technologies in big data
+* Ability to determine appropriate approaches towards new challenges
+* Proficiency in data analysis and performance evaluations
+* Application of models, combination of multiple approaches, adaptation to interdisciplinary fields
+
+
+Detailed topics covered in the course
+-------------------------------------
+
+
+* Foundations of interaction design
+* Data Preprocessing
+* Data Warehouse
+* Association Rules
+* Frequent Pattern mining
+* Classification
+* Clustering
+* Recommendation Systems
+* Mining graphs
+* Mining data streams
+* Neural Networks
+* Outlier Detection
+* Dimensionality Deduction
+
+
+Textbook
+--------
+
+
+* Jiawei Han, Micheline Kamber and Jian Pei. *Data Mining: Concepts and Techniques (3nd Edition)*
+
+
+Reference material
+------------------
+
+
+* Jure Leskovec, Anand Rajaraman and Jeffrey D. Ullman. *Mining of Massive Datasets*
+
+
+Required computer resources
+---------------------------
+
+
+NA
+
+
+
+Evaluation
+----------
+
+
+* Individual Assignments (30%)
+* Course Project (20%)
+* Mid-term Exam (20%)
+* Final Exam (30%)
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__data_structures_algorithms.md

@@ -0,0 +1,396 @@
+
+
+
+
+
+
+
+BSc: Data Structures Algorithms
+===============================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Data Structures and Algorithms](#Data_Structures_and_Algorithms)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Data Structures and Algorithms
+==============================
+
+
+* **Course name**: Data Structures and Algorithms
+* **Code discipline**: —
+* **Subject area**:
+
+
+Short Description
+-----------------
+
+
+This course provides an intensive treatment of a cross-section of the key elements of algorithms and data-structures, with an emphasis on implementing them in modern programming environments, and using them to solve real-world problems. The course will begin with the fundamentals of searching, sorting, lists, stacks, and queues, but will quickly build to cover more advanced topics, including trees, graphs, and algorithmic strategies. It will also cover the analysis of the performance and tractability of algorithms and will build on the concept of Abstract Data Types. A key focus of the course is on effective implementation and good design principles.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+* CSE101 - Introduction to Programming: OOP, Pointers, and Functional Programming
+* CSE201 - Mathematical Analysis I
+* CSE113 - Logic and Discrete Mathematics
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Elementary Data Structures, Algorithmic Complexity and Approaches | 1. Algorithms and Their Analysis
+2. Elementary Data Structures
+3. Hashing Map and Collision Handling
+4. Algorithmic Strategies
+ |
+| Sorting Algorithms and Trees | 1. Comparison and Non-comparison Sort
+2. Binary Search Tree
+3. Balanced Binary Search Trees
+4. Tree Traversals
+5. Priority Queues and Binary Heaps
+ |
+| Graphs | 1. Graph Representations
+2. Searching in Graphs
+3. Minimum Spanning Tree
+4. Shortest Path
+5. Max-flow Min-cut
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+This course helps you master the following concepts: Algorithms; Algorithm Analysis; Algorithmic Strategies; Data Structures.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Algorithms
+* Abstract Data Types
+* Data Structures
+* Algorithmic Strategies
+* Asymptotic Analysis
+* Amortized Analysis
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Difference between different abstract data types and data structures
+* How to perform asymptotic and amortized analysis
+* Difference between various algorithmic strategies
+* Different algorithms: such as sorting, searching, etc.
+* Different types of tree ADTs, their properties related algorithms
+* Graphs, their properties, and related algorithms
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Algorithmic strategies to solve real-life problems
+* Asymptotic analysis to Analyze algorithms and software’s complexity
+* Trees and Graphs (and their theory) to solve complex problems
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Labs/seminar classes | 0
+ |
+| Interim performance assessment | 30
+ |
+| Exams | 70
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. Introduction to Algorithms. The MIT Press 2009.
+* M. T. Goodrich, R. Tamassia, and M. H. Goldwasser. Data Structures and Algorithms in Java. WILEY 2014.
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Teaching and Learning Methods within each section
+| Teaching Techniques | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Development of individual parts of software product code | 1 | 1 | 1
+ |
+| Homework and group projects | 1 | 1 | 1
+ |
+| Midterm evaluation | 1 | 1 | 1
+ |
+| Testing (written or computer based) | 1 | 1 | 1
+ |
+| Discussions | 1 | 1 | 1
+ |
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Question | 0 | 1 | 0
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | For a given function give an asymptotic upper bound using “big-Oh” notation | 1
+ |
+| Question | Compute the worst case running time of a given algorithm. | 1
+ |
+| Question | Insert items into a hashmap given a hash function and a collision handling scheme. | 1
+ |
+| Question | Given an algorithm, identify its algorithmic strategy | 1
+ |
+| Question | How to implement various data structures? | 0
+ |
+| Question | Implement an algorithm for a given task having a desired worst case time complexity | 0
+ |
+| Question | Describe the difference between different types algorithmic strategies | 0
+ |
+| Question | Implement a hashmap | 0
+ |
+| Question | Solve various practical problems using different algorithmic strategies | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Given a BST, answer different questions, such as (a) is the tree an AVL tree? What is the predecessor of a certain node? (b) Will after the removal of a certain node, the resulting tree will be a AVL tree or not? | 1
+ |
+| Question | Similar question as above but for other types of balanced binary search trees, including randomly built binary search trees. | 1
+ |
+| Question | Questions related to tree algorithms, such as tree traversals | 1
+ |
+| Question | Given a sorting problem defined under some constraints, what sorting algorithm will you use and why? | 1
+ |
+| Question | Implement different types of binary search trees | 0
+ |
+| Question | Implement tree traversals | 0
+ |
+| Question | Implement different sorting algorithms, such as quicksort, countsort, bucketsort, etc. | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Given a graph with a certain number of vertices and connected components, compute the largest number of edges that it might have? | 1
+ |
+| Question | What is the difference between adjacency list and adjacency matrix representation of a graph? | 1
+ |
+| Question | Implement various graph representations | 0
+ |
+| Question | Given a computing problem, devise an algorithm to solve it using Graphs and then implement your algorithm. | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. For a given function give an asymptotic upper bound using “big-Oh” notation
+2. Compute the worst case running time of a given algorithm.
+3. Insert items into a hashmap given a hash function and a collision handling scheme.
+4. Given an algorithm, identify its algorithmic strategy
+
+
+**Section 2**
+
+
+
+1. Given an unbalanced AVL tree, perform double rotation and show the resulting tree.
+2. Given a sequence of elements to be sorted, explain which sorting algorithm you would use to sort the input the fastest and why you chose this sorting algorithm.
+3. Implement a sorting algorithm given a problem and specify the big-Oh running time for your algorithm.
+
+
+**Section 3**
+
+
+
+1. Give pseudocode for performing a certain operation in a required time complexity using the adjacency list representation.
+2. Give pseudocode for performing a certain operation in a required time complexity using the adjacency list representation.
+3. Calculate the maximum flow for a given flow network
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__dev_ops_engineering.md

@@ -0,0 +1,369 @@
+
+
+
+
+
+
+
+BSc: Dev Ops Engineering
+========================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 DevOps Engineering](#DevOps_Engineering)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+			* [2.2.1.4 Section 4](#Section_4)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+DevOps Engineering
+==================
+
+
+* **Course name**: DevOps Engineering
+* **Code discipline**: XYZ
+* **Subject area**: xxx
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: DevOps Engineering concepts:.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Introduction to subject, computer networks basics, transport layer protocols, and socket programming | 1. General introduction to the course
+2. Computer networks basic
+3. Socket programming
+4. UDP socket programming
+5. TCP socket programming
+ |
+|  |  |
+| Coordination, consistency, and replication in distributed systems |  |
+| Fault tolerance and security in distributed systems |  |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+Advanced Compilers Construction and Program Analysis have become
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+  
+
+
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+  
+
+
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Laboratory assignments | 55%
+ |
+| Final exam | 35%
+ |
+| Attendance | 10%
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Textbook:. Available online:
+* Reference:. Available online:
+* Reference:. Available online: h
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4
+ |
+| --- | --- | --- | --- | --- |
+| Development of individual parts of software product code | 1 | 1 | 1 | 1
+ |
+| Homework and group projects | 1 | 1 | 1 | 1
+ |
+| Testing (written or computer based) | 1 | 1 | 1 | 1
+ |
+| Oral polls | 1 | 1 | 1 | 1
+ |
+| Discussions | 1 | 1 | 1 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | ? | 1
+ |
+| Question | . | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | You have a list of large numbers, and you need to find if they are prime or not. Would you use multithreading, multiprocessing, or sequential programming in order to complete the task asap? Prove it in practice. | 0
+ |
+| Question | You need to send multiple requests to a server and receive responses. Assume there is a few msecs of delay before you receive the response from the server. Would you use multithreading, multiprocessing, or sequential programming in order to complete the task asap? Prove it in practice. (Order of the requests/responses doesn't matter) | 0
+ |
+| Question | Discuss two ways of creating the threads using threading module in Python: 1) passing the worker function as a target, 2) subclassing the Thread class | 0
+ |
+| Question | Given the function implemented locally, make it available to be called through RPC from remote process? Use xmlRPC. | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+| Question | ? | 1
+ |
+
+
+#### Section 4
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Same as above | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. ?
+2. ?
+3. ?
+4. ?
+
+
+**Section 2**
+
+
+
+1. 
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+
+1. Same as above
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__differential_equations.f22.md

@@ -0,0 +1,394 @@
+
+
+
+
+
+
+
+BSc: Differential Equations.f22
+===============================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Differential Equations](#Differential_Equations)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Course Topics](#Course_Topics)
+	+ [1.3 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.3.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.3.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.3.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.3.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.3.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.4 Grading](#Grading)
+		- [1.4.1 Course grading range](#Course_grading_range)
+		- [1.4.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.4.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.5 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.5.1 Open access resources](#Open_access_resources)
+	+ [1.6 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [1.7 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [1.7.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [1.7.1.1 Section 1](#Section_1)
+			* [1.7.1.2 Section 2](#Section_2)
+			* [1.7.1.3 Section 3](#Section_3)
+		- [1.7.2 Final assessment](#Final_assessment)
+			* [1.7.2.1 Section 1](#Section_1_2)
+			* [1.7.2.2 Section 2](#Section_2_2)
+			* [1.7.2.3 Section 3](#Section_3_2)
+		- [1.7.3 The retake exam](#The_retake_exam)
+
+
+
+Differential Equations
+======================
+
+
+* **Course name**: Differential Equations
+* **Code discipline**: CSE205
+* **Subject area**: Math
+
+
+Short Description
+-----------------
+
+
+The course is designed to provide Software Engineers and Computer Scientists by knowledge of basic (core) concepts, definitions, theoretical results and techniques of ordinary differential equations theory, basics of power series and numerical methods, applications of the all above in sciences. All definitions and theorem statements (that will be given in lectures and that are needed to explain the keywords listed above) will be formal, but just few of these theorems will be proven formally. Instead (in the tutorial and practice classes) we will try these definitions and theorems on work with routine exercises and applied problems.
+
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| First-order equations and their applications | 1. Separable equation
+2. Initial value problem
+3. Homogeneous nonlinear equations
+4. Substitutions
+5. Linear ordinary equations
+6. Bernoulli & Riccati equations
+7. Exact differential equations, integrating factor
+8. Examples of applications to modeling the real world problems
+ |
+| Introduction to Numerical Methods | 1. Method of sections (Newton method)
+2. Method of tangent lines (Euler method)
+3. Improved Euler method
+4. Runge-Kutta methods
+ |
+| Higher-order equations and systems | 1. Homogeneous linear equations
+2. Constant coefficient equations
+3. A method of undetermined coefficients
+4. A method of variation of parameters
+5. A method of the reduction of order
+6. Laplace transform. Inverse Laplace transform.
+7. Application of the Laplace transform to solving differential equations.
+8. Series solution of differential equations.
+9. Homogeneous linear systems
+10. Non-homogeneous systems
+11. Matrices, eigenvalues and matrix form of the systems of ODE
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+The course is designed to provide Software Engineers and Computer Scientists by knowledge of basic (core) concepts, definitions, theoretical results and techniques of ordinary differential equations theory, basics of power series and numerical methods, applications of the all above in sciences. All definitions and theorem statements (that will be given in lectures and that are needed to explain the keywords listed above) will be formal, but just few of these theorems will be proven formally. Instead (in the tutorial and practice classes) we will try these definitions and theorems on work with routine exercises and applied problems.
+
+
+
+### ILOs defined at three levels
+
+
+We specify the intended learning outcomes at three levels: conceptual knowledge, practical skills, and comprehensive skills.
+
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* understand application value of ordinary differential equations,
+* explain situation when the analytical solution of an equation cannot be found,
+* give the examples of functional series for certain simple functions,
+* describe the common goal of the numeric methods,
+* restate the given ordinary equation with the Laplace Transform.
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* recognize the type of the equation,
+* identify the method of analytical solution,
+* define an initial value problem,
+* list alternative approaches to solving ordinary differential equations,
+* match the concrete numerical approach with the necessary level of accuracy.
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* solve the given ordinary differential equation analytically (if possible),
+* apply the method of the Laplace Transform for the given initial value problem,
+* predict the number of terms in series solution of the equation depending on the given accuracy,
+* implement a certain numerical method in self-developed computer software.
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Fail | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Midterm | 20
+ |
+| Interim Assessment | 20
+ |
+| Final exam | 30
+ |
+| Computational assignment | 25
+ |
+| In-class participation | 5
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+* Participation is important. Attending lectures is the key to success in this course.
+* Review lecture materials before classes to do well.
+* Reading the recommended literature is obligatory, and will give you a deeper understanding of the material.
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Elementary Differential Equations by William F. Trench. Brooks/Cole Thomson Learning, 2001 [link](https://digitalcommons.trinity.edu/mono/8/)
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Teaching and Learning Methods within each section
+| Teaching Techniques | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Problem-based learning (students learn by solving open-ended problems without a strictly-defined solution) | 1 | 1 | 1
+ |
+| Project-based learning (students work on a project) | 0 | 1 | 0
+ |
+| Modular learning (facilitated self-study) | 0 | 0 | 0
+ |
+| Differentiated learning (provide tasks and activities at several levels of difficulty to fit students needs and level) | 1 | 1 | 1
+ |
+| Contextual learning (activities and tasks are connected to the real world to make it easier for students to relate to them) | 0 | 0 | 0
+ |
+| Business game (learn by playing a game that incorporates the principles of the material covered within the course) | 0 | 0 | 0
+ |
+| Inquiry-based learning | 0 | 0 | 0
+ |
+| Just-in-time teaching | 0 | 0 | 0
+ |
+| Process oriented guided inquiry learning (POGIL) | 0 | 0 | 0
+ |
+| Studio-based learning | 0 | 0 | 0
+ |
+| Universal design for learning | 0 | 0 | 0
+ |
+| Task-based learning | 0 | 0 | 0
+ |
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Lectures | 1 | 1 | 1
+ |
+| Interactive Lectures | 1 | 1 | 1
+ |
+| Lab exercises | 1 | 1 | 1
+ |
+| Experiments | 0 | 0 | 0
+ |
+| Modeling | 0 | 0 | 0
+ |
+| Cases studies | 0 | 0 | 0
+ |
+| Development of individual parts of software product code | 0 | 0 | 0
+ |
+| Individual Projects | 0 | 1 | 0
+ |
+| Group projects | 0 | 0 | 0
+ |
+| Flipped classroom | 0 | 0 | 0
+ |
+| Quizzes (written or computer based) | 1 | 1 | 1
+ |
+| Peer Review | 0 | 0 | 0
+ |
+| Discussions | 1 | 1 | 1
+ |
+| Presentations by students | 0 | 0 | 0
+ |
+| Written reports | 0 | 0 | 0
+ |
+| Simulations and role-plays | 0 | 0 | 0
+ |
+| Essays | 0 | 0 | 0
+ |
+| Oral Reports | 0 | 0 | 0
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+1. What is the type of the first order equation?
+2. Is the equation homogeneous or not?
+3. Which substitution may be used for solving the given equation?
+4. Is the equation linear or not?
+5. Which type of the equation have we obtained for the modeled real world problem?
+6. Is the equation exact or not?
+
+
+#### Section 2
+
+
+1. What is the difference between the methods of sections and tangent line approximations?
+2. What is the approximation error for the given method?
+3. How to improve the accuracy of Euler method?
+4. How to obtain a general formula of the Runge-Kutta methods?
+
+
+#### Section 3
+
+
+1. What is the type of the second order equation?
+2. Is the equation homogeneous or not?
+3. What is a characteristic equation of differential equation?
+4. In which form a general solution may be found?
+5. What is the form of the particular solution of non-homogeneous equation?
+6. How to compose the Laplace transform for a certain function?
+7. How to apply the method of Laplace transform for solving ordinary differential equations?
+8. How to differentiate a functional series?
+
+
+### Final assessment
+
+
+#### Section 1
+
+
+1. Determine the type of the first order equation and solve it with the use of appropriate method.
+2. Find the integrating factor for the given equation.
+3. Solve the initial value problem of the first order.
+4. Construct a mathematical model of the presented real world problem in terms of differential equations and answer for the specific question about it.
+
+
+#### Section 2
+
+
+1. For the given initial value problem with the ODE of the first order implement in your favorite programming Euler, improved Euler and general Runge-Kutta methods of solving.
+2. Using the developed software construct corresponding approximation of the solution of a given initial value problem (provide the possibility of changing of the initial conditions, implement the exact solution to be able to compare the obtained results).
+3. Investigate the convergence of the numerical methods on different grid sizes.
+4. Compare approximation errors of these methods plotting the corresponding chart for the dependency of approximation error on a grid size.
+
+
+#### Section 3
+
+
+1. Compose a characteristic equation and find its roots.
+2. Find the general of second order equation.
+3. Determine the form of a particular solution of the equation and reduce the order.
+4. Solve a homogeneous constant coefficient equation.
+5. Solve a non-homogeneous constant coefficient equation.
+6. Find the Laplace transform for a given function. Analyze its radius of convergence.
+7. Find the inverse Laplace transform for a given expression.
+8. Solve the second order differential equation with the use of a Laplace transform.
+9. Solve the second order differential equation with the use of Series approach.
+
+
+### The retake exam
+
+
+Retakes will be run as a comprehensive exam, where the student will be assessed the acquired knowledge coming from the textbooks, the lectures, the labs, and the additional required reading material, as supplied by the instructor. During such comprehensive oral/written the student could be asked to solve exercises and to explain theoretical and practical aspects of the course.
+
+
+
+
+
+
+
+
+
+
+

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+
+
+
+
+
+
+
+BSc: Differential Equations.f23
+===============================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Differential Equations](#Differential_Equations)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Course Topics](#Course_Topics)
+	+ [1.3 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.3.1 Course objectives](#Course_objectives)
+	+ [1.4 Grading](#Grading)
+		- [1.4.1 Course grading range](#Course_grading_range)
+		- [1.4.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+	+ [1.5 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.5.1 Open access resources](#Open_access_resources)
+
+
+
+Differential Equations
+======================
+
+
+* **Course name**: Differential Equations
+* **Code discipline**: CSE205
+* **Subject area**: Math
+
+
+Short Description
+-----------------
+
+
+This course is an introduction to ordinary differential equations(ODEs) and their applications. Topics covered include first order ODEs, second order linear ODEs, Laypunov’s stability theory and numerical methods.The course will also introduce students to systems of linear equations and eigenvalue problems.
+
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Differential equations of the first order | 1. Introduction into differential equations. Origins and examples of the differential equations.
+2. A geometrical interpretation of the differential equations of the first order. A field of directions and solutions of the differential equations as trajectories
+3. Theorem about existence of the solution of the differential equations. Proof of the theorem.
+4. Equations with separable variables and linear equations of the first order.
+5. Homogeneous equations and exact equations and integration factors.
+ |
+| Differential equations of the second order | 1. Linear equations of the second order. Phase portraits, trajectories and conservation laws. Singular points of the second order equations.
+2. Non-homogeneous equations and method of undetermined coefficients. Resonances.
+3. Variations parameters for the second order equations.
+4. Boundary value problems for the second-order equations and Green's function.
+5. Applications of Laplace transform.
+ |
+| Nonlinear equations and Lyapunov's stability | 1. Nonlinear equations of the second order. Conservation laws and trajectories.
+2. Lyapunov's stability. Lyapunov's function and Lyapunov stability theorems.
+3. Chetaev's instability theorem and examples of chaotic systems.
+4. Partial differential equations of the first order and method of characteristics.
+ |
+| Systems of the differential equations | 1. Linear systems of differential equations of the first order and matrix of fundamental solutions.
+2. Method of variations parameters for the non-homogeneous linear systems.
+ |
+| Numerical methods | 1. Euler's method.
+2. Runge-Kutta method.
+3. Stability and accuracy of numerical methods.
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### Course objectives
+
+
+Upon completion of this course, students should be able to:
+
+
+
+* Realize conditions of existence for the equations of the first order and solve first-order ordinary differential equations using various techniques such as separation of variables, integration factors.
+* Solve second-order linear differential equations with constant coefficients using techniques such as the characteristic equation and the method of undetermined coefficients and applications of Laplace transform for the linear equations.
+* Define the resonant conditions for the linear and nonlinear equations of the second order equation.
+* Apply the Lyapunov's stability theory for the linear and nonlinear systems.
+* Know the properties of the solutions of first-order partial differential equations.
+* Apply numerical methods to approximate solutions to differential equations.
+* Understand the concept of eigenvalues and eigenvectors and use them to solve systems of linear differential equations.
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Fail | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Midterm | 20
+ |
+| Interim Assessment | 20 pts (2 tests by 10 pts)
+ |
+| Final exam | 30
+ |
+| Computational assignment | 30
+ |
+| Attendance and In-class participation | 7
+ |
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Elementary Differential Equations by William F. Trench. Brooks/Cole Thomson Learning, 2001 [link](https://digitalcommons.trinity.edu/mono/8/)
+* Stephen L. Campbell and Richard Haberman, Introduction to differential equations with dynamical systems
+* J.L.Brenner, Problems in DifferentialEquations(adapted from ”Problems in differential equations” by A.F.Filippov)
+* S.G.Glebov, O.M.Kiselev, N.Tarkhanov. Nonlinear equations with small parameter. Volume I:Oscillations and resonances
+
+
+
+
+
+
+
+
+
+

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+
+
+
+
+
+
+
+BSc: Differential Equations
+===========================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Differential Equations](#Differential_Equations)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+			* [2.2.1.4 Section 4](#Section_4)
+			* [2.2.1.5 Section 5](#Section_5)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Differential Equations
+======================
+
+
+* **Course name**: Differential Equations
+* **Code discipline**: XYZ
+* **Subject area**: Math
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: Ordinary differential equations; Basic numerical methods.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| First-order equations and their applications | 1. The simplest type of differential equation
+2. Separable equation
+3. Initial value problem
+4. Homogeneous nonlinear equations, substitutions
+5. Linear ordinary equations, Bernoulli & Riccati equations
+6. Examples of applications to modeling the real world problems
+7. Exact differential equations, integrating factor
+ |
+| Introduction to numeric methods for algebraic and first-order differential equations | 1. Method of sections (Newton method)
+2. Method of tangent lines approximation (Euler method)
+3. Improved Euler method
+4. Runge-Kutta methods
+ |
+| Second-order differential equations and their applications | 1. Homogeneous linear equations.
+2. Constant coefficient homogeneous equations.
+3. Constant coefficient non-homogeneous equations.
+4. A method of undetermined coefficients.
+5. A method of variation of parameters.
+6. A method of the reduction of order.
+ |
+| Laplace transform | 1. Improper integrals. Convergence / Divergence.
+2. Laplace transform of a function
+3. Existence of the Laplace transform.
+4. Inverse Laplace transform.
+5. Application of the Laplace transform to solving differential equations.
+ |
+| Series approach to linear differential equations | 1. Functional series.
+2. Taylor and Maclaurin series.
+3. Differentiation of power series.
+4. Series solution of differential equations.
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+The course is designed to provide Software Engineers and Computer Scientists by knowledge of basic (core) concepts, definitions, theoretical results and techniques of ordinary differential equations theory, basics of power series and numerical methods, applications of the all above in sciences. All definitions and theorem statements (that will be given in lectures and that are needed to explain the keywords listed above) will be formal, but just few of these theorems will be proven formally. Instead (in the tutorial and practice classes) we will try these definitions and theorems on work with routine exercises and applied problems.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* recognize the type of the equation,
+* identify the method of analytical solution,
+* define an initial value problem,
+* list alternative approaches to solving ordinary differential equations,
+* match the concrete numerical approach with the necessary level of accuracy.
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* understand application value of ordinary differential equations,
+* explain situation when the analytical solution of an equation cannot be found,
+* give the examples of functional series for certain simple functions,
+* describe the common goal of the numeric methods,
+* restate the given ordinary equation with the Laplace Transform.
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* solve the given ordinary differential equation analytically (if possible),
+* apply the method of the Laplace Transform for the given initial value problem,
+* predict the number of terms in series solution of the equation depending on the given accuracy,
+* implement a certain numerical method in self-developed computer software.
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 136-170 | -
+ |
+| B. Good | 102-135 | -
+ |
+| C. Satisfactory | 68-101 | -
+ |
+| D. Poor | 0-68 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Labs/seminar classes | 20
+ |
+| Interim performance assessment | 70
+ |
+| Exams | 80
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4 | Section 5
+ |
+| --- | --- | --- | --- | --- | --- |
+| Homework and group projects | 1 | 1 | 1 | 1 | 1
+ |
+| Midterm evaluation | 1 | 1 | 1 | 1 | 1
+ |
+| Testing (written or computer based) | 1 | 1 | 1 | 1 | 1
+ |
+| Oral polls | 1 | 0 | 0 | 0 | 0
+ |
+| Discussions | 1 | 1 | 1 | 1 | 1
+ |
+| Development of individual parts of software product code | 0 | 1 | 0 | 0 | 0
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is the type of the first order equation? | 1
+ |
+| Question | Is the equation homogeneous or not? | 1
+ |
+| Question | Which substitution may be used for solving the given equation? | 1
+ |
+| Question | Is the equation linear or not? | 1
+ |
+| Question | Which type of the equation have we obtained for the modeled real world problem? | 1
+ |
+| Question | Is the equation exact or not? | 1
+ |
+| Question | Determine the type of the first order equation and solve it with the use of appropriate method. | 0
+ |
+| Question | Find the integrating factor for the given equation. | 0
+ |
+| Question | Solve the initial value problem of the first order. | 0
+ |
+| Question | Construct a mathematical model of the presented real world problem in terms of differential equations and answer for the specific question about it. | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is the difference between the methods of sections and tangent line approximations? | 1
+ |
+| Question | What is the approximation error for the given method? | 1
+ |
+| Question | How to improve the accuracy of Euler method? | 1
+ |
+| Question | How to obtain a general formula of the Runge-Kutta methods? | 1
+ |
+| Question | For the given initial value problem with the ODE of the first order implement in your favorite programming Euler, improved Euler and general Runge-Kutta methods of solving. | 0
+ |
+| Question | Using the developed software construct corresponding approximation of the solution of a given initial value problem (provide the possibility of changing of the initial conditions, implement the exact solution to be able to compare the obtained results). | 0
+ |
+| Question | Investigate the convergence of the numerical methods on different grid sizes. | 0
+ |
+| Question | Compare approximation errors of these methods plotting the corresponding chart for the dependency of approximation error on a grid size. | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is the type of the second order equation? | 1
+ |
+| Question | Is the equation homogeneous or not? | 1
+ |
+| Question | What is a characteristic equation of differential equation? | 1
+ |
+| Question | In which form a general solution may be found? | 1
+ |
+| Question | What is the form of the particular solution of non-homogeneous equation? | 1
+ |
+| Question | Compose a characteristic equation and find its roots. | 0
+ |
+| Question | Find the general of second order equation. | 0
+ |
+| Question | Determine the form of a particular solution of the equation and reduce the order. | 0
+ |
+| Question | Solve a homogeneous constant coefficient equation. | 0
+ |
+| Question | Solve a non-homogeneous constant coefficient equation. | 0
+ |
+
+
+#### Section 4
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is an improper integral? | 1
+ |
+| Question | How to compose the Laplace transform for a certain function? | 1
+ |
+| Question | What is a radius of convergence of the Laplace transform? | 1
+ |
+| Question | How to determine the inverse Laplace transform for a given expression? | 1
+ |
+| Question | How to apply the method of Laplace transform for solving ordinary differential equations? | 1
+ |
+| Question | Find the Laplace transform for a given function. Analyze its radius of convergence. | 0
+ |
+| Question | Find the inverse Laplace transform for a given expression. | 0
+ |
+| Question | Solve the first order differential equation with the use of a Laplace transform. | 0
+ |
+| Question | Solve the second order differential equation with the use of a Laplace transform. | 0
+ |
+
+
+#### Section 5
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What are the power and functional series? | 1
+ |
+| Question | How to find the radius of convergence of a series? | 1
+ |
+| Question | What is a Taylor series? | 1
+ |
+| Question | How to differentiate a functional series? | 1
+ |
+| Question | Find the radius of convergence of a given series. | 0
+ |
+| Question | Compose the Taylor series for a given function. | 0
+ |
+| Question | Solve the first order differential equation with the use of Series approach. | 0
+ |
+| Question | Solve the second order differential equation with the use of Series approach. | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. Linear first order equation. Integrating factor.
+2. Bernoulli & Riccati equations.
+3. Homogeneous nonlinear equations equations.
+4. Exact equations. Substitutions.
+
+
+**Section 2**
+
+
+
+1. Newton’s approximation method.
+2. Euler approximation method.
+3. Improved Euler method.
+4. Runge-Kutta methods.
+
+
+**Section 3**
+
+
+
+1. Homogeneous linear second order equations.
+2. Constant coefficient equations. A method of undetermined coefficients.
+3. Constant coefficient equations. A method of variation of parameters.
+4. Non-homogeneous linear second order equations. Reduction of order.
+
+
+**Section 4**
+
+
+
+1. Laplace transform, its radius of convergence and properties.
+2. Inverse Laplace transform. The method of rational functions.
+3. Application of Laplace transform to solving differential equations.
+
+
+**Section 5**
+
+
+
+1. Taylor and Maclaurin series as functional series. Radius of convergence.
+2. Uniqueness of power series. Its differentiation.
+3. Application of power series to solving differential equations
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+**Section 5**
+
+
+
+
+
+
+
+
+
+
+

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+
+
+
+
+
+
+
+BSc: Distributed And Network Programming
+========================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Distributed and Network Programming](#Distributed_and_Network_Programming)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+			* [2.2.1.4 Section 4](#Section_4)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Distributed and Network Programming
+===================================
+
+
+* **Course name**: Distributed and Network Programming
+* **Code discipline**: XYZ
+* **Subject area**: xxx
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: Network programming concepts: Layered architecture, TCP and UDP sockets, multithreaded servers; Distributed systems concepts: system architecture, inter-process communication, remote procedure calls, peer-to-peer systems, coordination, replication, and fault tolerance..
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+* **Networks**: 1) Understanding Application, Transport, and Network layers, 2) Basic socket programming experience
+* **Operating systems**
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Introduction to subject, computer networks basics, transport layer protocols, and socket programming | 1. General introduction to the course
+2. Computer networks basic
+3. Socket programming
+4. UDP socket programming
+5. TCP socket programming
+ |
+| Multithreaded socket programming, RPCs, and distributed system architecture | 1. Multithreading and multithreaded socket programming
+2. Remote procedure calls (RPCs)
+3. Distributed system architectures
+ |
+| Coordination, consistency, and replication in distributed systems | 1. Clock synchronization algorithms (NTP, Berkeley)
+2. Logical clock (Lamport clocks)
+3. Mutual exclusion algorithms: permission-based, token-based
+4. Election algorithms: Bully, Ring
+5. Consistency models
+6. Replica management
+7. Consistency protocols
+ |
+| Fault tolerance and security in distributed systems | 1. Intro to fault tolerance: Failure models, Failure masking by redundancy
+2. Process resilience: process groups, process replication, consensus in faulty systems, failure detection
+3. Reliable group communication: atomic multicast,
+4. Distributed commit
+5. Recovery: checkpointing
+6. Intro to security: threats, design issues, cryptography
+7. Secure channels: authentication, message integrity and confidentiality, secure group communication
+8. Access control: general issues, firewalls, secure mobile code, denial of service
+9. Secure naming
+10. Security management: Key management, secure group management, authorization management
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+Distributed and networked systems have become an integral part of our life, we use various applications such as chatting, online transactions, or cloud storage apps. All these popular applications are supported by an infrastructure (of servers) that is organized based on some concepts of distributed systems. The purpose of this course is to provide the students with the necessary concepts, models, and real-world problem-solving techniques of network programming and distributed systems.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Concepts of network programming
+* Different distributed system architectures
+* Various synchronization and coordination techniques
+* Different consistency models and replication methods
+* Approaches to achieve fault tolerance and security in distributed systems
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Difference between different transport protocols, when and why one is preferred over another
+* Difference between different distributed system architectures (centralized, decentralized, and hybrid)
+* How a mutual exclusion is achieved between concurrent servers (centralized, distributed, token-ring, and decentralized)
+* How a new leader is elected in peer-to-peer systems (bully, ring)
+* How to achieve a consistent replicas across distributed systems (consistency models and protocols, content replication and placement)
+* Some methods to achieve the fault tolerance in distributed systems
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Building a custom application protocols on top of the existing transport protocols
+* Writing multithreaded server and client apps with sockets
+* Using RPC for inter-process communication: command execution, file transfer
+* Building peer-to-peer systems with distributed protocol such as Chord
+* Building fault-tolerant systems with failure detection and leader election
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Laboratory assignments | 55%
+ |
+| Final exam | 35%
+ |
+| Attendance | 10%
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Textbook: Maarten Van Steen, and Andrew S. Tanenbaum. Distributed systems (3rd Edition) Leiden, The Netherlands: Maarten van Steen, 2017. Available online: <https://www.distributed-systems.net/>
+* Reference: George F. Coulouris, Jean Dollimore, and Tim Kindberg. Distributed systems: concepts and design (5th Edition) Addision Wesley, 2012. Available online: <https://www.cdk5.net/wp/>
+* Reference: Sukumar Ghosh. Distributed systems: an algorithmic approach (2nd Edition) Chapman&Hall /CRC, Author’s own course material, Spring 2015. Available online: <http://homepage.divms.uiowa.edu/~ghosh/16615.html>
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4
+ |
+| --- | --- | --- | --- | --- |
+| Development of individual parts of software product code | 1 | 1 | 1 | 1
+ |
+| Homework and group projects | 1 | 1 | 1 | 1
+ |
+| Testing (written or computer based) | 1 | 1 | 1 | 1
+ |
+| Oral polls | 1 | 1 | 1 | 1
+ |
+| Discussions | 1 | 1 | 1 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What are the distributed systems? | 1
+ |
+| Question | Give an example of distributed systems. | 1
+ |
+| Question | What are the advantages of layered architecture? | 1
+ |
+| Question | What are the roles of transport protocols? | 1
+ |
+| Question | How the TCP and UDP differ from each other? When one is preferred over the other? | 1
+ |
+| Question | What is socket programming? | 1
+ |
+| Question | How socket programming is different for UDP and TCP? | 1
+ |
+| Question | Write a simple UDP/TCP client-server echo program | 0
+ |
+| Question | Write a simple chatting program using UDP/TCP sockets | 0
+ |
+| Question | Given the simple echo server program, apply socket timeouts and catch timeout exceptions | 0
+ |
+| Question | Write a UDP-based reliable file transfer protocol | 0
+ |
+| Question | Write a program that parallelly executes the CPU-bound tasks using multiple processes | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | How the threads differ from processes? | 1
+ |
+| Question | What are the I/O and CPU-bound tasks? | 1
+ |
+| Question | For what kind of tasks, using threads is preferred than using processes? | 1
+ |
+| Question | What is a remote procedure call? | 1
+ |
+| Question | What are some well-known distributed system architectures? | 1
+ |
+| Question | Discuss the structured and unstructured decentralized architectures. | 1
+ |
+| Question | You have a list of large numbers, and you need to find if they are prime or not. Would you use multithreading, multiprocessing, or sequential programming in order to complete the task asap? Prove it in practice. | 0
+ |
+| Question | You need to send multiple requests to a server and receive responses. Assume there is a few msecs of delay before you receive the response from the server. Would you use multithreading, multiprocessing, or sequential programming in order to complete the task asap? Prove it in practice. (Order of the requests/responses doesn't matter) | 0
+ |
+| Question | Discuss two ways of creating the threads using threading module in Python: 1) passing the worker function as a target, 2) subclassing the Thread class | 0
+ |
+| Question | Given the function implemented locally, make it available to be called through RPC from remote process? Use xmlRPC. | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | How NTP protocol works? | 1
+ |
+| Question | How Berkeley protocol works? | 1
+ |
+| Question | Discuss the mutual exclusion algorithms. | 1
+ |
+| Question | Discuss the permanent and server-initiated replicas and their difference | 1
+ |
+| Question | Explain the Primary-backup protocol. | 1
+ |
+| Question | Given three machines with drifting clocks, adjust their clocks using Berkeley algorithm. | 0
+ |
+| Question | Explain how Bully algorithm for election works | 0
+ |
+| Question | Explain how Ring algorithm for election works | 0
+ |
+| Question | Explain the centralized (permission-based) method of mutual exclusion | 0
+ |
+
+
+#### Section 4
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Discuss the failure models | 1
+ |
+| Question | Discuss different failure masking techniques by redundancy | 1
+ |
+| Question | What is k-fault tolerant group? | 1
+ |
+| Question | What is general model of failure detection? | 1
+ |
+| Question | Explain basic reliable multicasting | 1
+ |
+| Question | Explain what is authentication | 1
+ |
+| Question | Explain what are message confidentiality and integrity | 1
+ |
+| Question | Same as above | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. Describe an advantage of layered architecture?
+2. Describe the differences between TCP and UDP protocols?
+3. Provide examples when using UDP can be more reasonable than TCP?
+4. Describe how UDP and TCP socket programming differ from each other?
+
+
+**Section 2**
+
+
+
+1. Discuss the differences between the threads and processes.
+2. What is the Race condition?
+3. Discuss the ways to protect the shared data from the race condition
+4. You're given the worker function that just sleeps for a second and quits, implement the same behavior in a subclass of the Thread.
+5. Discuss the RPC and its advantages over using the low-level socket programming?
+6. Discuss the decentralized architecture: structured and unstructured p2p systems.
+
+
+**Section 3**
+
+
+
+1. Discuss NTP and Berkeley protocols for synchronization and explain their key difference
+2. Discuss permission-based and token-based solution for mutual exclusion.
+3. Discuss content replication: permanent, server-initiated, and client-initiated replicas.
+4. Explain the Primary-backup protocol, its advantages and disadvantages.
+
+
+**Section 4**
+
+
+
+1. Same as above
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__fundamentals_of_computer_security.md

@@ -0,0 +1,499 @@
+
+
+
+
+
+
+
+BSc: Fundamentals of Computer Security
+======================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Fundamentals of Information Security](#Fundamentals_of_Information_Security)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+			* [2.2.1.4 Section 4](#Section_4)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Fundamentals of Information Security
+====================================
+
+
+* **Course name**: Fundamentals of Information Security
+* **Code discipline**: XYZ
+* **Subject area**: xxx
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: User authentication and authorization; Database and data center security; Reverse engineering and malicious software; Buffer overflow and software security; OS security; Symmetric encryption; Public-key cryptography.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Computer security technology and principles | 1. Introduction to computer security
+2. User authentication and authorization
+3. Database and data center security
+4. Network security of data center
+5. Reverse engineering and malicious software
+ |
+| Software and system security | 1. Buffer overflow and software security
+2. OS security
+3. Guest lecture from industry
+ |
+| Cryptographic algorithms | 1. Symmetric encryption and message confidentiality
+2. Public key cryptography and message authentication
+ |
+| Additional | 1. Compliances and documentation in computer security
+2. New technologies and research areas in cyber security
+3. Cybercrime and forensics, incident response
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+The purpose of this course is to teach the students the important aspects of cryptography, authentication, access control, DoS attacks, intrusion detection, etc. The students will learn major types of attacks and methods of protection from them.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Message and user authentication
+* Encryption algorithms
+* Authorization and access control mechanisms
+* Different types of attacks
+* Firewalls and intrusion detection methods
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* The importance of authentication and authentication protocols
+* Encryption algorithms used for authentication and message integrity
+* The importance of authorization and access control, different protocols
+* Major types of attacks and methods of protection from them
+* Importance of intrusion detection and firewalls
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Authentication protocols
+* Encryption techniques and algorithms
+* Well-known access control techniques
+* Mitigate the DoS attacks
+* Intrusion detection algorithms
+* Using firewalls
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Laboratory assignments | 50%
+ |
+| Weekly quizzes | 14%
+ |
+| Attendance | 6%
+ |
+| Final exam | 30%
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Required textbook: William Stallings and Lawrie Brown, "Computer Security: Principles and Practice,“ 4th edition, Pearson, 2017.
+* Additional textbook: William Stallings, "Cryptography and Network Security: Principles and Practice," 7th Edition, Pearson, 2017.
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4
+ |
+| --- | --- | --- | --- | --- |
+| Development of individual parts of software product code | 1 | 1 | 1 | 1
+ |
+| Homework and group projects | 1 | 1 | 1 | 1
+ |
+| Testing (written or computer based) | 1 | 1 | 1 | 1
+ |
+| Oral polls | 1 | 1 | 1 | 1
+ |
+| Discussions | 1 | 1 | 1 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is meant by the CIA triad? | 1
+ |
+| Question | What is the difference between data integrity and system integrity? | 1
+ |
+| Question | How is cryptanalysis different from brute-force attack? | 1
+ |
+| Question | List and briefly explain the different approaches to attacking a symmetric encryption scheme. | 1
+ |
+| Question | In general terms, what are four means of authenticating a user’s identity? | 1
+ |
+| Question | What is a Trojan horse attack? | 1
+ |
+| Question | What is the difference between authentication and authorization? | 1
+ |
+| Question | How does RBAC relate to DAC and MAC? | 1
+ |
+| Question | Define the terms database, database management system, and query language. | 1
+ |
+| Question | What is a relational database and what are its principal ingredients? | 1
+ |
+| Question | What is an SQL injection attack? What are the implications of an SQL injection attack? | 1
+ |
+| Question | List the categories for grouping different types of SQLi attacks. | 1
+ |
+| Question | Why is RBAC considered fit for database access control? | 1
+ |
+| Question | What are three broad mechanisms that malware can use to propagate? | 1
+ |
+| Question | What is a blended attack? | 1
+ |
+| Question | Define a denial-of-service (DoS) attack | 1
+ |
+| Question | State the difference between a SYN flooding attack and a SYN spoofing attack. | 1
+ |
+| Question | What is the goal of an HTTP flood attack? | 1
+ |
+| Question | What is a poison packet attack? Give two examples of such an attack. | 1
+ |
+| Question | How are intruders classified according to skill level? | 1
+ |
+| Question | List and briefly describe the classifications of intrusion detection systems based on the source and the type of data analyzed. | 1
+ |
+| Question | Consider the given general code for allowing access to a resource: a) Explain the security flaw in this program, b) Rewrite the code to avoid the flaw | 0
+ |
+| Question | Develop an attack tree for gaining access to the contents of a physical safe | 0
+ |
+| Question | Typically, in practice, the length of the message is greater than the block size of the encryption algorithm. The simplest approach to handle such encryption is known as electronic codebook (ECB) mode. Explain this mode. Mention a scenario where it cannot be applied. Explain briefly why it is not a secure mode of encryption | 0
+ |
+| Question | Consider a very simple symmetric block encryption algorithm, in which 64-bits blocks of plaintext are encrypted using a 128-bit key. Show the decryption equation. | 0
+ |
+| Question | Explain the suitability or unsuitability of the given passwords | 0
+ |
+| Question | Assume that Personal Identification Numbers (PINs) are formed by nine-digit combinations of numbers 0 to 9. Assume that an adversary is able to attempt three PINs per second.Assuming no feedback to the adversary until each attempt has been completed, what is the expected time to discover the correct PIN?Assuming feedback to the adversary flagging an error as each incorrect digit is entered, what is the expected time to discover the correct PIN? | 0
+ |
+| Question | Assume an application requires access control policies based on the applicant’s age and the type of funding to be provided. Using an ABAC approach, write policy rules for each of the following scenarios:If the applicant’s age is more than 35, only “Research Grants (RG)” can be provided.If the applicant’s age is less than or equal to 35, both “RG and Travel Grants (TG)” can be provided. | 0
+ |
+| Question | Assume a system with K subject attributes, M object attributes and Range () denotes the range of possible values that each attribute can take. What are the number of roles and permissions required for an RBAC model? What is the problem with this approach if additional attributes are added? | 0
+ |
+| Question | Consider a simplified database for an organization that includes information of several departments (identity, name, manager, number of employees) and of managers and employees of the respective departments. Suggest a relational database for efficiently managing this information | 0
+ |
+| Question | Users hulkhogan and undertaker do not have the SELECT access right to the Inventory table and the Item table. These tables were created by and are owned by user bruno-s. Write the SQL commands that would enable bruno-s to grant SELECT access to these tables to hulkhogan and undertaker. | 0
+ |
+| Question | Consider the given fragment of code. What type of malware is this? | 0
+ |
+| Question | Consider the given fragment embedded in a webpage. What type of malicious software is this? | 0
+ |
+| Question | In order to implement a classic DoS flood attack, the attacker must generate a sufficiently large volume of packets to exceed the capacity of the link to the target organization. Consider an attack using ICMP echo request (ping) packets that are 100 bytes in size (ignoring framing overhead). How many of these packets per second must the attacker send to flood a target organization using a 8-Mbps link? How many per second if the packets are 1000 bytes in size? Or 1460 bytes? | 0
+ |
+| Question | It is discussed that an amplification attack, which is a variant of reflection attack, can be launched by using any type of a suitable UDP service, such as the echo service. However, TCP services cannot be used in this attack. Why? | 0
+ |
+| Question | Consider the first step of the common attack methodology we describe, which is to gather publicly available information on possible targets. What types of information could be used? What does this use suggest to you about the content and detail of such information? How does this correlate with the organization’s business and legal requirements? How do you reconcile these conflicting demands? | 0
+ |
+| Question | As was mentioned in this chapter, the application gateway does not permit an end-toend TCP connection; rather, it sets up two TCP connections, one between itself and a TCP user on an inner host and one between itself and a TCP user on an outside host. The disadvantage of this approach is the additional processing overhead on each connection since the gateway must examine and forward all traffic in both directions. Describe at least one more limitation of this approach which is not discussed. | 0
+ |
+| Question | Given table shows a sample of a packet filter firewall ruleset for an imaginary network of IP address that range from 192.168.1.0 to 192.168.1.254. Describe the effect of each rule. | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Define buffer overflow. | 1
+ |
+| Question | Define an off-by-one attack. | 1
+ |
+| Question | Define an injection attack. List some examples of injection attacks. What are the general circumstances in which injection attacks are found? | 1
+ |
+| Question | State the similarities and differences between command injection and SQL injection attacks | 1
+ |
+| Question | What are the basic steps needed in the process of securing a system? | 1
+ |
+| Question | State different types of full virtualization with their security requirements. | 1
+ |
+| Question | List five essential characteristics of cloud computing. | 1
+ |
+| Question | List and briefly define three cloud service models. | 1
+ |
+| Question | Briefly explain the most prominent deployment models for cloud computing. | 1
+ |
+| Question | Describe some of the main cloud-specific security threats. | 1
+ |
+| Question | Investigate each of the unsafe standard C library functions shown in the figure using the UNIX man pages or any C programming text, and determine a safer alternative to use. | 0
+ |
+| Question | Investigate the use of a replacement standard C string library, such as Libsafe, bstring, vstr, or other. Determine how significant the required code changes are, if any, to use the chosen library. | 0
+ |
+| Question | Investigate the issues that arise while using sequence number as both identifier and authenticator of packets. Identify the root cause of the problem. | 0
+ |
+| Question | Investigate the various types of cross-site scripting (XSS) attacks. How can such attacks be prevented? | 0
+ |
+| Question | How can we use the TCP Wrappers and tcpd daemon to achieve secure remote control access? What if the network servers are heavily loaded? | 0
+ |
+| Question | Why is it important to secure the boot process? Is it required to limit which media the system must boot from? | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What are different types of cryptanalysis attacks? | 1
+ |
+| Question | Why do some block cipher modes of operation only use encryption while others use both encryption and decryption? | 1
+ |
+| Question | In the context of a hash function, what is a compression function? | 1
+ |
+| Question | Briefly explain Diffie-Hellman key exchange. | 1
+ |
+| Question | Suppose that your organization wants you to ensure the security of its data while the data is in transit. Which one out of stream cipher and block cipher would you select and why? | 0
+ |
+| Question | Can we perform encryption operations in parallel on multiple blocks of plaintext in any of the five modes? How about decryption? | 0
+ |
+| Question | Consider a 32-bit hash function defined as the concatenation of two 16-bit functions: XOR and RXOR, defined as “two simple hash functions.”Will this checksum detect all errors caused by an odd number of error bits? Explain.Will this checksum detect all errors caused by an even number of error bits? If not, characterize the error patterns that will cause the checksum to fail.Comment on the effectiveness of this function for use as a hash function for authentication | 0
+ |
+| Question | It is possible to use a hash function to construct a block cipher with a structure similar to DES. Because a hash function is one way and a block cipher must be reversible (to decrypt), how is it possible? | 0
+ |
+
+
+#### Section 4
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What are different types of cryptanalysis attacks? | 1
+ |
+| Question | Why do some block cipher modes of operation only use encryption while others use both encryption and decryption? | 1
+ |
+| Question | In the context of a hash function, what is a compression function? | 1
+ |
+| Question | Briefly explain Diffie-Hellman key exchange. | 1
+ |
+| Question | Suppose that your organization wants you to ensure the security of its data while the data is in transit. Which one out of stream cipher and block cipher would you select and why? | 0
+ |
+| Question | Can we perform encryption operations in parallel on multiple blocks of plaintext in any of the five modes? How about decryption? | 0
+ |
+| Question | Consider a 32-bit hash function defined as the concatenation of two 16-bit functions: XOR and RXOR, defined as “two simple hash functions.”Will this checksum detect all errors caused by an odd number of error bits? Explain.Will this checksum detect all errors caused by an even number of error bits? If not, characterize the error patterns that will cause the checksum to fail.Comment on the effectiveness of this function for use as a hash function for authentication | 0
+ |
+| Question | It is possible to use a hash function to construct a block cipher with a structure similar to DES. Because a hash function is one way and a block cipher must be reversible (to decrypt), how is it possible? | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. Questions from previous two subsections can be used.
+
+
+**Section 2**
+
+
+
+1. Questions from previous two subsections can be used.
+
+
+**Section 3**
+
+
+
+1. Questions from previous two subsections can be used.
+
+
+**Section 4**
+
+
+
+1. Questions from previous two subsections can be used.
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__game_theory.md

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+
+
+
+
+
+
+
+BSc: Game Theory
+================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Game Theory](#Game_Theory)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Game Theory
+===========
+
+
+* **Course name**: Game Theory
+* **Code discipline**: R-01
+* **Subject area**:
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: Game Theory: Basics of the mathematical theory of games, including Nash Equilibrium, Mixed Strategies, and Evolutionary Game Theory; Applications of Computer Programming: Implementation of Game Playing agents.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+* [CSE204 — Analytic Geometry And Linear Algebra II](https://eduwiki.innopolis.university/index.php/BSc:AnalyticGeometryAndLinearAlgebraII): real vector and matrix operations, convex hull and span.
+* [CSE206 — Probability And Statistics](https://eduwiki.innopolis.university/index.php/BSc:ProbabilityAndStatistics): probability distribution and mean function.
+* [CSE201 — Mathematical Analysis II](https://eduwiki.innopolis.university/index.php/BSc:MathematicalAnalysisI): extreme values of differentiable functions.
+* [CSE113 — Philosophy I - (Discrete Math and Logic)](https://eduwiki.innopolis.university/index.php/BSc:Logic_and_Discrete_Mathematics): paths in directed acyclic weighted graphs.
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Domination and Nash | 1. 2 by 2 classical games (Chicken, Prisoner’s dilemma, Battle of the Sexes, coin flips)
+2. n by m games and methods of reduction
+3. Domination and Nash Equilibrium
+4. Game Tree Roll Out
+ |
+| Advanced strategics | 1. Multiple player and random player games
+2. Higher level Strategic planning including - Shelling’s theory of credible threats and promises
+3. Introduction to Evolutionary Game theory
+ |
+| Tournament and Agents | 1. Agent players
+2. Computer Tournaments and Evolutionary Tournaments
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+Game Theory is a powerful method to make predictive decisions about common business cases and acts as a foundational course to decision making in AI systems, such as Bayesian techniques and game trees and Monte Carlo Tree Search. As such the purpose of this course is to provide a solid foundation on the basic structures of mathematical games including the canonical 2 by 2 structures of the Prisoner’s Dilemma, Chicken, Hawk and Dove, and Battle of the Sexes. Then looks at more complicated business examples such as price setting, making creditable threats and promises. It also gives practical instruction on the application of computers in game playing, especially tournament play and development of decision making models.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Should be able to define Nash Equilibrium, Domination, Mixed v. Pure Strategies
+* Should be able to define Evolutionary Stability
+* Should be able to define a number of common agent types (always cooperate/defect, Tit-for-tat, Grudger)
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* A student should understand how game theory affects common daily situations, such as internet trade (as a PD)
+* Should understand the role of Evolutionary Stable Strategies
+* Should understand the history of tournaments as methods to evaluate agent play
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Program a finite state machine to play iterated games
+* Apply both domination and Nash equilibrium to solve pure games
+* Apply both domination, Nash equilibrium, and mixed strategies to solve mixed strategic games
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Labs/seminar classes | 10
+ |
+| Interim performance assessment | 40
+ |
+| Midterm and Exam | 50
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Andrew McEachern, Game Theory : A Classical Introduction, Mathematical Games, and the Tournament
+* Thomas Schelling, Strategy and Conflict
+* William Poundstone, Prisoner’s Dilemma
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Homework and group projects | 1 | 1 | 1
+ |
+| Midterm evaluation | 1 | 0 | 0
+ |
+| Testing (written or computer based) | 1 | 1 | 1
+ |
+| Oral polls | 1 | 0 | 1
+ |
+| Discussions | 1 | 1 | 1
+ |
+| Development of individual parts of software product code | 0 | 1 | 1
+ |
+| Reports | 0 | 0 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is an externality in PD? | 1
+ |
+| Question | Give the Nash Equilibrium of an example 2 by 2 game | 1
+ |
+| Question | Give the Domination in an example n by m game | 1
+ |
+| Question | What is the payoff matrix for a given game | 1
+ |
+| Question | List and example the set of externalities of PD | 0
+ |
+| Question | Worked examples of Nash Equlibrium | 0
+ |
+| Question | Worked examples of Domination | 0
+ |
+| Question | Given the payoff matrix for a given game, what is the outcome of play. | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Using Domination and Nash Equilibrium find a mixed strategy solution for a given game. | 1
+ |
+| Question | How does this game differ if we only allow for pure strategies rather than mixed? | 1
+ |
+| Question | What is the difference between Evolutionary Stable Strategies and Dominator Theory | 1
+ |
+| Question | What is the ESS for an Iterated Prisoner’s Dilemma? | 1
+ |
+| Question | Why does IPD not have a clear Nash Equilibrium and why should we use a Evolutionary Stable Strategies | 0
+ |
+| Question | Show the finite state representation for TFT | 0
+ |
+| Question | Demonstrate the Outcome of a population of half ALLC and half ALLD | 0
+ |
+| Question | Demonstrate the Best Response method on an example matrix | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Define the meaning of a lock box. | 1
+ |
+| Question | Define the meaning of a nice strategy. | 1
+ |
+| Question | How can we make a strategy more cooperative by changing its structure? | 1
+ |
+| Question | Give a listing of IPD agents and a short description of their ruleset | 1
+ |
+| Question | Program a finite state machine for IPD which implements a Lock Box | 0
+ |
+| Question | What properties does a finite state machine have (i.e. is it nice) | 0
+ |
+| Question | If a state machine is nice - what does it’s transitions matrix look like? | 0
+ |
+| Question | How can a 3 and 4 state lockbox reach cooperation? | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. List and example the set of externalities of PD
+2. Worked examples of Nash Equilibrium and Domination
+3. Given the payoff matrix for a given game, what is the outcome of play.
+4. A button is put before you. If you don’t press the button you get a low passing grade on this question. If you press the button and less than half the class presses the button you get a high passing grade for this question. If more than half the class presses the button then those who press the button get a failing grade for this question. Do you press the button?
+
+
+**Section 2**
+
+
+
+1. Simulate the IPD, does the ESS occur?
+2. When the time-line of an ESS is extended but we include the restriction of a finite space, what happens to the equilibriumum
+3. Demonstrate the Best Response method on an example matrix
+
+
+**Section 3**
+
+
+
+1. Show a working finite state machine IPD model of Trifecta.
+2. Create a Tournament agent to compete against your classmates for a given game.
+3. Given a set of players for a IPD model, what is the most likely equilibrium outcome, explain.
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__history.md

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+
+
+
+
+
+
+
+BSc: History
+============
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 History](#History)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+			* [2.2.1.4 Section 4](#Section_4)
+			* [2.2.1.5 Section 5](#Section_5)
+			* [2.2.1.6 Section 6](#Section_6)
+			* [2.2.1.7 Section 7](#Section_7)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+History
+=======
+
+
+* **Course name**: History
+* **Code discipline**: HSS601
+* **Subject area**:
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: Origins of science and its connection with technology in different periods of human’s history; Science and society: how one impacts another and vice versa; Scientific revolution: its nature, causes and consequences for the history of science • The role of Russian science in the World scientific progress.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Introduction to the history of science. Science and technology of ancient civilizations | 1. the concept of science and technology and their role in the history of civilization
+2. scientific knowledge of the pre-civilization period and the first \*ancient Eastern civilizations
+3. features and main achievements of Greek and Roman science
+4. ancient technologies and the problem of their loss
+ |
+| Science and technology in Medieval Europe, Asia and America from 6th to 14th centuries | 1. Main features of the Medieval science
+2. Chinese and Arab science and their impact on European
+3. Science and technology of Medieval Europe
+4. Scientific and technological achievements of pre-Columbian American civilizations
+ |
+| Scientific and technological progress in the era of Renaissance (15th-16th centuries)s | 1. The Age of Discovery: the exploration of new territories.
+2. The emergence of scientific anatomy and chemistry.
+3. Revolution in astronomy: N. Copernicus, I. Kepler, G. Galileo.
+4. Technical achievements of the Renaissance
+ |
+| Scientific revolution of the 17th century and science in the age of Enlightenment | 1. Signs of the coming of the Modern Time. Recognition of science: the emergence of scientific societies and academies.
+2. Chemistry and Natural Science in the 17th-18th centuries.
+3. Advances in maths and physics in the 17-th-18th century.
+ |
+| Industrial revolution of the 19th century: the role of science and technology | 1. Development of the education system and the formation of the disciplinary structure of science
+2. Physics in the 19th century: discoveries in classical thermodynamics and electrodynamics
+3. Chemistry and biology in the 19th century. Charles Darwin's theory of evolution.
+4. The development of technology in the "age of the industrial revolution".
+ |
+| Science and technology from late 19th to the middle of 20th centuries: formation of non-classical science | 1. A revolution in physics: radioactivity and the atomic model, quantum mechanics.
+2. General theory of relativity and astrophysics.
+3. Discoveries in genetics and medicine of the first half of the 20th century.
+4. Technological progress in the late 19th - first half of the 20th centuries.
+ |
+| Modern science and technology: the role of IT | 1. "Post-non-classical science": new forms of organization of science and technology
+2. Modern physics: problems of substance and space research
+3. Revolution of the second half of the 20th century in genetics and microbiology
+4. Information revolution at the turn of the 20th and 21st centuries: perspectives of information technologies
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+The main purpose of this course to make the student aware of basic notions of mathematical programming and of its importance in the area of engineering.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Main achievements of ancient and medieval science
+* Key scientific revolutions from 17th to 20th centuries and their main directions • Technological inventions underlying modern human civilization
+* Main stages of IT development
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Features of scientific development at different stages of human history
+* Logic of the development of the scientific revolution
+* Relationship of scientific and technological progress in the history of mankind • Social factors influencing the development of science and technology
+* Role of Russian science in the history of world science and technology
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Use some methods of the humanitarian studies and their professional field
+* Find and critically analyze information relevant to professional development • Evaluate the possible prospects of a particular scientific and technical product from a historical point of view
+* Argue personal position on the development of science and technology
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Labs/seminar classes | 30
+ |
+| Interim performance assessment | 30
+ |
+| Exams | 40
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* <https://www.physlink.com/education/history.cfm>
+* <https://www.museogalileo.it/en/>
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4 | Section 5 | Section 6 | Section 7
+ |
+| --- | --- | --- | --- | --- | --- | --- | --- |
+| Homework and group projects | 1 | 1 | 1 | 1 | 1 | 1 | 0
+ |
+| Testing (written or computer based) | 1 | 0 | 0 | 0 | 0 | 0 | 1
+ |
+| Discussions | 1 | 1 | 0 | 0 | 1 | 1 | 1
+ |
+| Reports | 0 | 1 | 1 | 1 | 1 | 1 | 1
+ |
+| Midterm evaluation | 0 | 0 | 1 | 0 | 0 | 0 | 0
+ |
+| Essays | 0 | 0 | 0 | 1 | 0 | 0 | 0
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is the science and technology? Why is it important to study their history? | 1
+ |
+| Question | What we owe to the science of ancient Egypt, Mesopotamia and India? | 1
+ |
+| Question | What were the main features of ancient science? What were the reasons for its decline? | 1
+ |
+| Question | What are the main technical achievements of the ancient world? | 1
+ |
+| Question | Discussion – “Paleocontact hypothesis: pro et contra”. | 0
+ |
+| Question | Inventions ahead of their time: the problem of the demand for technology in the ancient world. | 0
+ |
+| Question | Problem of the beginnings of science: existing theories. | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | How has the man's attitude to nature changed in the Middle Ages? Why does the method of experiment appear in the Middle Ages? | 1
+ |
+| Question | What are the main achievements of Arab and Chinese science? How they influenced European science? | 1
+ |
+| Question | How was medieval science related to Christian doctrine? What was the significance of the emergence of universities in Europe during the Middle Ages? | 1
+ |
+| Question | What are the main scientific and technical achievements of pre-Columbian American civilizations (Maya, Inca and Aztec)? | 1
+ |
+| Question | Middle Ages: Era of Decline or Development of Science? (discussion) | 0
+ |
+| Question | Impact of the Crusades on the development of European science (report) | 0
+ |
+| Question | Strategy and tactics of medieval armies: the evolution of military technology (report) | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What changes have occurred in the scientific view of the Renaissance? What is humanism and on what basis does it arise? | 1
+ |
+| Question | What were the prerequisites and reasons for the great geographical discoveries? What were the most important geographical expeditions of the 15th-16th centuries and what discoveries were made as a result? | 1
+ |
+| Question | How did scientific anatomy originate in Europe? What is the significance of William Harvey's discoveries? | 1
+ |
+| Question | What was the revolutionary nature of Copernicus's discovery and why was it not recognized during his lifetime? What laws of planetary motion was able to formulate I. Kepler? How did G. Galileo manage to prove the validity of the Copernican hypothesis? Midterm test based on the questions of the first 3 sections. | 1
+ |
+| Question | Inventions in navigation that made long-distance ocean voyages possible (report) 2. Model of the Universe in the works of D. Bruno (report) | 0
+ |
+| Question | Leonardo da Vinci – a technical genius or a visionary? (report) | 0
+ |
+
+
+#### Section 4
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is “Protestant Ethic” and what are its features? When and why does science become a socially recognized phenomenon? | 1
+ |
+| Question | What system of classification of all living things did Karl Linnaeus suggest? Which scientist was the first to put forward the idea of the evolution of living organisms? | 1
+ |
+| Question | What mathematical discoveries made possible the formation of a mechanistic picture of the world? What is the significance of Isaac Newton's discoveries? What experience did L. Galvani set and what was its significance? | 1
+ |
+| Question | What is the difference between J. Watt's steam engine and T. Newcomen's steam engine? How did the lathe change in the 18th century? | 1
+ |
+| Question | Essay on the personality of one of the scientists of the Early Modern period. | 0
+ |
+| Question | French Enlightement and its role in the development of science (Voltaire, Diderot, Rousseau, and Montesquieu) (report) | 0
+ |
+| Question | Emergence of Russian science: Saint Petersburg Academy of science and the researches of M.V. Lomonosov (report) | 0
+ |
+
+
+#### Section 5
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | How and why did science acquire a disciplinary character? What new educational institutions appeared at this time? | 1
+ |
+| Question | What was the significance of the discoveries of J. Joule and R. Brown for classical thermodynamics? What is the significance of H. Oersted's experiment? Why did M. Faraday's discovery cast doubt on the mechanistic philosophy? | 1
+ |
+| Question | What is the significance of the periodic table of elements of D. I. Mendeleev? Who was the founder of modern microbiology and immunology? On what concepts was Charles Darwin's theory of evolution based? | 1
+ |
+| Question | What were the main stages of using the steam engine in industry and transport? When and by whom was the internal combustion engine invented? How did the communication system of the 19th century develop? | 1
+ |
+| Question | The role of science and technology in transforming Western Europe into the intellectual center of the world (discussion) | 0
+ |
+| Question | Research in 19th century medicine: germ theory of disease (report) | 0
+ |
+| Question | Polzunov or Watt: who was the creator of the steam engine? (report) | 0
+ |
+
+
+#### Section 6
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Why by the end of the 19th century can we talk about the crisis of "classical science" and what were its symptoms? How radioactivity discovered and what was the significance of this discovery? What models of the atom were proposed at the beginning of the 20th century? | 1
+ |
+| Question | What is the significance of A. Einstein's theory of relativity? What astronomical phenomena could it predict? How was the expansion of the universe discovered and what were its first scientific models? | 1
+ |
+| Question | Who is considered the founder of genetics and why? When and how did the first antibiotics appear? | 1
+ |
+| Question | When did the first radio broadcast take place? Who is the inventor of television? What were the first flying machines? How did the world wars affect the development of science and technology? | 1
+ |
+| Question | Weapons that changed the methods of warfare at the turn of the 19th and 20th centuries (report) | 0
+ |
+| Question | Struggle for the atom: the creation of atomic weapons and the use of atomic energy (discussion) | 0
+ |
+| Question | From daguerreotype to photography and from silent cinema to modern television (report) | 0
+ |
+
+
+#### Section 7
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What are the characteristic features of "post-non-classical science"? | 1
+ |
+| Question | What is the meaning of the quark hypothesis and how does it explain the structure of matter? What tasks are being set for the Large Hadron Collider and the International Experimental Thermonuclear Reactor? | 1
+ |
+| Question | What discoveries in genetics in the 1940s produced the decoding of the DNA molecule? What discoveries paved the way for genetic engineering? | 1
+ |
+| Question | What are the major generations of computers in the 20th century? How did the creation of the Internet begin? What are the prospects for the development of information technology? Final testing based on the questions of all sections. | 1
+ |
+| Question | Science and technology as a factor in modern geopolitics (discussion) | 0
+ |
+| Question | What opportunities open up nanotechnology for humanity? (report) | 0
+ |
+| Question | Genetic editing and bioethics issues (report) | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. The problem of the emergence of science in the ancient world. Typical features of ancient science and technology.
+2. The development of astronomical and mathematical knowledge in the ancient world.
+3. Ancient technologies and the problem of their loss.
+
+
+**Section 2**
+
+
+
+1. Education and its connection with science in the Middle Ages.
+2. Heritage of Arab and Chinese science.
+3. Medieval ideas about space and the place of man in the universe.
+
+
+**Section 3**
+
+
+
+1. Preconditions and reasons for the discovery of America.
+2. The development of astronomical knowledge and its impact on the transformation of the scientific views of the inhabitants of Medieval Europe.
+
+
+**Section 4**
+
+
+
+1. Scientific revolution of Early Modern Europe: formation of the mechanical philosophy.
+2. The influence of the development of science and technology on the emergence of the Enlightenment.
+
+
+**Section 5**
+
+
+
+1. The development of transport in the 19th century and its role in changing the way of life in Europe.
+2. The folding of industrial society in the 19th century.
+
+
+**Section 6**
+
+
+
+1. The role of the theory of relativity in shaping the modern worldview.
+2. Radioactivity and its study: implications for the world in the 20th Century.
+3. The development of astronomy in the 20th century and its influence on the formation of the modern worldview.
+
+
+**Section 7**
+
+
+
+1. Study of the microcosm and its influence on the development of technology in the XX XXI centuries
+2. The development of communications and the formation of a modern lifestyle.
+3. IT technologies and their perspectives.
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+**Section 5**
+
+
+**Section 6**
+
+
+**Section 7**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__human-ai_interaction_design.md

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+
+
+
+
+
+
+
+BSc: Human-AI Interaction Design
+================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Animal and human brain representation in neuroscience](#Animal_and_human_brain_representation_in_neuroscience)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+			* [2.2.1.4 Section 4](#Section_4)
+			* [2.2.1.5 Section 5](#Section_5)
+			* [2.2.1.6 Section 6](#Section_6)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Animal and human brain representation in neuroscience
+=====================================================
+
+
+* **Course name**: Animal and human brain representation in neuroscience
+* **Code discipline**: P.1.1 Course Characteristics
+* **Subject area**:
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: Anatomy and physiology of nervous system, sensory organs and musculoskeletal system; Localization in the brain of the different physiological and behavioural aspects of human life.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Anatomy and physiology | 1. Physiology of the brain cell
+2. Anatomy of brain and nervous system
+ |
+| Sensory organs | 1. Taste
+2. Smell
+3. Touch and pain
+4. Sight
+5. Hearing
+ |
+| Resting brain, attention, consciousness, sleep | 1. Mechanism of attention
+2. Resting brain and default mode network
+ |
+| Communication | 1. Language
+2. Brain control of communication
+3. Learning a second language
+4. Handwriting
+ |
+| Emotions, addiction and memory | 1. Neural basis of behaviour
+2. Neural basis of addiction
+ |
+| Movement | 1. Anatomy and physiology of muscles
+2. Tests to evaluate brain and muscle function during movement
+3. Neuronal control of muscles and movement
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+Brain and nervous system are being studied more and more in the last years, as the basis for human computer interface, robotics and so on. Aim of this study is giving a brief overview of key concepts of anatomy and physiology of nervous system, sensory organs and musculoskeletal system, and to understand the localization in the brain of the different physiological and behavioural aspects of human and animal life (e.g. attention, emotions, communication, etc.)
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Anatomy and physiology of the brain and central nervous system
+* Anatomy and physiology of sensory organs (sight, smell, touch, hearing, taste)
+* Anatomy and physiology of musculoskeletal system (muscles, tendons)
+* Brain representation of movement, communication, behaviour, attention, emotions, behaviour, and addiction
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Localization of the different areas of the brain involved in different processes
+* Possible uses of fMRI and other scientific instruments in neurosciences
+* Possible applications of IT in neuroscience
+* Differences in brain activity between humans and animals
+* Different methodologies to explore the brain activity in different situations
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Medical instrumentations to neuroscience
+* IT to neuroscience
+* IT to medical instrumentation
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Labs/seminar classes | 0
+ |
+| Interim performance assessment | 30
+ |
+| Exams | 50
+ |
+| Assigments (personal) | 20
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* M.F. Bear, B.W. Connors, M.A. Paradiso, Neuroscience – Exploring the brain, 4th edition, Wolters Kluwer, 2016
+* Hall, Guyton and Hall Textbook of Medical Physiology, Thirteenth Edition, Elsevier, 2016
+* Platform for large-scale, automated synthesis of functional magnetic resonance imaging (fMRI) data,
+* Kubios HRV analysis software,
+* DICOM Viewer,
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4 | Section 5 | Section 6
+ |
+| --- | --- | --- | --- | --- | --- | --- |
+| Homework and group projects | 1 | 1 | 1 | 1 | 1 | 1
+ |
+| Midterm evaluation | 1 | 1 | 1 | 1 | 1 | 1
+ |
+| Testing (written or computer based) | 1 | 1 | 1 | 1 | 1 | 1
+ |
+| Discussions | 1 | 1 | 1 | 1 | 1 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is the difference between unipolar, bipolar and multipolar neurons | 1
+ |
+| Question | What are the parts of the peripheral nervous system? | 1
+ |
+| Question | What is the action potential? | 1
+ |
+| Question | What are the main parts of the brain? | 1
+ |
+| Question | In the MRI pictures presented, identify the prefrontal cortex | 0
+ |
+| Question | Using heart rate variability, identify which tasks activate primarily the sympathetic nervous system | 0
+ |
+| Question | Design an experiment to evaluate the parasympathetic nervous system | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | How can the brain differentiate between different tastes? | 1
+ |
+| Question | Do receptors adapt to the stimulus? | 1
+ |
+| Question | What is the role of the tapetum lucidum? | 1
+ |
+| Question | Using the MRI pictures presented, identify the auditory cortex | 0
+ |
+| Question | Using the MRI pictures presented, identify the visual cortex | 0
+ |
+| Question | Manipulate the MRI picture provided to highlight the olfactory cortex | 0
+ |
+| Question | Is there a difference in the response of the autonomic nervous system to different kinds of music? Answer using heart rate variability | 0
+ |
+| Question | Is there a difference in the response of the automonic nervous system to different visual stimuli? Answer using heart rate variability | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What are the functions of the default mode network? | 1
+ |
+| Question | What is a zeitgeber? | 1
+ |
+| Question | What are the different functional states of the brain? | 1
+ |
+| Question | What are the two kinds of attention? | 1
+ |
+| Question | How many phases of sleep are there? | 1
+ |
+| Question | Using the MRI pictures provided identify the pituitary gland and the hypothalamus | 0
+ |
+| Question | Using the EEG waves provided identify the functional states of the brain | 0
+ |
+| Question | Develop a way to identify the different phases of the sleep cycle using activity trackers | 0
+ |
+| Question | Design an experiment to identify the different functional states of the brain using heart rate variability | 0
+ |
+
+
+#### Section 4
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Which of these forms of communication comes naturally (you do not have to learn it)? | 1
+ |
+| Question | How are called the two main areas of the brain that control language? | 1
+ |
+| Question | Which hemisphere is usually the one responsible for the language? | 1
+ |
+| Question | What parts of our body are responsible for our voice and spoken letters? | 1
+ |
+| Question | How do we learn to recognize spoken words? | 1
+ |
+| Question | Using the MRI pictures provided identify the areas of the brain responsible for language processing and understanding | 0
+ |
+| Question | Based on the 13 pictures of dogs provided decode what the animals want to tell us | 0
+ |
+| Question | Based on the videos of dogs provided identify the communication of the animals with the humans and with each other | 0
+ |
+| Question | Discuss the possibility of creating an app to decode dog-human or dog-dog communication | 0
+ |
+
+
+#### Section 5
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | How are called the two main memory systems? | 1
+ |
+| Question | Which memory helps us remember facts and events? | 1
+ |
+| Question | What are the main mediators of emotions and behaviour? | 1
+ |
+| Question | Which neurotransmitter is responsible for motivating our behaviour? | 1
+ |
+| Question | Which part of the brain controls fear? | 1
+ |
+| Question | Using the MRI pictures provided identify the parts of the brain involved in memory retaining | 0
+ |
+| Question | I will show you a written text, after 5 minutes I will cover it and you will be asked to write down as many parts of the text as possible, afterwards I will read you a text, at the end you will be asked to write down as many parts of the text as possible. Comparing the answers, you will be able to determine what kind of learner you are | 0
+ |
+| Question | Based on the tests you will find on the website provided, <http://www.whatismylearningstyle.com/index.html>, determine your learning style: is it accurate? How can you improve your study time and skills based on these results? | 0
+ |
+
+
+#### Section 6
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is the function of the musculoskeletal system? | 1
+ |
+| Question | How many types of neurons are involved in the neural regulation of movement? | 1
+ |
+| Question | How is the movement regulated in the brain? | 1
+ |
+| Question | What is the role of the cerebellum? | 1
+ |
+| Question | Using the MRI pictures provided identify the parts of the brain involved in the control of movement and the cerebellum | 0
+ |
+| Question | Analyse the EMG waves provided and confront them with the EEG waves | 0
+ |
+| Question | From the website provided, <https://physionet.org/>, and working in pairs, select and discuss a study that uses either EEG or EMG | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. Please describe the different phases of the action potential of the neural cell
+2. Please describe the differences between sympathetic and parasympathetic nervous system
+3. Please describe the methods used for evaluation of the brain and nervous system
+
+
+**Section 2**
+
+
+
+1. Describe the mechanism by which we are able to localize an auditory stimulus in the space
+2. Describe the mechanism of sight
+3. Describe how tactile receptors work
+4. Describe how the vestibular system works
+5. Describe how pain receptors work
+
+
+**Section 3**
+
+
+
+1. Outline the characteristics of a zeitgeber
+2. Describe the characteristics of the functional states of the brain based on EEG findings
+3. Comment on the cyclical variations of eye movement, heart rate and respiratory rate during sleep
+4. Describe the neural mechanism of sleep
+
+
+**Section 4**
+
+
+
+1. Describe the brain basis of language processing
+2. Describe the effect of learning a second language on the fluency of the first language
+3. What are the characteristics of brain control of handwriting?
+4. List the different ways animals can communicate
+
+
+**Section 5**
+
+
+
+1. Describe and comment on endocrine control of emotions
+2. Describe the stress response
+3. Comment on neuronal effects of addiction and possible differences between different kinds of addictions
+4. Describe and comment on the different kinds of memory
+
+
+**Section 6**
+
+
+
+1. Describe the physiology of muscle cells
+2. Describe the role of cerebellum in the control of movement
+3. What is the homunculus? Compare and comment on the different types described
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+**Section 5**
+
+
+**Section 6**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__information_retrieval.md

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+
+
+
+
+
+
+
+BSc: Information Retrieval
+==========================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Information Retrieval](#Information_Retrieval)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+			* [2.2.1.4 Section 4](#Section_4)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Information Retrieval
+=====================
+
+
+* **Course name**: Information Retrieval
+* **Code discipline**: CSE306
+* **Subject area**: Data Science; Computer systems organization; Information systems; Real-time systems; Information retrieval; World Wide Web; Recommender systems
+
+
+Short Description
+-----------------
+
+
+The course gives an introduction to practical and theoretical aspects of information search and recommender systems.
+This course covers the following concepts: Indexing; Search quality assessment; Relevance; Ranking; Information retrieval; Query; Recommendations; Multimedia retrieval.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+* CSE204 — Analytic Geometry And Linear Algebra II: matrix multiplication, matrix decomposition (SVD, ALS) and approximation (matrix norm), sparse matrix, stability of solution (decomposition), vector spaces, metric spaces, manifold, eigenvector and eigenvalue.
+* CSE113 — Philosophy I - (Discrete Math and Logic): graphs, trees, binary trees, balanced trees, metric (proximity) graphs, diameter, clique, path, shortest path.
+* CSE206 — Probability And Statistics: probability, likelihood, conditional probability, Bayesian rule, stochastic matrix and properties. Analysis: DFT, [discrete] gradient.
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Information retrieval basics | 1. Introduction to IR, major concepts.
+2. Crawling and Web.
+3. Quality assessment.
+ |
+| Text processing and indexing | 1. Building inverted index for text documents. Boolean retrieval model.
+2. Language, tokenization, stemming, searching, scoring.
+3. Spellchecking and wildcard search.
+4. Suggest and query expansion.
+5. Language modelling. Topic modelling.
+ |
+| Vector model and vector indexing | 1. Vector model
+2. Machine learning for vector embedding
+3. Vector-based index structures
+ |
+| Advanced topics. Media processing | 1. Image and video processing, understanding and indexing
+2. Content-based image retrieval
+3. Audio retrieval
+4. Relevance feedback
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+The course is designed to prepare students to understand background theories of information retrieval systems and introduce different information retrieval systems. The course will focus on the evaluation and analysis of such systems as well as how they are implemented. Throughout the course, students will be involved in discussions, readings, and assignments to experience real world systems. The technologies and algorithms covered in this class include machine learning, data mining, natural language processing, data indexing, and so on.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Terms and definitions used in area of information retrieval,
+* Search engine and recommender system essential parts,
+* Quality metrics of information retrieval systems,
+* Contemporary approaches to semantic data analysis,
+* Indexing strategies.
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Understand background theories behind information retrieval systems,
+* How to design a recommender system from scratch,
+* How to evaluate quality of a particular information retrieval system,
+* Core ideas and system implementation and maintenance,
+* How to identify and fix information retrieval system problems.
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Build a recommender service from scratch,
+* Implement a proper index for an unstructured dataset,
+* Plan quality measures for a new recommender service,
+* Run initial data analysis and problem evaluation for a business task, related to information retrieval.
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Assignments | 60
+ |
+| Quizzes | 40
+ |
+| Exams | 0
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+The simples way to succeed is to participate in labs and pass coding assignments in timely manner. This guarantees up to 60% of the grade. Participation in lecture quizzes allow to differentiate the grade.
+
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Manning, Raghavan, Schütze, An Introduction to Information Retrieval, 2008, Cambridge University Press
+* Baeza-Yates, Ribeiro-Neto, Modern Information Retrieval, 2011, Addison-Wesley
+* Buttcher, Clarke, Cormack, Information Retrieval: Implementing and Evaluating Search Engines, 2010, MIT Press
+* [Course repository in github](https://github.com/IUCVLab/information-retrieval).
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4
+ |
+| --- | --- | --- | --- | --- |
+| Development of individual parts of software product code | 1 | 1 | 1 | 1
+ |
+| Homework and group projects | 1 | 1 | 1 | 1
+ |
+| Testing (written or computer based) | 1 | 1 | 1 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Enumerate limitations for web crawling. | 1
+ |
+| Question | Propose a strategy for A/B testing. | 1
+ |
+| Question | Propose recommender quality metric. | 1
+ |
+| Question | Implement DCG metric. | 1
+ |
+| Question | Discuss relevance metric. | 1
+ |
+| Question | Crawl website with respect to robots.txt. | 1
+ |
+| Question | What is typical IR system architecture? | 0
+ |
+| Question | Show how to parse a dynamic web page. | 0
+ |
+| Question | Provide a framework to accept/reject A/B testing results. | 0
+ |
+| Question | Compute DCG for an example query for random search engine. | 0
+ |
+| Question | Implement a metric for a recommender system. | 0
+ |
+| Question | Implement pFound. | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Build inverted index for a text. | 1
+ |
+| Question | Tokenize a text. | 1
+ |
+| Question | Implement simple spellchecker. | 1
+ |
+| Question | Implement wildcard search. | 1
+ |
+| Question | Build inverted index for a set of web pages. | 0
+ |
+| Question | build a distribution of stems/lexemes for a text. | 0
+ |
+| Question | Choose and implement case-insensitive index for a given text collection. | 0
+ |
+| Question | Choose and implement semantic vector-based index for a given text collection. | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Embed the text with an ML model. | 1
+ |
+| Question | Build term-document matrix. | 1
+ |
+| Question | Build semantic index for a dataset using Annoy. | 1
+ |
+| Question | Build kd-tree index for a given dataset. | 1
+ |
+| Question | Why kd-trees work badly in 100-dimensional environment? | 1
+ |
+| Question | What is the difference between metric space and vector space? | 1
+ |
+| Question | Choose and implement persistent index for a given text collection. | 0
+ |
+| Question | Visualize a dataset for text classification. | 0
+ |
+| Question | Build (H)NSW index for a dataset. | 0
+ |
+| Question | Compare HNSW to Annoy index. | 0
+ |
+| Question | What are metric space index structures you know? | 0
+ |
+
+
+#### Section 4
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Extract semantic information from images. | 1
+ |
+| Question | Build an image hash. | 1
+ |
+| Question | Build a spectral representation of a song. | 1
+ |
+| Question | Whats is relevance feedback? | 1
+ |
+| Question | Build a "search by color" feature. | 0
+ |
+| Question | Extract scenes from video. | 0
+ |
+| Question | Write a voice-controlled search. | 0
+ |
+| Question | Semantic search within unlabelled image dataset. | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. Implement text crawler for a news site.
+2. What is SBS (side-by-side) and how is it used in search engines?
+3. Compare pFound with CTR and with DCG.
+4. Explain how A/B testing works.
+5. Describe PageRank algorithm.
+
+
+**Section 2**
+
+
+
+1. Explain how (and why) KD-trees work.
+2. What are weak places of inverted index?
+3. Compare different text vectorization approaches.
+4. Compare tolerant retrieval to spellchecking.
+
+
+**Section 3**
+
+
+
+1. Compare inverted index to HNSW in terms of speed, memory consumption?
+2. Choose the best index for a given dataset.
+3. Implement range search in KD-tree.
+
+
+**Section 4**
+
+
+
+1. What are the approaches to image understanding?
+2. How to cluster a video into scenes and shots?
+3. How speech-to-text technology works?
+4. How to build audio fingerprints?
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+
+1. Solve a complex coding problem similar to one of the homework or lab.
+
+
+**Section 2**
+
+
+
+1. Solve a complex coding problem similar to one of the homework or lab.
+
+
+**Section 3**
+
+
+
+1. Solve a complex coding problem similar to one of the homework or lab.
+
+
+**Section 4**
+
+
+
+1. Solve a complex coding problem similar to one of the homework or lab.
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__introduction_to_artificial_intelligence.md

@@ -0,0 +1,386 @@
+
+
+
+
+
+
+
+BSc: Introduction To Artificial Intelligence
+============================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Introduction to Artificial Intelligence](#Introduction_to_Artificial_Intelligence)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Introduction to Artificial Intelligence
+=======================================
+
+
+* **Course name**: Introduction to Artificial Intelligence
+* **Code discipline**: ?????
+* **Subject area**:
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: Artificial Intelligence: Introduction to the ethical use of AI and the framework of development of AI systems; Artificial Intelligence: Evolutionary Algorithms.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| History and Philosophy of AI | 1. Introduction to the practical applications of AI
+2. History of Epistemology, particularly on the issue of knowledge creation and intelligence.
+3. Understanding of the Chinese room and Turing test
+4. Appreciation for the role of AI in Industries and the the application
+5. Application of the PEAS model
+6. Application of the Thinking/Acting Humanly/Rationally
+7. Appreciation of the Ethical Issues in AI
+ |
+| Title 2 | 1. Searching Algorithms
+2. Tree Searches and logic, including basics of PROLOG as a lanuage for answering such problems
+3. First and Second order logic
+ |
+| Topics in Evolutionary Algorithms | 1. Understanding of the four base Evolutionary Algorithms: GA, GP, ES, EP
+2. Application of one of these four.
+3. Analysis of the application of these four types to a number of problem instances.
+4. Application of the appropriate statistical models and scientific method (i.e. Hypothesis testing) to evaluate the EA.
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+Have you ever wondered about how computers decide on what your credit worthiness is, or how they can play chess as good as a world master, or how world class circuits can be built with a minimal number of crossed wires? Perhaps you have wanted to build a human like robot, or have wanted to explore the stars with automated probes. Artificial Intelligence is the field which examines such problems. The goal is to provide a diverse theoretical overview of historical and current thought in the realm of Artificial Intelligence, Computational Intelligence, Robotics and Machine Learning Techniques.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Gather an appreciation of the history of AI founders
+* Solve simple problems using random, guided, and directed, search methods and be able to compare their abilities to solve the problem using a statistical argument
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Understand the PEAS model of problem definition
+* Understand the Environment Model
+* Understand the role of AI within computer science in a variety of fields and applications
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Apply Evolutionary Algorithms to a number of problems
+* Apply the PEAS model of problem definition
+* Apply the apply the Environment Model
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Assignment 1 | 20
+ |
+| Assignment 2 | 20
+ |
+| Lab Participation | 10
+ |
+| Midterm | 25
+ |
+| Final | 25
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Russell & Norvig - Artificial Intelligence: A Modern Approach, 3rd Edition
+* Ashlock - Evolutionary Computation for Modeling and Optimization
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Homework and group projects | 1 | 1 | 1
+ |
+| Midterm evaluation | 1 | 1 | 0
+ |
+| Essays | 1 | 0 | 0
+ |
+| Discussions | 1 | 1 | 1
+ |
+| Development of individual parts of software product code | 0 | 1 | 1
+ |
+| Testing (written or computer based) | 0 | 1 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | State and apply the PEAS model to a set of problems. | 1
+ |
+| Question | State the difference between Plato and Aristotle’s conceptions of knowledge - refer to Socrates definition? | 1
+ |
+| Question | Are you intelligent? What marks you as such? What is the definition? | 1
+ |
+| Question | Are you creative? What marks you as such? What is the definition? | 1
+ |
+| Question | Apply the PEAS model as a group to a real world instance. | 0
+ |
+| Question | Discuss - Humans in many low skilled tasks are being replaced by automation, what role do practitioners have in protecting its abuse | 0
+ |
+| Question | Discuss - Asimov’s laws of robotics are used as a science fiction application of ethics in AI, do you think they have a role in the real world. | 0
+ |
+| Question | Discuss - how can we prevent bias from entering into systems. | 0
+ |
+| Question | Discuss - What does it mean for a Computer to be Creative? | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Apply Prolog to an example of a family tree | 1
+ |
+| Question | Apply Prolog to an example of a logic problem | 1
+ |
+| Question | Compare and Contrast between two different search algorithms shown in class and implement. | 1
+ |
+| Question | Given an example data set which search would you use and why? | 1
+ |
+| Question | How does Prolog implement a tree? | 0
+ |
+| Question | Does this program work - mark out any errors. | 0
+ |
+| Question | What is the difference between a red and green cut? | 0
+ |
+| Question | What is the result of this Query? | 0
+ |
+| Question | What is the time complexity of this algorithm? | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Define a particular EA by its data structure | 1
+ |
+| Question | Implement an EA, write a Report about the implementation with sufficient search of the parameter space justified by statistical evaluations | 1
+ |
+| Question | Analysis of two EA types base upon their representation and variation operators and suitability to a problem space. | 1
+ |
+| Question | Produce a new type of EA based upon the concepts seen in class and speculate as to its effectivenesss on a problem via hypothesis testing. | 1
+ |
+| Question | Labs within this section are primarily for supporting assistance with the above objectives, e.g. work periods with TA assistance. | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. Apply the PEAS model to a real world instance.
+2. You have a classification problem involving images, from the perspective of Plato and Aristotle on knowledge, which algorithm would they implement, justify your decision.
+3. Write a short essay based upon either the prosecution or defense of a trial of an Android who has passed the Turing test who is petitioning the court for human rights. What would be your case for or against using concepts in class such as Turing test, Chinese room, etc.?
+
+
+**Section 2**
+
+
+
+1. Here is an example family tree. Given a simple Prolog Query - what would be the result?
+2. Here is an example logic problem. Given a Prolog Query - what would be the result.
+3. Compare and Contrast two different search algorithms in terms of time and space complexity
+4. Given data of type X, what search algorithm should you use and why?
+
+
+**Section 3**
+
+
+
+1. Show an analysis on a problem instance as to which EA method you would use, justify your answer based on the representation of the problem data.
+2. Implement an EA for a problem, show statistical justification of your result.
+3. Produce a report about a new creation of an EA system with sufficient justification with hypothesis tests.
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__introduction_to_artificial_intelligence.s22.md

@@ -0,0 +1,437 @@
+
+
+
+
+
+
+
+BSc: Introduction To Artificial Intelligence.s22
+================================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Introduction to Artificial Intelligence](#Introduction_to_Artificial_Intelligence)
+	+ [1.1 Course Characteristics](#Course_Characteristics)
+		- [1.1.1 Key concepts of the class](#Key_concepts_of_the_class)
+		- [1.1.2 What is the purpose of this course?](#What_is_the_purpose_of_this_course.3F)
+	+ [1.2 Course Objectives Based on Bloom’s Taxonomy](#Course_Objectives_Based_on_Bloom.E2.80.99s_Taxonomy)
+		- [1.2.1 What should a student remember at the end of the course?](#What_should_a_student_remember_at_the_end_of_the_course.3F)
+		- [1.2.2 What should a student be able to understand at the end of the course?](#What_should_a_student_be_able_to_understand_at_the_end_of_the_course.3F)
+		- [1.2.3 What should a student be able to apply at the end of the course?](#What_should_a_student_be_able_to_apply_at_the_end_of_the_course.3F)
+		- [1.2.4 Course evaluation](#Course_evaluation)
+		- [1.2.5 Grades range](#Grades_range)
+		- [1.2.6 Resources and reference material](#Resources_and_reference_material)
+	+ [1.3 Course Sections](#Course_Sections)
+		- [1.3.1 Section 1](#Section_1)
+			* [1.3.1.1 Section title:](#Section_title:)
+		- [1.3.2 Topics covered in this section:](#Topics_covered_in_this_section:)
+		- [1.3.3 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F)
+		- [1.3.4 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section)
+		- [1.3.5 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section)
+		- [1.3.6 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section)
+		- [1.3.7 Section 2](#Section_2)
+			* [1.3.7.1 Section title:](#Section_title:_2)
+		- [1.3.8 Topics covered in this section:](#Topics_covered_in_this_section:_2)
+		- [1.3.9 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_2)
+		- [1.3.10 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_2)
+		- [1.3.11 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_2)
+		- [1.3.12 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_2)
+		- [1.3.13 Section 3](#Section_3)
+			* [1.3.13.1 Section title:](#Section_title:_3)
+			* [1.3.13.2 Topics covered in this section:](#Topics_covered_in_this_section:_3)
+		- [1.3.14 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_3)
+		- [1.3.15 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_3)
+			* [1.3.15.1 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_3)
+			* [1.3.15.2 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_3)
+
+
+
+Introduction to Artificial Intelligence
+=======================================
+
+
+* **Course name:** Introduction to Artificial Intelligence
+* **Course number:** ?????
+
+
+Course Characteristics
+----------------------
+
+
+### Key concepts of the class
+
+
+* Artificial Intelligence: Introduction to the ethical use of AI and the framework of development of AI systems
+* Artificial Intelligence: Evolutionary Algorithms
+
+
+### What is the purpose of this course?
+
+
+Have you ever wondered about how computers decide on what your credit worthiness is, or how they can play chess as good as a world master, or how world class circuits can be built with a minimal number of crossed wires? Perhaps you have wanted to build a human like robot, or have wanted to explore the stars with automated probes. Artificial Intelligence is the field which examines such problems. The goal is to provide a diverse theoretical overview of historical and current thought in the realm of Artificial Intelligence, Computational Intelligence, Robotics and Machine Learning Techniques.
+
+
+
+Course Objectives Based on Bloom’s Taxonomy
+-------------------------------------------
+
+
+#### What should a student remember at the end of the course?
+
+
+By the end of the course, the students should be able to
+
+
+
+* Gather an appreciation of the history of AI founders
+* Solve simple problems using random, guided, and directed, search methods and be able to compare their abilities to solve the problem using a statistical argument
+
+
+#### What should a student be able to understand at the end of the course?
+
+
+* Understand the PEAS model of problem definition
+* Understand the Environment Model
+* Understand the role of AI within computer science in a variety of fields and applications
+
+
+#### What should a student be able to apply at the end of the course?
+
+
+* Apply Evolutionary Algorithms to a number of problems
+* Apply the PEAS model of problem definition
+* Apply the apply the Environment Model
+
+
+### Course evaluation
+
+
+
+
+Course grade breakdown
+| Type | Points
+ |
+| --- | --- |
+| Assignment 1 | 20
+ |
+| Assignment 2 | 20
+ |
+| Lab Participation | 10
+ |
+| Midterm | 25
+ |
+| Final | 25
+ |
+
+
+  
+
+This course has a required class element of practical work on course elements, the retake is not a substitute for practical knowledge, and it is inherently unfair that students who have not submitted these practical elements are graded the same as those who have accomplished course materials. In order to be eligible for the retake, a student is required to have submitted all course assignments, and have a passing grade on those elements. The lacking/failing elements, can be presented for this purpose up to 3 business days before the retake for evaluation. In the case of the resubmission of a failing element, a document should be attached noting which changes have been made to the assignment in order to lead to a passing mark. Lack of these elements in a passing state presented to the committee will be considered a failing grade for the retake.
+
+
+The retake grade will count as the final course grade, with the first retake giving no more than a B as final grade, and the second retake giving no more than a C. The first retake will be a written exam submitted to the professor, and the second retake as an oral commission.
+
+
+
+### Grades range
+
+
+
+
+Course grading range
+|  |  | **Proposed range** |
+| --- | --- | --- |
+| A. Excellent
+ | 90-100
+ |  |
+| B. Good
+ | 75-89
+ |  |
+| C. Satisfactory
+ | 60-74
+ |  |
+| D. Poor
+ | 0-59
+ |  |
+
+
+If necessary, please indicate freely your course’s grading features.
+
+
+
+### Resources and reference material
+
+
+* Russell & Norvig - Artificial Intelligence: A Modern Approach, 3rd Edition
+* Ashlock - Evolutionary Computation for Modeling and Optimization
+
+
+Course Sections
+---------------
+
+
+The main sections of the course and approximate hour distribution between them is as follows:
+
+
+
+
+
+Course Sections
+| **Section** | **Section Title** | **Teaching Hours** |
+| --- | --- | --- |
+| 1
+ | History and Philosophy of AI
+ | 16
+ |
+| 2
+ | Searching as Optimization
+ | 16
+ |
+| 3
+ | Topics in Evolutionary Algorithms
+ | 16
+ |
+
+
+### Section 1
+
+
+#### Section title:
+
+
+History and Philosophy of AI
+
+
+
+### Topics covered in this section:
+
+
+* Introduction to the practical applications of AI
+* History of Epistemology, particularly on the issue of knowledge creation and intelligence.
+* Understanding of the Chinese room and Turing test
+* Appreciation for the role of AI in Industries and the the application
+* Application of the PEAS model
+* Application of the Thinking/Acting Humanly/Rationally
+* Appreciation of the Ethical Issues in AI
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+|a|c| & **Yes/No**  
+
+Development of individual parts of software product code & 0  
+
+Homework and group projects & 1  
+
+Midterm evaluation & 1  
+
+Testing (written or computer based) & 0  
+
+Reports & 0  
+
+Essays & 1  
+
+Oral polls & 0  
+
+Discussions & 1  
+
+
+
+  
+
+
+
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. State and apply the PEAS model to a set of problems.
+2. State the difference between Plato and Aristotle’s conceptions of knowledge - refer to Socrates definition?
+3. Are you intelligent? What marks you as such? What is the definition?
+4. Are you creative? What marks you as such? What is the definition?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Apply the PEAS model as a group to a real world instance.
+2. Discuss - Humans in many low skilled tasks are being replaced by automation, what role do practitioners have in protecting its abuse
+3. Discuss - Asimov’s laws of robotics are used as a science fiction application of ethics in AI, do you think they have a role in the real world.
+4. Discuss - how can we prevent bias from entering into systems.
+5. Discuss - What does it mean for a Computer to be Creative?
+
+
+### Test questions for final assessment in this section
+
+
+1. Apply the PEAS model to a real world instance.
+2. You have a classification problem involving images, from the perspective of Plato and Aristotle on knowledge, which algorithm would they implement, justify your decision.
+3. Write a short essay based upon either the prosecution or defense of a trial of an Android who has passed the Turing test who is petitioning the court for human rights. What would be your case for or against using concepts in class such as Turing test, Chinese room, etc.?
+
+
+### Section 2
+
+
+#### Section title:
+
+
+Title 2
+
+
+
+### Topics covered in this section:
+
+
+* Searching Algorithms
+* Tree Searches and logic, including basics of PROLOG as a lanuage for answering such problems
+* First and Second order logic
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+|a|c| & **Yes/No**  
+
+Development of individual parts of software product code & 1  
+
+Homework and group projects & 1  
+
+Midterm evaluation & 1  
+
+Testing (written or computer based) & 1  
+
+Reports & 0  
+
+Essays & 0  
+
+Oral polls & 0  
+
+Discussions & 1  
+
+
+
+  
+
+
+
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. Apply Prolog to an example of a family tree
+2. Apply Prolog to an example of a logic problem
+3. Compare and Contrast between two different search algorithms shown in class and implement.
+4. Given an example data set which search would you use and why?
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. How does Prolog implement a tree?
+2. Does this program work - mark out any errors.
+3. What is the difference between a red and green cut?
+4. What is the result of this Query?
+5. What is the time complexity of this algorithm?
+
+
+### Test questions for final assessment in this section
+
+
+1. Here is an example family tree. Given a simple Prolog Query - what would be the result?
+2. Here is an example logic problem. Given a Prolog Query - what would be the result.
+3. Compare and Contrast two different search algorithms in terms of time and space complexity
+4. Given data of type X, what search algorithm should you use and why?
+
+
+### Section 3
+
+
+#### Section title:
+
+
+Topics in Evolutionary Algorithms
+
+
+
+#### Topics covered in this section:
+
+
+* Understanding of the four base Evolutionary Algorithms: GA, GP, ES, EP
+* Application of one of these four.
+* Analysis of the application of these four types to a number of problem instances.
+* Application of the appropriate statistical models and scientific method (i.e. Hypothesis testing) to evaluate the EA.
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+|a|c| & **Yes/No**  
+
+Development of individual parts of software product code & 1  
+
+Homework and group projects & 1  
+
+Midterm evaluation & 0  
+
+Testing (written or computer based) & 1  
+
+Reports & 0  
+
+Essays & 0  
+
+Oral polls & 0  
+
+Discussions & 1  
+
+
+
+  
+
+
+
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. Define a particular EA by its data structure
+2. Implement an EA, write a Report about the implementation with sufficient search of the parameter space justified by statistical evaluations
+3. Analysis of two EA types base upon their representation and variation operators and suitability to a problem space.
+4. Produce a new type of EA based upon the concepts seen in class and speculate as to its effectivenesss on a problem via hypothesis testing.
+
+
+#### Typical questions for seminar classes (labs) within this section
+
+
+1. Labs within this section are primarily for supporting assistance with the above objectives, e.g. work periods with TA assistance.
+
+
+#### Test questions for final assessment in this section
+
+
+1. Show an analysis on a problem instance as to which EA method you would use, justify your answer based on the representation of the problem data.
+2. Implement an EA for a problem, show statistical justification of your result.
+3. Produce a report about a new creation of an EA system with sufficient justification with hypothesis tests.
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__introduction_to_big_data.md

@@ -0,0 +1,549 @@
+
+
+
+
+
+
+
+BSc: Introduction To Big Data
+=============================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Introduction to Big Data](#Introduction_to_Big_Data)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+			* [2.2.1.4 Section 4](#Section_4)
+			* [2.2.1.5 Section 5](#Section_5)
+			* [2.2.1.6 Section 6](#Section_6)
+			* [2.2.1.7 Section 7](#Section_7)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Introduction to Big Data
+========================
+
+
+* **Course name**: Introduction to Big Data
+* **Code discipline**: N/A
+* **Subject area**:
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: Distributed data organization; Distributed data processing.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Introduction | 1. What is Big Data
+2. Characteristics of Big Data
+3. Data Structures
+4. Types of Analytics
+ |
+| Hadoop | 1. Data storage
+2. Clustering
+3. Design decisions
+4. Scaling
+5. Distributed systems
+6. The ecosystem
+ |
+| HDFS | 1. Distributed storage
+2. Types of nodes
+3. Files and blocks
+4. Replication
+5. Memory usage
+ |
+| MapReduce | 1. Distributed processing
+2. MapReduce model
+3. Applications
+4. Tasks management
+5. Patterns
+ |
+| YARN | 1. Resource manager
+2. Components
+3. Run an application
+4. Schedules
+ |
+| Optimizing Data Processing | 1. CAP theorem
+2. Distributed storage and computation
+3. Batch Processing
+4. Stream Processing
+5. Usage patterns
+6. NoSQL databases
+ |
+| Spark | 1. Architecture
+2. Use cases
+3. Job scheduling
+4. Data types
+5. SparkML
+6. GraphX
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+Software systems are increasingly based on large amount of data that come from a wide range of sources (e.g., logs, sensors, user-generated content, etc.). However, data are useful only if it can be analyzed properly to extract meaningful information can be used (e.g., to take decisions, to make predictions, etc.). This course provides an overview of the state-of-the-art technologies, tools, architectures, and systems constituting the big data computing solutions landscape. Particular attention will be given to the Hadoop ecosystem that is widely adopted in the industry.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* The most common structures of distributed storage.
+* Batch processing techniques
+* Stream processing techniques
+* Basic distributed data processing algorithms
+* Basic tools to address specific processing needs
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* The basis of the CAP theorem
+* The structure of the MapReduce
+* How to process batch data
+* How to process stream data
+* The characteristics of a NoSQL database
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Use a NoSQL database
+* Write a program for batch processing
+* Write a program for stream processing
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Labs/seminar classes | 30
+ |
+| Interim performance assessment | 30
+ |
+| Exams | 40
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Slides and material provided during the course.
+* Vignesh Prajapati. Big Data Analytics with R and Hadoop. Packt Publishing, 2013
+* Jules J. Berman. Principles of Big Data: Preparing, Sharing, and Analyzing Complex Information. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 2013
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4 | Section 5 | Section 6 | Section 7
+ |
+| --- | --- | --- | --- | --- | --- | --- | --- |
+| Testing (written or computer based) | 1 | 1 | 1 | 1 | 1 | 1 | 1
+ |
+| Discussions | 1 | 1 | 1 | 1 | 1 | 1 | 1
+ |
+| Development of individual parts of software product code | 0 | 0 | 1 | 1 | 1 | 1 | 1
+ |
+| Homework and group projects | 0 | 0 | 1 | 1 | 1 | 1 | 1
+ |
+| Midterm evaluation | 0 | 0 | 1 | 1 | 1 | 1 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Describe the 6 Vs | 1
+ |
+| Question | Describe the types of analytics | 1
+ |
+| Question | Design the structure of a DB to address a specific analytics type | 0
+ |
+| Question | Give examples of the 6 Vs in real systems | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Describe the Hadoop ecosystem | 1
+ |
+| Question | Structure of an Hadoop cluster | 1
+ |
+| Question | Describe the scaling techniques | 1
+ |
+| Question | Configure a basic Hadoop node | 0
+ |
+| Question | Configure a basic Hadoop cluster | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Describe the characteristics of the different nodes | 1
+ |
+| Question | How files and blocks are managed | 1
+ |
+| Question | How memory is managed | 1
+ |
+| Question | How replication works | 1
+ |
+| Question | Configure a HDFS cluster | 0
+ |
+| Question | Configure different replication approaches | 0
+ |
+| Question | Build a HDFS client | 0
+ |
+| Question | Use a HDFS command line | 0
+ |
+
+
+#### Section 4
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Describe the MapReduce model | 1
+ |
+| Question | Describe tasks management | 1
+ |
+| Question | Describe patterns of usage | 1
+ |
+| Question | Solve with MapReduce a specific problem | 0
+ |
+| Question | Implement a usage pattern | 0
+ |
+
+
+#### Section 5
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Describe the resource manager | 1
+ |
+| Question | Describe the lifecycle of an application | 1
+ |
+| Question | Describe and compare the scheduling approaches | 1
+ |
+| Question | Compare the performance of the different schedules in different load conditions | 0
+ |
+| Question | Configure YARN | 0
+ |
+| Question | Evaluate the overall performance of YARN | 0
+ |
+
+
+#### Section 6
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Analyze the CAP theorem | 1
+ |
+| Question | Define the kinds of data storage available | 1
+ |
+| Question | Characteristics of batch processing | 1
+ |
+| Question | Characteristics of stream processing | 1
+ |
+| Question | Describe the usage patterns | 1
+ |
+| Question | Compare NoSQL databases | 1
+ |
+| Question | Build a program to solve a problem with batch processing | 0
+ |
+| Question | Build a program to solve a problem with stream processing | 0
+ |
+| Question | Interact with a NoSQL database | 0
+ |
+
+
+#### Section 7
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Describe the architecture of Spark | 1
+ |
+| Question | Describe the types of schedulers | 1
+ |
+| Question | Different characteristics of the data types | 1
+ |
+| Question | Features of SparkML | 1
+ |
+| Question | Features of GraphX | 1
+ |
+| Question | Analyze the performance of different schedulers | 0
+ |
+| Question | Write a program exploiting the features of each data type | 0
+ |
+| Question | Write a program using SparkML | 0
+ |
+| Question | Write a program using GraphX | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. Design the structure of a DB to address a specific analytics type
+2. Give examples of the 6 Vs in real systems
+
+
+**Section 2**
+
+
+
+1. Identify the Hadoop components useful to address a specific problem.
+2. Configure an multi-node Hadoop system.
+
+
+**Section 3**
+
+
+
+1. Configure a HDFS cluster with some specific replication approaches
+2. Build a HDFS client
+
+
+**Section 4**
+
+
+
+1. Describe the advantages and disadvantages of the MapReduce model
+2. Solve a task designing the solution using MapReduce
+3. Solve a task designing the solution using a composition of usage patterns
+
+
+**Section 5**
+
+
+
+1. Evaluate the performance of a specific configuration
+2. Compare the different schedules
+
+
+**Section 6**
+
+
+
+1. Identify problems and solutions related to the CAP theorem
+2. Compare solutions with batch and stream processing approaches
+3. Design a system using a NoSQL database
+
+
+**Section 7**
+
+
+
+1. Compare the performance of different schedules with different loads
+2. Extend the SparkML library with a custom algorithm
+3. Extend the GraphX library with a custom algorithm
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+**Section 5**
+
+
+**Section 6**
+
+
+**Section 7**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__introduction_to_computer_vision.md

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+
+
+
+
+
+
+
+BSc: Introduction To Computer Vision
+====================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Introduction to Computer Vision](#Introduction_to_Computer_Vision)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+
+
+
+Introduction to Computer Vision
+===============================
+
+
+* **Course name**: Introduction to Computer Vision
+* **Code discipline**: XXX
+* **Subject area**:
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: Computer vision using machine learning models.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Representation of images and videos | 1. Computer representation
+2. Rescaling/manipulating images
+ |
+| Image Classification | 1. Loss Functions
+2. Backpropagation
+3. Neural Networks
+4. Training
+ |
+| Convolutional Neural Networks | 1. Training
+2. Architectures
+ |
+| Recurrent Neural Networks | 1. Training
+2. Architectures
+ |
+| Image Segmentation and object detection | 1. Techniques
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+This course provides an introductory but detailed treatment of computer vision techniques using machine learning, with an emphasis on implementing the computer vision algorithms from the scratch and using them to solve real-world problems. The course will begin with the image representation, but will quickly transition to computer vision techniques using machine learning, finishing with image segmentation and object detection and recognition. A key focus of the course is on providing students with not only theory but also hands-on practice of building their computer vision applications.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Significant exposure to real-world implementations
+* To develop research interest in the theory and application of computer vision
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Suitability of different computer vision models in different scenarios
+* Ability to choose the right model for the given task
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Hands on experience to implement different models to know inside behavior
+* Sufficient exposure to train and deploy model for the given task
+* Fine tune the deployed model in the real-world settings
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 91-100 | -
+ |
+| B. Good | 78-90 | -
+ |
+| C. Satisfactory | 60-77 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Weekly Labs | 50
+ |
+| Weekly Quizzes | 10
+ |
+| Midterm Exam | 15
+ |
+| Final Exam | 25
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Handouts supplied by the instructor
+* Materials from the internet and research papers shared by instructor
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__introduction_to_machine_learning.md

@@ -0,0 +1,499 @@
+
+
+
+
+
+
+
+BSc: Introduction To Machine Learning
+=====================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Introduction to Machine Learning](#Introduction_to_Machine_Learning)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+			* [2.2.1.4 Section 4](#Section_4)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Introduction to Machine Learning
+================================
+
+
+* **Course name**: Introduction to Machine Learning
+* **Code discipline**: R-01
+* **Subject area**:
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: Machine learning paradigms; Machine Learning approaches, and algorithms.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+* CSE202 — Analytical Geometry and Linear Algebra I
+* CSE204 — Analytical Geometry and Linear Algebra II
+* CSE201 — Mathematical Analysis I
+* CSE203 — Mathematical Analysis II
+* CSE206 — Probability And Statistics
+* CSE117 — Data Structures and Algorithms: python, numpy, basic object-oriented concepts, memory management.
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Supervised Learning | 1. Introduction to Machine Learning
+2. Derivatives and Cost Function
+3. Data Pre-processing
+4. Linear Regression
+5. Multiple Linear Regression
+6. Gradient Descent
+7. Polynomial Regression
+8. Bias-varaince Tradeoff
+9. Difference between classification and regression
+10. Logistic Regression
+11. Naive Bayes
+12. KNN
+13. Confusion Metrics
+14. Performance Metrics
+15. Regularization
+16. Hyperplane Based Classification
+17. Perceptron Learning Algorithm
+18. Max-Margin Classification
+19. Support Vector Machines
+20. Slack Variables
+21. Lagrangian Support Vector Machines
+22. Kernel Trick
+ |
+| Decision Trees and Ensemble Methods | 1. Decision Trees
+2. Bagging
+3. Boosting
+4. Random Forest
+5. Adaboost
+ |
+| Unsupervised Learning | 1. K-means Clustering
+2. K-means++
+3. Hierarchical Clustering
+4. DBSCAN
+5. Mean-shift
+ |
+| Deep Learning | 1. Artificial Neural Networks
+2. Back-propagation
+3. Convolutional Neural Networks
+4. Autoencoder
+5. Variatonal Autoencoder
+6. Generative Adversairal Networks
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+There is a growing business need of individuals skilled in artificial intelligence, data analytics, and machine learning. Therefore, the purpose of this course is to provide students with an intensive treatment of a cross-section of the key elements of machine learning, with an emphasis on implementing them in modern programming environments, and using them to solve real-world data science problems.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Different learning paradigms
+* A wide variety of learning approaches and algorithms
+* Various learning settings
+* Performance metrics
+* Popular machine learning software tools
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Difference between different learning paradigms
+* Difference between classification and regression
+* Concept of learning theory (bias/variance tradeoffs and large margins etc.)
+* Kernel methods
+* Regularization
+* Ensemble Learning
+* Neural or Deep Learning
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Classification approaches to solve supervised learning problems
+* Clustering approaches to solve unsupervised learning problems
+* Ensemble learning to improve a model’s performance
+* Regularization to improve a model’s generalization
+* Deep learning algorithms to solve real-world problems
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Labs/seminar classes | 0
+ |
+| Interim performance assessment | 40
+ |
+| Exams | 60
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* T. Hastie, R. Tibshirani, D. Witten and G. James. An Introduction to Statistical Learning. Springer 2013.
+* T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning. Springer 2011.
+* Tom M Mitchel. Machine Learning, McGraw Hill
+* Christopher M. Bishop. Pattern Recognition and Machine Learning, Springer
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4
+ |
+| --- | --- | --- | --- | --- |
+| Development of individual parts of software product code | 1 | 1 | 1 | 1
+ |
+| Homework and group projects | 1 | 1 | 1 | 1
+ |
+| Midterm evaluation | 1 | 1 | 1 | 1
+ |
+| Testing (written or computer based) | 1 | 1 | 1 | 1
+ |
+| Discussions | 1 | 1 | 1 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Is it true that in simple linear regression 
+
+
+
+
+
+
+R
+
+2
+
+
+
+
+
+
+{\displaystyle {\textstyle R^{2}}}
+
+{\displaystyle {\textstyle R^{2}}} and the squared correlation between X and Y are identical? | 1
+ |
+| Question | What are the two assumptions that the Linear regression model makes about the Error Terms? | 1
+ |
+| Question | Fit a regression model to a given data problem, and support your choice of the model. | 1
+ |
+| Question | In a list of given tasks, choose which are regression and which are classification tasks. | 1
+ |
+| Question | In a given graphical model of binary random variables, how many parameters are needed to define the Conditional Probability Distributions for this Bayes Net? | 1
+ |
+| Question | Write the mathematical form of the minimization objective of Rosenblatt’s perceptron learning algorithm for a two-dimensional case. | 1
+ |
+| Question | What is perceptron learning algorithm? | 1
+ |
+| Question | Write the mathematical form of its minimization objective for a two-dimensional case. | 1
+ |
+| Question | What is a max-margin classifier? | 1
+ |
+| Question | Explain the role of slack variable in SVM. | 1
+ |
+| Question | How to implement various regression models to solve different regression problems? | 0
+ |
+| Question | Describe the difference between different types of regression models, their pros and cons, etc. | 0
+ |
+| Question | Implement various classification models to solve different classification problems. | 0
+ |
+| Question | Describe the difference between Logistic regression and naive bayes. | 0
+ |
+| Question | Implement perceptron learning algorithm, SVMs, and its variants to solve different classification problems. | 0
+ |
+| Question | Solve a given optimization problem using the Lagrange multiplier method. | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What are pros and cons of decision trees over other classification models? | 1
+ |
+| Question | Explain how tree-pruning works. | 1
+ |
+| Question | What is the purpose of ensemble learning? | 1
+ |
+| Question | What is a bootstrap, and what is its role in Ensemble learning? | 1
+ |
+| Question | Explain the role of slack variable in SVM. | 1
+ |
+| Question | Implement different variants of decision trees to solve different classification problems. | 0
+ |
+| Question | Solve a given classification problem problem using an ensemble classifier. | 0
+ |
+| Question | Implement Adaboost for a given problem. | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Which implicit or explicit objective function does K-means implement? | 1
+ |
+| Question | Explain the difference between k-means and k-means++. | 1
+ |
+| Question | Whaat is single-linkage and what are its pros and cons? | 1
+ |
+| Question | Explain how DBSCAN works. | 1
+ |
+| Question | Implement different clustering algorithms to solve to solve different clustering problems. | 0
+ |
+| Question | Implement Mean-shift for video tracking | 0
+ |
+
+
+#### Section 4
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is a fully connected feed-forward ANN? | 1
+ |
+| Question | Explain different hyperparameters of CNNs. | 1
+ |
+| Question | Calculate KL-divergence between two probability distributions. | 1
+ |
+| Question | What is a generative model and how is it different from a discriminative model? | 1
+ |
+| Question | Implement different types of ANNs to solve to solve different classification problems. | 0
+ |
+| Question | Calculate KL-divergence between two probability distributions. | 0
+ |
+| Question | Implement different generative models for different problems. | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. What does it mean for the standard least squares coefficient estimates of linear regression to be scale equivariant?
+2. Given a fitted regression model to a dataset, interpret its coefficients.
+3. Explain which regression model would be a better fit to model the relationship between response and predictor in a given data.
+4. If the number of training examples goes to infinity, how will it affect the bias and variance of a classification model?
+5. Given a two dimensional classification problem, determine if by using Logistic regression and regularization, a linear boundary can be estimated or not.
+6. Explain which classification model would be a better fit to for a given classification problem.
+7. Consider the Leave-one-out-CV error of standard two-class SVM. Argue that under a given value of slack variable, a given mathematical statement is either correct or incorrect.
+8. How does the choice of slack variable affect the bias-variance tradeoff in SVM?
+9. Explain which Kernel would be a better fit to be used in SVM for a given data.
+
+
+**Section 2**
+
+
+
+1. When a decision tree is grown to full depth, how does it affect tree’s bias and variance, and its response to noisy data?
+2. Argue if an ensemble model would be a better choice for a given classification problem or not.
+3. Given a particular iteration of boosting and other important information, calculate the weights of the Adaboost classifier.
+
+
+**Section 3**
+
+
+
+1. K-Means does not explicitly use a fitness function. What are the characteristics of the solutions that K-Means finds? Which fitness function does it implicitly minimize?
+2. Suppose we clustered a set of N data points using two different specified clustering algorithms. In both cases we obtained 5 clusters and in both cases the centers of the clusters are exactly the same. Can 3 points that are assigned to different clusters in one method be assigned to the same cluster in the other method?
+3. What are the characterics of noise points in DBSCAN?
+
+
+**Section 4**
+
+
+
+1. Explain what is ReLU, what are its different variants, and what are their pros and cons?
+2. Calculate the number of parameters to be learned during training in a CNN, given all important information.
+3. Explain how a VAE can be used as a generative model.
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__introduction_to_optimization.f22.md

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+
+
+
+
+
+
+
+BSc: Introduction to Optimization.F22
+=====================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Introduction to Optimization](#Introduction_to_Optimization)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+	+ [1.7 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [1.8 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [1.8.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [1.8.1.1 Section 1](#Section_1)
+			* [1.8.1.2 Section 2](#Section_2)
+			* [1.8.1.3 Section 3](#Section_3)
+		- [1.8.2 Final assessment](#Final_assessment)
+			* [1.8.2.1 Section 1](#Section_1_2)
+			* [1.8.2.2 Section 2](#Section_2_2)
+			* [1.8.2.3 Section 3](#Section_3_2)
+		- [1.8.3 The retake exam](#The_retake_exam)
+
+
+
+Introduction to Optimization
+============================
+
+
+* **Course name**: Introduction to Optimization
+* **Code discipline**: CSE???
+* **Subject area**: Data Science and Artificial Intelligence
+
+
+Short Description
+-----------------
+
+
+The course outlines the classification and mathematical foundations of optimization methods, and presents algorithms for solving linear and nonlinear optimization.
+The purpose of the course is to introduce students to methods of linear and convex optimization and their application in solving problems of linear, network, integer, and nonlinear optimization.
+Course starts with linear programming and moving on to more complex problems. primal and dual simplex methods, network flow algorithms, branch and bound, interior point methods, Newton and quasi-Newton methods, and heuristic methods.
+Current states, literature, techniques, theories, and methodologies are presented and discussed during the semester.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+* CSE201: Mathematical Analysis I
+* CSE202: Analytical Geometry and Linear Algebra I
+* CSE203: Mathematical Analysis II
+* CSE204: Analytical Geometry and Linear Algebra II
+
+
+### Prerequisite topics
+
+
+* Basic programming skills.
+* OOP, and software design.
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Linear programming | 1. Optimization Applications
+2. Formulation of Optimization Models
+3. Graphical Solution of Linear Programs
+4. Simplex Method
+5. Linear Programming Duality and Sensitivity Analysis
+ |
+| Nonlinear programming | 1. Nonlinear Optimization Theory
+2. Steepest Descent and Conjugate Gradient Methods
+3. Newton and Quasi-Newton Methods
+4. Quadratic Programming
+ |
+| Extensions | 1. Network Models
+2. Dynamic Programming
+3. Multi-objective Programming
+4. Optimization Heuristics
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+The main purpose of this course is to enable a student to go from an idea to implementation of different optimization algorithms to solve problems in different fields of studies like machine and deep learning, etc.
+
+
+
+### ILOs defined at three levels
+
+
+We specify the intended learning outcomes at three levels: conceptual knowledge, practical skills, and comprehensive skills.
+
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* remember the different classifications and mathematical foundations of optimization methods
+* remember basic properties of the corresponding mathematical objects
+* remember the fundamental concepts, laws, and methods of linear and convex optimization
+* distinguish between different types of optimization methods
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Funderstand the basic concepts of optimization problems
+* evaluate the correctness of problem statements
+* explain which algorithm is suitable for solving problems
+* evaluate the correctness of results
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* understand the basic foundations behind optimization problems.
+* classify optimization problems.
+* choose a proper algorithm to solve optimization problems.
+* validate algorithms that students choose to solve optimization problems.
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Fail | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Midterm | 30
+ |
+| 2 Intermediate tests | 30 (15 for each)
+ |
+| Final exam | 40
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+* Participation is important. Attending lectures is the key to success in this course.
+* Review lecture materials before classes to do well.
+* Reading the recommended literature is optional, and will give you a deeper understanding of the material.
+
+
+  
+
+
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Convex Optimization – Boyd and Vandenberghe. Cambridge University Press.
+
+
+### Closed access resources
+
+
+* Engineering Optimization: Theory and Practice, by Singiresu S. Rao, John Wiley and Sons.
+* Bertsimas, Dimitris, and John Tsitsiklis. Introduction to Linear Optimization. Belmont, MA: Athena Scientific, 1997. ISBN: 9781886529199.
+
+
+### Software and tools used within the course
+
+
+* MATLAB
+* Python
+* Excel
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Teaching and Learning Methods within each section
+| Teaching Techniques | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Problem-based learning (students learn by solving open-ended problems without a strictly-defined solution) | 0 | 0 | 0
+ |
+| Project-based learning (students work on a project) | 1 | 1 | 1
+ |
+| Modular learning (facilitated self-study) | 0 | 0 | 0
+ |
+| Differentiated learning (provide tasks and activities at several levels of difficulty to fit students needs and level) | 1 | 1 | 1
+ |
+| Contextual learning (activities and tasks are connected to the real world to make it easier for students to relate to them) | 0 | 0 | 0
+ |
+| Business game (learn by playing a game that incorporates the principles of the material covered within the course) | 0 | 0 | 0
+ |
+| Inquiry-based learning | 0 | 0 | 0
+ |
+| Just-in-time teaching | 0 | 0 | 0
+ |
+| Process oriented guided inquiry learning (POGIL) | 0 | 0 | 0
+ |
+| Studio-based learning | 0 | 0 | 0
+ |
+| Universal design for learning | 0 | 0 | 0
+ |
+| Task-based learning | 0 | 0 | 0
+ |
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Lectures | 1 | 1 | 1
+ |
+| Interactive Lectures | 1 | 1 | 1
+ |
+| Lab exercises | 1 | 1 | 1
+ |
+| Experiments | 0 | 0 | 0
+ |
+| Modeling | 0 | 0 | 0
+ |
+| Cases studies | 0 | 0 | 0
+ |
+| Development of individual parts of software product code | 0 | 0 | 0
+ |
+| Individual Projects | 1 | 1 | 1
+ |
+| Group projects | 0 | 0 | 0
+ |
+| Flipped classroom | 0 | 0 | 0
+ |
+| Quizzes (written or computer based) | 0 | 0 | 0
+ |
+| Peer Review | 0 | 0 | 0
+ |
+| Discussions | 1 | 1 | 1
+ |
+| Presentations by students | 1 | 1 | 1
+ |
+| Written reports | 0 | 0 | 0
+ |
+| Simulations and role-plays | 0 | 0 | 0
+ |
+| Essays | 0 | 0 | 0
+ |
+| Oral Reports | 0 | 0 | 0
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+1. A steel company must decide how to allocate next week’s time on a rolling mill, which is a machine that takes unfinished slabs of steel as input and can produce either of two semi-finished products: bands and coils. The mill’s two products come off the rolling line at different rates:
+Bands 200 tons/hr
+Coils 140 tons/hr.
+They also produce different profits:
+Bands $ 25/ton
+Coils $ 30/ton.
+Based on currently booked orders, the following upper bounds are placed on the amount of each product to produce:
+Bands 6000 tons
+Coils 4000 tons.
+Given that there are 40 hours of production time available this week, the problem is to decide how many tons of bands and how many tons of coils should be produced to yield the greatest profit. Formulate this problem as a linear programming problem. Can you solve this problem by inspection?
+2. Solve the following linear programming problems.
+maximize 
+
+
+
+6
+
+x
+
+1
+
+
++
+8
+
+x
+
+2
+
+
++
+5
+
+x
+
+3
+
+
++
+9
+
+x
+
+4
+
+
+
+
+{\displaystyle 6x\_{1}+8x\_{2}+5x\_{3}+9x\_{4}}
+
+![{\displaystyle 6x_{1}+8x_{2}+5x_{3}+9x_{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ce2ab3c39825342e1f821d2d045d014fcd42e3be)
+subject to 
+
+
+
+2
+
+x
+
+1
+
+
++
+
+x
+
+2
+
+
++
+
+x
+
+3
+
+
++
+3
+
+x
+
+4
+
+
+≤
+5
+
+
+{\displaystyle 2x\_{1}+x\_{2}+x\_{3}+3x\_{4}\leq 5}
+
+![{\displaystyle 2x_{1}+x_{2}+x_{3}+3x_{4}\leq 5}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1e0ed5929293f10e2e0ae2aec7c2efb2d5f126e3)
+
+
+
+
+
+x
+
+1
+
+
++
+3
+
+x
+
+2
+
+
++
+
+x
+
+3
+
+
++
+2
+
+x
+
+4
+
+
+≤
+3
+
+
+{\displaystyle x\_{1}+3x\_{2}+x\_{3}+2x\_{4}\leq 3}
+
+![{\displaystyle x_{1}+3x_{2}+x_{3}+2x_{4}\leq 3}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dce99dfc351059f2575c4601e280ef71541f4348)
+
+
+
+
+x
+1
+,
+x
+2
+,
+x
+3
+,
+x
+4
+≥
+0
+
+
+{\displaystyle x1,x2,x3,x4\geq 0}
+
+![{\displaystyle x1,x2,x3,x4\geq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/932a2ebf6b713fcf449c6cafec3ce11add6d4345)
+3. Give an example showing that the variable that becomes basic in one iteration of the simplex method can become nonbasic in the next iteration.
+4. Solve the given linear program using the dual–primal two phase algorithm.
+maximize 
+
+
+
+2
+
+x
+
+1
+
+
+−
+6
+
+x
+
+2
+
+
+
+
+{\displaystyle 2x\_{1}-6x\_{2}}
+
+![{\displaystyle 2x_{1}-6x_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/881bc2534b793fa7ca32fac8fc36c81b70d303b6)
+subject to 
+
+
+
+−
+
+x
+
+1
+
+
+−
+
+x
+
+2
+
+
+−
+
+x
+
+3
+
+
+≤
+−
+2
+
+
+{\displaystyle -x\_{1}-x\_{2}-x\_{3}\leq -2}
+
+![{\displaystyle -x_{1}-x_{2}-x_{3}\leq -2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/88ff2b0cd8e197a1ecb742cd3882f107fd787b85)
+
+
+
+
+2
+
+x
+
+1
+
+
+−
+
+x
+
+2
+
+
++
+
+x
+
+3
+
+
+≤
+1
+
+
+{\displaystyle 2x\_{1}-x\_{2}+x\_{3}\leq 1}
+
+![{\displaystyle 2x_{1}-x_{2}+x_{3}\leq 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e35ccaa9729b136c0144638ac96d2e1e49488054)
+
+
+
+
+x
+1
+,
+x
+2
+,
+x
+3
+≥
+0
+
+
+{\displaystyle x1,x2,x3\geq 0}
+
+![{\displaystyle x1,x2,x3\geq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3b1d78faac4a1cc597eb376b19e6bea3cdef535c)
+
+
+#### Section 2
+
+
+1. Find the minimum of the function 
+
+
+
+f
+=
+λ
+
+/
+
+l
+o
+g
+λ
+
+
+{\displaystyle f=\lambda /log\lambda }
+
+![{\displaystyle f=\lambda /log\lambda }](https://wikimedia.org/api/rest_v1/media/math/render/svg/e64c38e5c3c9279ec5b037fa4d7a41bcf5ca941a) using the following methods:
+	* Newton method
+	* Quasi-Newton method
+	* Quadratic interpolation method
+2. State possible convergence criteria that can be used in direct search methods.
+3. Why is the steepest descent method not efficient in practice, although the directions used are the best directions?
+4. What is the difference between quadratic and cubic interpolation methods?
+5. Why is refitting necessary in interpolation methods?
+6. What is a direct root method?
+7. What is the basis of the interval halving method?
+8. What is the difference between Newton and quasi-Newton methods?
+
+
+#### Section 3
+
+
+1. Solve the following LP problem by dynamic programming:
+Maximize 
+
+
+
+f
+(
+
+x
+
+1
+
+
+,
+
+x
+
+2
+
+
+)
+=
+10
+
+x
+
+1
+
+
++
+8
+
+x
+
+2
+
+
+
+
+{\displaystyle f(x\_{1},x\_{2})=10x\_{1}+8x\_{2}}
+
+![{\displaystyle f(x_{1},x_{2})=10x_{1}+8x_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4ab765d633735118a14ce88384bc285b278956fc)
+subject to 
+
+
+
+2
+
+x
+
+1
+
+
++
+
+x
+
+2
+
+
+≤
+25
+
+
+{\displaystyle 2x\_{1}+x\_{2}\leq 25}
+
+![{\displaystyle 2x_{1}+x_{2}\leq 25}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e3e22bad412fe51fccd3e185076fece3f2b9eba0)
+
+
+
+
+3
+
+x
+
+1
+
+
++
+2
+
+x
+
+2
+
+
+≤
+45
+
+
+{\displaystyle 3x\_{1}+2x\_{2}\leq 45}
+
+![{\displaystyle 3x_{1}+2x_{2}\leq 45}](https://wikimedia.org/api/rest_v1/media/math/render/svg/60f89747d24cdf6f585c95555f7063678d510f73)
+
+
+
+
+
+x
+
+2
+
+
+≤
+10
+
+
+{\displaystyle x\_{2}\leq 10}
+
+![{\displaystyle x_{2}\leq 10}](https://wikimedia.org/api/rest_v1/media/math/render/svg/714b627484f0a69ef033170a587ab98ebacdb08d)
+
+
+
+
+x
+1
+,
+x
+2
+≥
+0
+
+
+{\displaystyle x1,x2\geq 0}
+
+![{\displaystyle x1,x2\geq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c873b834081899fb65c0a29631a2e08995d9b0d9)
+Verify your solution by solving it graphically.
+2. Consider the following tree solution for a minimum cost network flow problem:
+[![ItO p1.png](/img_auth.php/f/fe/ItO_p1.png)](/index.php/File:ItO_p1.png)
+As usual, bold arcs represent arcs on the spanning tree, numbers next to the bold arcs are primal flows, numbers next to non-bold arcs are dual slacks, and numbers next to nodes are dual variables.
+	* For what values of is this tree solution optimal?
+	* What are the entering and leaving arcs?
+	* After one pivot, what is the new tree solution?
+	* For what values of is the new tree solution optimal?
+
+
+### Final assessment
+
+
+#### Section 1
+
+
+1. Solve the following linear programming problems.
+maximize 
+
+
+
+
+x
+
+1
+
+
++
+3
+
+x
+
+2
+
+
+
+
+{\displaystyle x\_{1}+3x\_{2}}
+
+![{\displaystyle x_{1}+3x_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aa8ab277e3f341eab98b1681777938522110e092)
+subject to 
+
+
+
+−
+
+x
+
+1
+
+
+−
+
+x
+
+2
+
+
+≤
+−
+3
+
+
+{\displaystyle -x\_{1}-x\_{2}\leq -3}
+
+![{\displaystyle -x_{1}-x_{2}\leq -3}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a8ac67f209d89b530e9dff4c0fefad43351952ea)
+
+
+
+
+−
+
+x
+
+1
+
+
++
+
+x
+
+2
+
+
+≤
+−
+1
+
+
+{\displaystyle -x\_{1}+x\_{2}\leq -1}
+
+![{\displaystyle -x_{1}+x_{2}\leq -1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d659c53576d0a195ffe890400cf4cca532cc2437)
+
+
+
+
+−
+
+x
+
+1
+
+
++
+2
+
+x
+
+2
+
+
+≤
+2
+
+
+{\displaystyle -x\_{1}+2x\_{2}\leq 2}
+
+![{\displaystyle -x_{1}+2x_{2}\leq 2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e3920b38db67a9a9e7dc4b1262aeb028a2c6d742)
+
+
+
+
+x
+1
+,
+x
+2
+≥
+0
+
+
+{\displaystyle x1,x2\geq 0}
+
+![{\displaystyle x1,x2\geq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c873b834081899fb65c0a29631a2e08995d9b0d9)
+2. Give an example showing that the variable that becomes basic in one iteration of the simplex method can become nonbasic in the next iteration.
+3. Solve the given linear program using the dual–primal two phase algorithm.
+maximize 
+
+
+
+6
+
+x
+
+1
+
+
++
+8
+
+x
+
+2
+
+
++
+5
+
+x
+
+3
+
+
++
+9
+
+x
+
+4
+
+
+
+
+{\displaystyle 6x\_{1}+8x\_{2}+5x\_{3}+9x\_{4}}
+
+![{\displaystyle 6x_{1}+8x_{2}+5x_{3}+9x_{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ce2ab3c39825342e1f821d2d045d014fcd42e3be)
+subject to 
+
+
+
+
+x
+
+1
+
+
++
+
+x
+
+2
+
+
++
+
+x
+
+3
+
+
++
+
+x
+
+4
+
+
+=
+1
+
+
+{\displaystyle x\_{1}+x\_{2}+x\_{3}+x\_{4}=1}
+
+![{\displaystyle x_{1}+x_{2}+x_{3}+x_{4}=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/722b48280c1ac0810ec440bce224b4554e1d994a)
+
+
+
+
+
+x
+
+1
+
+
+,
+
+x
+
+2
+
+
+,
+
+x
+
+3
+
+
+,
+
+x
+
+4
+
+
+≥
+0
+
+
+{\displaystyle x\_{1},x\_{2},x\_{3},x\_{4}\geq 0}
+
+![{\displaystyle x_{1},x_{2},x_{3},x_{4}\geq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4a8915f5444dd2ef59f41b0b63427d91496e2c0a)
+
+
+#### Section 2
+
+
+1. Perform two iterations of the steepest descent method to minimize the function given from the stated starting point 
+
+
+
+(
+−
+1.2
+,
+1
+)
+
+
+{\displaystyle (-1.2,1)}
+
+![{\displaystyle (-1.2,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/abc9164d20051248169d1d825032e66a6f80a258)
+
+
+
+
+f
+(
+
+x
+
+1
+
+
+,
+
+x
+
+2
+
+
+)
+=
+100
+(
+
+x
+
+2
+
+
+−
+
+x
+
+1
+
+
+2
+
+
+
+)
+
+2
+
+
++
+(
+1
+−
+
+x
+
+1
+
+
+
+)
+
+2
+
+
+
+
+{\displaystyle f(x\_{1},x\_{2})=100(x\_{2}-x\_{1}^{2})^{2}+(1-x\_{1})^{2}}
+
+![{\displaystyle f(x_{1},x_{2})=100(x_{2}-x_{1}^{2})^{2}+(1-x_{1})^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ccb7b67f6f89e7785255b57eb148508365dbd4f3)
+2. Minimize 
+
+
+
+f
+=
+2
+
+x
+
+1
+
+
+2
+
+
++
+
+x
+
+2
+
+
+2
+
+
+
+
+{\displaystyle f=2x\_{1}^{2}+x\_{2}^{2}}
+
+![{\displaystyle f=2x_{1}^{2}+x_{2}^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e1188f60e52c56d9e3d592bafed16bcb783da002) by using the steepest descent method with the starting point 
+
+
+
+(
+1
+,
+2
+)
+
+
+{\displaystyle (1,2)}
+
+![{\displaystyle (1,2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1d0c72462a85992b95f90cc4a69048c9d83e8cbf) (two iterations only).
+3. Minimize 
+
+
+
+f
+=
+
+x
+
+1
+
+
+2
+
+
++
+3
+
+x
+
+2
+
+
+2
+
+
++
+6
+
+x
+
+3
+
+
+2
+
+
+
+
+{\displaystyle f=x\_{1}^{2}+3x\_{2}^{2}+6x\_{3}^{2}}
+
+![{\displaystyle f=x_{1}^{2}+3x_{2}^{2}+6x_{3}^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b44bc0dae6791c1c9e3fc3ee7d3ae79d6088bfcd) by Newton's method using the starting point as 
+
+
+
+(
+2
+,
+−
+1
+,
+1
+)
+
+
+{\displaystyle (2,-1,1)}
+
+![{\displaystyle (2,-1,1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/db0c7d8f3b67a090510e69eb9fdab854287b3246) .
+
+
+#### Section 3
+
+
+* It is proposed to build thermal stations at three different sites. The total budget available is 3 units (1 unit = $10 million) and the feasible levels of investment on any thermal station are 0, 1, 2, or 3 units. The electric power obtainable (return function) for different investments is given below. Find the investment policy for maximizing the total electric power generated.
+
+
+
+
+| Return function Ri(x) | i = 1 | i = 2 | i = 3
+ |
+| --- | --- | --- | --- |
+| R0(x) | 0 | 0 | 0
+ |
+| R1(x) | 2 | 1 | 3
+ |
+| R2(x) | 4 | 5 | 5
+ |
+| R3(x) | 6 | 6 | 6
+ |
+
+
+* A fertilizer company needs to supply 50 tons of fertilizer at the end of the first month, 70 tons at the end of the second month, and 90 tons at the end of the third month. The cost of producing x tons of fertilizer in any month is given by $
+
+
+
+(
+4500
+x
++
+20
+
+x
+
+2
+
+
+)
+
+
+{\displaystyle (4500x+20x^{2})}
+
+![{\displaystyle (4500x+20x^{2})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/09c172df4dd1b8177e2dc5514459fcd4ca694be5). It can produce more fertilizer in any month and supply it in the next month. However, there is an inventory carrying cost of $400 per ton per month. Find the optimal level of production in each of the three periods and the total cost involved by solving it as an initial value problem.
+* Consider the following tree solution for a minimum cost network flow problem:
+[![ItO p2.png](/img_auth.php/a/a7/ItO_p2.png)](/index.php/File:ItO_p2.png)
+As usual, bold arcs represent arcs on the spanning tree, numbers next to the bold arcs are primal flows, numbers next to non-bold arcs are dual slacks, and numbers next to nodes are dual variables.
+For what values of is this tree solution optimal?
+What are the entering and leaving arcs?
+After one pivot, what is the new tree solution?
+For what values of is the new tree solution optimal?
+
+
+### The retake exam
+
+
+Retakes will be run as a comprehensive exam, where the student will be assessed the acquired knowledge coming from the textbooks, the lectures, the labs, and the additional required reading material, as supplied by the instructor. During such comprehensive oral/written the student could be asked to solve exercises and to explain theoretical and practical aspects of the course.
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__introduction_to_programming.md

@@ -0,0 +1,462 @@
+
+
+
+
+
+
+
+BSc: Introduction To Programming
+================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Introduction to Programming](#Introduction_to_Programming)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+			* [2.2.1.4 Section 4](#Section_4)
+			* [2.2.1.5 Section 5](#Section_5)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Introduction to Programming
+===========================
+
+
+* **Course name**: Introduction to Programming
+* **Code discipline**: CSE101
+* **Subject area**: Programming Languages and Software Engineering
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: Basic concept - algorithm, program, data; Computer architecture basics; Structured programming; Object-oriented programming; Generic programming; Exception handling; Programming by contract (c); Functional programming; Concurrent programming.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Introduction to programming | 1. Basic definitions – algorithm, program, computer, von Neumann architecture, CPU lifecycle.
+2. Programming languages history and overview. Imperative (procedural) and functional approaches.
+3. Translation – compilation vs. interpretation. JIT, AOT. Hybrid modes.
+4. Introduction to typification. Static and dynamic typing. Type inference. Basic types – integer, real, character, boolean, bit. Arrays and strings. Records-structures.
+5. Programming – basic concepts. Statements and expressions. 3 atomic statements - assignment, if-check, goto. Control structures – conditional, assignment, goto, case-switch-inspect, loops.
+6. Variables and constants.
+7. Routines – procedures and functions.
+ |
+| Introduction to object-oriented programming | 1. Key principles of object-oriented programming
+2. Overloading is not overriding
+3. Concepts of class and object
+4. How objects can be created?
+5. Single and multiple inheritance
+ |
+| Introduction to generics, exception handling and programming by contract (C) | 1. Introduction to generics
+2. Introduction to exception handling
+3. Introduction to programming by contract (C)
+ |
+| Introduction to programming environments | 1. Concept of libraries as the basis for reuse.
+2. Concept of interfaces/API. Separate compilation.
+3. Approaches to software documentation.
+4. Persistence. Files.
+5. How to building a program. Recompilation problem. Name clashes, name spaces
+ |
+| Introduction to concurrent and functional programming | 1. Concurrent programming.
+2. Functional programming within imperative programming languages.
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+The Introduction to Programming course teaches the fundamental concepts and skills necessary to perform programming at a professional level. Students will learn how to master the fundamental control structures, data structures, reasoning patterns and programming language mechanisms characterizing modern programming, as well as the fundamental rules of producing high-quality software. They will acquire the necessary programming background for later courses introducing programming skills in specialized application areas. The course focuses on Object Oriented paradigm.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Basic concepts of programming. What is algorithm, program.
+* Concept of typification. Dynamic and static types.
+* Concepts of structured programming, object-oriented one.
+* Concepts of exception handling and generic programming.
+* Concurrent programming and functional programming in imperative programming languages.
+* verification of the software based on programming by contract (C)
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* How to create high quality software using mainstream concepts of programming.
+* What is object-oriented programming and its main advantages
+* How to increase the level of abstraction with help of genericity.
+* How to create concurrent programs and what are the main issues related to this kind of programming
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* To be able to create quality programs in Java.
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 85-100 | -
+ |
+| B. Good | 75-84 | -
+ |
+| C. Satisfactory | 60-75 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Labs/seminar classes | 40
+ |
+| Interim performance assessment | 30
+ |
+| Exams | 30
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4 | Section 5
+ |
+| --- | --- | --- | --- | --- | --- |
+| Homework and group projects | 1 | 1 | 1 | 1 | 1
+ |
+| Midterm evaluation | 1 | 1 | 1 | 0 | 0
+ |
+| Testing (written or computer based) | 1 | 0 | 0 | 1 | 1
+ |
+| Oral polls | 1 | 1 | 1 | 1 | 1
+ |
+| Discussions | 1 | 1 | 1 | 1 | 1
+ |
+| Development of individual parts of software product code | 0 | 1 | 0 | 0 | 0
+ |
+| Reports | 0 | 1 | 0 | 0 | 0
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is the difference between compiler and interpreter? | 1
+ |
+| Question | What is the difference between type and variable? | 1
+ |
+| Question | What is the background of structured programming? | 1
+ |
+| Question | How to compile a program? | 0
+ |
+| Question | How to run a program? | 0
+ |
+| Question | How to debug a program? | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is the meaning of polymorphism? | 1
+ |
+| Question | How to check the dynamic type of an object? | 1
+ |
+| Question | What are the limitations of single inheritance? | 1
+ |
+| Question | What are the issues related with multiple inheritance? | 1
+ |
+| Question | How to handle array of objects of some class type? | 0
+ |
+| Question | How to implement the class which logically has to have 2 constructors with the same signature but with different semantics? | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is constrained genericity? | 1
+ |
+| Question | What is exception? | 1
+ |
+| Question | What is assertion? | 1
+ |
+| Question | How constrained genericity may be used for sorting of objects? | 0
+ |
+| Question | In which order catch blocks are being processed? | 0
+ |
+| Question | Where is the problem when precondition is violated? | 0
+ |
+
+
+#### Section 4
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | How reuse helps to develop software? | 1
+ |
+| Question | How concept of libraries and separate compilation co-relate? | 1
+ |
+| Question | What are the benefits of integrating documentation into the source code? | 1
+ |
+| Question | Why is it essential to have persistent data structures? | 1
+ |
+| Question | What is to be done to design and develop a library? | 0
+ |
+| Question | How to add documenting comments into the source code? | 0
+ |
+| Question | What ways exists in Java to support persistence ? | 0
+ |
+
+
+#### Section 5
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Explain the key differences parallelism and concurrency | 1
+ |
+| Question | What are the key issues related to parallel execution? | 1
+ |
+| Question | What are the models of parallel execution? | 1
+ |
+| Question | What is the difference between function and object? | 1
+ |
+| Question | Which Java construction support concurrency? | 0
+ |
+| Question | What is a thread? | 0
+ |
+| Question | What is in-line lambda function? | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. What are the basic control structure of structured programming?
+2. What is the difference between statements and expressions?
+3. What are the benefits of type inference?
+
+
+**Section 2**
+
+
+
+1. Name all principles of object-oriented programming?
+2. Explain what conformance means?
+3. Explain why cycles are prohibited in the inheritance graph?
+
+
+**Section 3**
+
+
+
+1. Can array be treated as generic class?
+2. What is the difference between throw and throws in Java?
+3. What is purpose of the class invariant?
+
+
+**Section 4**
+
+
+
+1. How to deal with name clashes?
+2. What is the main task of the recompilation module?
+3. What are the differences between different formats of persistence files?
+
+
+**Section 5**
+
+
+
+1. What is the meaning of SIMD and MIMD?
+2. What are the implications of the Amdahl’s law?
+3. What model of concurrency Java relies on?
+4. Which function can be considered as pure?
+5. How to declare a function to accept a functional object as its argument?
+6. How Java supports high-order functions?
+7. How capturing variables works in Java?
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+**Section 5**
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__introduction_to_programming_ii.md

@@ -0,0 +1,146 @@
+
+
+
+
+
+
+
+BSc: Introduction To Programming II
+===================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Introduction to Programming II](#Introduction_to_Programming_II)
+	+ [1.1 Course characteristics](#Course_characteristics)
+		- [1.1.1 Key concepts of the class](#Key_concepts_of_the_class)
+		- [1.1.2 What is the purpose of this course?](#What_is_the_purpose_of_this_course.3F)
+			* [1.1.2.1 What should a student remember at the end of the course?](#What_should_a_student_remember_at_the_end_of_the_course.3F)
+			* [1.1.2.2 What should a student be able to understand at the end of the course?](#What_should_a_student_be_able_to_understand_at_the_end_of_the_course.3F)
+			* [1.1.2.3 What should a student be able to apply at the end of the course?](#What_should_a_student_be_able_to_apply_at_the_end_of_the_course.3F)
+		- [1.1.3 Course evaluation](#Course_evaluation)
+			* [1.1.3.1 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section)
+			* [1.1.3.2 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section)
+
+
+
+Introduction to Programming II
+==============================
+
+
+* **Course name:** Introduction to Programming II
+* **Course number:** XYZ
+* **Knowledge area:** Programming Languages and Software Engineering
+
+
+Course characteristics
+----------------------
+
+
+* **Faculty:** Computer Science and Engineering
+* **Year of instruction:** 1st year of BS
+* **Semester of instruction:** 2nd semester
+* **No. of Credits:** 4 ECTS
+* **Total workload on average:** 144 hours overall
+* **Class lecture hours:** 2 per week
+* **Class tutorial hours:** 2 per week
+* **Lab hours:** 2 per week
+* **Individual lab hours:** 0
+* **Frequency:** weekly throughout the semester
+* **Grading mode:** letters: A, B, C, D
+
+
+### Key concepts of the class
+
+
+* Introduction to Programming II concepts:
+
+
+### What is the purpose of this course?
+
+
+Introduction to Programming II is the continuation of an introductory course to programming. It teaches in a more in-depth look at programming and at the development of software. The course is project oriented and it focusses on problem-solving and how to program well. Students will learn how to master the fundamental control structures, data structures, reasoning patterns and programming language mechanisms characterizing modern programming, as well as the fundamental rules of producing high-quality software. The course also introduces functional programming.
+
+
+  
+
+
+
+
+#### What should a student remember at the end of the course?
+
+
+By the end of the course, the students should be able to recognize and define
+
+
+
+* 
+* 
+* 
+* 
+* 
+
+
+#### What should a student be able to understand at the end of the course?
+
+
+By the end of the course, the students should be able to describe and explain (with examples)
+
+
+
+* 
+* 
+* 
+* 
+* 
+* 
+
+
+#### What should a student be able to apply at the end of the course?
+
+
+By the end of the course, the students should be able to apply
+
+
+
+* 
+* 
+* 
+* 
+* 
+
+
+### Course evaluation
+
+
+* Course Project (50%)
+* Final Exam (40%)
+* Class and lab participation (10%)
+
+
+#### Typical questions for seminar classes (labs) within this section
+
+
+1. Same as above
+
+
+#### Test questions for final assessment in this section
+
+
+1. Same as above
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__introduction_to_robotics.md

@@ -0,0 +1,464 @@
+
+
+
+
+
+
+
+BSc: Introduction To Robotics
+=============================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Fundamentals of Robotics](#Fundamentals_of_Robotics)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+			* [2.2.1.4 Section 4](#Section_4)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Fundamentals of Robotics
+========================
+
+
+* **Course name**: Fundamentals of Robotics
+* **Code discipline**: R-01
+* **Subject area**:
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: Robotics; Robotic components; Robotic control..
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Introduction to robotics | 1. Introduction to Robotics, History of Robotics
+2. Introduction to Drones
+3. Introduction to Self driving cars
+4. Programming of Industrial Robot
+ |
+| Kinematics | 1. Rigid body and Homogeneous transformation
+2. Direct Kinematics
+3. Inverse Kinematics
+ |
+| Differential kinematics | 1. Differential kinematics
+2. Geometric calibration
+3. Trajectory Planning
+ |
+| Dynamics | 1. Dynamics of Rigid body
+2. Lagrange approach
+3. Newton-Euler approach
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+This course is an introduction to the field of robotics. It covers the fundamentals of kinematics, dynamics, and control of robot manipulators, robotic vision, and sensing. The course deals with forward and inverse kinematics of serial chain manipulators, the manipulator Jacobian, force relations, dynamics, and control. It presents elementary principles on proximity, tactile, and force sensing, vision sensors, camera calibration, stereo construction, and motion detection. The course concludes with current applications of robotics in active perception, medical robotics, autonomous vehicles, and other areas.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Model the kinematics of robotic systems.
+* Compute end-effector position and orientation from joint angles of a robotic system.
+* Compute the joint angles of a robotic system to reach the desired end-effector position and orientation.
+* Compute the linear and angular velocities of the end-effector of a robotic system from the joint angle velocities.
+* Convert a robot’s workspace to its configuration space and represent obstacles in the configuration space.
+* Compute valid path in a configuration space with motion planning algorithms.
+* Apply the generated motion path to the robotic system to generate a proper motion trajectory.
+* Apply the learned knowledge to several robotic systems: including robotic manipulators, humanoid robots.
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Name various applications of robots
+* Describe the current and potential economic and societal impacts of robot technology
+* Use the Jacobian to transform velocities and forces from joint space to operational space
+* Determine the singularities of a robot manipulator
+* Formulate the dynamic equations of a robot manipulator in joint space and in Cartesian space
+* List the major design parameters for robot manipulators and mobile robots
+* List the typical sensing and actuation methods used in robots
+* Analyze the workspace of a robot manipulator
+* List the special requirements of haptic devices and medical robots
+* Effectively communicate research results
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Describe rigid body motions using positions, orientations, frames, and mappings
+* Describe orientations using Euler angles, fixed angles, and quaternions
+* Develop the forward kinematic equations for an articulated manipulator
+* Describe the position and orientations of a robot in terms of joint space, Cartesian space, and operational space
+* Develop the Jacobian for a specific manipulator
+* Determine the singularities of a robot manipulator
+* Write the dynamic equations of a robot manipulator using the Lagrangian Formulation
+* Analyze the workspace of a robot manipulator
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 92-100 | -
+ |
+| B. Good | 80-91 | -
+ |
+| C. Satisfactory | 65-79 | -
+ |
+| D. Poor/Fail | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Weekly quizzes | 20
+ |
+| Home assignments | 20
+ |
+| Project | 20
+ |
+| Midterm Exam | 20
+ |
+| Final Exam | 20
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Siciliano, Sciavicco, Villani, and Oriolo, Robotics: Modeling, Planning and Control, Springe
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4
+ |
+| --- | --- | --- | --- | --- |
+| Development of individual parts of software product code | 1 | 1 | 1 | 1
+ |
+| Homework and group projects | 1 | 1 | 1 | 1
+ |
+| Midterm evaluation | 1 | 1 | 1 | 1
+ |
+| Testing (written or computer based) | 1 | 1 | 1 | 1
+ |
+| Discussions | 1 | 1 | 1 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is the difference between the manipulator arm and manipulator wrist | 1
+ |
+| Question | What is Node in ROS | 1
+ |
+| Question | What are the disadvantages of ROS | 1
+ |
+| Question | Write sensors which are used in self driving cars. | 1
+ |
+| Question | Describe the classical approach for deign self driving car | 1
+ |
+| Question | Advantages and drawbacks of robotic manipulators | 0
+ |
+| Question | Programming industrial robots | 0
+ |
+| Question | Developing self driving car | 0
+ |
+| Question | Drones and controllers for them | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Properties of Rotation Matrix | 1
+ |
+| Question | How to find Euler angles from rotation matrix | 1
+ |
+| Question | How to compute rotation matrix from knowing Euler angles | 1
+ |
+| Question | How to derive equations for direct kinematic problem | 1
+ |
+| Question | How to solve inverse kinematics problem | 1
+ |
+| Question | Structure, properties, and advantages of Homogeneous transformation | 0
+ |
+| Question | Expression for rotation around an arbitrary axis | 0
+ |
+| Question | Euler angles | 0
+ |
+| Question | Difference between Joint and Operational spaces | 0
+ |
+| Question | Direct kinematics for serial kinematic chain | 0
+ |
+| Question | Piper approach for inverse kinematics | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Write the matrix of differential transformation | 1
+ |
+| Question | What is Jacobian matrix | 1
+ |
+| Question | Difference between parametric and non-parametric robot calibration. | 1
+ |
+| Question | Why we need complete and irreducible model | 1
+ |
+| Question | How trajectory planning is realised | 1
+ |
+| Question | What is trajectory junction | 1
+ |
+| Question | Jacobian matrix calculation | 0
+ |
+| Question | Jacobian matrices for typical serial manipulators | 0
+ |
+| Question | Robot calibration procedure | 0
+ |
+| Question | complete, irreducible geometric model | 0
+ |
+| Question | robot control strategies with offline errors compensation | 0
+ |
+| Question | Trajectory planning in joint and Cartesian spaces | 0
+ |
+| Question | Trajectory junction | 0
+ |
+
+
+#### Section 4
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Energy of rigid body | 1
+ |
+| Question | Dynamics of rigid body | 1
+ |
+| Question | What is Direct and Inverse Dynamics | 1
+ |
+| Question | Difference between Newton Euler and Lagrange Euler approaches | 1
+ |
+| Question | Dynamics of rigid body | 0
+ |
+| Question | Direct and Inverse Dynamic | 0
+ |
+| Question | Newton-Euler Approach | 0
+ |
+| Question | Lagrange-Euler Approach | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. Typical commands for programming industrial manipulator motions
+2. Types of robots and their application ares
+3. Control of self driving car
+
+
+**Section 2**
+
+
+
+1. Transformation between reference frames
+2. Find Euler angles for given orientation matrix and transformation order
+3. Transformation between Cartesian and operational spaces
+4. Direct kinematic for SCARA robot
+5. Inverse kinematic for SCARA robot
+
+
+**Section 3**
+
+
+
+1. Write Jacobian for Polarrobot
+2. Advantages and disadvantages parametric and non-parametric robot calibration.
+3. complete, irreducible geometric model for spherical manipulator
+4. Compute the joint trajectory q(t) from q(0) = 1 to q(2) = 4 with null initial and final velocities and accelerations. (polynomial)
+5. Obtain manipulator trajectory for given manipulator kinematics, initial and final states and velocity and acceleration limits/
+
+
+**Section 4**
+
+
+
+1. Solve inverse dynamics problem for Cartesian robot
+2. Solve direct dynamics problem for RRR spherical manipulator
+3. Moving frame approach for dynamics modelling
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+**Section 4**
+
+
+
+
+
+
+
+
+
+
+

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+
+BSc: It Product Development
+===========================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 IT Product Development](#IT_Product_Development)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+IT Product Development
+======================
+
+
+* **Course name**: IT Product Development
+* **Code discipline**: CSE807
+* **Subject area**: Software Engineering
+
+
+Short Description
+-----------------
+
+
+This course has two parts: 1) building and launching a user-facing software product with the special emphasis on understanding user needs and 2) the application of data-driven product development techniques to iteratively improve the product. Students will learn how to transform an idea into software requirements through user research, prototyping and usability tests, then they will proceed to launch the MVP version of the product. In the second part of the course, the students will apply an iterative data-driven approach to developing a product, integrate event analytics, and run controlled experiments.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+* CSE101
+* CSE112
+* CSE122 or CSE804 or CSE809 or CSE812
+
+
+### Prerequisite topics
+
+
+* Basic programming skills.
+* OOP, and software design.
+* Familiarity with some development framework or technology (web or mobile)
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| From idea to MVP | 1. Introduction to Product Development
+2. Exploring the domain: User Research and Customer Conversations
+3. Documenting Requirements: MVP and App Features
+4. Prototyping and usability testing
+ |
+| Development and Launch | 1. Product backlog and iterative development
+2. Estimation Techniques, Acceptance Criteria, and Definition of Done
+3. UX/UI Design
+4. Software Engineering vs Product Management
+ |
+| Hypothesis-driven development | 1. Hypothesis-driven product development
+2. Measuring a product
+3. Controlled Experiments and A/B testing
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+What is the main goal of this course formulated in one sentence?
+The main purpose of this course is to enable a student to go from an idea to an MVP with the focus on delivering value to the customer and building the product in a data-driven evidence-based manner.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Describe the formula for stating a product idea and the importance of delivering value
+* Remember the definition and main attributes of MVP
+* Explain what are the main principles for building an effective customer conversation
+* Describe various classification of prototypes and where each one is applied
+* State the characteristics of a DEEP product backlog
+* Elaborate on the main principles of an effective UI/UX product design (hierarchy, navigation, color, discoverability, understandability)
+* List the key commonalities and differences between the mentality of a software engineer and a product manager
+* Explain what is hypothesis-driven development
+* Describe the important aspects and elements of a controlled experiment
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Formulate and assess the product ideas
+* Perform market research for existing products
+* Design effective customer conversations
+* Prototype UI, design and conduct usability tests
+* Prototype user interface
+* Design and conduct usability testing
+* Populate and groom a product backlog
+* Conduct Sprint Planning and Review
+* Choose product metrics and apply GQM
+* Integrate a third-party Analytics tools
+* Design, run and conclude Controlled experiments
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Conduct user and domain research to identify user needs and possible solutions
+* Elicit and document software requirements
+* Organize a software process to swiftly launch an MVP and keep improving it in an iterative manner.
+* Build a data pipeline to monitor metrics based on business goals and assess product progress in regards to design changes.
+* Evolve and improve a product in a data-driven evidence-based iterative manner
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Fail | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Assignment | 50
+ |
+| Quizzes | 15
+ |
+| Peer review | 15
+ |
+| Demo day | 20
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Participation is important. Showing up is the key to success in this course.  
+You will work in teams, so coordinating teamwork will be an important factor for success. This is also reflected in the peer review being a graded item.  
+Review lecture materials before classes to do well in quizzes.  
+Reading the recommended literature is optional, and will give you a deeper understanding of the material.
+
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Jackson, Michael. "The world and the machine." ICSE '95: Proceedings of the 17th international conference on Software engineeringApril 1995 Pages 283–292,
+* The Guide to Product Metrics:
+
+
+### Closed access resources
+
+
+* Fitzpatrick, R. (2013). The Mom Test: How to talk to customers & learn if your business is a good idea when everyone is lying to you. Robfitz Ltd.
+* Reis, E. (2011). The lean startup. New York: Crown Business, 27.
+* Rubin, K. S. (2012). Essential Scrum: A practical guide to the most popular Agile process. Addison-Wesley.
+
+
+### Software and tools used within the course
+
+
+* Firebase Analytics and A/B Testing, <https://firebase.google.com/>
+* Amplitude Product Analytics, <https://www.amplitude.com/>
+* MixPanel Product Analytics, <https://mixpanel.com/>
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Teaching and Learning Methods within each section
+| Teaching Techniques | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Problem-based learning (students learn by solving open-ended problems without a strictly-defined solution) | 1 | 1 | 1
+ |
+| Project-based learning (students work on a project) | 1 | 1 | 1
+ |
+| Differentiated learning (provide tasks and activities at several levels of difficulty to fit students needs and level) | 1 | 1 | 1
+ |
+| развивающего обучения (задания и материал "прокачивают" ещё нераскрытые возможности студентов); | 1 | 1 | 1
+ |
+| концентрированного обучения (занятия по одной большой теме логически объединяются); | 1 | 1 | 1
+ |
+| inquiry-based learning | 1 | 1 | 1
+ |
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Lectures | 1 | 1 | 1
+ |
+| Interactive Lectures | 1 | 1 | 1
+ |
+| Lab exercises | 1 | 1 | 1
+ |
+| Development of individual parts of software product code | 1 | 1 | 1
+ |
+| Group projects | 1 | 1 | 1
+ |
+| Quizzes (written or computer based) | 1 | 1 | 1
+ |
+| Peer Review | 1 | 1 | 1
+ |
+| Discussions | 1 | 1 | 1
+ |
+| Presentations by students | 1 | 1 | 1
+ |
+| Written reports | 1 | 1 | 1
+ |
+| Experiments | 0 | 0 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Quiz | 1. What is a product? What are the techniques for describing a product idea in a clear concise manner?2. What user research techniques do you know? In what situations are they applied?3. What are the key customer conversation principles according to the Mom Test technique? Bring an example of bad and good questions to ask.4. What are the 4 phases of the requirements engineering process? 5. How do we document requirements? What techniques do you know? | 1
+ |
+| Presentation | Prepare a short 2-minutes pitch for your project idea (2-5 slides). Suggested structure:What problem you are solving:- State the problem clearly in 2-3 short sentences.Who are you solving it for:- Who is your user/customer?- Why will they be attracted to it?What is your proposed solution to solve that problem:- One sentence description- What main feature(s) will it have? | 0
+ |
+| Individual Assignments | A1: Product Ideation and Market ResearchFormulate 3 project ideas in the following format:X helps Y to do Z – where X is your product’s name, Y is the target user, and Z is what user activity product help with.Submit Link to Screenshot board and Feature Analysis Table:- Pick and explore 5 apps similar to your idea- Take screenshots along the way and collect them on a board.- Make a qualitative analysis table for app features.Prepare a short 2-minutes pitch for your project idea (2-5 slides). Suggested structure:What problem you are solving:- State the problem clearly in 2-3 short sentences.Who are you solving it for:- Who is your user/customer?- Why will they be attracted to it?What is your proposed solution to solve that problem:- One sentence description- What main feature(s) will it have? | 1
+ |
+| Group Project Work | A2: Forming Teams and Identifying StakeholdersStudents are distributed into teams. Meet your team Discuss the ideaAgree on the rolesSetup task tracker (Trello or similar)Identify 3-5 stakeholders and how to approach themCompose a set of 5 most important questions you would ask from each stakeholder when interviewing themSubmitA pdf with the idea description, roles distribution among the team, identified stakeholders, ways to approach them, a set of questions for each stakeholder.An invite link to join your task trackerA3: Domain Exploration and RequirementsUser Research Process:Compose the questionnaire for each stakeholder type. Talk to 5-7 stakeholders.Keep updating the questionnaire throughout the processCompose an interview results tableProduce personasSummarize most important learning pointsDescribe features your MVP will have (use case diagram + user story mapping)Submit a pdf report with:Personas + corresponding questionnairesInterview results table (can provide a link to spreadsheet, make sure to open access)Learning points summaryMVP features.Optional: Start implementation of the functionality you are certain about.Assignment 4. UI design, Prototyping, MVP, and Usability TestingBreak down MVP features into phases and cut down the specification to implement MVP V1Produce low and high fidelity designs for your product.Review the phases breakdown.Follow either the Prototyping or MVP path to complete the assignment.Prototyping path:Make a clickable prototype with Figma or a similar toolMake 5-10 offline stakeholders use your prototype, observe them and gather feedbackEmbed your prototype into an online usability testing tool (e.g. Maze).Run an online usability test with 5-10 online stakeholders.Summarize key learning pointsMVP path:Review your MVP phases.Build MVP V1 Make 5-10 offline stakeholders use your MVP, observe them and gather feedbackIntegrate an online usability testing tool to observe user sessions (e.g. Smartlook).Distribute the MVP to 5-10 online stakeholders and run an online usability test.Summarize key learning pointsSubmit all of the below in one PDF:Link to sketches and designs.Link to your MVP/Clickable prototype.Link to online usability test.Names of people you conducted the tests with and which stakeholder type are they.Key learning points summary.Make sure all links are accessible/viewable. | 1
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Quiz | 1. What does the acronym MVP stand for? What types of MVP do you know of?2. Define roles, activities, and artefacts of Scrum. What differentiates Scrum from other Agile frameworks, e.g. Kanban?3. What does DEEP criteria stand for when discussing Product Backlog? Explain each of the aspects with examples.4. Describe how Scrum activities are performed. Which of them are essential and which of them can vary depending on the product. | 1
+ |
+| Presentation | Prepare a 5-mins presentation describing your: product backlogsprint resultsMVP-launch planEach team will present at the class. The assessment will be based on the presentation delivery, reasoning for decision making and asking questions and providing suggestions for other teams. | 0
+ |
+| Group Project Work | Assignment 5. Launching an MVP1. Populate and groom product backlog: Comply with the DEEP criteria. 2. Run two one-week sprints:Conduct two Sprint plannings, i.e. pick the tasks for Sprint Backlog.Conduct two Sprint reviewsRun one Sprint Retrospective3. Make a launch plan and release:You need to launch in the following two weeks.Decide what functionality will go into the release.Release your first version in Google Play.Hint: Focus on a small set of features solving a specific problem for a specific user, i.e. MVP.4. Prepare a 5-mins presentation describing your: product backlogsprint resultsMVP-launch plan.Demo for your launched MVP.Each team will present at the class. The assessment will be based on the presentation delivery, reasoning for decision making and asking questions and providing suggestions for other teams.5. Submit a PDF with:Backlogs and Launch planLink to the launched productAssignment 6. AC, DoD and Midterm Presentation1. Produce acceptance criteria for 3-5 most important user stories in your product.2. Produce definition of done checklist3. Estimate the items in your product backlog4. Prepare a midterm presentation for 10-mins in which you cover:The problem you are trying to solveYour users and customers (personas)Your solution and it's core value propositionCurrent state of your productClear plan for the upcoming weeksYour team and distribution of responsibilitiesDemoRetrospective and learning pointsLink to your appSubmit a pdf with:Items 1, 2, 3link to the presentation | 1
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Quiz | 1. What are common product hypotheses present? How can we formulate them as questions about our UX?2. Explain what is hypothesis-driven development3. Describe the important aspects and elements of a controlled experiment | 1
+ |
+| Presentation | Prepare a short 2-minutes pitch for your project idea (2-5 slides). Suggested structure:What problem you are solving:- State the problem clearly in 2-3 short sentences.Who are you solving it for:- Who is your user/customer?- Why will they be attracted to it?What is your proposed solution to solve that problem:- One sentence description- What main feature(s) will it have? | 0
+ |
+| Group project work | Assignment 7: Development, Observation, and Product Events.1. Continue with your development process:- Hold sprint planning and reviews.- Revisit estimations and keep track for velocity calculation.- Host demos and release new versions to your users2. Observing users:- Integrate a user sessions recording tool into your product- As a team: watch 100 user sessions and outline common user behavior patterns.- Each team member: give product to 3 new people and observe them use it.3. Product events:Create a product events table.Integrate a free analytics tool that supports events reporting (e.g. Amplitude, MixPanel).Write and submit a report:- describe user behavior patterns (main ways how people use your product).- learning points from the observations- add the events table.- describe which analytics tool you chose and whyAssignment 8: GQM, Metrics, and Hypothesis-testing.1. GQM and Metrics Dashboard- Compose a GQM for your product.- Identify your focus and L1 metrics- Setup an Analytics Dashboard with the metrics you chose.- Add the instructors to your Analytics Dashboard.Hypothesis-testing:- answer clarity and hypotheses: do users understand your product, is it easy for them to get started, and do they return?- suggest product improvements to increase clarity, ease of starting and retention.- based on the suggestions formulate 3 falsifiable hypotheses- design a simple test to check each of them- pick one test that could be conducted by observing your users- conduct the testSubmit:- GQM, Focus and L1 Metrics breakdown.- Report on the hypothesis-testing activities- Access link to the dashboard.Assignment 9: Running an A/B testCompose an A/B test:- Design a change in your product- Hypothesis: Clearly state what you expect to improve as the result of the change.- Parameter and Variants: Describe both A and B variants (and other if you have more).- Intended sample size.- OEC: Determine the target metric to run the experiment against.Then do one of the two options:Option 1: Conduct the A/B test using a remote control and A/B testing tool (Firebase, Optimizely or like)Option 2: Do the statistical math yourselfConduct an A/B test and collect data.Do the math manually using the standard Student T-test.Submit a PDF with:- the A/B test description - report on how the experiment went.- either screenshots from the tool or math calculations. | 1
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. Grading criteria for the final project presentation:
+2. 1. Problem: short clear statement on what you are solving, and why it’s important.
+3. 2. User: should be a specific user, can start from generic and then show how you narrowed it.
+4. 3. Solution: how do you target the problem, what were the initial assumptions/hypotheses
+5. 4. Elicitation process: interviews, how many people, what questions you asked, what you learnt.
+
+
+**Section 2**
+
+
+
+1. 5. Arriving at MVP: how you chose features, describe prototyping and learning from it, when did you launch, and how it went.
+2. 6. Team and development process: how it evolved, what were the challenges, what fixes you made to keep progressing.
+3. 7. Product demo: make it clear what your current product progress is.
+
+
+**Section 3**
+
+
+
+1. 7. Hypothesis-driven development: how did you verify value and understandability of your product, what were the main hypotheses you had to check through MVP.
+2. 8. Measuring product: what metrics you chose, why, what funnels did you set for yourself, and what was the baseline for your MVP.
+3. 9. Experimentation: What usability tests and experiments you conducted, what did you learn, how did it affect your funnels and metrics.
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+
+1. For the retake, students have to implement a product and follow the guidelines of the course. The complexity of the product can be reduced, if it is one person working on it. The grading criteria for each section are the same as for the final project presentation. There has to be a meeting before the retake itself to plan and agree on the product ideas, and to answer questions.
+2. P7. Activities and Teaching Methods by Sections
+3. Mark what techniques and methods are used in each section (1 is used, 0 is not used).
+4. Table A1: Teaching and Learning Methods within each section
+5. Table A2: Activities within each section
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+
+
+
+
+
+
+
+
+

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+BSc: Lean Software Development
+==============================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Lean Software Development](#Lean_Software_Development)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+		- [1.5.4 Course activities and grading breakdown](#Course_activities_and_grading_breakdown_2)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+			* [2.2.1.4 Section 4](#Section_4)
+			* [2.2.1.5 Section 5](#Section_5)
+			* [2.2.1.6 Section 6](#Section_6)
+			* [2.2.1.7 Section 7](#Section_7)
+		- [2.2.2 Final assessment](#Final_assessment)
+
+
+
+Lean Software Development
+=========================
+
+
+* **Course name**: Lean Software Development
+* **Code discipline**: XYZ
+* **Subject area**:
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: Fundamental principles of producing software as a creative act of the human mind; Techniques to optimize such production, with specific focus on agile methods.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+### Prerequisite topics
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Software as a creative activity | 1. Nature of software
+2. Software and art
+3. Core resources for the production of software
+4. Tame and wicked projects
+5. Organizing the activities based on the GQM approach
+ |
+| Measurement in software | 1. Meaning of measures
+2. The representational theory of measurement
+3. Measurement scales
+4. Fundamental measures for the production of software
+5. Procedural measures
+6. Object Oriented measures
+ |
+| Taylorism and Fordism | 1. The increase of productivity in the idea of Taylor
+2. The role of division of work
+3. Planning and formalization of tasks
+4. Economies of scale
+5. Problems in understanding tasks
+6. Taylorism/Fordism and software development
+ |
+| Lean and Agile | 1. Taiichi Ono and the Toyota Production System
+2. Creating a “Radiography” of the Production Process
+3. Workers involvement
+4. “Pull” and Not “Push”
+5. Kanban
+6. Quality management
+7. Process control
+8. Job enrichment
+9. Control and coordination mechanisms
+10. Case study: Extreme Programming
+ |
+| Issues in Lean and Agile | 1. The “Hype of Agile”
+2. The dark side of agile
+3. Skepticism about agile methods
+4. Knowledge and software engineering
+5. Using burn-down charts
+6. The Zen of agile
+ |
+| Structuring a Lean Approach to software development | 1. Existing proposals to create a “Lean Software Development”
+2. Sharing a common vision
+3. Depriving gurus of their power
+4. GQM+
+5. Applying the GQM+ step-by-step
+6. Business alignment
+7. GQM+ for business alignment
+ |
+| Optimizing the development process | 1. Why the PDSA does not work in software
+2. The experience factory
+3. The QIP cycle
+4. Non invasive measurement
+5. The big-brother effect
+6. The role of autonomation
+7. Employing Andon boards
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+This course exposes the student to the core concepts behind Lean Development in Software Engineering, beyond myths and legends, emphasizing how it relates to the general principles of Lean Development. It discusses the different possible software processes, how they can be tailored, enacted, and measured. In addition, a significant part of the course is centered around the application of lean to software development to knowledge intensive areas not necessarily connected to software.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* creative nature of software production as an act of creativity of the human mind,
+* the substantial differences between tame and wicked problems,
+* the core concepts of measurement in software engineering,
+* the fundamentals of Taylorist/Fordist approaches to (software) production,
+* the basis of lean and agile software development,
+* the “dark” side of agility,
+* the importance of knowledge and knowledge sharing in producing software,
+* how to create an ad-hoc process for a development organization.
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* when a problem is “easy to solve” provided enough effort is put to such solution and when it is not,
+* what is a measure in general,
+* why it is important and how we can define and perform measurements in software engineering, especially in lean and agile development environments,
+* how to organize the development process to collect metrics non invasively,
+* the difference between pulling and pushing in (software) development,
+* the fundamental principle of agility,
+* the risk intrinsic in the dark side of agile,
+* how to organize an agile development process based on the definition of overall Goals, associated Question, and milestones based on Metrics,
+* an environment based on experience, like the Experience Factory.
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Compute the fundamental software metrics to track the evolution of a project,
+* Organize the aims of a (software) development organization in terms of Goals, Questions, and Metrics,
+* Create a tailored (lean and agile) development process for an organization producing software,
+* Define a path to insert and manage such (lean and agile) development process into an organization producing software,
+* Structure the experience gathering during inside an organization to based on it the future strategic decision of such organization,
+* Relate the various proposals for Agile Methods to the overall principles of Lean Management,
+* Define a suitable (lean) process for a new organization, a process to introduce and institutionalize it, and an approach to measure the outcome of such introduction and institutionalization.
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 91-100 | -
+ |
+| B. Good | 76-90 | -
+ |
+| C. Satisfactory | 51-75 | -
+ |
+| D. Poor | 0-50 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Class and lab participation (including class quizzes) | 20
+ |
+| Project | 40
+ |
+| Oral Exam | 40
+ |
+
+
+Each activity is mandatory and failing any component of the course implies failing the entire course and go to the retake, apart from the students declaring at the beginning of the course that they aim for a C, in which case the rule below applies.
+
+
+Students will be asked to define their learning goals at the beginning of the course and will have a personalized evaluation framework. In particular:
+
+
+
+* Students aiming for a C can focus on attending lectures and having a pre-oral at the end of week 2, passing which they can achieve their goal, provided that they actively attend and participate at all lectures, including the final presentations;
+* Students aiming for a B and A in addition to attending lecture and labs, sustaining an oral, also need to have a project with a clear output as written below, including a report and a presentation at the end.
+
+
+### Recommendations for students on how to succeed in the course
+
+
+The goal of the project is to read the book and understand what is the takeaway for software engineering, considering three fundamental aspects: a) the process to follow, b) the product being built c) the structure of the team and its organization. The projects will be executed in weekly iteration on traceable files.
+
+
+The projects will be partially graded weekly (30%) and part at the end (70%). Moreover, at the end you will need to give a 5-minute presentation of your work.
+
+
+During the first week of the project you will create the overall GQM of the project and you will be evaluated based on it during the second week. During the second week of the project you will also create the vision of your project with a roadmap. From the third week onward you will start to have the reviews of your project increments in terms of the a) progresses toward the completion b) accurate planning based on the defined GQM, and c) quality of the work. Weekly grade ranges from 0 to 2 points.
+
+
+The overall project success will be evaluated as following:
+
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Grade | Project outcome
+ |
+| --- | --- |
+| A (100%) | In-depth analysis of the subject under investigation with original ideas for SE and practical experiments
+ |
+| B (80%) | In-depth analysis of the subject under investigation with original ideas for SE
+ |
+| C (60%) | Analysis of the subject under investigation, highlighting general ideas for SE, without novelty
+ |
+| D (0%) | No activities
+ |
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Textbook: Andrea Janes and Giancarlo Succi. Lean Software Development in Action. Springer, Heidelberg, Germany, 2014. ISBN 978-3-662-44178-7. doi: 10.1007/978-3-642-00503-9.
+* Reference: James P. Womack and Daniel T. Jones. Lean Thinking: banish waste and create wealth in your corporation. Lean Enterprise Institute. Simon & Schuster, 1996. ISBN 9780684810355.
+* Reference: Taiichi Ohno. Toyota production system: beyond large-scale production. CRC Press, 1988
+* Reference: James P. Womack. Lean Thinking. Simon & Schuster, Limited, 1997. ISBN 9780671004712.
+* Reference: James P. Womack, Daniel T. Jones, and Daniel Roos. The Machine That Changed the World: The Story of Lean Production. Harper Perennial modern classics. HarperCollins, 1991. ISBN 9780060974176.
+* Reference: Mary Poppendieck and Tom Poppendieck. Implementing Lean Software Development: From Concept to Cash. A Kent Beck signature book. Addison-Wesley, 2007. ISBN 9780321437389.
+* Reference: C.M. Christensen. The Innovator’s Dilemma: When New Technologies Cause Great Firms to Fail. Management of innovation and change series. Harvard Business School Press, 1997. ISBN 9780875845852.
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Moodle, Miro, Overleaf
+
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4 | Section 5 | Section 6 | Section 7
+ |
+| --- | --- | --- | --- | --- | --- | --- | --- |
+| Homework and group projects | 1 | 1 | 1 | 1 | 1 | 1 | 1
+ |
+| Reports | 1 | 1 | 1 | 1 | 1 | 1 | 1
+ |
+| Oral polls | 1 | 1 | 1 | 1 | 1 | 1 | 1
+ |
+| Discussions | 1 | 1 | 1 | 1 | 1 | 1 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Provide examples of creativity in the production of software. | 1
+ |
+| Question | Describe the differences between tame and wicked projects. | 1
+ |
+| Question | Discuss the key resources needed for the production of software. | 1
+ |
+| Question | What are key issues in creative production of software for distributed teams? | 1
+ |
+| Question | Provide examples of wicked problems from your everyday life | 0
+ |
+| Question | Evidence wickedness in different aspects of software production | 0
+ |
+| Question | Create a GQM for your aims of the semester | 0
+ |
+| Question | Discuss the role of GQM in tame and wicked projects | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Provide examples of the representational theory of measurement | 1
+ |
+| Question | List the measurement scales | 1
+ |
+| Question | Present for each measurement scale the operations that can be performed on it | 1
+ |
+| Question | Discuss the representational condition | 1
+ |
+| Question | What are key size metrics? | 1
+ |
+| Question | What are key complexity metrics? | 1
+ |
+| Question | Provide examples of subjective and objective metrics | 0
+ |
+| Question | List 3 direct and 3 indirect measures, evidencing also the problems connected to the construction of indirect measures | 0
+ |
+| Question | Compute LOC and other size metrics for code snippets | 0
+ |
+| Question | Compute MCC and other complexity metrics for code snippets | 0
+ |
+| Question | Compute the metrics of the CK suite for portions of Object Oriented systems | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Detail the fundamental assumptions by Taylor | 1
+ |
+| Question | What are the fundamental activities of managers according to Taylor? | 1
+ |
+| Question | In which sense Taylor has influenced what we now consider “good management practices?” | 1
+ |
+| Question | How does creativity relates to the “good management practices” of Taylor? | 1
+ |
+| Question | What are the problems in applying Fordism/Taylorism to software development? | 1
+ |
+| Question | Provide examples of companies where the approach by Taylor has been successful | 0
+ |
+| Question | Discuss how the approach of Taylor can be useful in attracting and/or retaining employees | 0
+ |
+| Question | Analyse the fundamental activities of managers according to Taylor and determine their limits | 0
+ |
+| Question | Determine the fundamental activities of managers according to Taylor can have an implication in the software crisis | 0
+ |
+| Question | Outline how flexibility and variable requirements can be handled in the context of Taylorism and Fordism | 0
+ |
+
+
+#### Section 4
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Present the key problems in batch production | 1
+ |
+| Question | Outline the key principles of the approach of Ono at Toyota | 1
+ |
+| Question | What are the fundamental steps in eliminating waste according to Ono? | 1
+ |
+| Question | Details the role of the customers and of the workers in the approach of Ono | 1
+ |
+| Question | Explain the difference between “Pulling” and “Pushing” | 1
+ |
+| Question | What are key steps in improving quality according to Ono? | 1
+ |
+| Question | What are the key control and coordination mechanisms available? | 1
+ |
+| Question | What are the fundamental two actions needed to perform a Lean transformation according to Ono? | 0
+ |
+| Question | What are the associated three major needs? | 0
+ |
+| Question | What are the 5 steps to enact Lean Thinking according to Womak and Jones? | 0
+ |
+| Question | Discuss the 8 constantly ongoing activities in a lean company like Toyota | 0
+ |
+| Question | How can activities been classified in a decision matrix in an environment like Toyota? | 0
+ |
+| Question | Provide concrete examples of “Push” and of “Pull” in software production. | 0
+ |
+| Question | Details the control and coordination mechanisms present in agile and in traditional development environments. | 0
+ |
+
+
+#### Section 5
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | What is the Gartner’s Innovation Hype Cycle? Could you provide examples of application of it to a different field of knowledge? | 1
+ |
+| Question | Describe the so-called “Dark Agile Manifesto” | 1
+ |
+| Question | What are the sources of the skepticism present with respect to Agile? | 1
+ |
+| Question | What makes agile awkward in the eyes of “traditional” managers? | 1
+ |
+| Question | Given a production system, how do you determine what is the value of every step, how much improvement can be considered enough, and when is the point reached where value is not increased anymore but destroyed? | 1
+ |
+| Question | How is it possible to obtain knowledge about the production process? How can I create visibility of the ongoing activities or problems? | 1
+ |
+| Question | Identify in other areas of software engineering phenomenon similar to the “Dark Side of Agile.” | 0
+ |
+| Question | Identify in other knowledge-intensive fields phenomena similar to the “Dark Side of Agile” and discuss how they can be tackled. | 0
+ |
+| Question | Given a production process, determine strategies to store knowledge to create experience? | 0
+ |
+| Question | How can you design the production process so that the team uses the gained experience? | 0
+ |
+| Question | How can you systematically improve your process, also building on the experience to anticipate problems (create wisdom)? | 0
+ |
+
+
+#### Section 6
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Reflect on the seven principles for characterizing Lean Software Development by Mary and Tom Poppendieck. | 1
+ |
+| Question | What is the semantic gap and which threats it poses to effective software development? | 1
+ |
+| Question | Map the structure of Extreme Programming to the layered structure of Shalloway et al. | 1
+ |
+| Question | How does the scientific method deprives gurus from their power? | 1
+ |
+| Question | What are the steps to implement the GQM+? | 1
+ |
+| Question | For what reason measurement goals and business goals should be interconnected? | 1
+ |
+| Question | How do the practices of Lean Management defined by Hibbs and colleagues relate to the seven principles by Mary and Tom Poppendieck | 0
+ |
+| Question | Propose how you could develop software and hardware tools to promote common visions in companies. | 0
+ |
+| Question | Elaborate a proposal to create some kind of Balanced Scorecards to evaluate your current study. | 0
+ |
+| Question | Discuss the opinion of Ono about following plans and the extent to which such opinion contradicts (a) the practices, and (b) the principles of the tayloristic/fordistic approach | 0
+ |
+| Question | Propose a SWAT analysis to introduce a Lean approach to your most recent software development endavour | 0
+ |
+
+
+#### Section 7
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Details the major components of an experience factory. | 1
+ |
+| Question | What are Reflection, Retrospective, and Post-Mortem Analysis? Why are they useful in Lean Software Development? | 1
+ |
+| Question | What are the key components of a non invasive software measurement systems? | 1
+ |
+| Question | What is the big brother effect and how it is possible to alleviate it. | 1
+ |
+| Question | Discuss how autonomation is present in Extreme Programming. | 1
+ |
+| Question | Where is the term “Dashboard” coming from and what is its use in Lean Software Development? | 1
+ |
+| Question | List the steps of a QIP. | 0
+ |
+| Question | Discuss the risks of a measurement program and how non invasive software measurement can help alleviating them. | 0
+ |
+| Question | Are there cases in which Theory X of management could be more effective than Theory Y? Discuss your findings. | 0
+ |
+| Question | For which aspects of software production autonomation could be useful? | 0
+ |
+| Question | Which tools could be used to promote autonomation? | 0
+ |
+| Question | Prototype by paper and pencil an Andon board that you would consider useful in a software production environment. | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. Present the salient aspects of wicked problems
+2. List the key aspects of software that make it a wicked problem
+3. Provide a link between wickedness and creativity in software production
+4. Discuss what promotes and what inhibit creativity in general and in software production
+5. Outline meaning and limitation of the concept of “engineering” the production of software
+
+
+**Section 2**
+
+
+
+1. Structure the aims of a company using the GQM and detailing the metrics to compute, also explaining the deductions and the predictions that can be made with such metrics.
+2. Given an index computed as a combination of metrics, determine if it is a metrics according to the representational theory of measurement.
+3. Analyse a portion of a system and determine suitable metrics to extract and the information that would be provided by such metrics.
+4. Given a website performing a service (like flight reservations), compute the Function Points for such website.
+5. Discuss how to structure a taxonomy of quality for a specific company, explaining the role of reliability in it, and detailing how to compute the reliability again in the context of such company; please make the assumptions that you need to perform such computation.
+
+
+**Section 3**
+
+
+
+1. What aspects of making software feel like an art, which like a craft to you and how could you bend Taylorism and Fordism to handle it?
+2. How does Fordism and Taylorism can explain that companies producing software containing bugs can still stay in the market, and, in certain case, also be successful?
+3. Based on your experience and previous courses, which development models can refer to Fordism and Taylorism and which cannot be reduced to it?
+4. How does the specialization of work in software development can be linked to Fordism and Taylorism?
+5. Provide an example for each of the fundamental activities of managers according to Taylor that shows how such activity is very useful in software development and one that shows that is is inadequate.
+
+
+**Section 4**
+
+
+
+1. Structure a model like PDSA for a company producing websites for online marketing.
+2. How can the right part and the right information be always available without waste according to the Toyota approach?
+3. Compare a street crossing based on traffic lights with a roundabout and determine the approach that is safest and the one with the a highest throughput according to Waterfall and to Lean.
+4. Discuss the involvements of workers in tayloristic/fordistic and in Lean development processes and their implications for the retention and the improvement of the quality of the workforce.
+5. Outline the extent of which economies of scale exist in Lean development processes.
+6. Imagine you had to introduce Extreme Programming in a software development team that follows a waterfall process. Which problems do you foresee? How will the clients react (that until now are used to work with a team that used the waterfall process)? How would you address them?
+
+
+**Section 5**
+
+
+
+1. Imagine you are the boss of a small software development company. Which actions would you do or which practices would you introduce to prevent that your programmers fall into the trap of following a software guru?
+2. Elaborate possible extreme (and damaging) positions that can be taken by gurus of agile.
+3. Explain the differences in introducing a methodology by a guru and by a smart and effective coach.
+4. Detail why Extreme Programming produces an informative workspace.
+5. Discuss effective ways of packaging and “distributing” knowledge in software teams, starting with the guru approach of organizing knowledge into simple, clear practices which are easy to explain and to follow.
+
+
+**Section 6**
+
+
+
+1. Discuss the role of customer on-site under the perspective of lean and outline it relevance in the earlier and then in the later proposals of agile software development.
+2. Suppose that you have to develop Balanced Scorecards for a software development team. Which perspectives would you use? Which goals would you use for each perspective?
+3. What is a socio-technical system and how can it be used to describe an (agile) software production environement?
+4. Imagine you want to evaluate how readable the source code of some program is. Define a GQM+ model to describe what and why you would measure.
+5. The development in company M occurs according to the following schema: when a new project is started, a developer takes an old project that is the most similar to the new requirements and makes a copy and starts implementing the required modifications. To improve this process and to help the company to adopt a component-based approach, we want to understand which pieces of code are the best candidates for future components and which variability points they have. Define a suitable GQM+ for such purpose.
+
+
+**Section 7**
+
+
+
+1. What type of wisdom (in the sense of “know-why”) would you manage in an Experience Factory to support Lean Thinking? Distinguish between organizational learning and project learning.
+2. Assume you are a manager convinced that Theory X is true. Which non-invasive measurement probes would you want to develop to maximize productivity? Now assume you are convinced that Theory Y is true. Which non-invasive measurement probes would you need now?
+3. We discussed that we foresee two ways to collect measurements non- invasively: in batch and in background mode. What are the advantages and disadvantages of each approach?
+4. There are many interrelated building blocks (or concepts) of Lean Software Development and each contributes differently to it. What types of data are handled by each of these building blocks (or concepts)? How do the contribution to the overall value stream, to the creation of knowledge, and to the overall improvement?
+5. Assume you set up a fantastic dashboard for your team. As you collect the data and visualize it, you notice that all the measurements show problematic values. You let the dashboard in place for some days and also show it to your collaborators, but nobody cares; everybody continues his job as if everything would be fine. What is going wrong?
+
+
+
+
+
+
+
+
+
+

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+
+
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+
+
+BSc: Logic and Discrete Mathematics
+===================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Logic and Discrete Mathematics (Philosophy 1)](#Logic_and_Discrete_Mathematics_.28Philosophy_1.29)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Course Topics](#Course_Topics)
+	+ [1.3 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.3.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.3.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.3.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.3.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.3.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.4 Grading](#Grading)
+		- [1.4.1 Course grading range](#Course_grading_range)
+		- [1.4.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.4.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.5 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.5.1 Open access resources](#Open_access_resources)
+	+ [1.6 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [1.7 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [1.7.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [1.7.1.1 Section 1](#Section_1)
+			* [1.7.1.2 Section 2](#Section_2)
+			* [1.7.1.3 Section 3](#Section_3)
+		- [1.7.2 Final assessment](#Final_assessment)
+			* [1.7.2.1 Section 1](#Section_1_2)
+			* [1.7.2.2 Section 2](#Section_2_2)
+			* [1.7.2.3 Section 3](#Section_3_2)
+		- [1.7.3 The retake exam](#The_retake_exam)
+
+
+
+Logic and Discrete Mathematics (Philosophy 1)
+=============================================
+
+
+* **Course name**: Logic and Discrete Mathematics (Philosophy 1)
+* **Code discipline**: CSE113
+* **Subject area**: Math, Computer Science
+
+
+Short Description
+-----------------
+
+
+This course consists of two distinct but overlapping parts: i. Logic; and ii. Discrete Mathematics.
+The first part of the course is an introduction to formal symbolic logic. Philosopher John Locke once wrote that ``logic is the anatomy of thought. *This part of the course will teach* 
+students to analyse and evaluate arguments using the formal techniques of modern symbolic logic.
+The second part of the is designed for students to teach them basic notions of graph theory, discrete optimization and dynamic programming. This part will give practical experience with basic algorithms in discrete mathematics. 
+
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Basic of Logic | 1. Logical Operators
+2. Truth Tables for Propositions
+3. Propositional calculus
+4. Quantifiers
+5. Predicate Logic
+6. Basic Proof Techniques in Math
+7. Fundamental proofs
+8. Use of propositional calculus to do proofs
+ |
+| Set Theory & Finite combinatorics
+ | 1. Fundamentals of the set theory
+2. From sets to relations
+3. Functions and numbers
+4. Algebra of binary relations
+5. Principles of finite combinatorics
+6. Recursion and Discrete Optimization
+7. Linear recurrence relations
+ |
+| Basic of Graphs | 1. From set and relations to graphs
+2. Euler tours and graphs
+3. Hamilton paths and graphs
+4. Planar graphs and Euler formula
+5. Trees and Kőnig's infinity lemma
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+This calculus course will provide an opportunity for participants to:
+
+
+
+* understand key principles involved in differentiation and integration of functions
+* solve problems that connect small-scale (differential) quantities to large-scale (integrated) quantities
+* become familiar with the fundamental theorems of Calculus
+* get hands-on experience with the integral and derivative applications and of the inverse relationship between integration and differentiation.
+
+
+### ILOs defined at three levels
+
+
+We specify the intended learning outcomes at three levels: conceptual knowledge, practical skills, and comprehensive skills.
+
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* know the categorical logic
+* know the propositional logic
+* know the predicate logic
+* explain the difference between deduction and induction
+* know the trees and spanning trees
+* remember the Euler and Hamilton graphs
+* know what is planar graphs
+* explain the Dijkstra’s algorithm
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* use Venn diagrams
+* calculate truth values
+* analyse formal structures of some arguments
+* differ the deduction and induction
+* build spanning trees
+* find Euler tour and Hamilton path
+* use Dijkstra’s algorithm
+* solve maximum flow problem
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+...
+
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 85-100 | -
+ |
+| B. Good | 75-84 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Fail | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Midterm | 40
+ |
+| Final exam | 40
+ |
+| In-class participation | 20
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+* Participation is important. Attending lectures is the key to success in this course.
+* Review lecture materials before classes to do well.
+* Reading the recommended literature is obligatory, and will give you a deeper understanding of the material.
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* K.H. Rosen, Discrete Mathematics and Its Applications (7th Edition). McGraw Hill, 2012.
+* Lehman, E., Leighton, F. T., Meyer, A. R. (2017). *Mathematics for Computer Science. Massachusetts Institute of Technology Press.*
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Teaching and Learning Methods within each section
+| Teaching Techniques | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Problem-based learning (students learn by solving open-ended problems without a strictly-defined solution) | 1 | 1 | 1
+ |
+| Project-based learning (students work on a project) | 0 | 0 | 0
+ |
+| Modular learning (facilitated self-study) | 0 | 0 | 0
+ |
+| Differentiated learning (provide tasks and activities at several levels of difficulty to fit students needs and level) | 1 | 1 | 1
+ |
+| Contextual learning (activities and tasks are connected to the real world to make it easier for students to relate to them) | 0 | 0 | 0
+ |
+| Business game (learn by playing a game that incorporates the principles of the material covered within the course) | 0 | 0 | 0
+ |
+| Inquiry-based learning | 0 | 0 | 0
+ |
+| Just-in-time teaching | 0 | 0 | 0
+ |
+| Process oriented guided inquiry learning (POGIL) | 0 | 0 | 0
+ |
+| Studio-based learning | 0 | 0 | 0
+ |
+| Universal design for learning | 0 | 0 | 0
+ |
+| Task-based learning | 0 | 0 | 0
+ |
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Lectures | 1 | 1 | 1
+ |
+| Interactive Lectures | 1 | 1 | 1
+ |
+| Lab exercises | 1 | 1 | 1
+ |
+| Experiments | 0 | 0 | 0
+ |
+| Modeling | 0 | 0 | 0
+ |
+| Cases studies | 0 | 0 | 0
+ |
+| Development of individual parts of software product code | 0 | 0 | 0
+ |
+| Individual Projects | 0 | 0 | 0
+ |
+| Group projects | 0 | 0 | 0
+ |
+| Flipped classroom | 0 | 0 | 0
+ |
+| Quizzes (written or computer based) | 1 | 1 | 1
+ |
+| Peer Review | 0 | 0 | 0
+ |
+| Discussions | 1 | 1 | 1
+ |
+| Presentations by students | 0 | 0 | 0
+ |
+| Written reports | 0 | 0 | 0
+ |
+| Simulations and role-plays | 0 | 0 | 0
+ |
+| Essays | 0 | 0 | 0
+ |
+| Oral Reports | 0 | 0 | 0
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+1. Solve Truth Tables
+2. Use Truth Tables to analyse arguments
+3. Use Quantifiers to assess inferences
+4. What is Propositional Logic used for?
+5. What is Predicate Logic used for?
+
+
+#### Section 2
+
+
+#### Section 3
+
+
+1. What is the characteristic property of trees?
+2. How to find an Euler tour?
+3. What is a Hamilton path?
+4. Why are K3 and K5,5 not planar?
+5. What is the difference between undirected and directed graphs?
+6. Why do we consider weighted graphs?
+7. What practical problems are solved using Dijkstra's algorithm?
+8. What is the maximum flow problem?
+
+
+### Final assessment
+
+
+#### Section 1
+
+
+1. What is the difference between Categorical and Propositional Logic?
+2. How does Predicate Logic differ from Categorical and Propositional Logic?
+3. Why is Predicate Logic so important?
+4. What are Truth-Functions and why do we use them?
+5. Compute True Tables for Propositions
+6. Compute True Tables for Arguments
+
+
+#### Section 2
+
+
+1. 
+
+
+#### Section 3
+
+
+1. Explain handshaking lemma.
+2. Give necessary and sufficient conditions for the existence of an Euler tour.
+3. Give sufficient conditions for the existence of a Hamilton path (theorems of Dirac and Ore).
+4. Explain Kuratowski’s theorem.
+5. Explain the difference between undirected and directed graphs.
+6. Give the definition of weighted graphs?
+7. Explain Dijkstra's algorithm?
+8. What is the solution of the maximum flow problem (the Ford-Fulkerson algorithm)?
+
+
+### The retake exam
+
+
+Retakes will be run as a comprehensive exam, where the student will be assessed the acquired knowledge coming from the textbooks, the lectures, the labs, and the additional required reading material, as supplied by the instructor. During such comprehensive oral/written the student could be asked to solve exercises and to explain theoretical and practical aspects of the course.
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__mathematical_analysis_i.f21.md

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+
+
+
+
+
+
+
+BSc: Mathematical Analysis I.F21.test
+=====================================
+
+
+
+(Redirected from [BSc: Mathematical Analysis I.F21](/index.php?title=BSc:_Mathematical_Analysis_I.F21&redirect=no "BSc: Mathematical Analysis I.F21"))
+
+
+  
+
+
+
+
+Contents
+--------
+
+
+* [1 Mathematical Analysis I](#Mathematical_Analysis_I)
+	+ [1.1 Course Characteristics](#Course_Characteristics)
+		- [1.1.1 Key concepts of the class](#Key_concepts_of_the_class)
+		- [1.1.2 What is the purpose of this course?](#What_is_the_purpose_of_this_course.3F)
+	+ [1.2 Course Objectives Based on Bloom’s Taxonomy](#Course_Objectives_Based_on_Bloom.E2.80.99s_Taxonomy)
+		- [1.2.1 What should a student remember at the end of the course?](#What_should_a_student_remember_at_the_end_of_the_course.3F)
+		- [1.2.2 What should a student be able to understand at the end of the course?](#What_should_a_student_be_able_to_understand_at_the_end_of_the_course.3F)
+		- [1.2.3 What should a student be able to apply at the end of the course?](#What_should_a_student_be_able_to_apply_at_the_end_of_the_course.3F)
+		- [1.2.4 Course evaluation](#Course_evaluation)
+		- [1.2.5 Grades range](#Grades_range)
+		- [1.2.6 Resources and reference material](#Resources_and_reference_material)
+	+ [1.3 Course Sections](#Course_Sections)
+		- [1.3.1 Section 1](#Section_1)
+			* [1.3.1.1 Section title:](#Section_title:)
+		- [1.3.2 Topics covered in this section:](#Topics_covered_in_this_section:)
+		- [1.3.3 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F)
+		- [1.3.4 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section)
+		- [1.3.5 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section)
+		- [1.3.6 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section)
+		- [1.3.7 Section 2](#Section_2)
+			* [1.3.7.1 Section title:](#Section_title:_2)
+		- [1.3.8 Topics covered in this section:](#Topics_covered_in_this_section:_2)
+		- [1.3.9 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_2)
+		- [1.3.10 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_2)
+		- [1.3.11 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_2)
+		- [1.3.12 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_2)
+		- [1.3.13 Section 3](#Section_3)
+			* [1.3.13.1 Section title:](#Section_title:_3)
+			* [1.3.13.2 Topics covered in this section:](#Topics_covered_in_this_section:_3)
+		- [1.3.14 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_3)
+		- [1.3.15 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_3)
+			* [1.3.15.1 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_3)
+			* [1.3.15.2 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_3)
+
+
+
+Mathematical Analysis I
+=======================
+
+
+Course Characteristics
+----------------------
+
+
+### Key concepts of the class
+
+
+* Differentiation
+* Integration
+* Series
+
+
+### What is the purpose of this course?
+
+
+This calculus course covers differentiation and integration of functions of one variable, with applications. The basic objective of Calculus is to relate small-scale (differential) quantities to large-scale (integrated) quantities. This is accomplished by means of the Fundamental Theorem of Calculus. Should be understanding of the integral as a cumulative sum, of the derivative as a rate of change, and of the inverse relationship between integration and differentiation.
+
+
+This calculus course will provide an opportunity for participants to:
+
+
+
+* understand key principles involved in differentiation and integration of functions
+* solve problems that connect small-scale (differential) quantities to large-scale (integrated) quantities
+* become familiar with the fundamental theorems of Calculus
+* get hands-on experience with the integral and derivative applications and of the inverse relationship between integration and differentiation.
+
+
+Course Objectives Based on Bloom’s Taxonomy
+-------------------------------------------
+
+
+### What should a student remember at the end of the course?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Derivative. Differential. Applications
+* Indefinite integral. Definite integral. Applications
+* Sequences. Series. Convergence. Power Series
+
+
+### What should a student be able to understand at the end of the course?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Derivative. Differential. Applications
+* Indefinite integral. Definite integral. Applications
+* Sequences. Series. Convergence. Power Series
+* Taylor Series
+
+
+### What should a student be able to apply at the end of the course?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* find multiple, path, surface integrals
+* find the range of a function in a given domain
+* decompose a function into infinite series
+
+
+### Course evaluation
+
+
+
+
+Course grade breakdown
+|  |  | **Proposed points** |
+| --- | --- | --- |
+| Labs/seminar classes
+ | 20
+ |  |
+| Interim performance assessment
+ | 30
+ |  |
+| Exams
+ | 50
+ |  |
+
+
+If necessary, please indicate freely your course’s features in terms of students’ performance assessment.
+
+
+
+### Grades range
+
+
+
+
+Course grading range
+|  |  | **Proposed range** |
+| --- | --- | --- |
+| A. Excellent
+ | 90-100
+ |  |
+| B. Good
+ | 75-89
+ |  |
+| C. Satisfactory
+ | 60-74
+ |  |
+| D. Poor
+ | 0-59
+ |  |
+
+
+If necessary, please indicate freely your course’s grading features.
+
+
+
+### Resources and reference material
+
+
+* Zorich, V. A. “Mathematical Analysis I, Translator: Cooke R.” (2004)
+* 
+* 
+
+
+Course Sections
+---------------
+
+
+The main sections of the course and approximate hour distribution between them is as follows:
+
+
+
+
+
+Course Sections
+| **Section** | **Section Title** | **Teaching Hours** |
+| --- | --- | --- |
+| 1
+ | Sequences and Limits
+ | 28
+ |
+| 2
+ | Differentiation
+ | 24
+ |
+| 3
+ | Integration and Series
+ | 28
+ |
+
+
+### Section 1
+
+
+#### Section title:
+
+
+Sequences and Limits
+
+
+
+### Topics covered in this section:
+
+
+* Sequences. Limits of sequences
+* Limits of sequences. Limits of functions
+* Limits of functions. Continuity. Hyperbolic functions
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. A sequence, limiting value
+2. Limit of a sequence, convergent and divergent sequences
+3. Increasing and decreasing sequences, monotonic sequences
+4. Bounded sequences. Properties of limits
+5. Theorem about bounded and monotonic sequences.
+6. Cauchy sequence. The Cauchy Theorem (criterion).
+7. Limit of a function. Properties of limits.
+8. The first remarkable limit.
+9. The Cauchy criterion for the existence of a limit of a function.
+10. Second remarkable limit.
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Find a limit of a sequence
+2. Find a limit of a function
+
+
+### Test questions for final assessment in this section
+
+
+1. Find limits of the following sequences or prove that they do not exist:
+2. a
+
+n
+
+
+=
+n
+−
+
+
+
+n
+
+2
+
+
+−
+70
+n
++
+1400
+
+
+
+
+{\displaystyle a\_{n}=n-{\sqrt {n^{2}-70n+1400}}}
+
+![{\displaystyle a_{n}=n-{\sqrt {n^{2}-70n+1400}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aeca3ea0fc01bed1f98eb199a9819614e88e793f);
+3. d
+
+n
+
+
+=
+
+
+(
+
+
+
+2
+n
+−
+4
+
+
+2
+n
++
+1
+
+
+
+)
+
+
+n
+
+
+
+
+{\textstyle d\_{n}=\left({\frac {2n-4}{2n+1}}\right)^{n}}
+
+![{\textstyle d_{n}=\left({\frac {2n-4}{2n+1}}\right)^{n}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/389a3735f2899205a00b490e482acbcfa39b3edb);
+4. x
+
+n
+
+
+=
+
+
+
+
+
+(
+
+2
+
+n
+
+2
+
+
++
+1
+
+)
+
+
+6
+
+
+(
+n
+−
+1
+
+)
+
+2
+
+
+
+
+
+(
+
+
+n
+
+7
+
+
++
+1000
+
+n
+
+6
+
+
+−
+3
+
+)
+
+
+2
+
+
+
+
+
+
+{\textstyle x\_{n}={\frac {\left(2n^{2}+1\right)^{6}(n-1)^{2}}{\left(n^{7}+1000n^{6}-3\right)^{2}}}}
+
+![{\textstyle x_{n}={\frac {\left(2n^{2}+1\right)^{6}(n-1)^{2}}{\left(n^{7}+1000n^{6}-3\right)^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5f2e2a41471540c1cb5f3f8b2ad3d96ef91cf7e9).
+
+
+### Section 2
+
+
+#### Section title:
+
+
+Differentiation
+
+
+
+### Topics covered in this section:
+
+
+* Derivatives. Differentials
+* Mean-Value Theorems
+* l’Hopital’s rule
+* Taylor Formula with Lagrange and Peano remainders
+* Taylor formula and limits
+* Increasing / decreasing functions. Concave / convex functions
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. A plane curve is given by 
+
+
+
+x
+(
+t
+)
+=
+−
+
+
+
+
+t
+
+2
+
+
++
+4
+t
++
+8
+
+
+t
++
+2
+
+
+
+
+
+{\displaystyle x(t)=-{\frac {t^{2}+4t+8}{t+2}}}
+
+![{\displaystyle x(t)=-{\frac {t^{2}+4t+8}{t+2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d5c87d1bcdd432a16c052b35df5eeafde36d5f1c), 
+
+
+
+y
+(
+t
+)
+=
+
+
+
+
+t
+
+2
+
+
++
+9
+t
++
+22
+
+
+t
++
+6
+
+
+
+
+
+{\textstyle y(t)={\frac {t^{2}+9t+22}{t+6}}}
+
+![{\textstyle y(t)={\frac {t^{2}+9t+22}{t+6}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5053f85973bbe307983c1751cf8555915e010966). Find
+	1. the asymptotes of this curve;
+	2. the derivative 
+	
+	
+	
+	
+	y
+	
+	x
+	
+	′
+	
+	
+	
+	{\textstyle y'\_{x}}
+	
+	![{\textstyle y'_{x}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef2ed2d5f61e3172938257665534af01f608117f).
+2. Derive the Maclaurin expansion for 
+
+
+
+f
+(
+x
+)
+=
+
+
+
+1
++
+
+e
+
+−
+2
+x
+
+
+
+
+3
+
+
+
+
+
+{\textstyle f(x)={\sqrt[{3}]{1+e^{-2x}}}}
+
+![{\textstyle f(x)={\sqrt[{3}]{1+e^{-2x}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/14bfa69ed7bcfd7de396a3360c031c64292828b3) up to 
+
+
+
+o
+
+(
+
+x
+
+3
+
+
+)
+
+
+
+{\textstyle o\left(x^{3}\right)}
+
+![{\textstyle o\left(x^{3}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2e23f841ca36ac3c4d7ccc3920dbe12d69f5b304).
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Differentiation techniques: inverse, implicit, parametric etc.
+2. Find a derivative of a function
+3. Apply Leibniz formula
+4. Draw graphs of functions
+5. Find asymptotes of a parametric function
+
+
+### Test questions for final assessment in this section
+
+
+1. Find a derivative of a (implicit/inverse) function
+2. Apply Leibniz formula Find 
+
+
+
+
+y
+
+(
+n
+)
+
+
+(
+x
+)
+
+
+{\textstyle y^{(n)}(x)}
+
+![{\textstyle y^{(n)}(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f7589798b5f12dd4045984596bdeef45c97ebbb2) if 
+
+
+
+y
+(
+x
+)
+=
+
+(
+
+
+x
+
+2
+
+
+−
+2
+
+)
+
+cos
+⁡
+2
+x
+sin
+⁡
+3
+x
+
+
+{\textstyle y(x)=\left(x^{2}-2\right)\cos 2x\sin 3x}
+
+![{\textstyle y(x)=\left(x^{2}-2\right)\cos 2x\sin 3x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec58b46b813170ce96a00bff16a41f464508272a).
+3. Draw graphs of functions
+4. Find asymptotes
+5. Apply l’Hopital’s rule
+6. Find the derivatives of the following functions:
+	1. f
+	(
+	x
+	)
+	=
+	
+	log
+	
+	
+	|
+	
+	sin
+	⁡
+	x
+	
+	|
+	
+	
+	
+	⁡
+	
+	
+	
+	
+	x
+	
+	2
+	
+	
+	+
+	6
+	
+	
+	6
+	
+	
+	
+	
+	
+	{\textstyle f(x)=\log \_{|\sin x|}{\sqrt[{6}]{x^{2}+6}}}
+	
+	![{\textstyle f(x)=\log _{|\sin x|}{\sqrt[{6}]{x^{2}+6}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f4dd86bbb69d9a98691da7b8c676178d856cbd6f);
+	2. y
+	(
+	x
+	)
+	
+	
+	{\textstyle y(x)}
+	
+	![{\textstyle y(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4639e7d86a9d2274f64a48570e7fe4ef17f7efa) that is given implicitly by 
+	
+	
+	
+	
+	x
+	
+	3
+	
+	
+	+
+	5
+	x
+	y
+	+
+	
+	y
+	
+	3
+	
+	
+	=
+	0
+	
+	
+	{\textstyle x^{3}+5xy+y^{3}=0}
+	
+	![{\textstyle x^{3}+5xy+y^{3}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0ee197bafd124ae61986c15d077d9183dbcd3cc8).
+
+
+### Section 3
+
+
+#### Section title:
+
+
+Integration and Series
+
+
+
+#### Topics covered in this section:
+
+
+* Antiderivative. Indefinite integral
+* Definite integral
+* The Fundamental Theorem of Calculus
+* Improper Integrals
+* Convergence tests. Dirichlet’s test
+* Series. Convergence tests
+* Absolute / Conditional convergence
+* Power Series. Radius of convergence
+* Functional series. Uniform convergence
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 0
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. Find the indefinite integral 
+
+
+
+
+∫
+x
+ln
+⁡
+
+(
+
+x
++
+
+
+
+x
+
+2
+
+
+−
+1
+
+
+
+)
+
+
+d
+x
+
+
+
+{\textstyle \displaystyle \int x\ln \left(x+{\sqrt {x^{2}-1}}\right)\,dx}
+
+![{\textstyle \displaystyle \int x\ln \left(x+{\sqrt {x^{2}-1}}\right)\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cecb2d4bbc0d780bd1a3833c2dcb3a512f8a745d).
+2. Find the length of a curve given by 
+
+
+
+y
+=
+ln
+⁡
+sin
+⁡
+x
+
+
+{\textstyle y=\ln \sin x}
+
+![{\textstyle y=\ln \sin x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d9f39b93580dbed62ccb3b5560e4e2fa35b8900b), 
+
+
+
+
+
+π
+4
+
+
+⩽
+x
+⩽
+
+
+π
+2
+
+
+
+
+{\textstyle {\frac {\pi }{4}}\leqslant x\leqslant {\frac {\pi }{2}}}
+
+![{\textstyle {\frac {\pi }{4}}\leqslant x\leqslant {\frac {\pi }{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a70476c552255c896a29ea67b3eea049324922f0).
+3. Find all values of parameter 
+
+
+
+α
+
+
+{\textstyle \alpha }
+
+![{\textstyle \alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d86dbd6183264b2f8569da1751380b173c7b185) such that series 
+
+
+
+
+
+∑
+
+k
+=
+1
+
+
++
+∞
+
+
+
+
+(
+
+
+
+3
+k
++
+2
+
+
+2
+k
++
+1
+
+
+
+)
+
+
+k
+
+
+
+α
+
+k
+
+
+
+
+
+{\textstyle \displaystyle \sum \limits \_{k=1}^{+\infty }\left({\frac {3k+2}{2k+1}}\right)^{k}\alpha ^{k}}
+
+![{\textstyle \displaystyle \sum \limits _{k=1}^{+\infty }\left({\frac {3k+2}{2k+1}}\right)^{k}\alpha ^{k}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f6dabe061cfa1e87b7fc4629f85418142fa7b1d) converges.
+
+
+#### Typical questions for seminar classes (labs) within this section
+
+
+1. Integration techniques
+2. Integration by parts
+3. Calculation of areas, lengths, volumes
+4. Application of convergence tests
+5. Calculation of Radius of convergence
+
+
+#### Test questions for final assessment in this section
+
+
+1. Find the following integrals:
+2. ∫
+
+
+
+
+
+4
++
+
+x
+
+2
+
+
+
+
++
+2
+
+
+4
+−
+
+x
+
+2
+
+
+
+
+
+
+16
+−
+
+x
+
+4
+
+
+
+
+
+
+d
+x
+
+
+{\textstyle \int {\frac {{\sqrt {4+x^{2}}}+2{\sqrt {4-x^{2}}}}{\sqrt {16-x^{4}}}}\,dx}
+
+![{\textstyle \int {\frac {{\sqrt {4+x^{2}}}+2{\sqrt {4-x^{2}}}}{\sqrt {16-x^{4}}}}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a336f5054ecdaaf721dd26521ceea178d0538e7f);
+3. ∫
+
+2
+
+2
+x
+
+
+
+e
+
+x
+
+
+
+d
+x
+
+
+{\textstyle \int 2^{2x}e^{x}\,dx}
+
+![{\textstyle \int 2^{2x}e^{x}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e670c4f2b17ea6c370f8a531d165d79245d3dc45);
+4. ∫
+
+
+
+d
+x
+
+
+3
+
+x
+
+2
+
+
+−
+
+x
+
+4
+
+
+
+
+
+
+
+{\textstyle \int {\frac {dx}{3x^{2}-x^{4}}}}
+
+![{\textstyle \int {\frac {dx}{3x^{2}-x^{4}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dfc1a209cc0faf2f924c6f8af0e31d8024eb8769).
+5. Use comparison test to determine if the following series converge.
+
+
+
+
+
+
+
+∑
+
+k
+=
+1
+
+
+∞
+
+
+
+
+
+3
++
+(
+−
+1
+
+)
+
+k
+
+
+
+
+k
+
+2
+
+
+
+
+
+
+{\textstyle \sum \limits \_{k=1}^{\infty }{\frac {3+(-1)^{k}}{k^{2}}}}
+
+![{\textstyle \sum \limits _{k=1}^{\infty }{\frac {3+(-1)^{k}}{k^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3e87788ec917e8c1f759186838a02cfc24cdd912);
+6. Use Cauchy criterion to prove that the series 
+
+
+
+
+∑
+
+k
+=
+1
+
+
+∞
+
+
+
+
+
+k
++
+1
+
+
+
+k
+
+2
+
+
++
+3
+
+
+
+
+
+{\textstyle \sum \limits \_{k=1}^{\infty }{\frac {k+1}{k^{2}+3}}}
+
+![{\textstyle \sum \limits _{k=1}^{\infty }{\frac {k+1}{k^{2}+3}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1db1b7d2a764a327ba2530374b1f9452eabe866c) is divergent.
+7. Find the sums of the following series:
+8. ∑
+
+k
+=
+1
+
+
+∞
+
+
+
+
+1
+
+16
+
+k
+
+2
+
+
+−
+8
+k
+−
+3
+
+
+
+
+
+{\textstyle \sum \limits \_{k=1}^{\infty }{\frac {1}{16k^{2}-8k-3}}}
+
+![{\textstyle \sum \limits _{k=1}^{\infty }{\frac {1}{16k^{2}-8k-3}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/912efbbc162ea622ba6e3d18f8e519149ef054b7);
+9. ∑
+
+k
+=
+1
+
+
+∞
+
+
+
+
+
+k
+−
+
+
+
+k
+
+2
+
+
+−
+1
+
+
+
+
+
+k
+
+2
+
+
++
+k
+
+
+
+
+
+{\textstyle \sum \limits \_{k=1}^{\infty }{\frac {k-{\sqrt {k^{2}-1}}}{\sqrt {k^{2}+k}}}}
+
+![{\textstyle \sum \limits _{k=1}^{\infty }{\frac {k-{\sqrt {k^{2}-1}}}{\sqrt {k^{2}+k}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4ce35076e06e2b6f92f5e7adf17507591f658f0d).
+
+
+
+
+
+
+
+[Category](/index.php/Special:Categories "Special:Categories"): * [TRD](/index.php?title=Category:TRD&action=edit&redlink=1 "Category:TRD (page does not exist)")
+
+
+

raw/raw_bsc__mathematical_analysis_i.f21.test.md

@@ -0,0 +1,1282 @@
+
+
+
+
+
+
+
+BSc: Mathematical Analysis I.F21.test
+=====================================
+
+
+
+
+
+
+  
+
+
+
+
+Contents
+--------
+
+
+* [1 Mathematical Analysis I](#Mathematical_Analysis_I)
+	+ [1.1 Course Characteristics](#Course_Characteristics)
+		- [1.1.1 Key concepts of the class](#Key_concepts_of_the_class)
+		- [1.1.2 What is the purpose of this course?](#What_is_the_purpose_of_this_course.3F)
+	+ [1.2 Course Objectives Based on Bloom’s Taxonomy](#Course_Objectives_Based_on_Bloom.E2.80.99s_Taxonomy)
+		- [1.2.1 What should a student remember at the end of the course?](#What_should_a_student_remember_at_the_end_of_the_course.3F)
+		- [1.2.2 What should a student be able to understand at the end of the course?](#What_should_a_student_be_able_to_understand_at_the_end_of_the_course.3F)
+		- [1.2.3 What should a student be able to apply at the end of the course?](#What_should_a_student_be_able_to_apply_at_the_end_of_the_course.3F)
+		- [1.2.4 Course evaluation](#Course_evaluation)
+		- [1.2.5 Grades range](#Grades_range)
+		- [1.2.6 Resources and reference material](#Resources_and_reference_material)
+	+ [1.3 Course Sections](#Course_Sections)
+		- [1.3.1 Section 1](#Section_1)
+			* [1.3.1.1 Section title:](#Section_title:)
+		- [1.3.2 Topics covered in this section:](#Topics_covered_in_this_section:)
+		- [1.3.3 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F)
+		- [1.3.4 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section)
+		- [1.3.5 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section)
+		- [1.3.6 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section)
+		- [1.3.7 Section 2](#Section_2)
+			* [1.3.7.1 Section title:](#Section_title:_2)
+		- [1.3.8 Topics covered in this section:](#Topics_covered_in_this_section:_2)
+		- [1.3.9 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_2)
+		- [1.3.10 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_2)
+		- [1.3.11 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_2)
+		- [1.3.12 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_2)
+		- [1.3.13 Section 3](#Section_3)
+			* [1.3.13.1 Section title:](#Section_title:_3)
+			* [1.3.13.2 Topics covered in this section:](#Topics_covered_in_this_section:_3)
+		- [1.3.14 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_3)
+		- [1.3.15 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_3)
+			* [1.3.15.1 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_3)
+			* [1.3.15.2 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_3)
+
+
+
+Mathematical Analysis I
+=======================
+
+
+Course Characteristics
+----------------------
+
+
+### Key concepts of the class
+
+
+* Differentiation
+* Integration
+* Series
+
+
+### What is the purpose of this course?
+
+
+This calculus course covers differentiation and integration of functions of one variable, with applications. The basic objective of Calculus is to relate small-scale (differential) quantities to large-scale (integrated) quantities. This is accomplished by means of the Fundamental Theorem of Calculus. Should be understanding of the integral as a cumulative sum, of the derivative as a rate of change, and of the inverse relationship between integration and differentiation.
+
+
+This calculus course will provide an opportunity for participants to:
+
+
+
+* understand key principles involved in differentiation and integration of functions
+* solve problems that connect small-scale (differential) quantities to large-scale (integrated) quantities
+* become familiar with the fundamental theorems of Calculus
+* get hands-on experience with the integral and derivative applications and of the inverse relationship between integration and differentiation.
+
+
+Course Objectives Based on Bloom’s Taxonomy
+-------------------------------------------
+
+
+### What should a student remember at the end of the course?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Derivative. Differential. Applications
+* Indefinite integral. Definite integral. Applications
+* Sequences. Series. Convergence. Power Series
+
+
+### What should a student be able to understand at the end of the course?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Derivative. Differential. Applications
+* Indefinite integral. Definite integral. Applications
+* Sequences. Series. Convergence. Power Series
+* Taylor Series
+
+
+### What should a student be able to apply at the end of the course?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* find multiple, path, surface integrals
+* find the range of a function in a given domain
+* decompose a function into infinite series
+
+
+### Course evaluation
+
+
+
+
+Course grade breakdown
+|  |  | **Proposed points** |
+| --- | --- | --- |
+| Labs/seminar classes
+ | 20
+ |  |
+| Interim performance assessment
+ | 30
+ |  |
+| Exams
+ | 50
+ |  |
+
+
+If necessary, please indicate freely your course’s features in terms of students’ performance assessment.
+
+
+
+### Grades range
+
+
+
+
+Course grading range
+|  |  | **Proposed range** |
+| --- | --- | --- |
+| A. Excellent
+ | 90-100
+ |  |
+| B. Good
+ | 75-89
+ |  |
+| C. Satisfactory
+ | 60-74
+ |  |
+| D. Poor
+ | 0-59
+ |  |
+
+
+If necessary, please indicate freely your course’s grading features.
+
+
+
+### Resources and reference material
+
+
+* Zorich, V. A. “Mathematical Analysis I, Translator: Cooke R.” (2004)
+* 
+* 
+
+
+Course Sections
+---------------
+
+
+The main sections of the course and approximate hour distribution between them is as follows:
+
+
+
+
+
+Course Sections
+| **Section** | **Section Title** | **Teaching Hours** |
+| --- | --- | --- |
+| 1
+ | Sequences and Limits
+ | 28
+ |
+| 2
+ | Differentiation
+ | 24
+ |
+| 3
+ | Integration and Series
+ | 28
+ |
+
+
+### Section 1
+
+
+#### Section title:
+
+
+Sequences and Limits
+
+
+
+### Topics covered in this section:
+
+
+* Sequences. Limits of sequences
+* Limits of sequences. Limits of functions
+* Limits of functions. Continuity. Hyperbolic functions
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. A sequence, limiting value
+2. Limit of a sequence, convergent and divergent sequences
+3. Increasing and decreasing sequences, monotonic sequences
+4. Bounded sequences. Properties of limits
+5. Theorem about bounded and monotonic sequences.
+6. Cauchy sequence. The Cauchy Theorem (criterion).
+7. Limit of a function. Properties of limits.
+8. The first remarkable limit.
+9. The Cauchy criterion for the existence of a limit of a function.
+10. Second remarkable limit.
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Find a limit of a sequence
+2. Find a limit of a function
+
+
+### Test questions for final assessment in this section
+
+
+1. Find limits of the following sequences or prove that they do not exist:
+2. a
+
+n
+
+
+=
+n
+−
+
+
+
+n
+
+2
+
+
+−
+70
+n
++
+1400
+
+
+
+
+{\displaystyle a\_{n}=n-{\sqrt {n^{2}-70n+1400}}}
+
+![{\displaystyle a_{n}=n-{\sqrt {n^{2}-70n+1400}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aeca3ea0fc01bed1f98eb199a9819614e88e793f);
+3. d
+
+n
+
+
+=
+
+
+(
+
+
+
+2
+n
+−
+4
+
+
+2
+n
++
+1
+
+
+
+)
+
+
+n
+
+
+
+
+{\textstyle d\_{n}=\left({\frac {2n-4}{2n+1}}\right)^{n}}
+
+![{\textstyle d_{n}=\left({\frac {2n-4}{2n+1}}\right)^{n}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/389a3735f2899205a00b490e482acbcfa39b3edb);
+4. x
+
+n
+
+
+=
+
+
+
+
+
+(
+
+2
+
+n
+
+2
+
+
++
+1
+
+)
+
+
+6
+
+
+(
+n
+−
+1
+
+)
+
+2
+
+
+
+
+
+(
+
+
+n
+
+7
+
+
++
+1000
+
+n
+
+6
+
+
+−
+3
+
+)
+
+
+2
+
+
+
+
+
+
+{\textstyle x\_{n}={\frac {\left(2n^{2}+1\right)^{6}(n-1)^{2}}{\left(n^{7}+1000n^{6}-3\right)^{2}}}}
+
+![{\textstyle x_{n}={\frac {\left(2n^{2}+1\right)^{6}(n-1)^{2}}{\left(n^{7}+1000n^{6}-3\right)^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5f2e2a41471540c1cb5f3f8b2ad3d96ef91cf7e9).
+
+
+### Section 2
+
+
+#### Section title:
+
+
+Differentiation
+
+
+
+### Topics covered in this section:
+
+
+* Derivatives. Differentials
+* Mean-Value Theorems
+* l’Hopital’s rule
+* Taylor Formula with Lagrange and Peano remainders
+* Taylor formula and limits
+* Increasing / decreasing functions. Concave / convex functions
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. A plane curve is given by 
+
+
+
+x
+(
+t
+)
+=
+−
+
+
+
+
+t
+
+2
+
+
++
+4
+t
++
+8
+
+
+t
++
+2
+
+
+
+
+
+{\displaystyle x(t)=-{\frac {t^{2}+4t+8}{t+2}}}
+
+![{\displaystyle x(t)=-{\frac {t^{2}+4t+8}{t+2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d5c87d1bcdd432a16c052b35df5eeafde36d5f1c), 
+
+
+
+y
+(
+t
+)
+=
+
+
+
+
+t
+
+2
+
+
++
+9
+t
++
+22
+
+
+t
++
+6
+
+
+
+
+
+{\textstyle y(t)={\frac {t^{2}+9t+22}{t+6}}}
+
+![{\textstyle y(t)={\frac {t^{2}+9t+22}{t+6}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5053f85973bbe307983c1751cf8555915e010966). Find
+	1. the asymptotes of this curve;
+	2. the derivative 
+	
+	
+	
+	
+	y
+	
+	x
+	
+	′
+	
+	
+	
+	{\textstyle y'\_{x}}
+	
+	![{\textstyle y'_{x}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef2ed2d5f61e3172938257665534af01f608117f).
+2. Derive the Maclaurin expansion for 
+
+
+
+f
+(
+x
+)
+=
+
+
+
+1
++
+
+e
+
+−
+2
+x
+
+
+
+
+3
+
+
+
+
+
+{\textstyle f(x)={\sqrt[{3}]{1+e^{-2x}}}}
+
+![{\textstyle f(x)={\sqrt[{3}]{1+e^{-2x}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/14bfa69ed7bcfd7de396a3360c031c64292828b3) up to 
+
+
+
+o
+
+(
+
+x
+
+3
+
+
+)
+
+
+
+{\textstyle o\left(x^{3}\right)}
+
+![{\textstyle o\left(x^{3}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2e23f841ca36ac3c4d7ccc3920dbe12d69f5b304).
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Differentiation techniques: inverse, implicit, parametric etc.
+2. Find a derivative of a function
+3. Apply Leibniz formula
+4. Draw graphs of functions
+5. Find asymptotes of a parametric function
+
+
+### Test questions for final assessment in this section
+
+
+1. Find a derivative of a (implicit/inverse) function
+2. Apply Leibniz formula Find 
+
+
+
+
+y
+
+(
+n
+)
+
+
+(
+x
+)
+
+
+{\textstyle y^{(n)}(x)}
+
+![{\textstyle y^{(n)}(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f7589798b5f12dd4045984596bdeef45c97ebbb2) if 
+
+
+
+y
+(
+x
+)
+=
+
+(
+
+
+x
+
+2
+
+
+−
+2
+
+)
+
+cos
+⁡
+2
+x
+sin
+⁡
+3
+x
+
+
+{\textstyle y(x)=\left(x^{2}-2\right)\cos 2x\sin 3x}
+
+![{\textstyle y(x)=\left(x^{2}-2\right)\cos 2x\sin 3x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec58b46b813170ce96a00bff16a41f464508272a).
+3. Draw graphs of functions
+4. Find asymptotes
+5. Apply l’Hopital’s rule
+6. Find the derivatives of the following functions:
+	1. f
+	(
+	x
+	)
+	=
+	
+	log
+	
+	
+	|
+	
+	sin
+	⁡
+	x
+	
+	|
+	
+	
+	
+	⁡
+	
+	
+	
+	
+	x
+	
+	2
+	
+	
+	+
+	6
+	
+	
+	6
+	
+	
+	
+	
+	
+	{\textstyle f(x)=\log \_{|\sin x|}{\sqrt[{6}]{x^{2}+6}}}
+	
+	![{\textstyle f(x)=\log _{|\sin x|}{\sqrt[{6}]{x^{2}+6}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f4dd86bbb69d9a98691da7b8c676178d856cbd6f);
+	2. y
+	(
+	x
+	)
+	
+	
+	{\textstyle y(x)}
+	
+	![{\textstyle y(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4639e7d86a9d2274f64a48570e7fe4ef17f7efa) that is given implicitly by 
+	
+	
+	
+	
+	x
+	
+	3
+	
+	
+	+
+	5
+	x
+	y
+	+
+	
+	y
+	
+	3
+	
+	
+	=
+	0
+	
+	
+	{\textstyle x^{3}+5xy+y^{3}=0}
+	
+	![{\textstyle x^{3}+5xy+y^{3}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0ee197bafd124ae61986c15d077d9183dbcd3cc8).
+
+
+### Section 3
+
+
+#### Section title:
+
+
+Integration and Series
+
+
+
+#### Topics covered in this section:
+
+
+* Antiderivative. Indefinite integral
+* Definite integral
+* The Fundamental Theorem of Calculus
+* Improper Integrals
+* Convergence tests. Dirichlet’s test
+* Series. Convergence tests
+* Absolute / Conditional convergence
+* Power Series. Radius of convergence
+* Functional series. Uniform convergence
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 0
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. Find the indefinite integral 
+
+
+
+
+∫
+x
+ln
+⁡
+
+(
+
+x
++
+
+
+
+x
+
+2
+
+
+−
+1
+
+
+
+)
+
+
+d
+x
+
+
+
+{\textstyle \displaystyle \int x\ln \left(x+{\sqrt {x^{2}-1}}\right)\,dx}
+
+![{\textstyle \displaystyle \int x\ln \left(x+{\sqrt {x^{2}-1}}\right)\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cecb2d4bbc0d780bd1a3833c2dcb3a512f8a745d).
+2. Find the length of a curve given by 
+
+
+
+y
+=
+ln
+⁡
+sin
+⁡
+x
+
+
+{\textstyle y=\ln \sin x}
+
+![{\textstyle y=\ln \sin x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d9f39b93580dbed62ccb3b5560e4e2fa35b8900b), 
+
+
+
+
+
+π
+4
+
+
+⩽
+x
+⩽
+
+
+π
+2
+
+
+
+
+{\textstyle {\frac {\pi }{4}}\leqslant x\leqslant {\frac {\pi }{2}}}
+
+![{\textstyle {\frac {\pi }{4}}\leqslant x\leqslant {\frac {\pi }{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a70476c552255c896a29ea67b3eea049324922f0).
+3. Find all values of parameter 
+
+
+
+α
+
+
+{\textstyle \alpha }
+
+![{\textstyle \alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d86dbd6183264b2f8569da1751380b173c7b185) such that series 
+
+
+
+
+
+∑
+
+k
+=
+1
+
+
++
+∞
+
+
+
+
+(
+
+
+
+3
+k
++
+2
+
+
+2
+k
++
+1
+
+
+
+)
+
+
+k
+
+
+
+α
+
+k
+
+
+
+
+
+{\textstyle \displaystyle \sum \limits \_{k=1}^{+\infty }\left({\frac {3k+2}{2k+1}}\right)^{k}\alpha ^{k}}
+
+![{\textstyle \displaystyle \sum \limits _{k=1}^{+\infty }\left({\frac {3k+2}{2k+1}}\right)^{k}\alpha ^{k}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f6dabe061cfa1e87b7fc4629f85418142fa7b1d) converges.
+
+
+#### Typical questions for seminar classes (labs) within this section
+
+
+1. Integration techniques
+2. Integration by parts
+3. Calculation of areas, lengths, volumes
+4. Application of convergence tests
+5. Calculation of Radius of convergence
+
+
+#### Test questions for final assessment in this section
+
+
+1. Find the following integrals:
+2. ∫
+
+
+
+
+
+4
++
+
+x
+
+2
+
+
+
+
++
+2
+
+
+4
+−
+
+x
+
+2
+
+
+
+
+
+
+16
+−
+
+x
+
+4
+
+
+
+
+
+
+d
+x
+
+
+{\textstyle \int {\frac {{\sqrt {4+x^{2}}}+2{\sqrt {4-x^{2}}}}{\sqrt {16-x^{4}}}}\,dx}
+
+![{\textstyle \int {\frac {{\sqrt {4+x^{2}}}+2{\sqrt {4-x^{2}}}}{\sqrt {16-x^{4}}}}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a336f5054ecdaaf721dd26521ceea178d0538e7f);
+3. ∫
+
+2
+
+2
+x
+
+
+
+e
+
+x
+
+
+
+d
+x
+
+
+{\textstyle \int 2^{2x}e^{x}\,dx}
+
+![{\textstyle \int 2^{2x}e^{x}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e670c4f2b17ea6c370f8a531d165d79245d3dc45);
+4. ∫
+
+
+
+d
+x
+
+
+3
+
+x
+
+2
+
+
+−
+
+x
+
+4
+
+
+
+
+
+
+
+{\textstyle \int {\frac {dx}{3x^{2}-x^{4}}}}
+
+![{\textstyle \int {\frac {dx}{3x^{2}-x^{4}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dfc1a209cc0faf2f924c6f8af0e31d8024eb8769).
+5. Use comparison test to determine if the following series converge.
+
+
+
+
+
+
+
+∑
+
+k
+=
+1
+
+
+∞
+
+
+
+
+
+3
++
+(
+−
+1
+
+)
+
+k
+
+
+
+
+k
+
+2
+
+
+
+
+
+
+{\textstyle \sum \limits \_{k=1}^{\infty }{\frac {3+(-1)^{k}}{k^{2}}}}
+
+![{\textstyle \sum \limits _{k=1}^{\infty }{\frac {3+(-1)^{k}}{k^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3e87788ec917e8c1f759186838a02cfc24cdd912);
+6. Use Cauchy criterion to prove that the series 
+
+
+
+
+∑
+
+k
+=
+1
+
+
+∞
+
+
+
+
+
+k
++
+1
+
+
+
+k
+
+2
+
+
++
+3
+
+
+
+
+
+{\textstyle \sum \limits \_{k=1}^{\infty }{\frac {k+1}{k^{2}+3}}}
+
+![{\textstyle \sum \limits _{k=1}^{\infty }{\frac {k+1}{k^{2}+3}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1db1b7d2a764a327ba2530374b1f9452eabe866c) is divergent.
+7. Find the sums of the following series:
+8. ∑
+
+k
+=
+1
+
+
+∞
+
+
+
+
+1
+
+16
+
+k
+
+2
+
+
+−
+8
+k
+−
+3
+
+
+
+
+
+{\textstyle \sum \limits \_{k=1}^{\infty }{\frac {1}{16k^{2}-8k-3}}}
+
+![{\textstyle \sum \limits _{k=1}^{\infty }{\frac {1}{16k^{2}-8k-3}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/912efbbc162ea622ba6e3d18f8e519149ef054b7);
+9. ∑
+
+k
+=
+1
+
+
+∞
+
+
+
+
+
+k
+−
+
+
+
+k
+
+2
+
+
+−
+1
+
+
+
+
+
+k
+
+2
+
+
++
+k
+
+
+
+
+
+{\textstyle \sum \limits \_{k=1}^{\infty }{\frac {k-{\sqrt {k^{2}-1}}}{\sqrt {k^{2}+k}}}}
+
+![{\textstyle \sum \limits _{k=1}^{\infty }{\frac {k-{\sqrt {k^{2}-1}}}{\sqrt {k^{2}+k}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4ce35076e06e2b6f92f5e7adf17507591f658f0d).
+
+
+
+
+
+
+
+[Category](/index.php/Special:Categories "Special:Categories"): * [TRD](/index.php?title=Category:TRD&action=edit&redlink=1 "Category:TRD (page does not exist)")
+
+
+

raw/raw_bsc__mathematical_analysis_i.f22.md

@@ -0,0 +1,925 @@
+
+
+
+
+
+
+
+BSc: Mathematical Analysis I.f22
+================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Mathematical Analysis I](#Mathematical_Analysis_I)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Course Topics](#Course_Topics)
+	+ [1.3 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.3.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.3.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.3.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.3.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.3.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.4 Grading](#Grading)
+		- [1.4.1 Course grading range](#Course_grading_range)
+		- [1.4.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.4.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.5 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.5.1 Open access resources](#Open_access_resources)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+		- [2.2.2 Final assessment](#Final_assessment)
+			* [2.2.2.1 Section 1](#Section_1_2)
+			* [2.2.2.2 Section 2](#Section_2_2)
+			* [2.2.2.3 Section 3](#Section_3_2)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Mathematical Analysis I
+=======================
+
+
+* **Course name**: Mathematical Analysis I
+* **Code discipline**: CSE201
+* **Subject area**: Math
+
+
+Short Description
+-----------------
+
+
+This calculus course covers differentiation and integration of functions of one variable, with applications. The basic objective of Calculus is to relate small-scale (differential) quantities to large-scale (integrated) quantities. This is accomplished by means of the Fundamental Theorem of Calculus. Should be understanding of the integral as a cumulative sum, of the derivative as a rate of change, and of the inverse relationship between integration and differentiation.
+
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Limits | 1. Limits of Sequences
+2. Newton's Method
+3. Limits of Functions
+ |
+| Derivatives | 1. Derivative as a Limit
+2. Leibniz Notation
+3. Rates of Change
+4. The Chain Rule
+5. Fractional Powers and Implicit Differentiation
+6. Related Rates and Parametric Curves
+7. Inverse Functions and Differentiation
+8. Differentiation of the Trigonometric, Exponential and Logarithmic Functions
+9. L'Hopital's Rule
+10. Increasing and Decreasing Functions
+11. The Second Derivative and Concavity
+12. Maximum-Minimum Problems
+13. Graphing
+ |
+| Integrals | 1. Sums and Areas
+2. The Fundamental Theorem of Calculus
+3. Definite and Indefinite Integrals
+4. Integration by Substitution
+5. Changing Variables in the Definite Integral
+6. Integration by Parts
+7. Trigonometric Integrals
+8. Partial Fractions
+9. Parametric Curves
+10. Applications of the integrals
+11. Improper integrals
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+This calculus course will provide an opportunity for participants to:
+
+
+
+* understand key principles involved in differentiation and integration of functions
+* solve problems that connect small-scale (differential) quantities to large-scale (integrated) quantities
+* become familiar with the fundamental theorems of Calculus
+* get hands-on experience with the integral and derivative applications and of the inverse relationship between integration and differentiation.
+
+
+### ILOs defined at three levels
+
+
+We specify the intended learning outcomes at three levels: conceptual knowledge, practical skills, and comprehensive skills.
+
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* remember the differentiation techniques
+* remember the integration techniques
+* remember how to work with sequences and series
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* apply the derivatives to analyse the functions
+* integrate
+* understand the basics of approximation
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Take derivatives of various type functions and of various orders
+* Integrate
+* Apply definite integral
+* Expand functions into Taylor series
+* Apply convergence tests
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 85-100 | -
+ |
+| B. Good | 70-84 | -
+ |
+| C. Satisfactory | 50-69 | -
+ |
+| D. Fail | 0-49 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Midterm | 20
+ |
+| Tests | 28 (14 for each)
+ |
+| Final exam | 50
+ |
+| In-class participation | 7 (including 5 extras)
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+* Participation is important. Attending lectures is the key to success in this course.
+* Review lecture materials before classes to do well.
+* Reading the recommended literature is obligatory, and will give you a deeper understanding of the material.
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Jerrold E. Marsden and Alan Weinstein, Calculus I, II, and II. Springer-Verlag, Second Edition 1985 [link](https://www.cds.caltech.edu/~marsden/volume/Calculus/)
+* Zorich, V. A. Mathematical Analysis I, Translator: Cooke R. (2004)
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Teaching and Learning Methods within each section
+| Teaching Techniques | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Problem-based learning (students learn by solving open-ended problems without a strictly-defined solution) | 1 | 1 | 1
+ |
+| Project-based learning (students work on a project) | 0 | 0 | 0
+ |
+| Modular learning (facilitated self-study) | 0 | 0 | 0
+ |
+| Differentiated learning (provide tasks and activities at several levels of difficulty to fit students needs and level) | 1 | 1 | 1
+ |
+| Contextual learning (activities and tasks are connected to the real world to make it easier for students to relate to them) | 0 | 0 | 0
+ |
+| Business game (learn by playing a game that incorporates the principles of the material covered within the course) | 0 | 0 | 0
+ |
+| Inquiry-based learning | 0 | 0 | 0
+ |
+| Just-in-time teaching | 0 | 0 | 0
+ |
+| Process oriented guided inquiry learning (POGIL) | 0 | 0 | 0
+ |
+| Studio-based learning | 0 | 0 | 0
+ |
+| Universal design for learning | 0 | 0 | 0
+ |
+| Task-based learning | 0 | 0 | 0
+ |
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Lectures | 1 | 1 | 1
+ |
+| Interactive Lectures | 1 | 1 | 1
+ |
+| Lab exercises | 1 | 1 | 1
+ |
+| Experiments | 0 | 0 | 0
+ |
+| Modeling | 0 | 0 | 0
+ |
+| Cases studies | 0 | 0 | 0
+ |
+| Development of individual parts of software product code | 0 | 0 | 0
+ |
+| Individual Projects | 0 | 0 | 0
+ |
+| Group projects | 0 | 0 | 0
+ |
+| Flipped classroom | 0 | 0 | 0
+ |
+| Quizzes (written or computer based) | 1 | 1 | 1
+ |
+| Peer Review | 0 | 0 | 0
+ |
+| Discussions | 1 | 1 | 1
+ |
+| Presentations by students | 0 | 0 | 0
+ |
+| Written reports | 0 | 0 | 0
+ |
+| Simulations and role-plays | 0 | 0 | 0
+ |
+| Essays | 0 | 0 | 0
+ |
+| Oral Reports | 0 | 0 | 0
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+1. Find limits of the following sequences or prove that they do not exist:
+	* a
+	
+	n
+	
+	
+	=
+	n
+	−
+	
+	
+	
+	n
+	
+	2
+	
+	
+	−
+	70
+	n
+	+
+	1400
+	
+	
+	
+	
+	{\displaystyle a\_{n}=n-{\sqrt {n^{2}-70n+1400}}}
+	
+	![{\displaystyle a_{n}=n-{\sqrt {n^{2}-70n+1400}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aeca3ea0fc01bed1f98eb199a9819614e88e793f);
+	* d
+	
+	n
+	
+	
+	=
+	
+	
+	(
+	
+	
+	
+	2
+	n
+	−
+	4
+	
+	
+	2
+	n
+	+
+	1
+	
+	
+	
+	)
+	
+	
+	n
+	
+	
+	
+	
+	{\textstyle d\_{n}=\left({\frac {2n-4}{2n+1}}\right)^{n}}
+	
+	![{\textstyle d_{n}=\left({\frac {2n-4}{2n+1}}\right)^{n}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/389a3735f2899205a00b490e482acbcfa39b3edb);
+	* x
+	
+	n
+	
+	
+	=
+	
+	
+	
+	
+	
+	(
+	
+	2
+	
+	n
+	
+	2
+	
+	
+	+
+	1
+	
+	)
+	
+	
+	6
+	
+	
+	(
+	n
+	−
+	1
+	
+	)
+	
+	2
+	
+	
+	
+	
+	
+	(
+	
+	
+	n
+	
+	7
+	
+	
+	+
+	1000
+	
+	n
+	
+	6
+	
+	
+	−
+	3
+	
+	)
+	
+	
+	2
+	
+	
+	
+	
+	
+	
+	{\textstyle x\_{n}={\frac {\left(2n^{2}+1\right)^{6}(n-1)^{2}}{\left(n^{7}+1000n^{6}-3\right)^{2}}}}
+	
+	![{\textstyle x_{n}={\frac {\left(2n^{2}+1\right)^{6}(n-1)^{2}}{\left(n^{7}+1000n^{6}-3\right)^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5f2e2a41471540c1cb5f3f8b2ad3d96ef91cf7e9).
+
+
+#### Section 2
+
+
+1. A plane curve is given by 
+
+
+
+x
+(
+t
+)
+=
+−
+
+
+
+
+t
+
+2
+
+
++
+4
+t
++
+8
+
+
+t
++
+2
+
+
+
+
+
+{\displaystyle x(t)=-{\frac {t^{2}+4t+8}{t+2}}}
+
+![{\displaystyle x(t)=-{\frac {t^{2}+4t+8}{t+2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d5c87d1bcdd432a16c052b35df5eeafde36d5f1c), 
+
+
+
+y
+(
+t
+)
+=
+
+
+
+
+t
+
+2
+
+
++
+9
+t
++
+22
+
+
+t
++
+6
+
+
+
+
+
+{\textstyle y(t)={\frac {t^{2}+9t+22}{t+6}}}
+
+![{\textstyle y(t)={\frac {t^{2}+9t+22}{t+6}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5053f85973bbe307983c1751cf8555915e010966). Find
+the asymptotes of this curve;
+the derivative 
+
+
+
+
+y
+
+x
+
+′
+
+
+
+{\textstyle y'\_{x}}
+
+![{\textstyle y'_{x}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef2ed2d5f61e3172938257665534af01f608117f).
+2. Apply Leibniz formula Find 
+
+
+
+
+y
+
+(
+n
+)
+
+
+(
+x
+)
+
+
+{\textstyle y^{(n)}(x)}
+
+![{\textstyle y^{(n)}(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f7589798b5f12dd4045984596bdeef45c97ebbb2) if 
+
+
+
+y
+(
+x
+)
+=
+
+(
+
+
+x
+
+2
+
+
+−
+2
+
+)
+
+cos
+⁡
+2
+x
+sin
+⁡
+3
+x
+
+
+{\textstyle y(x)=\left(x^{2}-2\right)\cos 2x\sin 3x}
+
+![{\textstyle y(x)=\left(x^{2}-2\right)\cos 2x\sin 3x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec58b46b813170ce96a00bff16a41f464508272a).
+Draw graphs of functions
+Find asymptotes
+3. Find the derivatives of the following functions:
+	* f
+	(
+	x
+	)
+	=
+	
+	log
+	
+	
+	|
+	
+	sin
+	⁡
+	x
+	
+	|
+	
+	
+	
+	⁡
+	
+	
+	
+	
+	x
+	
+	2
+	
+	
+	+
+	6
+	
+	
+	6
+	
+	
+	
+	
+	
+	{\textstyle f(x)=\log \_{|\sin x|}{\sqrt[{6}]{x^{2}+6}}}
+	
+	![{\textstyle f(x)=\log _{|\sin x|}{\sqrt[{6}]{x^{2}+6}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f4dd86bbb69d9a98691da7b8c676178d856cbd6f);
+	* y
+	(
+	x
+	)
+	
+	
+	{\textstyle y(x)}
+	
+	![{\textstyle y(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4639e7d86a9d2274f64a48570e7fe4ef17f7efa) that is given implicitly by 
+	
+	
+	
+	
+	x
+	
+	3
+	
+	
+	+
+	5
+	x
+	y
+	+
+	
+	y
+	
+	3
+	
+	
+	=
+	0
+	
+	
+	{\textstyle x^{3}+5xy+y^{3}=0}
+	
+	![{\textstyle x^{3}+5xy+y^{3}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0ee197bafd124ae61986c15d077d9183dbcd3cc8).
+
+
+#### Section 3
+
+
+1. Find the following integrals:
+	* ∫
+	
+	
+	
+	
+	
+	4
+	+
+	
+	x
+	
+	2
+	
+	
+	
+	
+	+
+	2
+	
+	
+	4
+	−
+	
+	x
+	
+	2
+	
+	
+	
+	
+	
+	
+	16
+	−
+	
+	x
+	
+	4
+	
+	
+	
+	
+	
+	
+	d
+	x
+	
+	
+	{\textstyle \int {\frac {{\sqrt {4+x^{2}}}+2{\sqrt {4-x^{2}}}}{\sqrt {16-x^{4}}}}\,dx}
+	
+	![{\textstyle \int {\frac {{\sqrt {4+x^{2}}}+2{\sqrt {4-x^{2}}}}{\sqrt {16-x^{4}}}}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a336f5054ecdaaf721dd26521ceea178d0538e7f);
+	* ∫
+	
+	2
+	
+	2
+	x
+	
+	
+	
+	e
+	
+	x
+	
+	
+	
+	d
+	x
+	
+	
+	{\textstyle \int 2^{2x}e^{x}\,dx}
+	
+	![{\textstyle \int 2^{2x}e^{x}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e670c4f2b17ea6c370f8a531d165d79245d3dc45);
+	* ∫
+	
+	
+	
+	d
+	x
+	
+	
+	3
+	
+	x
+	
+	2
+	
+	
+	−
+	
+	x
+	
+	4
+	
+	
+	
+	
+	
+	
+	
+	{\textstyle \int {\frac {dx}{3x^{2}-x^{4}}}}
+	
+	![{\textstyle \int {\frac {dx}{3x^{2}-x^{4}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dfc1a209cc0faf2f924c6f8af0e31d8024eb8769).
+2. Find the indefinite integral 
+
+
+
+
+∫
+x
+ln
+⁡
+
+(
+
+x
++
+
+
+
+x
+
+2
+
+
+−
+1
+
+
+
+)
+
+
+d
+x
+
+
+
+{\textstyle \displaystyle \int x\ln \left(x+{\sqrt {x^{2}-1}}\right)\,dx}
+
+![{\textstyle \displaystyle \int x\ln \left(x+{\sqrt {x^{2}-1}}\right)\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cecb2d4bbc0d780bd1a3833c2dcb3a512f8a745d).
+3. Find the length of a curve given by 
+
+
+
+y
+=
+ln
+⁡
+sin
+⁡
+x
+
+
+{\textstyle y=\ln \sin x}
+
+![{\textstyle y=\ln \sin x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d9f39b93580dbed62ccb3b5560e4e2fa35b8900b), 
+
+
+
+
+
+π
+4
+
+
+⩽
+x
+⩽
+
+
+π
+2
+
+
+
+
+{\textstyle {\frac {\pi }{4}}\leqslant x\leqslant {\frac {\pi }{2}}}
+
+![{\textstyle {\frac {\pi }{4}}\leqslant x\leqslant {\frac {\pi }{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a70476c552255c896a29ea67b3eea049324922f0).
+
+
+### Final assessment
+
+
+#### Section 1
+
+
+1. Find a limit of a sequence
+2. Find a limit of a function
+
+
+#### Section 2
+
+
+1. Apply the appropriate differentiation technique to a given problem.
+2. Find a derivative of a function
+3. Apply Leibniz formula
+4. Draw graphs of functions
+5. Find asymptotes of a parametric function
+
+
+#### Section 3
+
+
+1. Apply the appropriate integration technique to the given problem
+2. Find the value of the devinite integral
+3. Calculate the area of the domain or the length of the curve
+
+
+### The retake exam
+
+
+Retakes will be run as a comprehensive exam, where the student will be assessed the acquired knowledge coming from the textbooks, the lectures, the labs, and the additional required reading material, as supplied by the instructor. During such comprehensive oral/written the student could be asked to solve exercises and to explain theoretical and practical aspects of the course.
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__mathematical_analysis_i.md

@@ -0,0 +1,1284 @@
+
+
+
+
+
+
+
+BSc: Mathematical Analysis I
+============================
+
+
+
+
+
+
+  
+
+
+
+
+Contents
+--------
+
+
+* [1 Mathematical Analysis I](#Mathematical_Analysis_I)
+	+ [1.1 Course Characteristics](#Course_Characteristics)
+		- [1.1.1 Key concepts of the class](#Key_concepts_of_the_class)
+		- [1.1.2 What is the purpose of this course?](#What_is_the_purpose_of_this_course.3F)
+	+ [1.2 Course Objectives Based on Bloom’s Taxonomy](#Course_Objectives_Based_on_Bloom.E2.80.99s_Taxonomy)
+		- [1.2.1 What should a student remember at the end of the course?](#What_should_a_student_remember_at_the_end_of_the_course.3F)
+		- [1.2.2 What should a student be able to understand at the end of the course?](#What_should_a_student_be_able_to_understand_at_the_end_of_the_course.3F)
+		- [1.2.3 What should a student be able to apply at the end of the course?](#What_should_a_student_be_able_to_apply_at_the_end_of_the_course.3F)
+		- [1.2.4 Course evaluation](#Course_evaluation)
+		- [1.2.5 Grades range](#Grades_range)
+		- [1.2.6 Resources and reference material](#Resources_and_reference_material)
+	+ [1.3 Course Sections](#Course_Sections)
+		- [1.3.1 Section 1](#Section_1)
+			* [1.3.1.1 Section title:](#Section_title:)
+		- [1.3.2 Topics covered in this section:](#Topics_covered_in_this_section:)
+		- [1.3.3 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F)
+		- [1.3.4 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section)
+		- [1.3.5 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section)
+		- [1.3.6 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section)
+		- [1.3.7 Section 2](#Section_2)
+			* [1.3.7.1 Section title:](#Section_title:_2)
+		- [1.3.8 Topics covered in this section:](#Topics_covered_in_this_section:_2)
+		- [1.3.9 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_2)
+		- [1.3.10 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_2)
+		- [1.3.11 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_2)
+		- [1.3.12 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_2)
+		- [1.3.13 Section 3](#Section_3)
+			* [1.3.13.1 Section title:](#Section_title:_3)
+			* [1.3.13.2 Topics covered in this section:](#Topics_covered_in_this_section:_3)
+		- [1.3.14 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_3)
+		- [1.3.15 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_3)
+			* [1.3.15.1 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_3)
+			* [1.3.15.2 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_3)
+
+
+
+Mathematical Analysis I
+=======================
+
+
+Course Characteristics
+----------------------
+
+
+### Key concepts of the class
+
+
+* Differentiation
+* Integration
+* Series
+
+
+### What is the purpose of this course?
+
+
+This calculus course covers differentiation and integration of functions of one variable, with applications. The basic objective of Calculus is to relate small-scale (differential) quantities to large-scale (integrated) quantities. This is accomplished by means of the Fundamental Theorem of Calculus. Should be understanding of the integral as a cumulative sum, of the derivative as a rate of change, and of the inverse relationship between integration and differentiation.
+
+
+This calculus course will provide an opportunity for participants to:
+
+
+
+* understand key principles involved in differentiation and integration of functions
+* solve problems that connect small-scale (differential) quantities to large-scale (integrated) quantities
+* become familiar with the fundamental theorems of Calculus
+* get hands-on experience with the integral and derivative applications and of the inverse relationship between integration and differentiation.
+
+
+Course Objectives Based on Bloom’s Taxonomy
+-------------------------------------------
+
+
+### What should a student remember at the end of the course?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Derivative. Differential. Applications
+* Indefinite integral. Definite integral. Applications
+* Sequences. Series. Convergence. Power Series
+
+
+### What should a student be able to understand at the end of the course?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Derivative. Differential. Applications
+* Indefinite integral. Definite integral. Applications
+* Sequences. Series. Convergence. Power Series
+* Taylor Series
+
+
+### What should a student be able to apply at the end of the course?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Take derivatives of various type functions and of various orders
+* Integrate
+* Apply definite integral
+* Expand functions into Taylor series
+* Apply convergence tests
+
+
+### Course evaluation
+
+
+
+
+Course grade breakdown
+|  |  | **Proposed points** |
+| --- | --- | --- |
+| Labs/seminar classes
+ | 20
+ |  |
+| Interim performance assessment
+ | 30
+ |  |
+| Exams
+ | 50
+ |  |
+
+
+If necessary, please indicate freely your course’s features in terms of students’ performance assessment.
+
+
+
+### Grades range
+
+
+
+
+Course grading range
+|  |  | **Proposed range** |
+| --- | --- | --- |
+| A. Excellent
+ | 90-100
+ |  |
+| B. Good
+ | 75-89
+ |  |
+| C. Satisfactory
+ | 60-74
+ |  |
+| D. Poor
+ | 0-59
+ |  |
+
+
+If necessary, please indicate freely your course’s grading features.
+
+
+
+### Resources and reference material
+
+
+* Zorich, V. A. “Mathematical Analysis I, Translator: Cooke R.” (2004)
+* 
+* 
+
+
+Course Sections
+---------------
+
+
+The main sections of the course and approximate hour distribution between them is as follows:
+
+
+
+
+
+Course Sections
+| **Section** | **Section Title** | **Teaching Hours** |
+| --- | --- | --- |
+| 1
+ | Sequences and Limits
+ | 28
+ |
+| 2
+ | Differentiation
+ | 24
+ |
+| 3
+ | Integration and Series
+ | 28
+ |
+
+
+### Section 1
+
+
+#### Section title:
+
+
+Sequences and Limits
+
+
+
+### Topics covered in this section:
+
+
+* Sequences. Limits of sequences
+* Limits of sequences. Limits of functions
+* Limits of functions. Continuity. Hyperbolic functions
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. A sequence, limiting value
+2. Limit of a sequence, convergent and divergent sequences
+3. Increasing and decreasing sequences, monotonic sequences
+4. Bounded sequences. Properties of limits
+5. Theorem about bounded and monotonic sequences.
+6. Cauchy sequence. The Cauchy Theorem (criterion).
+7. Limit of a function. Properties of limits.
+8. The first remarkable limit.
+9. The Cauchy criterion for the existence of a limit of a function.
+10. Second remarkable limit.
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Find a limit of a sequence
+2. Find a limit of a function
+
+
+### Test questions for final assessment in this section
+
+
+1. Find limits of the following sequences or prove that they do not exist:
+2. a
+
+n
+
+
+=
+n
+−
+
+
+
+n
+
+2
+
+
+−
+70
+n
++
+1400
+
+
+
+
+{\displaystyle a\_{n}=n-{\sqrt {n^{2}-70n+1400}}}
+
+![{\displaystyle a_{n}=n-{\sqrt {n^{2}-70n+1400}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aeca3ea0fc01bed1f98eb199a9819614e88e793f);
+3. d
+
+n
+
+
+=
+
+
+(
+
+
+
+2
+n
+−
+4
+
+
+2
+n
++
+1
+
+
+
+)
+
+
+n
+
+
+
+
+{\textstyle d\_{n}=\left({\frac {2n-4}{2n+1}}\right)^{n}}
+
+![{\textstyle d_{n}=\left({\frac {2n-4}{2n+1}}\right)^{n}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/389a3735f2899205a00b490e482acbcfa39b3edb);
+4. x
+
+n
+
+
+=
+
+
+
+
+
+(
+
+2
+
+n
+
+2
+
+
++
+1
+
+)
+
+
+6
+
+
+(
+n
+−
+1
+
+)
+
+2
+
+
+
+
+
+(
+
+
+n
+
+7
+
+
++
+1000
+
+n
+
+6
+
+
+−
+3
+
+)
+
+
+2
+
+
+
+
+
+
+{\textstyle x\_{n}={\frac {\left(2n^{2}+1\right)^{6}(n-1)^{2}}{\left(n^{7}+1000n^{6}-3\right)^{2}}}}
+
+![{\textstyle x_{n}={\frac {\left(2n^{2}+1\right)^{6}(n-1)^{2}}{\left(n^{7}+1000n^{6}-3\right)^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5f2e2a41471540c1cb5f3f8b2ad3d96ef91cf7e9).
+
+
+### Section 2
+
+
+#### Section title:
+
+
+Differentiation
+
+
+
+### Topics covered in this section:
+
+
+* Derivatives. Differentials
+* Mean-Value Theorems
+* l’Hopital’s rule
+* Taylor Formula with Lagrange and Peano remainders
+* Taylor formula and limits
+* Increasing / decreasing functions. Concave / convex functions
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. A plane curve is given by 
+
+
+
+x
+(
+t
+)
+=
+−
+
+
+
+
+t
+
+2
+
+
++
+4
+t
++
+8
+
+
+t
++
+2
+
+
+
+
+
+{\displaystyle x(t)=-{\frac {t^{2}+4t+8}{t+2}}}
+
+![{\displaystyle x(t)=-{\frac {t^{2}+4t+8}{t+2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d5c87d1bcdd432a16c052b35df5eeafde36d5f1c), 
+
+
+
+y
+(
+t
+)
+=
+
+
+
+
+t
+
+2
+
+
++
+9
+t
++
+22
+
+
+t
++
+6
+
+
+
+
+
+{\textstyle y(t)={\frac {t^{2}+9t+22}{t+6}}}
+
+![{\textstyle y(t)={\frac {t^{2}+9t+22}{t+6}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5053f85973bbe307983c1751cf8555915e010966). Find
+	1. the asymptotes of this curve;
+	2. the derivative 
+	
+	
+	
+	
+	y
+	
+	x
+	
+	′
+	
+	
+	
+	{\textstyle y'\_{x}}
+	
+	![{\textstyle y'_{x}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ef2ed2d5f61e3172938257665534af01f608117f).
+2. Derive the Maclaurin expansion for 
+
+
+
+f
+(
+x
+)
+=
+
+
+
+1
++
+
+e
+
+−
+2
+x
+
+
+
+
+3
+
+
+
+
+
+{\textstyle f(x)={\sqrt[{3}]{1+e^{-2x}}}}
+
+![{\textstyle f(x)={\sqrt[{3}]{1+e^{-2x}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/14bfa69ed7bcfd7de396a3360c031c64292828b3) up to 
+
+
+
+o
+
+(
+
+x
+
+3
+
+
+)
+
+
+
+{\textstyle o\left(x^{3}\right)}
+
+![{\textstyle o\left(x^{3}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2e23f841ca36ac3c4d7ccc3920dbe12d69f5b304).
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Differentiation techniques: inverse, implicit, parametric etc.
+2. Find a derivative of a function
+3. Apply Leibniz formula
+4. Draw graphs of functions
+5. Find asymptotes of a parametric function
+
+
+### Test questions for final assessment in this section
+
+
+1. Find a derivative of a (implicit/inverse) function
+2. Apply Leibniz formula Find 
+
+
+
+
+y
+
+(
+n
+)
+
+
+(
+x
+)
+
+
+{\textstyle y^{(n)}(x)}
+
+![{\textstyle y^{(n)}(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f7589798b5f12dd4045984596bdeef45c97ebbb2) if 
+
+
+
+y
+(
+x
+)
+=
+
+(
+
+
+x
+
+2
+
+
+−
+2
+
+)
+
+cos
+⁡
+2
+x
+sin
+⁡
+3
+x
+
+
+{\textstyle y(x)=\left(x^{2}-2\right)\cos 2x\sin 3x}
+
+![{\textstyle y(x)=\left(x^{2}-2\right)\cos 2x\sin 3x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec58b46b813170ce96a00bff16a41f464508272a).
+3. Draw graphs of functions
+4. Find asymptotes
+5. Apply l’Hopital’s rule
+6. Find the derivatives of the following functions:
+	1. f
+	(
+	x
+	)
+	=
+	
+	log
+	
+	
+	|
+	
+	sin
+	⁡
+	x
+	
+	|
+	
+	
+	
+	⁡
+	
+	
+	
+	
+	x
+	
+	2
+	
+	
+	+
+	6
+	
+	
+	6
+	
+	
+	
+	
+	
+	{\textstyle f(x)=\log \_{|\sin x|}{\sqrt[{6}]{x^{2}+6}}}
+	
+	![{\textstyle f(x)=\log _{|\sin x|}{\sqrt[{6}]{x^{2}+6}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f4dd86bbb69d9a98691da7b8c676178d856cbd6f);
+	2. y
+	(
+	x
+	)
+	
+	
+	{\textstyle y(x)}
+	
+	![{\textstyle y(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4639e7d86a9d2274f64a48570e7fe4ef17f7efa) that is given implicitly by 
+	
+	
+	
+	
+	x
+	
+	3
+	
+	
+	+
+	5
+	x
+	y
+	+
+	
+	y
+	
+	3
+	
+	
+	=
+	0
+	
+	
+	{\textstyle x^{3}+5xy+y^{3}=0}
+	
+	![{\textstyle x^{3}+5xy+y^{3}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0ee197bafd124ae61986c15d077d9183dbcd3cc8).
+
+
+### Section 3
+
+
+#### Section title:
+
+
+Integration and Series
+
+
+
+#### Topics covered in this section:
+
+
+* Antiderivative. Indefinite integral
+* Definite integral
+* The Fundamental Theorem of Calculus
+* Improper Integrals
+* Convergence tests. Dirichlet’s test
+* Series. Convergence tests
+* Absolute / Conditional convergence
+* Power Series. Radius of convergence
+* Functional series. Uniform convergence
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 0
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. Find the indefinite integral 
+
+
+
+
+∫
+x
+ln
+⁡
+
+(
+
+x
++
+
+
+
+x
+
+2
+
+
+−
+1
+
+
+
+)
+
+
+d
+x
+
+
+
+{\textstyle \displaystyle \int x\ln \left(x+{\sqrt {x^{2}-1}}\right)\,dx}
+
+![{\textstyle \displaystyle \int x\ln \left(x+{\sqrt {x^{2}-1}}\right)\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cecb2d4bbc0d780bd1a3833c2dcb3a512f8a745d).
+2. Find the length of a curve given by 
+
+
+
+y
+=
+ln
+⁡
+sin
+⁡
+x
+
+
+{\textstyle y=\ln \sin x}
+
+![{\textstyle y=\ln \sin x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d9f39b93580dbed62ccb3b5560e4e2fa35b8900b), 
+
+
+
+
+
+π
+4
+
+
+⩽
+x
+⩽
+
+
+π
+2
+
+
+
+
+{\textstyle {\frac {\pi }{4}}\leqslant x\leqslant {\frac {\pi }{2}}}
+
+![{\textstyle {\frac {\pi }{4}}\leqslant x\leqslant {\frac {\pi }{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a70476c552255c896a29ea67b3eea049324922f0).
+3. Find all values of parameter 
+
+
+
+α
+
+
+{\textstyle \alpha }
+
+![{\textstyle \alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d86dbd6183264b2f8569da1751380b173c7b185) such that series 
+
+
+
+
+
+∑
+
+k
+=
+1
+
+
++
+∞
+
+
+
+
+(
+
+
+
+3
+k
++
+2
+
+
+2
+k
++
+1
+
+
+
+)
+
+
+k
+
+
+
+α
+
+k
+
+
+
+
+
+{\textstyle \displaystyle \sum \limits \_{k=1}^{+\infty }\left({\frac {3k+2}{2k+1}}\right)^{k}\alpha ^{k}}
+
+![{\textstyle \displaystyle \sum \limits _{k=1}^{+\infty }\left({\frac {3k+2}{2k+1}}\right)^{k}\alpha ^{k}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f6dabe061cfa1e87b7fc4629f85418142fa7b1d) converges.
+
+
+#### Typical questions for seminar classes (labs) within this section
+
+
+1. Integration techniques
+2. Integration by parts
+3. Calculation of areas, lengths, volumes
+4. Application of convergence tests
+5. Calculation of Radius of convergence
+
+
+#### Test questions for final assessment in this section
+
+
+1. Find the following integrals:
+2. ∫
+
+
+
+
+
+4
++
+
+x
+
+2
+
+
+
+
++
+2
+
+
+4
+−
+
+x
+
+2
+
+
+
+
+
+
+16
+−
+
+x
+
+4
+
+
+
+
+
+
+d
+x
+
+
+{\textstyle \int {\frac {{\sqrt {4+x^{2}}}+2{\sqrt {4-x^{2}}}}{\sqrt {16-x^{4}}}}\,dx}
+
+![{\textstyle \int {\frac {{\sqrt {4+x^{2}}}+2{\sqrt {4-x^{2}}}}{\sqrt {16-x^{4}}}}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a336f5054ecdaaf721dd26521ceea178d0538e7f);
+3. ∫
+
+2
+
+2
+x
+
+
+
+e
+
+x
+
+
+
+d
+x
+
+
+{\textstyle \int 2^{2x}e^{x}\,dx}
+
+![{\textstyle \int 2^{2x}e^{x}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e670c4f2b17ea6c370f8a531d165d79245d3dc45);
+4. ∫
+
+
+
+d
+x
+
+
+3
+
+x
+
+2
+
+
+−
+
+x
+
+4
+
+
+
+
+
+
+
+{\textstyle \int {\frac {dx}{3x^{2}-x^{4}}}}
+
+![{\textstyle \int {\frac {dx}{3x^{2}-x^{4}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dfc1a209cc0faf2f924c6f8af0e31d8024eb8769).
+5. Use comparison test to determine if the following series converge.
+
+
+
+
+
+
+
+∑
+
+k
+=
+1
+
+
+∞
+
+
+
+
+
+3
++
+(
+−
+1
+
+)
+
+k
+
+
+
+
+k
+
+2
+
+
+
+
+
+
+{\textstyle \sum \limits \_{k=1}^{\infty }{\frac {3+(-1)^{k}}{k^{2}}}}
+
+![{\textstyle \sum \limits _{k=1}^{\infty }{\frac {3+(-1)^{k}}{k^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3e87788ec917e8c1f759186838a02cfc24cdd912);
+6. Use Cauchy criterion to prove that the series 
+
+
+
+
+∑
+
+k
+=
+1
+
+
+∞
+
+
+
+
+
+k
++
+1
+
+
+
+k
+
+2
+
+
++
+3
+
+
+
+
+
+{\textstyle \sum \limits \_{k=1}^{\infty }{\frac {k+1}{k^{2}+3}}}
+
+![{\textstyle \sum \limits _{k=1}^{\infty }{\frac {k+1}{k^{2}+3}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1db1b7d2a764a327ba2530374b1f9452eabe866c) is divergent.
+7. Find the sums of the following series:
+8. ∑
+
+k
+=
+1
+
+
+∞
+
+
+
+
+1
+
+16
+
+k
+
+2
+
+
+−
+8
+k
+−
+3
+
+
+
+
+
+{\textstyle \sum \limits \_{k=1}^{\infty }{\frac {1}{16k^{2}-8k-3}}}
+
+![{\textstyle \sum \limits _{k=1}^{\infty }{\frac {1}{16k^{2}-8k-3}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/912efbbc162ea622ba6e3d18f8e519149ef054b7);
+9. ∑
+
+k
+=
+1
+
+
+∞
+
+
+
+
+
+k
+−
+
+
+
+k
+
+2
+
+
+−
+1
+
+
+
+
+
+k
+
+2
+
+
++
+k
+
+
+
+
+
+{\textstyle \sum \limits \_{k=1}^{\infty }{\frac {k-{\sqrt {k^{2}-1}}}{\sqrt {k^{2}+k}}}}
+
+![{\textstyle \sum \limits _{k=1}^{\infty }{\frac {k-{\sqrt {k^{2}-1}}}{\sqrt {k^{2}+k}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4ce35076e06e2b6f92f5e7adf17507591f658f0d).
+
+
+
+
+
+
+
+[Category](/index.php/Special:Categories "Special:Categories"): * [TRD](/index.php?title=Category:TRD&action=edit&redlink=1 "Category:TRD (page does not exist)")
+
+
+

raw/raw_bsc__mathematical_analysis_ii.md

@@ -0,0 +1,5081 @@
+
+
+
+
+
+
+
+BSc: Mathematical Analysis II
+=============================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 MathematicalAnalysis II](#MathematicalAnalysis_II)
+	+ [1.1 Course Characteristics](#Course_Characteristics)
+		- [1.1.1 Key concepts of the class](#Key_concepts_of_the_class)
+		- [1.1.2 What is the purpose of this course?](#What_is_the_purpose_of_this_course.3F)
+	+ [1.2 Course Objectives Based on Bloom’s Taxonomy](#Course_Objectives_Based_on_Bloom.E2.80.99s_Taxonomy)
+		- [1.2.1 - What should a student remember at the end of the course?](#-_What_should_a_student_remember_at_the_end_of_the_course.3F)
+		- [1.2.2 - What should a student be able to understand at the end of the course?](#-_What_should_a_student_be_able_to_understand_at_the_end_of_the_course.3F)
+		- [1.2.3 - What should a student be able to apply at the end of the course?](#-_What_should_a_student_be_able_to_apply_at_the_end_of_the_course.3F)
+		- [1.2.4 Course evaluation](#Course_evaluation)
+		- [1.2.5 Grades range](#Grades_range)
+		- [1.2.6 Resources and reference material](#Resources_and_reference_material)
+	+ [1.3 Course Sections](#Course_Sections)
+		- [1.3.1 Section 1](#Section_1)
+			* [1.3.1.1 Section title:](#Section_title:)
+		- [1.3.2 Topics covered in this section:](#Topics_covered_in_this_section:)
+		- [1.3.3 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F)
+		- [1.3.4 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section)
+		- [1.3.5 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section)
+		- [1.3.6 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section)
+		- [1.3.7 Section 2](#Section_2)
+			* [1.3.7.1 Section title:](#Section_title:_2)
+		- [1.3.8 Topics covered in this section:](#Topics_covered_in_this_section:_2)
+		- [1.3.9 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_2)
+		- [1.3.10 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_2)
+		- [1.3.11 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_2)
+		- [1.3.12 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_2)
+		- [1.3.13 Section 3](#Section_3)
+			* [1.3.13.1 Section title:](#Section_title:_3)
+			* [1.3.13.2 Topics covered in this section:](#Topics_covered_in_this_section:_3)
+		- [1.3.14 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_3)
+		- [1.3.15 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_3)
+			* [1.3.15.1 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_3)
+		- [1.3.16 Test questions for final assessment in the course](#Test_questions_for_final_assessment_in_the_course)
+		- [1.3.17 Section 1](#Section_1_2)
+			* [1.3.17.1 Section title:](#Section_title:_4)
+		- [1.3.18 Topics covered in this section:](#Topics_covered_in_this_section:_4)
+		- [1.3.19 What forms of evaluation were used to test students’ performance in this section?](#What_forms_of_evaluation_were_used_to_test_students.E2.80.99_performance_in_this_section.3F_4)
+		- [1.3.20 Typical questions for ongoing performance evaluation within this section](#Typical_questions_for_ongoing_performance_evaluation_within_this_section_4)
+		- [1.3.21 Typical questions for seminar classes (labs) within this section](#Typical_questions_for_seminar_classes_.28labs.29_within_this_section_4)
+		- [1.3.22 Test questions for final assessment in this section](#Test_questions_for_final_assessment_in_this_section_3)
+
+
+
+MathematicalAnalysis II
+=======================
+
+
+* **Course name:** Mathematical Analysis II
+* **Course number:** BS-01
+
+
+Course Characteristics
+----------------------
+
+
+### Key concepts of the class
+
+
+* Multivariate calculus: derivatives, differentials, maxima and minima
+* Multivariate integration
+* Functional series. Fourier series
+* Integrals with parameters
+
+
+### What is the purpose of this course?
+
+
+The goal of the course is to study basic mathematical concepts that will be required in further studies. The course is based on Mathematical Analysis I, and the concepts studied there are widely used in this course. The course covers differentiation and integration of functions of several variables. Some more advanced concepts, as uniform convergence of series and integrals, are also considered, since they are important for understanding applicability of many theorems of mathematical analysis. In the end of the course some useful applications are covered, such as gamma-function, beta-function, and Fourier transform.
+
+
+
+Course Objectives Based on Bloom’s Taxonomy
+-------------------------------------------
+
+
+### - What should a student remember at the end of the course?
+
+
+By the end of the course, the students should be able to:
+
+
+
+* find partial and directional derivatives of functions of several variables;
+* find maxima and minima for a function of several variables
+* use Fubini’s theorem for calculating multiple integrals
+* calculate line and path integrals
+* distinguish between point wise and uniform convergence of series and improper integrals
+* decompose a function into Fourier series
+* calculate Fourier transform of a function
+
+
+### - What should a student be able to understand at the end of the course?
+
+
+By the end of the course, the students should be able to understand:
+
+
+
+* how to find minima and maxima of a function subject to a constraint
+* how to represent double integrals as iterated integrals and vice versa
+* what the length of a curve and the area of a surface is
+* properties of uniformly convergent series and improper integrals
+* beta-function, gamma-function and their properties
+* how to find Fourier transform of a function
+
+
+### - What should a student be able to apply at the end of the course?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* find multiple, path, surface integrals
+* find the range of a function in a given domain
+* decompose a function into Fourier series
+
+
+### Course evaluation
+
+
+
+
+Course grade breakdown
+|  |  | **Proposed points** |
+| --- | --- | --- |
+| Test 1
+ | ?
+ | 10
+ |
+| Midterm
+ | ?
+ | 25
+ |
+| Test 2
+ | ?
+ | 10
+ |
+| Participation
+ | ?
+ | 5
+ |
+| Final exam
+ | ?
+ | 50
+ |
+
+
+### Grades range
+
+
+
+
+Course grading range
+|  |  | **Proposed range** |
+| --- | --- | --- |
+| A. Excellent
+ | 90-100
+ | 85-100
+ |
+| B. Good
+ | 75-89
+ | 65-84
+ |
+| C. Satisfactory
+ | 60-74
+ | 45-64
+ |
+| D. Poor
+ | 0-59
+ | 0-44
+ |
+
+
+### Resources and reference material
+
+
+* Robert A. Adams, Christopher Essex (2017) Calculus. A Complete Course, Pearson
+* Jerrold Marsden, Alan Weinstein (1985) Calculus (in three volumes; volumes 2 and 3), Springer
+
+
+Course Sections
+---------------
+
+
+The main sections of the course and approximate hour distribution between them is as follows:
+
+
+
+
+
+Course Sections
+| **Section** | **Section Title** | **Teaching Hours** |
+| --- | --- | --- |
+| 1
+ | Differential Analysis of Functions of Several Variables
+ | 24
+ |
+| 2
+ | Integration of Functions of Several Variables
+ | 30
+ |
+| 3
+ | Uniform Convergence of Functional Series. Fourier Series
+ | 18
+ |
+| 4
+ | Integrals with Parameter(s)
+ | 18
+ |
+| hline
+ |  |  |
+
+
+### Section 1
+
+
+#### Section title:
+
+
+Differential Analysis of Functions of Several Variables
+
+
+
+### Topics covered in this section:
+
+
+* Limits of functions of several variables
+* Partial and directional derivatives of functions of several variables. Gradient
+* Differentials of functions of several variables. Taylor formula
+* Maxima and minima for functions of several variables
+* Maxima and minima for functions of several variables subject to a constraint
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. Find 
+
+
+
+
+lim
+
+x
+→
+0
+
+
+
+lim
+
+y
+→
+0
+
+
+u
+(
+x
+;
+y
+)
+
+
+{\textstyle \lim \limits \_{x\to 0}\lim \limits \_{y\to 0}u(x;y)}
+
+![{\textstyle \lim \limits _{x\to 0}\lim \limits _{y\to 0}u(x;y)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/41fcf6ef0f4de155d38dc7b27a24cb3be9c95abc), 
+
+
+
+
+lim
+
+y
+→
+0
+
+
+
+lim
+
+x
+→
+0
+
+
+u
+(
+x
+;
+y
+)
+
+
+{\textstyle \lim \limits \_{y\to 0}\lim \limits \_{x\to 0}u(x;y)}
+
+![{\textstyle \lim \limits _{y\to 0}\lim \limits _{x\to 0}u(x;y)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/30b9ab013043fea23bc9bc3584592aa95379e778) and 
+
+
+
+
+lim
+
+(
+x
+;
+y
+)
+→
+(
+0
+;
+0
+)
+
+
+u
+(
+x
+;
+y
+)
+
+
+{\textstyle \lim \limits \_{(x;y)\to (0;0)}u(x;y)}
+
+![{\textstyle \lim \limits _{(x;y)\to (0;0)}u(x;y)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f181440f0fe3a34a0575a79be4be5e8e6aa37957) if 
+
+
+
+u
+(
+x
+;
+y
+)
+=
+
+
+
+
+x
+
+2
+
+
+y
++
+x
+
+y
+
+2
+
+
+
+
+
+x
+
+2
+
+
+−
+x
+y
++
+
+y
+
+2
+
+
+
+
+
+
+
+{\textstyle u(x;y)={\frac {x^{2}y+xy^{2}}{x^{2}-xy+y^{2}}}}
+
+![{\textstyle u(x;y)={\frac {x^{2}y+xy^{2}}{x^{2}-xy+y^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb7a5e54b99cd1e3fd00b1f8ae13ab79a21e5f56).
+2. Find the differential of a function: (a) 
+
+
+
+u
+(
+x
+;
+y
+)
+=
+ln
+⁡
+
+(
+
+x
++
+
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+
+
+
+)
+
+
+
+{\textstyle u(x;y)=\ln \left(x+{\sqrt {x^{2}+y^{2}}}\right)}
+
+![{\textstyle u(x;y)=\ln \left(x+{\sqrt {x^{2}+y^{2}}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5cc7b02dad3ea12644b4ecadf08fcaa6405d4529); (b) 
+
+
+
+u
+(
+x
+;
+y
+)
+=
+ln
+⁡
+sin
+⁡
+
+
+
+x
++
+1
+
+
+y
+
+
+
+
+
+{\textstyle u(x;y)=\ln \sin {\frac {x+1}{\sqrt {y}}}}
+
+![{\textstyle u(x;y)=\ln \sin {\frac {x+1}{\sqrt {y}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1c25c88f1c0c5fda11150ba0fe2212b28a40ecc7).
+3. Find the differential of 
+
+
+
+u
+(
+x
+;
+y
+)
+
+
+{\textstyle u(x;y)}
+
+![{\textstyle u(x;y)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/feeabc2f3e55a2a2f72b6ec04a08c1315c08699e) given implicitly by an equation 
+
+
+
+
+x
+
+3
+
+
++
+2
+
+y
+
+3
+
+
++
+
+u
+
+3
+
+
+−
+3
+x
+y
+u
++
+2
+y
+−
+3
+=
+0
+
+
+{\textstyle x^{3}+2y^{3}+u^{3}-3xyu+2y-3=0}
+
+![{\textstyle x^{3}+2y^{3}+u^{3}-3xyu+2y-3=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/911701538f15cf656e0dd261ad813f9c8a2c93f9) at points 
+
+
+
+M
+(
+1
+;
+1
+;
+1
+)
+
+
+{\textstyle M(1;1;1)}
+
+![{\textstyle M(1;1;1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/97b7d6ccd5c6763a4d4ea7e712c393483057239d) and 
+
+
+
+N
+(
+1
+;
+1
+;
+−
+2
+)
+
+
+{\textstyle N(1;1;-2)}
+
+![{\textstyle N(1;1;-2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/00c66cfa579443b4e19dcd7f9348d1ae9dfce8d4).
+4. Find maxima and minima of a function subject to a constraint (or several constraints):
+	1. u
+	=
+	
+	x
+	
+	2
+	
+	
+	
+	y
+	
+	3
+	
+	
+	
+	z
+	
+	4
+	
+	
+	
+	
+	{\textstyle u=x^{2}y^{3}z^{4}}
+	
+	![{\textstyle u=x^{2}y^{3}z^{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e9178002e5b4a33a04c2d25eb41d3311427efe6d), 
+	
+	
+	
+	2
+	x
+	+
+	3
+	y
+	+
+	4
+	z
+	=
+	18
+	
+	
+	{\textstyle 2x+3y+4z=18}
+	
+	![{\textstyle 2x+3y+4z=18}](https://wikimedia.org/api/rest_v1/media/math/render/svg/85a5abaa6c5cd03742a1c4a119e9c686645f2018), 
+	
+	
+	
+	x
+	>
+	0
+	
+	
+	{\textstyle x>0}
+	
+	![{\textstyle x>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4bd6212b5a778bded18868fc5cd19eb3b15844a0), 
+	
+	
+	
+	y
+	>
+	0
+	
+	
+	{\textstyle y>0}
+	
+	![{\textstyle y>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bad11e7747271c5d6ebd668b512129802597fc5c), 
+	
+	
+	
+	z
+	>
+	0
+	
+	
+	{\textstyle z>0}
+	
+	![{\textstyle z>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f3045a2beda2df2d38cfc9478a0eea2ddb453540);
+	2. u
+	=
+	x
+	−
+	y
+	+
+	2
+	z
+	
+	
+	{\textstyle u=x-y+2z}
+	
+	![{\textstyle u=x-y+2z}](https://wikimedia.org/api/rest_v1/media/math/render/svg/193769ce94ad54f9791ac7b0ebf6f4036bff6c79), 
+	
+	
+	
+	
+	x
+	
+	2
+	
+	
+	+
+	
+	y
+	
+	2
+	
+	
+	+
+	2
+	
+	z
+	
+	2
+	
+	
+	=
+	16
+	
+	
+	{\textstyle x^{2}+y^{2}+2z^{2}=16}
+	
+	![{\textstyle x^{2}+y^{2}+2z^{2}=16}](https://wikimedia.org/api/rest_v1/media/math/render/svg/84686b9dcda37f369eea56991236263c2a9de909);
+	3. u
+	=
+	
+	∑
+	
+	i
+	=
+	1
+	
+	
+	k
+	
+	
+	
+	a
+	
+	i
+	
+	
+	
+	x
+	
+	i
+	
+	
+	2
+	
+	
+	
+	
+	{\textstyle u=\sum \limits \_{i=1}^{k}a\_{i}x\_{i}^{2}}
+	
+	![{\textstyle u=\sum \limits _{i=1}^{k}a_{i}x_{i}^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8e3b99d12ee0032f9ceed49b13a60ce96318791f), 
+	
+	
+	
+	
+	∑
+	
+	i
+	=
+	1
+	
+	
+	k
+	
+	
+	
+	x
+	
+	i
+	
+	
+	=
+	1
+	
+	
+	{\textstyle \sum \limits \_{i=1}^{k}x\_{i}=1}
+	
+	![{\textstyle \sum \limits _{i=1}^{k}x_{i}=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7cb5ca3b9867373e2fafdbb2b03a4566e3dfdd01), 
+	
+	
+	
+	
+	a
+	
+	i
+	
+	
+	>
+	0
+	
+	
+	{\textstyle a\_{i}>0}
+	
+	![{\textstyle a_{i}>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/38bcfd15c6b9a443175f08979d756ae989ab5b2d);
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Let us consider 
+
+
+
+u
+(
+x
+;
+y
+)
+=
+
+
+{
+
+
+
+1
+,
+
+
+x
+=
+
+y
+
+2
+
+
+,
+
+
+
+
+0
+,
+
+
+x
+≠
+
+y
+
+2
+
+
+.
+
+
+
+
+
+
+
+
+{\textstyle u(x;y)={\begin{cases}1,&x=y^{2},\\0,&x\neq y^{2}.\end{cases}}}
+
+![{\textstyle u(x;y)={\begin{cases}1,&x=y^{2},\\0,&x\neq y^{2}.\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2ef639991c2d486e19194dcab47e79e89c4719cf) Show that this function has a limit at the origin along any straight line that passes through it (and all these limits are equal to each other), yet this function does not have limit as 
+
+
+
+(
+x
+;
+y
+)
+→
+(
+0
+;
+0
+)
+
+
+{\textstyle (x;y)\to (0;0)}
+
+![{\textstyle (x;y)\to (0;0)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1aad79e4e9cac7378243f902ec17a57220eb5af1).
+2. Find the largest possible value of directional derivative at point 
+
+
+
+M
+(
+1
+;
+−
+2
+;
+−
+3
+)
+
+
+{\textstyle M(1;-2;-3)}
+
+![{\textstyle M(1;-2;-3)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c6f479a92cfac0e7c81f759916f0d2a6dcd446b7) of function 
+
+
+
+f
+=
+ln
+⁡
+x
+y
+z
+
+
+{\textstyle f=\ln xyz}
+
+![{\textstyle f=\ln xyz}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2324355449882336524193afd9f3da43e6a6a1fc).
+3. Find maxima and minima of functions 
+
+
+
+u
+(
+x
+,
+y
+)
+
+
+{\textstyle u(x,y)}
+
+![{\textstyle u(x,y)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/26146447d087aba20bdc815b1359cfe72d1d5f03) given implicitly by the equations:
+	1. x
+	
+	2
+	
+	
+	+
+	
+	y
+	
+	2
+	
+	
+	+
+	
+	u
+	
+	2
+	
+	
+	−
+	4
+	x
+	−
+	6
+	y
+	−
+	4
+	u
+	+
+	8
+	=
+	0
+	
+	
+	{\textstyle x^{2}+y^{2}+u^{2}-4x-6y-4u+8=0}
+	
+	![{\textstyle x^{2}+y^{2}+u^{2}-4x-6y-4u+8=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/03e8c5cfc2bdda7aa0c924323e94ed791d346372), 
+	
+	
+	
+	u
+	>
+	2
+	
+	
+	{\textstyle u>2}
+	
+	![{\textstyle u>2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/41600e09220a0e3c7dc1f2970ecbf29e81c613f0);
+	2. x
+	
+	3
+	
+	
+	−
+	
+	y
+	
+	2
+	
+	
+	+
+	
+	u
+	
+	2
+	
+	
+	−
+	3
+	x
+	+
+	4
+	y
+	+
+	u
+	−
+	8
+	=
+	0
+	
+	
+	{\textstyle x^{3}-y^{2}+u^{2}-3x+4y+u-8=0}
+	
+	![{\textstyle x^{3}-y^{2}+u^{2}-3x+4y+u-8=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5746abcb8a0f27c804736f73b9cfc82c99347c05).
+4. Find maxima and minima of functions subject to constraints:
+	1. u
+	=
+	x
+	
+	y
+	
+	2
+	
+	
+	
+	
+	{\textstyle u=xy^{2}}
+	
+	![{\textstyle u=xy^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d85561033c5dddbfcdf5a25aace9fb86831a60b8), 
+	
+	
+	
+	x
+	+
+	2
+	y
+	−
+	1
+	=
+	0
+	
+	
+	{\textstyle x+2y-1=0}
+	
+	![{\textstyle x+2y-1=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0e48d00bd62efaf4195638b0e94cfe6c33db40e3);
+	2. u
+	=
+	x
+	y
+	+
+	y
+	z
+	
+	
+	{\textstyle u=xy+yz}
+	
+	![{\textstyle u=xy+yz}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a5b660b93b9234afd2ceb06e0cd3281e16a3c236), 
+	
+	
+	
+	
+	x
+	
+	2
+	
+	
+	+
+	
+	y
+	
+	2
+	
+	
+	=
+	2
+	
+	
+	{\textstyle x^{2}+y^{2}=2}
+	
+	![{\textstyle x^{2}+y^{2}=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f240ee91ca81c79c50513c5f25508f44e235601), 
+	
+	
+	
+	y
+	+
+	z
+	=
+	2
+	
+	
+	{\textstyle y+z=2}
+	
+	![{\textstyle y+z=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/78bc0e88f98fef66bc4577781598ec11e1fdfa0b), 
+	
+	
+	
+	y
+	>
+	0
+	
+	
+	{\textstyle y>0}
+	
+	![{\textstyle y>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bad11e7747271c5d6ebd668b512129802597fc5c).
+
+
+### Test questions for final assessment in this section
+
+
+1. Find all points where the differential of a function 
+
+
+
+f
+(
+x
+;
+y
+)
+=
+(
+5
+x
++
+7
+y
+−
+25
+)
+
+e
+
+−
+
+x
+
+2
+
+
+−
+x
+y
+−
+
+y
+
+2
+
+
+
+
+
+
+{\textstyle f(x;y)=(5x+7y-25)e^{-x^{2}-xy-y^{2}}}
+
+![{\textstyle f(x;y)=(5x+7y-25)e^{-x^{2}-xy-y^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fcef5187dd210178de071072338fc887676cb0c6) is equal to zero.
+2. Show that function 
+
+
+
+φ
+=
+f
+
+(
+
+
+
+x
+y
+
+
+;
+
+x
+
+2
+
+
++
+y
+−
+
+z
+
+2
+
+
+
+)
+
+
+
+{\textstyle \varphi =f\left({\frac {x}{y}};x^{2}+y-z^{2}\right)}
+
+![{\textstyle \varphi =f\left({\frac {x}{y}};x^{2}+y-z^{2}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1bb557bb21657f2b0c8229adce9ee9804acd1a18) satisfies the equation 
+
+
+
+2
+x
+z
+
+φ
+
+x
+
+
++
+2
+y
+z
+
+φ
+
+y
+
+
++
+
+(
+
+2
+
+x
+
+2
+
+
++
+y
+
+)
+
+
+φ
+
+z
+
+
+=
+0
+
+
+{\textstyle 2xz\varphi \_{x}+2yz\varphi \_{y}+\left(2x^{2}+y\right)\varphi \_{z}=0}
+
+![{\textstyle 2xz\varphi _{x}+2yz\varphi _{y}+\left(2x^{2}+y\right)\varphi _{z}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b3521dcad724a9685111a47bef3a86ae868278f4).
+3. Find maxima and minima of function 
+
+
+
+u
+=
+2
+
+x
+
+2
+
+
++
+12
+x
+y
++
+
+y
+
+2
+
+
+
+
+{\textstyle u=2x^{2}+12xy+y^{2}}
+
+![{\textstyle u=2x^{2}+12xy+y^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/09a2dd7f0d957f03692af28142af427d5e1791df) under condition that 
+
+
+
+
+x
+
+2
+
+
++
+4
+
+y
+
+2
+
+
+=
+25
+
+
+{\textstyle x^{2}+4y^{2}=25}
+
+![{\textstyle x^{2}+4y^{2}=25}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e2161246eedccf6d799aa1e5734b118c315f7150). Find the maximum and minimum value of a function
+4. u
+=
+
+(
+
+
+y
+
+2
+
+
+−
+
+x
+
+2
+
+
+
+)
+
+
+e
+
+1
+−
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+
+
+
+
+{\textstyle u=\left(y^{2}-x^{2}\right)e^{1-x^{2}+y^{2}}}
+
+![{\textstyle u=\left(y^{2}-x^{2}\right)e^{1-x^{2}+y^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/932e00eb2464b47b893d6fb18846cfcccb4e6d6b) on a domain given by inequality 
+
+
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+≤
+4
+
+
+{\textstyle x^{2}+y^{2}\leq 4}
+
+![{\textstyle x^{2}+y^{2}\leq 4}](https://wikimedia.org/api/rest_v1/media/math/render/svg/90eb8b71c5ce09a4ec482966f3de5479978b1e3d);
+
+
+### Section 2
+
+
+#### Section title:
+
+
+Integration of Functions of Several Variables
+
+
+
+### Topics covered in this section:
+
+
+* Z-test
+* Double integrals. Fubini’s theorem and iterated integrals
+* Substituting variables in double integrals. Polar coordinates
+* Triple integrals. Use of Fubini’s theorem
+* Spherical and cylindrical coordinates
+* Path integrals
+* Area of a surface
+* Surface integrals
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. Represent double integrals below as an iterated integrals (or a sum of iterated integrals) with different orders of integration: 
+
+
+
+
+∬
+
+D
+
+
+f
+(
+x
+;
+y
+)
+
+d
+x
+
+d
+y
+
+
+{\textstyle \iint \limits \_{D}f(x;y)\,dx\,dy}
+
+![{\textstyle \iint \limits _{D}f(x;y)\,dx\,dy}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e2b52bb56df4ec7f5416ec2e32f0903b2e1197b9) where 
+
+
+
+D
+=
+
+{
+
+(
+x
+;
+y
+)
+
+|
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+≤
+9
+,
+
+
+x
+
+2
+
+
++
+(
+y
++
+4
+
+)
+
+2
+
+
+≥
+25
+
+
+
+
+}
+
+
+
+{\textstyle D=\left\{(x;y)\left|x^{2}+y^{2}\leq 9,\,x^{2}+(y+4)^{2}\geq 25\right.\right\}}
+
+![{\textstyle D=\left\{(x;y)\left|x^{2}+y^{2}\leq 9,\,x^{2}+(y+4)^{2}\geq 25\right.\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cbf78bafb60b17a34676ba32d3cda4bb45f3c75e).
+2. Represent integral 
+
+
+
+I
+=
+
+
+∭
+
+D
+
+
+f
+(
+x
+;
+y
+;
+z
+)
+
+d
+x
+
+d
+y
+
+d
+z
+
+
+
+{\textstyle I=\displaystyle \iiint \limits \_{D}f(x;y;z)\,dx\,dy\,dz}
+
+![{\textstyle I=\displaystyle \iiint \limits _{D}f(x;y;z)\,dx\,dy\,dz}](https://wikimedia.org/api/rest_v1/media/math/render/svg/860cffcd0fc93fae6ac55ac594c5fa8928880ffb) as iterated integrals with all possible (i.e. 6) orders of integration; 
+
+
+
+D
+
+
+{\textstyle D}
+
+![{\textstyle D}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4e5200f518cb5afe304ec42ffdd4f6c63c702f77) is bounded by 
+
+
+
+x
+=
+0
+
+
+{\textstyle x=0}
+
+![{\textstyle x=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/95946e5db8fcf9ae99523bcd4f83433c8b2e441e), 
+
+
+
+x
+=
+a
+
+
+{\textstyle x=a}
+
+![{\textstyle x=a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/70e0fe729bde9223f1b509db0471471c21261b82), 
+
+
+
+y
+=
+0
+
+
+{\textstyle y=0}
+
+![{\textstyle y=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5c4b2729074b444ef801a0afa24160d074b52eec), 
+
+
+
+y
+=
+
+
+a
+x
+
+
+
+
+{\textstyle y={\sqrt {ax}}}
+
+![{\textstyle y={\sqrt {ax}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/acdf89c1a5d352bac27ef5bd553c3c3e2b07f8e3), 
+
+
+
+z
+=
+0
+
+
+{\textstyle z=0}
+
+![{\textstyle z=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0829ff59a6fdc19b44396956e8767fac4ba87ba3), 
+
+
+
+z
+=
+x
++
+y
+
+
+{\textstyle z=x+y}
+
+![{\textstyle z=x+y}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a04ad39377ab70df2722495d428ad59389561311).
+3. Find line integrals of a scalar fields 
+
+
+
+
+
+∫
+
+Γ
+
+
+(
+x
++
+y
+)
+
+d
+s
+
+
+
+{\textstyle \displaystyle \int \limits \_{\Gamma }(x+y)\,ds}
+
+![{\textstyle \displaystyle \int \limits _{\Gamma }(x+y)\,ds}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8d7a626ecc11638cd879e8c5dd84deec5f4ec95e) where 
+
+
+
+Γ
+
+
+{\textstyle \Gamma }
+
+![{\textstyle \Gamma }](https://wikimedia.org/api/rest_v1/media/math/render/svg/f677684faf84745068a3b602896ca59b0766be4a) is boundary of a triangle with vertices 
+
+
+
+(
+0
+;
+0
+)
+
+
+{\textstyle (0;0)}
+
+![{\textstyle (0;0)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e8cabde45f1dd10b936518c3de98d232d7c46150), 
+
+
+
+(
+1
+;
+0
+)
+
+
+{\textstyle (1;0)}
+
+![{\textstyle (1;0)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/97e7e03a49a76bc809417791254eb6c78fcc0836) and 
+
+
+
+(
+0
+;
+1
+)
+
+
+{\textstyle (0;1)}
+
+![{\textstyle (0;1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/047498b8de986e906f31c93d8870f2ad77819d71).
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Change order of integration in the iterated integral 
+
+
+
+
+∫
+
+0
+
+
+
+2
+
+
+
+d
+y
+
+∫
+
+y
+
+
+
+4
+−
+
+y
+
+2
+
+
+
+
+
+f
+(
+x
+;
+y
+)
+
+d
+x
+
+
+{\textstyle \int \limits \_{0}^{\sqrt {2}}dy\int \limits \_{y}^{\sqrt {4-y^{2}}}f(x;y)\,dx}
+
+![{\textstyle \int \limits _{0}^{\sqrt {2}}dy\int \limits _{y}^{\sqrt {4-y^{2}}}f(x;y)\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ed028a999470345e5f3d630c5d992c8c67156e84).
+2. Find the volume of a solid given by 
+
+
+
+0
+≤
+z
+≤
+
+x
+
+2
+
+
+
+
+{\textstyle 0\leq z\leq x^{2}}
+
+![{\textstyle 0\leq z\leq x^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/980fd1ccb56e85661acedd630abbd390e4b2003a), 
+
+
+
+x
++
+y
+≤
+5
+
+
+{\textstyle x+y\leq 5}
+
+![{\textstyle x+y\leq 5}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6171ff088c858f3829d9dd5b3139d11be00a5d7f), 
+
+
+
+x
+−
+2
+y
+≥
+2
+
+
+{\textstyle x-2y\geq 2}
+
+![{\textstyle x-2y\geq 2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aa1f70dd26698483c4066479e1bb099241cb9f1c), 
+
+
+
+y
+≥
+0
+
+
+{\textstyle y\geq 0}
+
+![{\textstyle y\geq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a4ab86d638e82193271bc685d8d977cbbcf4e65a).
+3. Change into polar coordinates and rewrite the integral as a single integral: 
+
+
+
+
+
+∬
+
+G
+
+
+f
+
+(
+
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+
+
+)
+
+
+d
+x
+
+d
+y
+
+
+
+{\textstyle \displaystyle \iint \limits \_{G}f\left({\sqrt {x^{2}+y^{2}}}\right)\,dx\,dy}
+
+![{\textstyle \displaystyle \iint \limits _{G}f\left({\sqrt {x^{2}+y^{2}}}\right)\,dx\,dy}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e6139ce46c9b40b5e98d6557634f3243b4c6a91c), 
+
+
+
+G
+=
+
+{
+
+(
+x
+;
+y
+)
+
+|
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+≤
+x
+;
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+≤
+y
+
+
+
+
+}
+
+
+
+{\textstyle G=\left\{(x;y)\left|x^{2}+y^{2}\leq x;\,x^{2}+y^{2}\leq y\right.\right\}}
+
+![{\textstyle G=\left\{(x;y)\left|x^{2}+y^{2}\leq x;\,x^{2}+y^{2}\leq y\right.\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8ab169f95c6e19bea58f06a0f2496b99adc8e4e2).
+4. Having ascertained that integrand is an exact differential, calculate the integral along a piecewise smooth plain curve that starts at 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) and finishes at 
+
+
+
+B
+
+
+{\textstyle B}
+
+![{\textstyle B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/de0b47ffc21636dc2df68f6c793177a268f10e9b): 
+
+
+
+
+
+∫
+
+Γ
+
+
+
+(
+
+
+x
+
+4
+
+
++
+4
+x
+
+y
+
+3
+
+
+
+)
+
+
+d
+x
++
+
+(
+
+6
+
+x
+
+2
+
+
+
+y
+
+2
+
+
+−
+5
+
+y
+
+4
+
+
+
+)
+
+
+d
+y
+
+
+
+{\textstyle \displaystyle \int \limits \_{\Gamma }\left(x^{4}+4xy^{3}\right)\,dx+\left(6x^{2}y^{2}-5y^{4}\right)\,dy}
+
+![{\textstyle \displaystyle \int \limits _{\Gamma }\left(x^{4}+4xy^{3}\right)\,dx+\left(6x^{2}y^{2}-5y^{4}\right)\,dy}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9479ff2e89c48d84cd99758176960aefefa3c2a3), 
+
+
+
+A
+(
+−
+2
+;
+−
+1
+)
+
+
+{\textstyle A(-2;-1)}
+
+![{\textstyle A(-2;-1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/28816a18116ec2bcd546b276cb0ac6201873d963), 
+
+
+
+B
+(
+0
+;
+3
+)
+
+
+{\textstyle B(0;3)}
+
+![{\textstyle B(0;3)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/67293f2836c5adc3c391fa564fcdc2fac94a2562);
+
+
+### Test questions for final assessment in this section
+
+
+1. Domain 
+
+
+
+G
+
+
+{\textstyle G}
+
+![{\textstyle G}](https://wikimedia.org/api/rest_v1/media/math/render/svg/febc2b9ff73bcca7b3fdb1432fddd1cdf3c8403c) is bounded by lines 
+
+
+
+y
+=
+2
+x
+
+
+{\textstyle y=2x}
+
+![{\textstyle y=2x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4d06a41ec951090ac63c9e967e4d2d827376c9ca), 
+
+
+
+y
+=
+x
+
+
+{\textstyle y=x}
+
+![{\textstyle y=x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/93343635ea42bd77e3e1ce347195e23ade09b5d3) and 
+
+
+
+y
+=
+2
+
+
+{\textstyle y=2}
+
+![{\textstyle y=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/887628e811c56cc94aaccb0f5e4c773f19231cf9). Rewrite integral 
+
+
+
+
+∬
+
+G
+
+
+f
+(
+x
+)
+
+d
+x
+
+d
+y
+
+
+{\textstyle \iint \limits \_{G}f(x)\,dx\,dy}
+
+![{\textstyle \iint \limits _{G}f(x)\,dx\,dy}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bbc886f1ea76c3bc7f81d3c334f7620147794855) as a single integral.
+2. Represent the integral 
+
+
+
+
+
+∬
+
+G
+
+
+f
+(
+x
+;
+y
+)
+
+d
+x
+
+d
+y
+
+
+
+{\textstyle \displaystyle \iint \limits \_{G}f(x;y)\,dx\,dy}
+
+![{\textstyle \displaystyle \iint \limits _{G}f(x;y)\,dx\,dy}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f11428df0d608e522a446f7cf8ee68cdbdbdee29) as iterated integrals with different order of integration in polar coordinates if 
+
+
+
+G
+=
+
+{
+
+(
+x
+;
+y
+)
+
+|
+
+
+a
+
+2
+
+
+≤
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+≤
+4
+
+a
+
+2
+
+
+;
+
+
+|
+
+x
+
+|
+
+−
+y
+≥
+0
+
+
+
+
+}
+
+
+
+{\textstyle G=\left\{(x;y)\left|a^{2}\leq x^{2}+y^{2}\leq 4a^{2};\,|x|-y\geq 0\right.\right\}}
+
+![{\textstyle G=\left\{(x;y)\left|a^{2}\leq x^{2}+y^{2}\leq 4a^{2};\,|x|-y\geq 0\right.\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/34dc3c913392b2188d0f55ce7885d44baa8a8f59).
+3. Find the integral making an appropriate substitution: 
+
+
+
+
+
+∭
+
+G
+
+
+
+(
+
+
+x
+
+2
+
+
+−
+
+y
+
+2
+
+
+
+)
+
+
+(
+
+z
++
+
+x
+
+2
+
+
+−
+
+y
+
+2
+
+
+
+)
+
+
+d
+x
+
+d
+y
+
+d
+z
+
+
+
+{\textstyle \displaystyle \iiint \limits \_{G}\left(x^{2}-y^{2}\right)\left(z+x^{2}-y^{2}\right)\,dx\,dy\,dz}
+
+![{\textstyle \displaystyle \iiint \limits _{G}\left(x^{2}-y^{2}\right)\left(z+x^{2}-y^{2}\right)\,dx\,dy\,dz}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3b7f604b225ae19524d76d6342cb44f0c7fe07ff), 
+
+
+
+G
+=
+
+{
+
+(
+x
+;
+y
+;
+z
+)
+
+|
+
+x
+−
+1
+<
+y
+<
+x
+;
+
+1
+−
+x
+<
+y
+<
+2
+−
+x
+;
+
+1
+−
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+<
+z
+<
+
+y
+
+2
+
+
+−
+
+x
+
+2
+
+
++
+2
+x
+
+
+
+
+}
+
+
+
+{\textstyle G=\left\{(x;y;z)\left|x-1<y<x;\,1-x<y<2-x;\,1-x^{2}+y^{2}<z<y^{2}-x^{2}+2x\right.\right\}}
+
+![{\textstyle G=\left\{(x;y;z)\left|x-1<y<x;\,1-x<y<2-x;\,1-x^{2}+y^{2}<z<y^{2}-x^{2}+2x\right.\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/28659bdf51117253f1eea6a8c57f76540a6ec159).
+4. Use divergence theorem to find the following integrals 
+
+
+
+
+
+∬
+
+S
+
+
+(
+1
++
+2
+x
+)
+
+d
+y
+
+d
+z
++
+(
+2
+x
++
+3
+y
+)
+
+d
+z
+
+d
+x
++
+(
+3
+y
++
+4
+z
+)
+
+d
+x
+
+d
+y
+
+
+
+{\textstyle \displaystyle \iint \limits \_{S}(1+2x)\,dy\,dz+(2x+3y)\,dz\,dx+(3y+4z)\,dx\,dy}
+
+![{\textstyle \displaystyle \iint \limits _{S}(1+2x)\,dy\,dz+(2x+3y)\,dz\,dx+(3y+4z)\,dx\,dy}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73a9a7b00f2cc15f508b9bf55224d55b9d1e7e14) where 
+
+
+
+S
+
+
+{\textstyle S}
+
+![{\textstyle S}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e10a3c52d186162ec8910ebc0288ce982aef842f) is the outer surface of a tetrahedron 
+
+
+
+
+
+x
+a
+
+
++
+
+
+y
+b
+
+
++
+
+
+z
+c
+
+
+≤
+1
+
+
+{\textstyle {\frac {x}{a}}+{\frac {y}{b}}+{\frac {z}{c}}\leq 1}
+
+![{\textstyle {\frac {x}{a}}+{\frac {y}{b}}+{\frac {z}{c}}\leq 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1377463cd4c0d1b190d99150ad4c7cecd93ca22f), 
+
+
+
+x
+≥
+0
+
+
+{\textstyle x\geq 0}
+
+![{\textstyle x\geq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c434fc1e2ab777786469de853c75e616007b3eb4), 
+
+
+
+y
+≥
+0
+
+
+{\textstyle y\geq 0}
+
+![{\textstyle y\geq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a4ab86d638e82193271bc685d8d977cbbcf4e65a), 
+
+
+
+z
+≥
+0
+
+
+{\textstyle z\geq 0}
+
+![{\textstyle z\geq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7298578ca3a51011394eff000d2c36a4b6cf9c7b);
+
+
+### Section 3
+
+
+#### Section title:
+
+
+Uniform Convergence of Functional Series. Fourier Series
+
+
+
+#### Topics covered in this section:
+
+
+* Uniform and point wise convergence of functional series
+* Properties of uniformly convergent series
+* Fourier series. Sufficient conditions of convergence and uniform convergence
+* Bessel’s inequality and Parseval’s identity.
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. Find out whether the following functional series converges uniformly on the indicated intervals. Justify your answer. 
+
+
+
+
+∑
+
+n
+=
+1
+
+
+∞
+
+
+
+e
+
+−
+n
+
+(
+
+
+x
+
+2
+
+
++
+2
+sin
+⁡
+x
+
+)
+
+
+
+
+
+{\textstyle \sum \limits \_{n=1}^{\infty }e^{-n\left(x^{2}+2\sin x\right)}}
+
+![{\textstyle \sum \limits _{n=1}^{\infty }e^{-n\left(x^{2}+2\sin x\right)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5683d5e640c22a7cd5b1d3520409c431056e30b0), 
+
+
+
+
+Δ
+
+1
+
+
+=
+(
+0
+;
+1
+]
+
+
+{\textstyle \Delta \_{1}=(0;1]}
+
+![{\textstyle \Delta _{1}=(0;1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b80239da7d74486d76788367da82b612e233dcf6), 
+
+
+
+
+Δ
+
+2
+
+
+=
+[
+1
+;
++
+∞
+)
+
+
+{\textstyle \Delta \_{2}=[1;+\infty )}
+
+![{\textstyle \Delta _{2}=[1;+\infty )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/767b97f867e082dfede53759fa2df79cd53a3869);
+2. ∑
+
+n
+=
+1
+
+
+∞
+
+
+
+
+
+n
+
+x
+
+3
+
+
+
+
+
+x
+
+2
+
+
++
+
+n
+
+2
+
+
+
+
+
+
+
+{\textstyle \sum \limits \_{n=1}^{\infty }{\frac {\sqrt {nx^{3}}}{x^{2}+n^{2}}}}
+
+![{\textstyle \sum \limits _{n=1}^{\infty }{\frac {\sqrt {nx^{3}}}{x^{2}+n^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/695d67fad209cd46deb8627d55eb112673a97d93), 
+
+
+
+
+Δ
+
+1
+
+
+=
+(
+0
+;
+1
+)
+
+
+{\textstyle \Delta \_{1}=(0;1)}
+
+![{\textstyle \Delta _{1}=(0;1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1c54e8b5a3c4d79037b0711372b6689de58b6e4d), 
+
+
+
+
+Δ
+
+2
+
+
+=
+(
+1
+;
++
+∞
+)
+
+
+{\textstyle \Delta \_{2}=(1;+\infty )}
+
+![{\textstyle \Delta _{2}=(1;+\infty )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3da88d3477a5cc6c7f3a8fcfd468e4202bf6d1b9)
+3. Show that sequence 
+
+
+
+
+f
+
+n
+
+
+(
+x
+)
+=
+n
+x
+
+
+(
+
+1
+−
+x
+
+)
+
+
+n
+
+
+
+
+{\textstyle f\_{n}(x)=nx\left(1-x\right)^{n}}
+
+![{\textstyle f_{n}(x)=nx\left(1-x\right)^{n}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a522a3890243ed03c901f3ef345528a6d7a25af5) converges non-uniformly on 
+
+
+
+[
+0
+;
+1
+]
+
+
+{\textstyle [0;1]}
+
+![{\textstyle [0;1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f62f697cdfa218d158d17c6c527ce72134efed64) to a continuous function 
+
+
+
+f
+(
+x
+)
+
+
+{\textstyle f(x)}
+
+![{\textstyle f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0a982c6635ab3b98d9e12d5f5a8533359bcb38a), but 
+
+
+
+
+lim
+
+n
+→
++
+∞
+
+
+
+∫
+
+0
+
+
+1
+
+
+
+f
+
+n
+
+
+(
+x
+)
+
+d
+x
+=
+
+lim
+
+n
+→
++
+∞
+
+
+
+∫
+
+0
+
+
+1
+
+
+f
+(
+x
+)
+
+d
+x
+
+
+{\textstyle \lim \limits \_{n\rightarrow +\infty }\int \limits \_{0}^{1}f\_{n}(x)\,dx=\lim \limits \_{n\rightarrow +\infty }\int \limits \_{0}^{1}f(x)\,dx}
+
+![{\textstyle \lim \limits _{n\rightarrow +\infty }\int \limits _{0}^{1}f_{n}(x)\,dx=\lim \limits _{n\rightarrow +\infty }\int \limits _{0}^{1}f(x)\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/26cdc6b877954d1ce3e2f9fbd8828b1a99c3f171).
+4. Decompose the following function determined on 
+
+
+
+[
+−
+π
+;
+π
+]
+
+
+{\textstyle [-\pi ;\pi ]}
+
+![{\textstyle [-\pi ;\pi ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8de05c42024ae085180a3cee60b8f13097d64f77) into Fourier series using the standard trigonometric system 
+
+
+
+
+
+
+
+{
+
+1
+;
+cos
+⁡
+k
+x
+;
+sin
+⁡
+k
+x
+
+}
+
+|
+
+
+k
+=
+1
+
+
+∞
+
+
+
+
+{\textstyle \left.\left\{1;\cos kx;\sin kx\right\}\right|\_{k=1}^{\infty }}
+
+![{\textstyle \left.\left\{1;\cos kx;\sin kx\right\}\right|_{k=1}^{\infty }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/29d968d30ab8a62c2a3a4fb4933f829c41690cb4). Draw the graph of the sum of Fourier series obtained. 
+
+
+
+f
+(
+x
+)
+=
+
+
+{
+
+
+
+1
+,
+
+0
+≤
+x
+≤
+π
+,
+
+
+
+
+0
+,
+
+−
+π
+≤
+x
+<
+0.
+
+
+
+
+
+
+
+
+{\textstyle f(x)={\begin{cases}1,\;0\leq x\leq \pi ,\\0,\;-\pi \leq x<0.\end{cases}}}
+
+![{\textstyle f(x)={\begin{cases}1,\;0\leq x\leq \pi ,\\0,\;-\pi \leq x<0.\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/60f52f8d6fd57ea3c17ddf34def837fd9d40bdd8)
+5. Prove that if for an absolutely integrable function 
+
+
+
+f
+(
+x
+)
+
+
+{\textstyle f(x)}
+
+![{\textstyle f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0a982c6635ab3b98d9e12d5f5a8533359bcb38a) on 
+
+
+
+[
+−
+π
+;
+π
+]
+
+
+{\textstyle [-\pi ;\pi ]}
+
+![{\textstyle [-\pi ;\pi ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8de05c42024ae085180a3cee60b8f13097d64f77)
+	1. f
+	(
+	x
+	+
+	π
+	)
+	=
+	f
+	(
+	x
+	)
+	
+	
+	{\textstyle f(x+\pi )=f(x)}
+	
+	![{\textstyle f(x+\pi )=f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0ce55ba2c7905d39f645e59d326dd2ee0b27ad9d) then 
+	
+	
+	
+	
+	a
+	
+	2
+	k
+	−
+	1
+	
+	
+	=
+	
+	b
+	
+	2
+	k
+	−
+	1
+	
+	
+	=
+	0
+	
+	
+	{\textstyle a\_{2k-1}=b\_{2k-1}=0}
+	
+	![{\textstyle a_{2k-1}=b_{2k-1}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cac4a716a7237168ccd3b284a630438598378535), 
+	
+	
+	
+	k
+	∈
+	
+	N
+	
+	
+	
+	{\textstyle k\in \mathbb {N} }
+	
+	![{\textstyle k\in \mathbb {N} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b359d27f09d61f7e77a0bae3c5d8b5e4227ec85f);
+	2. f
+	(
+	x
+	+
+	π
+	)
+	=
+	−
+	f
+	(
+	x
+	)
+	
+	
+	{\textstyle f(x+\pi )=-f(x)}
+	
+	![{\textstyle f(x+\pi )=-f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c070274d371f991894de6ca7284d9995f6ffded2) then 
+	
+	
+	
+	
+	a
+	
+	0
+	
+	
+	=
+	0
+	
+	
+	{\textstyle a\_{0}=0}
+	
+	![{\textstyle a_{0}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4fd55771bc2ed5ee8baca22b067055969c613664), 
+	
+	
+	
+	
+	a
+	
+	2
+	k
+	
+	
+	=
+	
+	b
+	
+	2
+	k
+	
+	
+	=
+	0
+	
+	
+	{\textstyle a\_{2k}=b\_{2k}=0}
+	
+	![{\textstyle a_{2k}=b_{2k}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c68e5e1d6f79d962c4b0464f988cf3f9c407bab1), 
+	
+	
+	
+	k
+	∈
+	
+	N
+	
+	
+	
+	{\textstyle k\in \mathbb {N} }
+	
+	![{\textstyle k\in \mathbb {N} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b359d27f09d61f7e77a0bae3c5d8b5e4227ec85f).
+
+
+#### Typical questions for seminar classes (labs) within this section
+
+
+1. Show that sequence 
+
+
+
+
+f
+
+n
+
+
+(
+x
+)
+=
+n
+x
+
+
+(
+
+1
+−
+
+x
+
+2
+
+
+
+)
+
+
+n
+
+
+
+
+{\textstyle f\_{n}(x)=nx\left(1-x^{2}\right)^{n}}
+
+![{\textstyle f_{n}(x)=nx\left(1-x^{2}\right)^{n}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a70725cc314abf72c5133f4e359c1e00dce20492) converges on 
+
+
+
+[
+0
+;
+1
+]
+
+
+{\textstyle [0;1]}
+
+![{\textstyle [0;1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f62f697cdfa218d158d17c6c527ce72134efed64) to a continuous function 
+
+
+
+f
+(
+x
+)
+
+
+{\textstyle f(x)}
+
+![{\textstyle f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0a982c6635ab3b98d9e12d5f5a8533359bcb38a), and at that 
+
+
+
+
+lim
+
+n
+→
++
+∞
+
+
+
+∫
+
+0
+
+
+1
+
+
+
+f
+
+n
+
+
+(
+x
+)
+
+d
+x
+≠
+
+lim
+
+n
+→
++
+∞
+
+
+
+∫
+
+0
+
+
+1
+
+
+f
+(
+x
+)
+
+d
+x
+
+
+{\textstyle \lim \limits \_{n\rightarrow +\infty }\int \limits \_{0}^{1}f\_{n}(x)\,dx\neq \lim \limits \_{n\rightarrow +\infty }\int \limits \_{0}^{1}f(x)\,dx}
+
+![{\textstyle \lim \limits _{n\rightarrow +\infty }\int \limits _{0}^{1}f_{n}(x)\,dx\neq \lim \limits _{n\rightarrow +\infty }\int \limits _{0}^{1}f(x)\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1e65a1b7cf3dc50480022a3bdc0330ecc91486b2).
+2. Show that sequence 
+
+
+
+
+f
+
+n
+
+
+(
+x
+)
+=
+
+x
+
+3
+
+
++
+
+
+1
+n
+
+
+sin
+⁡
+
+(
+
+n
+x
++
+
+
+
+n
+π
+
+2
+
+
+
+)
+
+
+
+{\textstyle f\_{n}(x)=x^{3}+{\frac {1}{n}}\sin \left(nx+{\frac {n\pi }{2}}\right)}
+
+![{\textstyle f_{n}(x)=x^{3}+{\frac {1}{n}}\sin \left(nx+{\frac {n\pi }{2}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/336a2e4259e83eb0aba76054a6168b6f5422cee9) converges uniformly on 
+
+
+
+
+R
+
+
+
+{\textstyle \mathbb {R} }
+
+![{\textstyle \mathbb {R} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/2031b33f0faf73d2d73a1da12544f00a37474f16), but 
+
+
+
+
+
+(
+
+
+lim
+
+n
+→
++
+∞
+
+
+
+f
+
+n
+
+
+(
+x
+)
+
+)
+
+′
+
+≠
+
+lim
+
+n
+→
++
+∞
+
+
+
+f
+
+n
+
+′
+
+(
+x
+)
+
+
+{\textstyle \left(\lim \limits \_{n\rightarrow +\infty }f\_{n}(x)\right)'\neq \lim \limits \_{n\rightarrow +\infty }f'\_{n}(x)}
+
+![{\textstyle \left(\lim \limits _{n\rightarrow +\infty }f_{n}(x)\right)'\neq \lim \limits _{n\rightarrow +\infty }f'_{n}(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8abb56db236e3697dc26dbda43c7e8b6f5f96013).
+3. Decompose 
+
+
+
+cos
+⁡
+α
+x
+
+
+{\textstyle \cos \alpha x}
+
+![{\textstyle \cos \alpha x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8019dd965515917fea1b504d73c914f060639f85), 
+
+
+
+α
+∉
+
+Z
+
+
+
+{\textstyle \alpha \notin \mathbb {Z} }
+
+![{\textstyle \alpha \notin \mathbb {Z} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a73399668b864d0692d6f1638e44c8d8dd4cb79) into Fourier series on 
+
+
+
+[
+−
+π
+;
+π
+]
+
+
+{\textstyle [-\pi ;\pi ]}
+
+![{\textstyle [-\pi ;\pi ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8de05c42024ae085180a3cee60b8f13097d64f77). Using this decomposition prove that 
+
+
+
+cot
+⁡
+y
+=
+
+
+1
+y
+
+
++
+
+∑
+
+k
+=
+1
+
+
+∞
+
+
+
+
+
+2
+y
+
+
+
+y
+
+2
+
+
+−
+
+π
+
+2
+
+
+
+k
+
+2
+
+
+
+
+
+
+
+{\textstyle \cot y={\frac {1}{y}}+\sum \limits \_{k=1}^{\infty }{\frac {2y}{y^{2}-\pi ^{2}k^{2}}}}
+
+![{\textstyle \cot y={\frac {1}{y}}+\sum \limits _{k=1}^{\infty }{\frac {2y}{y^{2}-\pi ^{2}k^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a0cf7b4883ec773362cf3d9bbc8fc0173d48d359).
+4. Function 
+
+
+
+f
+(
+x
+)
+
+
+{\textstyle f(x)}
+
+![{\textstyle f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0a982c6635ab3b98d9e12d5f5a8533359bcb38a) is absolutely integrable on 
+
+
+
+[
+0
+;
+π
+]
+
+
+{\textstyle [0;\pi ]}
+
+![{\textstyle [0;\pi ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eb0e57f19cbd824b48391708d429bf63d2e2a615), and 
+
+
+
+f
+(
+π
+−
+x
+)
+=
+f
+(
+x
+)
+
+
+{\textstyle f(\pi -x)=f(x)}
+
+![{\textstyle f(\pi -x)=f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7bb5fc6410ccd99c704b13a284d6e40916d19d64). Prove that
+	1. if it is decomposed into Fourier series of sines then 
+	
+	
+	
+	
+	b
+	
+	2
+	k
+	
+	
+	=
+	0
+	
+	
+	{\textstyle b\_{2k}=0}
+	
+	![{\textstyle b_{2k}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/46ded058e03d36e114e338e0462c569289aec786), 
+	
+	
+	
+	k
+	∈
+	
+	N
+	
+	
+	
+	{\textstyle k\in \mathbb {N} }
+	
+	![{\textstyle k\in \mathbb {N} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b359d27f09d61f7e77a0bae3c5d8b5e4227ec85f);
+	2. if it is decomposed into Fourier series of cosines then 
+	
+	
+	
+	
+	a
+	
+	2
+	k
+	−
+	1
+	
+	
+	=
+	0
+	
+	
+	{\textstyle a\_{2k-1}=0}
+	
+	![{\textstyle a_{2k-1}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/554d589645e1e9e2b0ee58935fc6a7dada40793e), 
+	
+	
+	
+	k
+	∈
+	
+	N
+	
+	
+	
+	{\textstyle k\in \mathbb {N} }
+	
+	![{\textstyle k\in \mathbb {N} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b359d27f09d61f7e77a0bae3c5d8b5e4227ec85f).
+5. ## Decompose 
+
+
+
+f
+(
+x
+)
+=
+
+
+{
+
+
+
+1
+,
+
+
+|
+
+x
+
+|
+
+<
+α
+,
+
+
+
+
+0
+,
+
+α
+⩽
+
+|
+
+x
+
+|
+
+<
+π
+
+
+
+
+
+
+
+
+{\textstyle f(x)={\begin{cases}1,\;|x|<\alpha ,\\0,\;\alpha \leqslant |x|<\pi \end{cases}}}
+
+![{\textstyle f(x)={\begin{cases}1,\;|x|<\alpha ,\\0,\;\alpha \leqslant |x|<\pi \end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9f6a3c99a69eb3442d864304b578e38b2ebe430d) into Fourier series using the standard trigonometric system.
+	1. Using Parseval’s identity find 
+	
+	
+	
+	
+	σ
+	
+	1
+	
+	
+	=
+	
+	∑
+	
+	k
+	=
+	1
+	
+	
+	∞
+	
+	
+	
+	
+	
+	
+	sin
+	
+	2
+	
+	
+	⁡
+	k
+	α
+	
+	
+	k
+	
+	2
+	
+	
+	
+	
+	
+	
+	{\textstyle \sigma \_{1}=\sum \limits \_{k=1}^{\infty }{\frac {\sin ^{2}k\alpha }{k^{2}}}}
+	
+	![{\textstyle \sigma _{1}=\sum \limits _{k=1}^{\infty }{\frac {\sin ^{2}k\alpha }{k^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/72c064ce830fdbf415754eb98bbb0ac306f44b13) and 
+	
+	
+	
+	
+	σ
+	
+	2
+	
+	
+	=
+	
+	∑
+	
+	k
+	=
+	1
+	
+	
+	∞
+	
+	
+	
+	
+	
+	
+	cos
+	
+	2
+	
+	
+	���
+	k
+	α
+	
+	
+	k
+	
+	2
+	
+	
+	
+	
+	
+	
+	{\textstyle \sigma \_{2}=\sum \limits \_{k=1}^{\infty }{\frac {\cos ^{2}k\alpha }{k^{2}}}}
+	
+	![{\textstyle \sigma _{2}=\sum \limits _{k=1}^{\infty }{\frac {\cos ^{2}k\alpha }{k^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3c65c79bd3377bd71cfe61bf6815fde7ae9123ac).
+
+
+### Test questions for final assessment in the course
+
+
+1. Find out whether the following functional series converge uniformly on the indicated intervals. Justify your answer. 
+
+
+
+
+∑
+
+n
+=
+1
+
+
+∞
+
+
+
+
+
+x
+n
++
+
+
+n
+
+
+
+
+n
++
+x
+
+
+
+ln
+⁡
+
+(
+
+1
++
+
+
+x
+
+n
+
+
+n
+
+
+
+
+
+
+)
+
+
+
+{\textstyle \sum \limits \_{n=1}^{\infty }{\frac {xn+{\sqrt {n}}}{n+x}}\ln \left(1+{\frac {x}{n{\sqrt {n}}}}\right)}
+
+![{\textstyle \sum \limits _{n=1}^{\infty }{\frac {xn+{\sqrt {n}}}{n+x}}\ln \left(1+{\frac {x}{n{\sqrt {n}}}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/633e458aace66350ea9ed9586785ddcfb7b0091f), 
+
+
+
+
+Δ
+
+1
+
+
+=
+(
+0
+;
+1
+)
+
+
+{\textstyle \Delta \_{1}=(0;1)}
+
+![{\textstyle \Delta _{1}=(0;1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1c54e8b5a3c4d79037b0711372b6689de58b6e4d), 
+
+
+
+
+Δ
+
+2
+
+
+=
+(
+1
+;
++
+∞
+)
+
+
+{\textstyle \Delta \_{2}=(1;+\infty )}
+
+![{\textstyle \Delta _{2}=(1;+\infty )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3da88d3477a5cc6c7f3a8fcfd468e4202bf6d1b9);
+2. Show that sequence 
+
+
+
+
+f
+
+n
+
+
+(
+x
+)
+=
+
+
+
+sin
+⁡
+n
+x
+
+
+n
+
+
+
+
+
+{\textstyle f\_{n}(x)={\frac {\sin nx}{\sqrt {n}}}}
+
+![{\textstyle f_{n}(x)={\frac {\sin nx}{\sqrt {n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b01913798491ead471b64c411c026cb5d9f77919) converges uniformly on 
+
+
+
+
+R
+
+
+
+{\textstyle \mathbb {R} }
+
+![{\textstyle \mathbb {R} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/2031b33f0faf73d2d73a1da12544f00a37474f16) to a differentiable function 
+
+
+
+f
+(
+x
+)
+
+
+{\textstyle f(x)}
+
+![{\textstyle f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0a982c6635ab3b98d9e12d5f5a8533359bcb38a), and at that 
+
+
+
+
+lim
+
+n
+→
++
+∞
+
+
+
+f
+
+n
+
+′
+
+(
+0
+)
+≠
+
+f
+′
+
+(
+0
+)
+
+
+{\textstyle \lim \limits \_{n\rightarrow +\infty }f'\_{n}(0)\neq f'(0)}
+
+![{\textstyle \lim \limits _{n\rightarrow +\infty }f'_{n}(0)\neq f'(0)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5bbe4b0d69f8fa0731a27506b57b049c891e3402).
+
+
+### Section 1
+
+
+#### Section title:
+
+
+Integrals with Parameter(s)
+
+
+
+### Topics covered in this section:
+
+
+* Definite integrals with parameters
+* Improper integrals with parameters. Uniform convergence
+* Properties of uniformly convergent integrals
+* Beta-function and gamma-function
+* Fourier transform
+
+
+### What forms of evaluation were used to test students’ performance in this section?
+
+
+
+
+|  | **Yes/No** |
+| --- | --- |
+| Development of individual parts of software product code
+ | 0
+ |
+| Homework and group projects
+ | 1
+ |
+| Midterm evaluation
+ | 1
+ |
+| Testing (written or computer based)
+ | 1
+ |
+| Reports
+ | 0
+ |
+| Essays
+ | 0
+ |
+| Oral polls
+ | 0
+ |
+| Discussions
+ | 1
+ |
+
+
+### Typical questions for ongoing performance evaluation within this section
+
+
+1. Find out if 
+
+
+
+
+
+∫
+
+0
+
+
+1
+
+
+
+(
+
+
+lim
+
+α
+→
+0
+
+
+
+
+
+2
+x
+
+α
+
+2
+
+
+
+
+
+(
+
+
+α
+
+2
+
+
++
+
+x
+
+2
+
+
+
+)
+
+
+2
+
+
+
+
+
+)
+
+
+d
+x
+=
+
+lim
+
+α
+→
+0
+
+
+
+∫
+
+0
+
+
+1
+
+
+
+
+
+2
+x
+
+α
+
+2
+
+
+
+
+
+(
+
+
+α
+
+2
+
+
++
+
+x
+
+2
+
+
+
+)
+
+
+2
+
+
+
+
+
+d
+x
+
+
+
+{\textstyle \displaystyle \int \limits \_{0}^{1}\left(\lim \limits \_{\alpha \to 0}{\frac {2x\alpha ^{2}}{\left(\alpha ^{2}+x^{2}\right)^{2}}}\right)\,dx=\lim \limits \_{\alpha \to 0}\int \limits \_{0}^{1}{\frac {2x\alpha ^{2}}{\left(\alpha ^{2}+x^{2}\right)^{2}}}\,dx}
+
+![{\textstyle \displaystyle \int \limits _{0}^{1}\left(\lim \limits _{\alpha \to 0}{\frac {2x\alpha ^{2}}{\left(\alpha ^{2}+x^{2}\right)^{2}}}\right)\,dx=\lim \limits _{\alpha \to 0}\int \limits _{0}^{1}{\frac {2x\alpha ^{2}}{\left(\alpha ^{2}+x^{2}\right)^{2}}}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2584f0a98c545141bcac904a0c1a37b2b3d1bada).
+2. Differentiating the integrals with respect to parameter 
+
+
+
+φ
+
+
+{\textstyle \varphi }
+
+![{\textstyle \varphi }](https://wikimedia.org/api/rest_v1/media/math/render/svg/99015519246670af1cb5592e439ad64a27fb4830), find it: 
+
+
+
+I
+(
+α
+)
+=
+
+∫
+
+0
+
+
+π
+
+/
+
+2
+
+
+ln
+⁡
+
+(
+
+
+α
+
+2
+
+
+−
+
+sin
+
+2
+
+
+⁡
+φ
+
+)
+
+
+d
+φ
+
+
+{\textstyle I(\alpha )=\int \limits \_{0}^{\pi /2}\ln \left(\alpha ^{2}-\sin ^{2}\varphi \right)\,d\varphi }
+
+![{\textstyle I(\alpha )=\int \limits _{0}^{\pi /2}\ln \left(\alpha ^{2}-\sin ^{2}\varphi \right)\,d\varphi }](https://wikimedia.org/api/rest_v1/media/math/render/svg/181b98d5fb603e05a6a64798b9099a29d7af21bb), 
+
+
+
+α
+>
+1
+
+
+{\textstyle \alpha >1}
+
+![{\textstyle \alpha >1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/77a6bb580edc9bebe0369a6c0e1eb7aa3a2fb39a).
+3. Prove that the following integral converges uniformly on the indicated set. 
+
+
+
+
+
+∫
+
+0
+
+
++
+∞
+
+
+
+e
+
+−
+α
+x
+
+
+cos
+⁡
+2
+x
+
+d
+x
+
+
+
+{\textstyle \displaystyle \int \limits \_{0}^{+\infty }e^{-\alpha x}\cos 2x\,dx}
+
+![{\textstyle \displaystyle \int \limits _{0}^{+\infty }e^{-\alpha x}\cos 2x\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ecc6145eb14a1ffea9f326df53ec147091507d8), 
+
+
+
+Δ
+=
+[
+1
+;
++
+∞
+)
+
+
+{\textstyle \Delta =[1;+\infty )}
+
+![{\textstyle \Delta =[1;+\infty )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fec69fd24d288553b369186751d5dacf9e2b0b9b);
+4. It is known that Dirichlet’s integral 
+
+
+
+
+∫
+
+0
+
+
++
+∞
+
+
+
+
+
+sin
+⁡
+x
+
+x
+
+
+
+d
+x
+
+
+{\textstyle \int \limits \_{0}^{+\infty }{\frac {\sin x}{x}}\,dx}
+
+![{\textstyle \int \limits _{0}^{+\infty }{\frac {\sin x}{x}}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/425b3fcfc6b0bf0eb1b06971b0e0876121010af0) is equal to 
+
+
+
+
+
+π
+2
+
+
+
+
+{\textstyle {\frac {\pi }{2}}}
+
+![{\textstyle {\frac {\pi }{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/313947d4107765408f902d3eaee6a719e7f01dae). Find the values of the following integrals using Dirichlet’s integral
+	1. ∫
+	
+	0
+	
+	
+	+
+	∞
+	
+	
+	
+	
+	sin
+	
+	α
+	x
+	
+	
+	
+	x
+	
+	d
+	x
+	
+	
+	{\textstyle \int \limits \_{0}^{+\infty }{\frac {\sin }{\alpha x}}x\,dx}
+	
+	![{\textstyle \int \limits _{0}^{+\infty }{\frac {\sin }{\alpha x}}x\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9258657dddf0c5f4665ac3cbe4005eba785c9b2e), 
+	
+	
+	
+	α
+	≠
+	0
+	
+	
+	{\textstyle \alpha \neq 0}
+	
+	![{\textstyle \alpha \neq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c2250c614e2711ae1e99c559b55902c9f213f0f6);
+	2. ∫
+	
+	0
+	
+	
+	+
+	∞
+	
+	
+	
+	
+	
+	sin
+	⁡
+	x
+	−
+	x
+	cos
+	⁡
+	x
+	
+	
+	x
+	
+	3
+	
+	
+	
+	
+	
+	d
+	x
+	
+	
+	{\textstyle \int \limits \_{0}^{+\infty }{\frac {\sin x-x\cos x}{x^{3}}}\,dx}
+	
+	![{\textstyle \int \limits _{0}^{+\infty }{\frac {\sin x-x\cos x}{x^{3}}}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4c41656006e60835bc2ee22cc9f54b55f63fe6d2).
+
+
+### Typical questions for seminar classes (labs) within this section
+
+
+1. Find out if 
+
+
+
+
+
+∫
+
+0
+
+
+1
+
+
+
+(
+
+
+∫
+
+0
+
+
+1
+
+
+f
+(
+x
+,
+α
+)
+
+d
+α
+
+)
+
+
+d
+x
+=
+
+∫
+
+0
+
+
+1
+
+
+
+(
+
+
+∫
+
+0
+
+
+1
+
+
+f
+(
+x
+,
+α
+)
+
+d
+x
+
+)
+
+
+d
+α
+
+
+
+{\textstyle \displaystyle \int \limits \_{0}^{1}\left(\int \limits \_{0}^{1}f(x,\alpha )\,d\alpha \right)\,dx=\int \limits \_{0}^{1}\left(\int \limits \_{0}^{1}f(x,\alpha )\,dx\right)\,d\alpha }
+
+![{\textstyle \displaystyle \int \limits _{0}^{1}\left(\int \limits _{0}^{1}f(x,\alpha )\,d\alpha \right)\,dx=\int \limits _{0}^{1}\left(\int \limits _{0}^{1}f(x,\alpha )\,dx\right)\,d\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/cee1e6d0944c1aaea36afba56d6075217953bb85) if 
+
+
+
+f
+(
+x
+;
+α
+)
+=
+
+
+
+α
+−
+x
+
+
+(
+α
++
+x
+
+)
+
+3
+
+
+
+
+
+
+
+{\textstyle f(x;\alpha )={\frac {\alpha -x}{(\alpha +x)^{3}}}}
+
+![{\textstyle f(x;\alpha )={\frac {\alpha -x}{(\alpha +x)^{3}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dc9c85d7bd50ebdf0924dc3b64407e78feb21300).
+2. Find 
+
+
+
+
+Φ
+′
+
+(
+α
+)
+
+
+{\textstyle \Phi '(\alpha )}
+
+![{\textstyle \Phi '(\alpha )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8047208a7b2d408b6cd8e6c9250ccf1d4c76c558) if 
+
+
+
+Φ
+(
+α
+)
+=
+
+∫
+
+1
+
+
+2
+
+
+
+
+
+e
+
+α
+
+x
+
+2
+
+
+
+
+x
+
+
+
+d
+x
+
+
+{\textstyle \Phi (\alpha )=\int \limits \_{1}^{2}{\frac {e^{\alpha x^{2}}}{x}}\,dx}
+
+![{\textstyle \Phi (\alpha )=\int \limits _{1}^{2}{\frac {e^{\alpha x^{2}}}{x}}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/617c37a94758ea74e6b211d64ef9f98dfdc0f00c).
+3. Differentiating the integral with respect to parameter 
+
+
+
+α
+
+
+{\textstyle \alpha }
+
+![{\textstyle \alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d86dbd6183264b2f8569da1751380b173c7b185), find it: 
+
+
+
+I
+(
+α
+)
+=
+
+∫
+
+0
+
+
+π
+
+
+
+
+1
+
+cos
+⁡
+x
+
+
+
+ln
+⁡
+
+
+
+1
++
+α
+cos
+⁡
+x
+
+
+1
+−
+α
+cos
+⁡
+x
+
+
+
+
+d
+x
+
+
+{\textstyle I(\alpha )=\int \limits \_{0}^{\pi }{\frac {1}{\cos x}}\ln {\frac {1+\alpha \cos x}{1-\alpha \cos x}}\,dx}
+
+![{\textstyle I(\alpha )=\int \limits _{0}^{\pi }{\frac {1}{\cos x}}\ln {\frac {1+\alpha \cos x}{1-\alpha \cos x}}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a92283d198c15b51ddb805f720f9926f2531a081), 
+
+
+
+
+|
+
+α
+
+|
+
+<
+1
+
+
+{\textstyle |\alpha |<1}
+
+![{\textstyle |\alpha |<1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3f3bc8657b6c933b86ca3a8eaec06cea2ce9ba5e).
+4. Find Fourier transform of the following functions:
+	1. f
+	(
+	x
+	)
+	=
+	
+	
+	{
+	
+	
+	
+	1
+	,
+	
+	
+	
+	|
+	
+	x
+	
+	|
+	
+	≤
+	1
+	,
+	
+	
+	
+	
+	0
+	,
+	
+	
+	
+	|
+	
+	x
+	
+	|
+	
+	>
+	1
+	;
+	
+	
+	
+	
+	
+	
+	
+	
+	{\textstyle f(x)={\begin{cases}1,&|x|\leq 1,\\0,&|x|>1;\end{cases}}}
+	
+	![{\textstyle f(x)={\begin{cases}1,&|x|\leq 1,\\0,&|x|>1;\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/761e36a557a92fc780c53dc0a2244d0f77575d6c)
+5. Let 
+
+
+
+
+
+
+f
+^
+
+
+
+(
+y
+)
+
+
+{\textstyle {\widehat {f}}(y)}
+
+![{\textstyle {\widehat {f}}(y)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7c96d3e1f2527643d3e650c7ceef5a050a68b877) be Fourier transform of 
+
+
+
+f
+(
+x
+)
+
+
+{\textstyle f(x)}
+
+![{\textstyle f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0a982c6635ab3b98d9e12d5f5a8533359bcb38a). Prove that Fourier transform of 
+
+
+
+
+e
+
+i
+α
+x
+
+
+f
+(
+x
+)
+
+
+{\textstyle e^{i\alpha x}f(x)}
+
+![{\textstyle e^{i\alpha x}f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c7c37e6524c1b14a0a114dce723ad9d75c431f55) is equal to 
+
+
+
+
+
+
+f
+^
+
+
+
+(
+y
+−
+α
+)
+
+
+{\textstyle {\widehat {f}}(y-\alpha )}
+
+![{\textstyle {\widehat {f}}(y-\alpha )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e67a18b35a42889d04a5a61ada189ddfee0d1509), 
+
+
+
+α
+∈
+
+R
+
+
+
+{\textstyle \alpha \in \mathbb {R} }
+
+![{\textstyle \alpha \in \mathbb {R} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/0e51aa19934069aa0256691a8bdb2703ba20459d).
+
+
+### Test questions for final assessment in this section
+
+
+1. Find out if 
+
+
+
+
+
+∫
+
+0
+
+
+1
+
+
+
+(
+
+
+∫
+
+0
+
+
+1
+
+
+f
+(
+x
+,
+α
+)
+
+d
+α
+
+)
+
+
+d
+x
+=
+
+∫
+
+0
+
+
+1
+
+
+
+(
+
+
+∫
+
+0
+
+
+1
+
+
+f
+(
+x
+,
+α
+)
+
+d
+x
+
+)
+
+
+d
+α
+
+
+
+{\textstyle \displaystyle \int \limits \_{0}^{1}\left(\int \limits \_{0}^{1}f(x,\alpha )\,d\alpha \right)\,dx=\int \limits \_{0}^{1}\left(\int \limits \_{0}^{1}f(x,\alpha )\,dx\right)\,d\alpha }
+
+![{\textstyle \displaystyle \int \limits _{0}^{1}\left(\int \limits _{0}^{1}f(x,\alpha )\,d\alpha \right)\,dx=\int \limits _{0}^{1}\left(\int \limits _{0}^{1}f(x,\alpha )\,dx\right)\,d\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/cee1e6d0944c1aaea36afba56d6075217953bb85) if 
+
+
+
+f
+(
+x
+;
+α
+)
+=
+
+
+
+
+α
+
+2
+
+
+−
+
+x
+
+2
+
+
+
+
+
+(
+
+
+α
+
+2
+
+
++
+
+x
+
+2
+
+
+
+)
+
+
+2
+
+
+
+
+
+
+{\textstyle f(x;\alpha )={\frac {\alpha ^{2}-x^{2}}{\left(\alpha ^{2}+x^{2}\right)^{2}}}}
+
+![{\textstyle f(x;\alpha )={\frac {\alpha ^{2}-x^{2}}{\left(\alpha ^{2}+x^{2}\right)^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ad3db9eccd713138b87c03d7c3f05a00070a2405).
+2. Find 
+
+
+
+
+Φ
+′
+
+(
+α
+)
+
+
+{\textstyle \Phi '(\alpha )}
+
+![{\textstyle \Phi '(\alpha )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8047208a7b2d408b6cd8e6c9250ccf1d4c76c558) if 
+
+
+
+Φ
+(
+α
+)
+=
+
+∫
+
+0
+
+
+α
+
+
+
+
+
+ln
+⁡
+(
+1
++
+α
+x
+)
+
+x
+
+
+
+d
+x
+
+
+{\textstyle \Phi (\alpha )=\int \limits \_{0}^{\alpha }{\frac {\ln(1+\alpha x)}{x}}\,dx}
+
+![{\textstyle \Phi (\alpha )=\int \limits _{0}^{\alpha }{\frac {\ln(1+\alpha x)}{x}}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/43d164fbebb756a47ff129f0db4d9fe3fa5f03fc).
+3. Prove that the following integral converges uniformly on the indicated set. 
+
+
+
+
+
+∫
+
+−
+∞
+
+
++
+∞
+
+
+
+
+
+cos
+⁡
+α
+x
+
+
+4
++
+
+x
+
+2
+
+
+
+
+
+
+d
+x
+
+
+
+{\textstyle \displaystyle \int \limits \_{-\infty }^{+\infty }{\frac {\cos \alpha x}{4+x^{2}}}\,dx}
+
+![{\textstyle \displaystyle \int \limits _{-\infty }^{+\infty }{\frac {\cos \alpha x}{4+x^{2}}}\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/885d09aefe0e523d4d5136a7edb22d0f13b21e3f), 
+
+
+
+Δ
+=
+
+R
+
+
+
+{\textstyle \Delta =\mathbb {R} }
+
+![{\textstyle \Delta =\mathbb {R} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/6467f37ddb43f890061ce5b6e5d7f98a41952efa);
+4. Find Fourier integral for 
+
+
+
+f
+(
+x
+)
+=
+
+
+{
+
+
+
+1
+,
+
+
+
+|
+
+x
+
+|
+
+≤
+τ
+,
+
+
+
+
+0
+,
+
+
+
+|
+
+x
+
+|
+
+>
+τ
+;
+
+
+
+
+
+
+
+
+{\textstyle f(x)={\begin{cases}1,&|x|\leq \tau ,\\0,&|x|>\tau ;\end{cases}}}
+
+![{\textstyle f(x)={\begin{cases}1,&|x|\leq \tau ,\\0,&|x|>\tau ;\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/83e284e1e648c9781bac545652c249d6ae375951)
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__mathematical_analysis_ii.s23.md

@@ -0,0 +1,2383 @@
+
+
+
+
+
+
+
+BSc: Mathematical Analysis II.s23
+=================================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Mathematical Analysis II](#Mathematical_Analysis_II)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Course Topics](#Course_Topics)
+	+ [1.3 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.3.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.3.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.3.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.3.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.3.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.4 Grading](#Grading)
+		- [1.4.1 Course grading range](#Course_grading_range)
+		- [1.4.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.4.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.5 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.5.1 Open access resources](#Open_access_resources)
+	+ [1.6 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [1.7 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [1.7.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [1.7.1.1 Section 1](#Section_1)
+			* [1.7.1.2 Section 2](#Section_2)
+			* [1.7.1.3 Section 3](#Section_3)
+			* [1.7.1.4 Section 4](#Section_4)
+		- [1.7.2 Final assessment](#Final_assessment)
+			* [1.7.2.1 Section 1](#Section_1_2)
+			* [1.7.2.2 Section 2](#Section_2_2)
+			* [1.7.2.3 Section 3](#Section_3_2)
+			* [1.7.2.4 Section 4](#Section_4_2)
+		- [1.7.3 The retake exam](#The_retake_exam)
+
+
+
+Mathematical Analysis II
+========================
+
+
+* **Course name**: Mathematical Analysis II
+* **Code discipline**: CSE203
+* **Subject area**: Math
+
+
+Short Description
+-----------------
+
+
+* Series: convergence, approximation
+* Multivariate calculus: derivatives, differentials, maxima and minima
+* Multivariate integration
+* Basics of vector analysis
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Infinite Series | 1. The Sum of an Infinite Series
+2. The Comparison Test
+3. The Integral and Ratio Tests
+4. Alternating Series
+5. Power Series
+6. Taylor's Formula
+ |
+| Partial Differentiation | 1. Limits of functions of several variables
+2. Introduction to Partial Derivatives
+3. The Chain Rule
+4. Gradients
+5. Level Surfaces and Implicit Differentiation
+6. Maximas and Minimas
+7. Constrained Extrema and Lagrange Multipliers
+ |
+| Multiple Integration | 1. The Double Integral and Iterated Integral
+2. The Double Integral over General Region
+3. Integrals in Polar coordinates, Substitutions in the double integrals
+4. Integrals in Cylindrical and Spherical Coordinates
+5. Applications of the Double and Triple Integrals
+ |
+| Vector Analysis | 1. Line Integrals, Path Independence
+2. Exact Differentials
+3. Green’s Theorem
+4. Circulation and Stoke’s Theorem
+5. Flux and Divergence Theorem
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+The goal of the course is to study basic mathematical concepts that will be required in further studies. The course is based on Mathematical Analysis I, and the concepts studied there are widely used in this course. The course covers differentiation and integration of functions of several variables. Some more advanced concepts, as uniform convergence of series and integrals, are also considered, since they are important for understanding applicability of many theorems of mathematical analysis. In the end of the course some useful applications are covered, such as gamma-function, beta-function, and Fourier transform.
+
+
+
+### ILOs defined at three levels
+
+
+We specify the intended learning outcomes at three levels: conceptual knowledge, practical skills, and comprehensive skills.
+
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* know how to find minima and maxima of a function subject to a constraint
+* know how to represent double integrals as iterated integrals and vice versa
+* know what the length of a curve and the area of a surface is
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* find partial and directional derivatives of functions of several variables;
+* find maxima and minima for a function of several variables
+* use Fubini theorem for calculating multiple integrals
+* calculate line and path integrals
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* find multiple, path, surface integrals
+* find the range of a function in a given domain
+* decompose a function into infinite series
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Fail | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Midterm | 20
+ |
+| Quizzes | 28 (2 for each)
+ |
+| Final exam | 50
+ |
+| In-class participation | 7 (including 5 extras)
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+* Participation is important. Attending lectures is the key to success in this course.
+* Review lecture materials before classes to do well.
+* Reading the recommended literature is obligatory, and will give you a deeper understanding of the material.
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Jerrold E. Marsden and Alan Weinstein, Calculus I, II, and II. Springer-Verlag, Second Edition 1985 [link](https://www.cds.caltech.edu/~marsden/volume/Calculus/)
+* Robert A. Adams, Christopher Essex (2017) Calculus. A Complete Course, Pearson
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Teaching and Learning Methods within each section
+| Teaching Techniques | Section 1 | Section 2 | Section 3 | Section 4
+ |
+| --- | --- | --- | --- | --- |
+| Problem-based learning (students learn by solving open-ended problems without a strictly-defined solution) | 0 | 0 | 0 | 0
+ |
+| Project-based learning (students work on a project) | 0 | 0 | 0 | 0
+ |
+| Modular learning (facilitated self-study) | 0 | 0 | 0 | 0
+ |
+| Differentiated learning (provide tasks and activities at several levels of difficulty to fit students needs and level) | 1 | 1 | 1 | 1
+ |
+| Contextual learning (activities and tasks are connected to the real world to make it easier for students to relate to them) | 0 | 0 | 0 | 0
+ |
+| Business game (learn by playing a game that incorporates the principles of the material covered within the course) | 0 | 0 | 0 | 0
+ |
+| Inquiry-based learning | 0 | 0 | 0 | 0
+ |
+| Just-in-time teaching | 0 | 0 | 0 | 0
+ |
+| Process oriented guided inquiry learning (POGIL) | 0 | 0 | 0 | 0
+ |
+| Studio-based learning | 0 | 0 | 0 | 0
+ |
+| Universal design for learning | 0 | 0 | 0 | 0
+ |
+| Task-based learning | 0 | 0 | 0 | 0
+ |
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3 | Section 4
+ |
+| --- | --- | --- | --- | --- |
+| Lectures | 1 | 1 | 1 | 1
+ |
+| Interactive Lectures | 1 | 1 | 1 | 1
+ |
+| Lab exercises | 1 | 1 | 1 | 1
+ |
+| Experiments | 0 | 0 | 0 | 0
+ |
+| Modeling | 0 | 0 | 0 | 0
+ |
+| Cases studies | 0 | 0 | 0 | 0
+ |
+| Development of individual parts of software product code | 0 | 0 | 0 | 0
+ |
+| Individual Projects | 0 | 0 | 0 | 0
+ |
+| Group projects | 0 | 0 | 0 | 0
+ |
+| Flipped classroom | 0 | 0 | 0 | 0
+ |
+| Quizzes (written or computer based) | 1 | 1 | 1 | 1
+ |
+| Peer Review | 0 | 0 | 0 | 0
+ |
+| Discussions | 1 | 1 | 1 | 1
+ |
+| Presentations by students | 0 | 0 | 0 | 0
+ |
+| Written reports | 0 | 0 | 0 | 0
+ |
+| Simulations and role-plays | 0 | 0 | 0 | 0
+ |
+| Essays | 0 | 0 | 0 | 0
+ |
+| Oral Reports | 0 | 0 | 0 | 0
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+1. Derive the Maclaurin expansion for 
+
+
+
+f
+(
+x
+)
+=
+
+
+
+1
++
+
+e
+
+−
+2
+x
+
+
+
+
+3
+
+
+
+
+
+{\textstyle f(x)={\sqrt[{3}]{1+e^{-2x}}}}
+
+![{\textstyle f(x)={\sqrt[{3}]{1+e^{-2x}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/14bfa69ed7bcfd7de396a3360c031c64292828b3) up to 
+
+
+
+o
+
+(
+
+x
+
+3
+
+
+)
+
+
+
+{\textstyle o\left(x^{3}\right)}
+
+![{\textstyle o\left(x^{3}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2e23f841ca36ac3c4d7ccc3920dbe12d69f5b304).
+2. Find 
+
+
+
+
+lim
+
+x
+→
+0
+
+
+
+lim
+
+y
+→
+0
+
+
+u
+(
+x
+;
+y
+)
+
+
+{\textstyle \lim \limits \_{x\to 0}\lim \limits \_{y\to 0}u(x;y)}
+
+![{\textstyle \lim \limits _{x\to 0}\lim \limits _{y\to 0}u(x;y)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/41fcf6ef0f4de155d38dc7b27a24cb3be9c95abc), 
+
+
+
+
+lim
+
+y
+→
+0
+
+
+
+lim
+
+x
+→
+0
+
+
+u
+(
+x
+;
+y
+)
+
+
+{\textstyle \lim \limits \_{y\to 0}\lim \limits \_{x\to 0}u(x;y)}
+
+![{\textstyle \lim \limits _{y\to 0}\lim \limits _{x\to 0}u(x;y)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/30b9ab013043fea23bc9bc3584592aa95379e778) and 
+
+
+
+
+lim
+
+(
+x
+;
+y
+)
+→
+(
+0
+;
+0
+)
+
+
+u
+(
+x
+;
+y
+)
+
+
+{\textstyle \lim \limits \_{(x;y)\to (0;0)}u(x;y)}
+
+![{\textstyle \lim \limits _{(x;y)\to (0;0)}u(x;y)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f181440f0fe3a34a0575a79be4be5e8e6aa37957) if 
+
+
+
+u
+(
+x
+;
+y
+)
+=
+
+
+
+
+x
+
+2
+
+
+y
++
+x
+
+y
+
+2
+
+
+
+
+
+x
+
+2
+
+
+−
+x
+y
++
+
+y
+
+2
+
+
+
+
+
+
+
+{\textstyle u(x;y)={\frac {x^{2}y+xy^{2}}{x^{2}-xy+y^{2}}}}
+
+![{\textstyle u(x;y)={\frac {x^{2}y+xy^{2}}{x^{2}-xy+y^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb7a5e54b99cd1e3fd00b1f8ae13ab79a21e5f56).
+
+
+#### Section 2
+
+
+1. Find the differential of a function: (a) 
+
+
+
+u
+(
+x
+;
+y
+)
+=
+ln
+⁡
+
+(
+
+x
++
+
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+
+
+
+)
+
+
+
+{\textstyle u(x;y)=\ln \left(x+{\sqrt {x^{2}+y^{2}}}\right)}
+
+![{\textstyle u(x;y)=\ln \left(x+{\sqrt {x^{2}+y^{2}}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5cc7b02dad3ea12644b4ecadf08fcaa6405d4529); (b) 
+
+
+
+u
+(
+x
+;
+y
+)
+=
+ln
+⁡
+sin
+⁡
+
+
+
+x
++
+1
+
+
+y
+
+
+
+
+
+{\textstyle u(x;y)=\ln \sin {\frac {x+1}{\sqrt {y}}}}
+
+![{\textstyle u(x;y)=\ln \sin {\frac {x+1}{\sqrt {y}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1c25c88f1c0c5fda11150ba0fe2212b28a40ecc7).
+2. Find the differential of 
+
+
+
+u
+(
+x
+;
+y
+)
+
+
+{\textstyle u(x;y)}
+
+![{\textstyle u(x;y)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/feeabc2f3e55a2a2f72b6ec04a08c1315c08699e) given implicitly by an equation 
+
+
+
+
+x
+
+3
+
+
++
+2
+
+y
+
+3
+
+
++
+
+u
+
+3
+
+
+−
+3
+x
+y
+u
++
+2
+y
+−
+3
+=
+0
+
+
+{\textstyle x^{3}+2y^{3}+u^{3}-3xyu+2y-3=0}
+
+![{\textstyle x^{3}+2y^{3}+u^{3}-3xyu+2y-3=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/911701538f15cf656e0dd261ad813f9c8a2c93f9) at points 
+
+
+
+M
+(
+1
+;
+1
+;
+1
+)
+
+
+{\textstyle M(1;1;1)}
+
+![{\textstyle M(1;1;1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/97b7d6ccd5c6763a4d4ea7e712c393483057239d) and 
+
+
+
+N
+(
+1
+;
+1
+;
+−
+2
+)
+
+
+{\textstyle N(1;1;-2)}
+
+![{\textstyle N(1;1;-2)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/00c66cfa579443b4e19dcd7f9348d1ae9dfce8d4).
+3. Find maxima and minima of a function subject to a constraint (or several constraints):
+	1. u
+	=
+	
+	x
+	
+	2
+	
+	
+	
+	y
+	
+	3
+	
+	
+	
+	z
+	
+	4
+	
+	
+	
+	
+	{\textstyle u=x^{2}y^{3}z^{4}}
+	
+	![{\textstyle u=x^{2}y^{3}z^{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e9178002e5b4a33a04c2d25eb41d3311427efe6d), 
+	
+	
+	
+	2
+	x
+	+
+	3
+	y
+	+
+	4
+	z
+	=
+	18
+	
+	
+	{\textstyle 2x+3y+4z=18}
+	
+	![{\textstyle 2x+3y+4z=18}](https://wikimedia.org/api/rest_v1/media/math/render/svg/85a5abaa6c5cd03742a1c4a119e9c686645f2018), 
+	
+	
+	
+	x
+	>
+	0
+	
+	
+	{\textstyle x>0}
+	
+	![{\textstyle x>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4bd6212b5a778bded18868fc5cd19eb3b15844a0), 
+	
+	
+	
+	y
+	>
+	0
+	
+	
+	{\textstyle y>0}
+	
+	![{\textstyle y>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bad11e7747271c5d6ebd668b512129802597fc5c), 
+	
+	
+	
+	z
+	>
+	0
+	
+	
+	{\textstyle z>0}
+	
+	![{\textstyle z>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f3045a2beda2df2d38cfc9478a0eea2ddb453540);
+	2. u
+	=
+	x
+	−
+	y
+	+
+	2
+	z
+	
+	
+	{\textstyle u=x-y+2z}
+	
+	![{\textstyle u=x-y+2z}](https://wikimedia.org/api/rest_v1/media/math/render/svg/193769ce94ad54f9791ac7b0ebf6f4036bff6c79), 
+	
+	
+	
+	
+	x
+	
+	2
+	
+	
+	+
+	
+	y
+	
+	2
+	
+	
+	+
+	2
+	
+	z
+	
+	2
+	
+	
+	=
+	16
+	
+	
+	{\textstyle x^{2}+y^{2}+2z^{2}=16}
+	
+	![{\textstyle x^{2}+y^{2}+2z^{2}=16}](https://wikimedia.org/api/rest_v1/media/math/render/svg/84686b9dcda37f369eea56991236263c2a9de909);
+	3. u
+	=
+	
+	∑
+	
+	i
+	=
+	1
+	
+	
+	k
+	
+	
+	
+	a
+	
+	i
+	
+	
+	
+	x
+	
+	i
+	
+	
+	2
+	
+	
+	
+	
+	{\textstyle u=\sum \limits \_{i=1}^{k}a\_{i}x\_{i}^{2}}
+	
+	![{\textstyle u=\sum \limits _{i=1}^{k}a_{i}x_{i}^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8e3b99d12ee0032f9ceed49b13a60ce96318791f), 
+	
+	
+	
+	
+	∑
+	
+	i
+	=
+	1
+	
+	
+	k
+	
+	
+	
+	x
+	
+	i
+	
+	
+	=
+	1
+	
+	
+	{\textstyle \sum \limits \_{i=1}^{k}x\_{i}=1}
+	
+	![{\textstyle \sum \limits _{i=1}^{k}x_{i}=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7cb5ca3b9867373e2fafdbb2b03a4566e3dfdd01), 
+	
+	
+	
+	
+	a
+	
+	i
+	
+	
+	>
+	0
+	
+	
+	{\textstyle a\_{i}>0}
+	
+	![{\textstyle a_{i}>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/38bcfd15c6b9a443175f08979d756ae989ab5b2d);
+
+
+#### Section 3
+
+
+1. Represent double integrals below as an iterated integrals (or a sum of iterated integrals) with different orders of integration: 
+
+
+
+
+∬
+
+D
+
+
+f
+(
+x
+;
+y
+)
+
+d
+x
+
+d
+y
+
+
+{\textstyle \iint \limits \_{D}f(x;y)\,dx\,dy}
+
+![{\textstyle \iint \limits _{D}f(x;y)\,dx\,dy}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e2b52bb56df4ec7f5416ec2e32f0903b2e1197b9) where 
+
+
+
+D
+=
+
+{
+
+(
+x
+;
+y
+)
+
+|
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+≤
+9
+,
+
+
+x
+
+2
+
+
++
+(
+y
++
+4
+
+)
+
+2
+
+
+≥
+25
+
+
+
+
+}
+
+
+
+{\textstyle D=\left\{(x;y)\left|x^{2}+y^{2}\leq 9,\,x^{2}+(y+4)^{2}\geq 25\right.\right\}}
+
+![{\textstyle D=\left\{(x;y)\left|x^{2}+y^{2}\leq 9,\,x^{2}+(y+4)^{2}\geq 25\right.\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cbf78bafb60b17a34676ba32d3cda4bb45f3c75e).
+2. Represent integral 
+
+
+
+I
+=
+
+
+∭
+
+D
+
+
+f
+(
+x
+;
+y
+;
+z
+)
+
+d
+x
+
+d
+y
+
+d
+z
+
+
+
+{\textstyle I=\displaystyle \iiint \limits \_{D}f(x;y;z)\,dx\,dy\,dz}
+
+![{\textstyle I=\displaystyle \iiint \limits _{D}f(x;y;z)\,dx\,dy\,dz}](https://wikimedia.org/api/rest_v1/media/math/render/svg/860cffcd0fc93fae6ac55ac594c5fa8928880ffb) as iterated integrals with all possible (i.e. 6) orders of integration; 
+
+
+
+D
+
+
+{\textstyle D}
+
+![{\textstyle D}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4e5200f518cb5afe304ec42ffdd4f6c63c702f77) is bounded by 
+
+
+
+x
+=
+0
+
+
+{\textstyle x=0}
+
+![{\textstyle x=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/95946e5db8fcf9ae99523bcd4f83433c8b2e441e), 
+
+
+
+x
+=
+a
+
+
+{\textstyle x=a}
+
+![{\textstyle x=a}](https://wikimedia.org/api/rest_v1/media/math/render/svg/70e0fe729bde9223f1b509db0471471c21261b82), 
+
+
+
+y
+=
+0
+
+
+{\textstyle y=0}
+
+![{\textstyle y=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5c4b2729074b444ef801a0afa24160d074b52eec), 
+
+
+
+y
+=
+
+
+a
+x
+
+
+
+
+{\textstyle y={\sqrt {ax}}}
+
+![{\textstyle y={\sqrt {ax}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/acdf89c1a5d352bac27ef5bd553c3c3e2b07f8e3), 
+
+
+
+z
+=
+0
+
+
+{\textstyle z=0}
+
+![{\textstyle z=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0829ff59a6fdc19b44396956e8767fac4ba87ba3), 
+
+
+
+z
+=
+x
++
+y
+
+
+{\textstyle z=x+y}
+
+![{\textstyle z=x+y}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a04ad39377ab70df2722495d428ad59389561311).
+3. Change order of integration in the iterated integral 
+
+
+
+
+∫
+
+0
+
+
+
+2
+
+
+
+d
+y
+
+∫
+
+y
+
+
+
+4
+−
+
+y
+
+2
+
+
+
+
+
+f
+(
+x
+;
+y
+)
+
+d
+x
+
+
+{\textstyle \int \limits \_{0}^{\sqrt {2}}dy\int \limits \_{y}^{\sqrt {4-y^{2}}}f(x;y)\,dx}
+
+![{\textstyle \int \limits _{0}^{\sqrt {2}}dy\int \limits _{y}^{\sqrt {4-y^{2}}}f(x;y)\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ed028a999470345e5f3d630c5d992c8c67156e84).
+4. Find the volume of a solid given by 
+
+
+
+0
+≤
+z
+≤
+
+x
+
+2
+
+
+
+
+{\textstyle 0\leq z\leq x^{2}}
+
+![{\textstyle 0\leq z\leq x^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/980fd1ccb56e85661acedd630abbd390e4b2003a), 
+
+
+
+x
++
+y
+≤
+5
+
+
+{\textstyle x+y\leq 5}
+
+![{\textstyle x+y\leq 5}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6171ff088c858f3829d9dd5b3139d11be00a5d7f), 
+
+
+
+x
+−
+2
+y
+≥
+2
+
+
+{\textstyle x-2y\geq 2}
+
+![{\textstyle x-2y\geq 2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aa1f70dd26698483c4066479e1bb099241cb9f1c), 
+
+
+
+y
+≥
+0
+
+
+{\textstyle y\geq 0}
+
+![{\textstyle y\geq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a4ab86d638e82193271bc685d8d977cbbcf4e65a).
+
+
+#### Section 4
+
+
+1. Find line integrals of a scalar fields 
+
+
+
+
+
+∫
+
+Γ
+
+
+(
+x
++
+y
+)
+
+d
+s
+
+
+
+{\textstyle \displaystyle \int \limits \_{\Gamma }(x+y)\,ds}
+
+![{\textstyle \displaystyle \int \limits _{\Gamma }(x+y)\,ds}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8d7a626ecc11638cd879e8c5dd84deec5f4ec95e) where 
+
+
+
+Γ
+
+
+{\textstyle \Gamma }
+
+![{\textstyle \Gamma }](https://wikimedia.org/api/rest_v1/media/math/render/svg/f677684faf84745068a3b602896ca59b0766be4a) is boundary of a triangle with vertices 
+
+
+
+(
+0
+;
+0
+)
+
+
+{\textstyle (0;0)}
+
+![{\textstyle (0;0)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e8cabde45f1dd10b936518c3de98d232d7c46150), 
+
+
+
+(
+1
+;
+0
+)
+
+
+{\textstyle (1;0)}
+
+![{\textstyle (1;0)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/97e7e03a49a76bc809417791254eb6c78fcc0836) and 
+
+
+
+(
+0
+;
+1
+)
+
+
+{\textstyle (0;1)}
+
+![{\textstyle (0;1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/047498b8de986e906f31c93d8870f2ad77819d71).
+2. Having ascertained that integrand is an exact differential, calculate the integral along a piecewise smooth plain curve that starts at 
+
+
+
+A
+
+
+{\textstyle A}
+
+![{\textstyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a118c6ad00742b3f5dccd2f0e74b5e369df6fd31) and finishes at 
+
+
+
+B
+
+
+{\textstyle B}
+
+![{\textstyle B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/de0b47ffc21636dc2df68f6c793177a268f10e9b): 
+
+
+
+
+
+∫
+
+Γ
+
+
+
+(
+
+
+x
+
+4
+
+
++
+4
+x
+
+y
+
+3
+
+
+
+)
+
+
+d
+x
++
+
+(
+
+6
+
+x
+
+2
+
+
+
+y
+
+2
+
+
+−
+5
+
+y
+
+4
+
+
+
+)
+
+
+d
+y
+
+
+
+{\textstyle \displaystyle \int \limits \_{\Gamma }\left(x^{4}+4xy^{3}\right)\,dx+\left(6x^{2}y^{2}-5y^{4}\right)\,dy}
+
+![{\textstyle \displaystyle \int \limits _{\Gamma }\left(x^{4}+4xy^{3}\right)\,dx+\left(6x^{2}y^{2}-5y^{4}\right)\,dy}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9479ff2e89c48d84cd99758176960aefefa3c2a3), 
+
+
+
+A
+(
+−
+2
+;
+−
+1
+)
+
+
+{\textstyle A(-2;-1)}
+
+![{\textstyle A(-2;-1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/28816a18116ec2bcd546b276cb0ac6201873d963), 
+
+
+
+B
+(
+0
+;
+3
+)
+
+
+{\textstyle B(0;3)}
+
+![{\textstyle B(0;3)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/67293f2836c5adc3c391fa564fcdc2fac94a2562);
+
+
+### Final assessment
+
+
+#### Section 1
+
+
+1. Find out whether the following functional series converges uniformly on the indicated intervals. Justify your answer. 
+
+
+
+
+∑
+
+n
+=
+1
+
+
+∞
+
+
+
+e
+
+−
+n
+
+(
+
+
+x
+
+2
+
+
++
+2
+sin
+⁡
+x
+
+)
+
+
+
+
+
+{\textstyle \sum \limits \_{n=1}^{\infty }e^{-n\left(x^{2}+2\sin x\right)}}
+
+![{\textstyle \sum \limits _{n=1}^{\infty }e^{-n\left(x^{2}+2\sin x\right)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5683d5e640c22a7cd5b1d3520409c431056e30b0), 
+
+
+
+
+Δ
+
+1
+
+
+=
+(
+0
+;
+1
+]
+
+
+{\textstyle \Delta \_{1}=(0;1]}
+
+![{\textstyle \Delta _{1}=(0;1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b80239da7d74486d76788367da82b612e233dcf6), 
+
+
+
+
+Δ
+
+2
+
+
+=
+[
+1
+;
++
+∞
+)
+
+
+{\textstyle \Delta \_{2}=[1;+\infty )}
+
+![{\textstyle \Delta _{2}=[1;+\infty )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/767b97f867e082dfede53759fa2df79cd53a3869);
+2. Find out whether the following functional series converges uniformly on the indicated intervals. Justify your answer. 
+
+
+
+
+∑
+
+n
+=
+1
+
+
+∞
+
+
+
+
+
+n
+
+x
+
+3
+
+
+
+
+
+x
+
+2
+
+
++
+
+n
+
+2
+
+
+
+
+
+
+
+{\textstyle \sum \limits \_{n=1}^{\infty }{\frac {\sqrt {nx^{3}}}{x^{2}+n^{2}}}}
+
+![{\textstyle \sum \limits _{n=1}^{\infty }{\frac {\sqrt {nx^{3}}}{x^{2}+n^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/695d67fad209cd46deb8627d55eb112673a97d93), 
+
+
+
+
+Δ
+
+1
+
+
+=
+(
+0
+;
+1
+)
+
+
+{\textstyle \Delta \_{1}=(0;1)}
+
+![{\textstyle \Delta _{1}=(0;1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1c54e8b5a3c4d79037b0711372b6689de58b6e4d), 
+
+
+
+
+Δ
+
+2
+
+
+=
+(
+1
+;
++
+∞
+)
+
+
+{\textstyle \Delta \_{2}=(1;+\infty )}
+
+![{\textstyle \Delta _{2}=(1;+\infty )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3da88d3477a5cc6c7f3a8fcfd468e4202bf6d1b9)
+
+
+#### Section 2
+
+
+1. Find all points where the differential of a function 
+
+
+
+f
+(
+x
+;
+y
+)
+=
+(
+5
+x
++
+7
+y
+−
+25
+)
+
+e
+
+−
+
+x
+
+2
+
+
+−
+x
+y
+−
+
+y
+
+2
+
+
+
+
+
+
+{\textstyle f(x;y)=(5x+7y-25)e^{-x^{2}-xy-y^{2}}}
+
+![{\textstyle f(x;y)=(5x+7y-25)e^{-x^{2}-xy-y^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fcef5187dd210178de071072338fc887676cb0c6) is equal to zero.
+2. Show that function 
+
+
+
+φ
+=
+f
+
+(
+
+
+
+x
+y
+
+
+;
+
+x
+
+2
+
+
++
+y
+−
+
+z
+
+2
+
+
+
+)
+
+
+
+{\textstyle \varphi =f\left({\frac {x}{y}};x^{2}+y-z^{2}\right)}
+
+![{\textstyle \varphi =f\left({\frac {x}{y}};x^{2}+y-z^{2}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1bb557bb21657f2b0c8229adce9ee9804acd1a18) satisfies the equation 
+
+
+
+2
+x
+z
+
+φ
+
+x
+
+
++
+2
+y
+z
+
+φ
+
+y
+
+
++
+
+(
+
+2
+
+x
+
+2
+
+
++
+y
+
+)
+
+
+φ
+
+z
+
+
+=
+0
+
+
+{\textstyle 2xz\varphi \_{x}+2yz\varphi \_{y}+\left(2x^{2}+y\right)\varphi \_{z}=0}
+
+![{\textstyle 2xz\varphi _{x}+2yz\varphi _{y}+\left(2x^{2}+y\right)\varphi _{z}=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b3521dcad724a9685111a47bef3a86ae868278f4).
+3. Find maxima and minima of function 
+
+
+
+u
+=
+2
+
+x
+
+2
+
+
++
+12
+x
+y
++
+
+y
+
+2
+
+
+
+
+{\textstyle u=2x^{2}+12xy+y^{2}}
+
+![{\textstyle u=2x^{2}+12xy+y^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/09a2dd7f0d957f03692af28142af427d5e1791df) under condition that 
+
+
+
+
+x
+
+2
+
+
++
+4
+
+y
+
+2
+
+
+=
+25
+
+
+{\textstyle x^{2}+4y^{2}=25}
+
+![{\textstyle x^{2}+4y^{2}=25}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e2161246eedccf6d799aa1e5734b118c315f7150). Find the maximum and minimum value of a function
+4. u
+=
+
+(
+
+
+y
+
+2
+
+
+−
+
+x
+
+2
+
+
+
+)
+
+
+e
+
+1
+−
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+
+
+
+
+{\textstyle u=\left(y^{2}-x^{2}\right)e^{1-x^{2}+y^{2}}}
+
+![{\textstyle u=\left(y^{2}-x^{2}\right)e^{1-x^{2}+y^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/932e00eb2464b47b893d6fb18846cfcccb4e6d6b) on a domain given by inequality 
+
+
+
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+≤
+4
+
+
+{\textstyle x^{2}+y^{2}\leq 4}
+
+![{\textstyle x^{2}+y^{2}\leq 4}](https://wikimedia.org/api/rest_v1/media/math/render/svg/90eb8b71c5ce09a4ec482966f3de5479978b1e3d);
+
+
+#### Section 3
+
+
+1. Domain 
+
+
+
+G
+
+
+{\textstyle G}
+
+![{\textstyle G}](https://wikimedia.org/api/rest_v1/media/math/render/svg/febc2b9ff73bcca7b3fdb1432fddd1cdf3c8403c) is bounded by lines 
+
+
+
+y
+=
+2
+x
+
+
+{\textstyle y=2x}
+
+![{\textstyle y=2x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4d06a41ec951090ac63c9e967e4d2d827376c9ca), 
+
+
+
+y
+=
+x
+
+
+{\textstyle y=x}
+
+![{\textstyle y=x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/93343635ea42bd77e3e1ce347195e23ade09b5d3) and 
+
+
+
+y
+=
+2
+
+
+{\textstyle y=2}
+
+![{\textstyle y=2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/887628e811c56cc94aaccb0f5e4c773f19231cf9). Rewrite integral 
+
+
+
+
+∬
+
+G
+
+
+f
+(
+x
+)
+
+d
+x
+
+d
+y
+
+
+{\textstyle \iint \limits \_{G}f(x)\,dx\,dy}
+
+![{\textstyle \iint \limits _{G}f(x)\,dx\,dy}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bbc886f1ea76c3bc7f81d3c334f7620147794855) as a single integral.
+2. Represent the integral 
+
+
+
+
+
+∬
+
+G
+
+
+f
+(
+x
+;
+y
+)
+
+d
+x
+
+d
+y
+
+
+
+{\textstyle \displaystyle \iint \limits \_{G}f(x;y)\,dx\,dy}
+
+![{\textstyle \displaystyle \iint \limits _{G}f(x;y)\,dx\,dy}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f11428df0d608e522a446f7cf8ee68cdbdbdee29) as iterated integrals with different order of integration in polar coordinates if 
+
+
+
+G
+=
+
+{
+
+(
+x
+;
+y
+)
+
+|
+
+
+a
+
+2
+
+
+≤
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+≤
+4
+
+a
+
+2
+
+
+;
+
+
+|
+
+x
+
+|
+
+−
+y
+≥
+0
+
+
+
+
+}
+
+
+
+{\textstyle G=\left\{(x;y)\left|a^{2}\leq x^{2}+y^{2}\leq 4a^{2};\,|x|-y\geq 0\right.\right\}}
+
+![{\textstyle G=\left\{(x;y)\left|a^{2}\leq x^{2}+y^{2}\leq 4a^{2};\,|x|-y\geq 0\right.\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/34dc3c913392b2188d0f55ce7885d44baa8a8f59).
+3. Find the integral making an appropriate substitution: 
+
+
+
+
+
+∭
+
+G
+
+
+
+(
+
+
+x
+
+2
+
+
+−
+
+y
+
+2
+
+
+
+)
+
+
+(
+
+z
++
+
+x
+
+2
+
+
+−
+
+y
+
+2
+
+
+
+)
+
+
+d
+x
+
+d
+y
+
+d
+z
+
+
+
+{\textstyle \displaystyle \iiint \limits \_{G}\left(x^{2}-y^{2}\right)\left(z+x^{2}-y^{2}\right)\,dx\,dy\,dz}
+
+![{\textstyle \displaystyle \iiint \limits _{G}\left(x^{2}-y^{2}\right)\left(z+x^{2}-y^{2}\right)\,dx\,dy\,dz}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3b7f604b225ae19524d76d6342cb44f0c7fe07ff), 
+
+
+
+G
+=
+
+{
+
+(
+x
+;
+y
+;
+z
+)
+
+|
+
+x
+−
+1
+<
+y
+<
+x
+;
+
+1
+−
+x
+<
+y
+<
+2
+−
+x
+;
+
+1
+−
+
+x
+
+2
+
+
++
+
+y
+
+2
+
+
+<
+z
+<
+
+y
+
+2
+
+
+−
+
+x
+
+2
+
+
++
+2
+x
+
+
+
+
+}
+
+
+
+{\textstyle G=\left\{(x;y;z)\left|x-1<y<x;\,1-x<y<2-x;\,1-x^{2}+y^{2}<z<y^{2}-x^{2}+2x\right.\right\}}
+
+![{\textstyle G=\left\{(x;y;z)\left|x-1<y<x;\,1-x<y<2-x;\,1-x^{2}+y^{2}<z<y^{2}-x^{2}+2x\right.\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/28659bdf51117253f1eea6a8c57f76540a6ec159).
+
+
+#### Section 4
+
+
+1. Find line integrals of a scalar fields 
+
+
+
+
+
+∫
+
+Γ
+
+
+(
+x
++
+y
+)
+
+d
+s
+
+
+
+{\textstyle \displaystyle \int \limits \_{\Gamma }(x+y)\,ds}
+
+![{\textstyle \displaystyle \int \limits _{\Gamma }(x+y)\,ds}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8d7a626ecc11638cd879e8c5dd84deec5f4ec95e) where 
+
+
+
+Γ
+
+
+{\textstyle \Gamma }
+
+![{\textstyle \Gamma }](https://wikimedia.org/api/rest_v1/media/math/render/svg/f677684faf84745068a3b602896ca59b0766be4a) is boundary of a triangle with vertices 
+
+
+
+(
+0
+;
+0
+)
+
+
+{\textstyle (0;0)}
+
+![{\textstyle (0;0)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e8cabde45f1dd10b936518c3de98d232d7c46150), 
+
+
+
+(
+1
+;
+0
+)
+
+
+{\textstyle (1;0)}
+
+![{\textstyle (1;0)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/97e7e03a49a76bc809417791254eb6c78fcc0836) and 
+
+
+
+(
+0
+;
+1
+)
+
+
+{\textstyle (0;1)}
+
+![{\textstyle (0;1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/047498b8de986e906f31c93d8870f2ad77819d71).
+2. Use divergence theorem to find the following integrals 
+
+
+
+
+
+∬
+
+S
+
+
+(
+1
++
+2
+x
+)
+
+d
+y
+
+d
+z
++
+(
+2
+x
++
+3
+y
+)
+
+d
+z
+
+d
+x
++
+(
+3
+y
++
+4
+z
+)
+
+d
+x
+
+d
+y
+
+
+
+{\textstyle \displaystyle \iint \limits \_{S}(1+2x)\,dy\,dz+(2x+3y)\,dz\,dx+(3y+4z)\,dx\,dy}
+
+![{\textstyle \displaystyle \iint \limits _{S}(1+2x)\,dy\,dz+(2x+3y)\,dz\,dx+(3y+4z)\,dx\,dy}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73a9a7b00f2cc15f508b9bf55224d55b9d1e7e14) where 
+
+
+
+S
+
+
+{\textstyle S}
+
+![{\textstyle S}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e10a3c52d186162ec8910ebc0288ce982aef842f) is the outer surface of a tetrahedron 
+
+
+
+
+
+x
+a
+
+
++
+
+
+y
+b
+
+
++
+
+
+z
+c
+
+
+≤
+1
+
+
+{\textstyle {\frac {x}{a}}+{\frac {y}{b}}+{\frac {z}{c}}\leq 1}
+
+![{\textstyle {\frac {x}{a}}+{\frac {y}{b}}+{\frac {z}{c}}\leq 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1377463cd4c0d1b190d99150ad4c7cecd93ca22f), 
+
+
+
+x
+≥
+0
+
+
+{\textstyle x\geq 0}
+
+![{\textstyle x\geq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c434fc1e2ab777786469de853c75e616007b3eb4), 
+
+
+
+y
+≥
+0
+
+
+{\textstyle y\geq 0}
+
+![{\textstyle y\geq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a4ab86d638e82193271bc685d8d977cbbcf4e65a), 
+
+
+
+z
+≥
+0
+
+
+{\textstyle z\geq 0}
+
+![{\textstyle z\geq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7298578ca3a51011394eff000d2c36a4b6cf9c7b);
+
+
+### The retake exam
+
+
+Retakes will be run as a comprehensive exam, where the student will be assessed the acquired knowledge coming from the textbooks, the lectures, the labs, and the additional required reading material, as supplied by the instructor. During such comprehensive oral/written the student could be asked to solve exercises and to explain theoretical and practical aspects of the course.
+
+
+
+
+
+
+
+
+
+
+

raw/raw_bsc__mechanics_and_machines.md

@@ -0,0 +1,430 @@
+
+
+
+
+
+
+
+BSc: Mechanics And Machines
+===========================
+
+
+
+
+
+
+Contents
+--------
+
+
+* [1 Mechanics and Machines](#Mechanics_and_Machines)
+	+ [1.1 Short Description](#Short_Description)
+	+ [1.2 Prerequisites](#Prerequisites)
+		- [1.2.1 Prerequisite subjects](#Prerequisite_subjects)
+		- [1.2.2 Prerequisite topics](#Prerequisite_topics)
+	+ [1.3 Course Topics](#Course_Topics)
+	+ [1.4 Intended Learning Outcomes (ILOs)](#Intended_Learning_Outcomes_.28ILOs.29)
+		- [1.4.1 What is the main purpose of this course?](#What_is_the_main_purpose_of_this_course.3F)
+		- [1.4.2 ILOs defined at three levels](#ILOs_defined_at_three_levels)
+			* [1.4.2.1 Level 1: What concepts should a student know/remember/explain?](#Level_1:_What_concepts_should_a_student_know.2Fremember.2Fexplain.3F)
+			* [1.4.2.2 Level 2: What basic practical skills should a student be able to perform?](#Level_2:_What_basic_practical_skills_should_a_student_be_able_to_perform.3F)
+			* [1.4.2.3 Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?](#Level_3:_What_complex_comprehensive_skills_should_a_student_be_able_to_apply_in_real-life_scenarios.3F)
+	+ [1.5 Grading](#Grading)
+		- [1.5.1 Course grading range](#Course_grading_range)
+		- [1.5.2 Course activities and grading breakdown](#Course_activities_and_grading_breakdown)
+		- [1.5.3 Recommendations for students on how to succeed in the course](#Recommendations_for_students_on_how_to_succeed_in_the_course)
+	+ [1.6 Resources, literature and reference materials](#Resources.2C_literature_and_reference_materials)
+		- [1.6.1 Open access resources](#Open_access_resources)
+		- [1.6.2 Closed access resources](#Closed_access_resources)
+		- [1.6.3 Software and tools used within the course](#Software_and_tools_used_within_the_course)
+* [2 Teaching Methodology: Methods, techniques, & activities](#Teaching_Methodology:_Methods.2C_techniques.2C_.26_activities)
+	+ [2.1 Activities and Teaching Methods](#Activities_and_Teaching_Methods)
+	+ [2.2 Formative Assessment and Course Activities](#Formative_Assessment_and_Course_Activities)
+		- [2.2.1 Ongoing performance assessment](#Ongoing_performance_assessment)
+			* [2.2.1.1 Section 1](#Section_1)
+			* [2.2.1.2 Section 2](#Section_2)
+			* [2.2.1.3 Section 3](#Section_3)
+		- [2.2.2 Final assessment](#Final_assessment)
+		- [2.2.3 The retake exam](#The_retake_exam)
+
+
+
+Mechanics and Machines
+======================
+
+
+* **Course name**: Mechanics and Machines
+* **Code discipline**:
+* **Subject area**: Mechanical engineering, modeling and design of mechanisms and machines
+
+
+Short Description
+-----------------
+
+
+This course covers the following concepts: Mechanical engineering: Methods of calculation and design of mechanisms and machines.
+
+
+
+Prerequisites
+-------------
+
+
+### Prerequisite subjects
+
+
+* [CSE203 — Mathematical Analysis II](https://eduwiki.innopolis.university/index.php/BSc:MathematicalAnalysisII)
+* [CSE205 — Differential Equations](https://eduwiki.innopolis.university/index.php/BSc:DifferentialEquations)
+
+
+### Prerequisite topics
+
+
+* [CSE203 — Mathematical Analysis II](https://eduwiki.innopolis.university/index.php/BSc:MathematicalAnalysisII): Linear algebra, vectors and matrices, partial derivatives, Theoretical Mechanics
+* [CSE205 — Differential Equations](https://eduwiki.innopolis.university/index.php/BSc:DifferentialEquations): ODE
+
+
+Course Topics
+-------------
+
+
+
+
+Course Sections and Topics
+| Section | Topics within the section
+ |
+| --- | --- |
+| Introduction to Engineering | 1. Reading engineering drawings.
+2. Types of joining machine parts.
+3. Overview of axles, shafts, bearings, couplings.
+4. Overview of materials used in mechanical engineering.
+5. Overview of parts manufacturing methods.
+6. Overview of surface treatments.
+7. Application of CAD / CAE systems for the design of machine parts.
+ |
+| Theory of mechanisms and machines | 1. Structural analysis of mechanisms
+2. Kinematic analysis of mechanisms
+3. Kinematic analysis of gears
+4. Force and dynamic analysis of mechanisms
+5. Dynamic characteristics of machines
+6. Synthesis of mechanisms
+7. Balancing mechanisms
+8. Vibration and vibration protection
+9. Application of CAD / CAE systems for kinematic and dynamic analysis of mechanisms
+ |
+| Strength of materials | 1. Introduction to the resistance of materials
+2. Stresses and deformations
+3. Stretching and compression
+4. Pure shift
+5. Torsion
+6. Bending
+7. Dynamic loads
+8. Cyclic loads
+ |
+
+
+Intended Learning Outcomes (ILOs)
+---------------------------------
+
+
+### What is the main purpose of this course?
+
+
+The purpose of the course is to give broad basic knowledge in mechanical engineering and to show the modern capabilities of computer technology for solving engineering problems. The course covers topics such as the strength of materials and the theory of mechanisms and machines. The objective of the course is to provide knowledge and skills that are useful in the development of new robots, and are also necessary for the effective use of industrial robots for various types of material processing.
+
+
+
+### ILOs defined at three levels
+
+
+#### Level 1: What concepts should a student know/remember/explain?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Various types of joining machine parts,
+* Various methods of manufacturing machine parts and processing their surfaces,
+* Various types of mechanisms and their scope,
+* Various types of gears and their main characteristics,
+* The main problems of the structural, kinematic and dynamic analysis of mechanisms,
+* Fundamental principles of strength of materials,
+* The main problems of strength and stiffness calculation.
+
+
+#### Level 2: What basic practical skills should a student be able to perform?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* How to read engineering drawings,
+* How to choose a method of joining machine parts,
+* How to choose the type of gears,
+* How to conduct structural, kinematic and dynamic analysis of mechanisms,
+* How to balance mechanisms,
+* How to choose the shape of the machine part depending on the type of loading,
+* How to evaluate the strength and stiffness of machine parts
+
+
+#### Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
+
+
+By the end of the course, the students should be able to ...
+
+
+
+* Design simple machinery using a CAD system
+* Perform kinematic and dynamic calculations of mechanisms and machines
+* Synthesize and optimize mechanisms in accordance with specified requirements
+* Perform strength and stiffness calculations manually and using a CAD system
+
+
+Grading
+-------
+
+
+### Course grading range
+
+
+
+
+
+| Grade | Range | Description of performance
+ |
+| --- | --- | --- |
+| A. Excellent | 90-100 | -
+ |
+| B. Good | 75-89 | -
+ |
+| C. Satisfactory | 60-74 | -
+ |
+| D. Poor | 0-59 | -
+ |
+
+
+### Course activities and grading breakdown
+
+
+
+
+
+| Activity Type | Percentage of the overall course grade
+ |
+| --- | --- |
+| Labs/seminar classes | 10
+ |
+| Interim performance assessment | 50
+ |
+| Exams | 40
+ |
+
+
+### Recommendations for students on how to succeed in the course
+
+
+Resources, literature and reference materials
+---------------------------------------------
+
+
+### Open access resources
+
+
+* Michael M. Stanišic Mechanisms and Machines: Kinematics, Dynamics, and Synthesis, 2015
+* Dietmar Gross et al. Engineering Mechanics 2: Mechanics of Materials, 2018
+* Vitor Dias da Silva Mechanics and Strength of Materials 2006
+* Frolov K.V. at al. Teoriya mechanizmov i mashin 1987 - in Russian
+* Artobolevski I.I. Teoriya mechanizmov i mashin 1988 - in Russian
+* Artobolevski I.I., Edelstein B.V. Sbornik zadach po teorii mechanizmov i mashin 1975 - in Russian
+* Jukov V.G. Mechanika. Soprotivlenie materialov 2012 - in Russian
+* Volmir A.S. at al. Sbornik zadach po soprotivleniu materialov 1984 - in Russian
+* Mary Kathryn Thompson, John Martin Thompson ANSYS Mechanical APDL for Finite Element Analysis, 2017
+* Alawadhi, Esam M. Finite element simulations using ANSYS, 2016
+* Fedorova N.N. at al. Osnovy paboty v ANSYS 17, 2017 - in Russian
+
+
+### Closed access resources
+
+
+### Software and tools used within the course
+
+
+Teaching Methodology: Methods, techniques, & activities
+=======================================================
+
+
+Activities and Teaching Methods
+-------------------------------
+
+
+
+
+Activities within each section
+| Learning Activities | Section 1 | Section 2 | Section 3
+ |
+| --- | --- | --- | --- |
+| Homework and group projects | 1 | 1 | 1
+ |
+| Midterm evaluation | 1 | 1 | 0
+ |
+| Testing (written or computer based) | 1 | 1 | 1
+ |
+| Oral polls | 1 | 1 | 1
+ |
+
+
+Formative Assessment and Course Activities
+------------------------------------------
+
+
+### Ongoing performance assessment
+
+
+#### Section 1
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Make projections the part according to its 3D model or image. | 1
+ |
+| Question | Make a 3D model of the part according to its drawing. | 1
+ |
+| Question | Suggest a method of manufacturing a part according to its drawing and description. | 1
+ |
+| Question | Suggest a way to connect parts according to their description. | 1
+ |
+| Question | Suggest a method for transmitting movement in a machinery by describing its functions. | 1
+ |
+| Question | Analyze the parts of a given mechanism or construction. | 0
+ |
+| Question | Using a CAD-system, make solid-state 3D-models of parts of a given mechanism or construction | 0
+ |
+| Question | Make a 3D model of the assembly of a given mechanism or construction | 0
+ |
+| Question | Make and describe drawings of parts of a given mechanism or construction | 0
+ |
+
+
+#### Section 2
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Propose the structure of the mechanism for the implementation of the given functions | 1
+ |
+| Question | Calculate the trajectories, velocities and accelerations of specific points and links of the mechanism | 1
+ |
+| Question | Calculate gear transfer functions | 1
+ |
+| Question | Calculate the forces arising in the mechanism during its movement | 1
+ |
+| Question | Calculate mechanism balancing parameters | 1
+ |
+| Question | Make a 3D model of the mechanism in a CAD system, check its operability | 1
+ |
+| Question | Apply kinematic and dynamic analysis of mechanisms and gears. | 0
+ |
+| Question | Perform a synthesis of mechanisms to implement the specified functions. | 0
+ |
+| Question | Make engine selection according to dynamic characteristics. | 0
+ |
+| Question | Calculate balancing mechanisms, including the use of flywheels. | 0
+ |
+| Question | Perform vibration analysis and vibration protection design. | 0
+ |
+
+
+#### Section 3
+
+
+
+
+
+| Activity Type | Content | Is Graded?
+ |
+| --- | --- | --- |
+| Question | Calculate stresses and strains in a bar loaded with stretching or compressive force. | 1
+ |
+| Question | Calculate stresses in shear stresses in riveted or welded joints. | 1
+ |
+| Question | Calculate stress and strain of a shaft loaded with torque. | 1
+ |
+| Question | Calculate stress and strain of a beam loaded with bending moments. | 1
+ |
+| Question | Using a CAD system, calculate stresses and deformations of parts of the developed mechanism. | 1
+ |
+| Question | Apply methods of resistance of materials to assess the operability of parts in cases of simple loading. | 0
+ |
+| Question | Apply a CAD system to calculate and evaluate the operability of parts in cases of complex loading. | 0
+ |
+| Question | Design and optimize the shape of parts depending on the conditions of their loading. | 0
+ |
+| Question | Apply a method for evaluating the durability and reliability of parts. | 0
+ |
+
+
+### Final assessment
+
+
+**Section 1**
+
+
+
+1. Describe the principles of solid modeling in CAD systems.
+2. Describe the scope, advantages and disadvantages of various ways of joining machine parts.
+3. Describe the scope, advantages and disadvantages of various bearings.
+4. Describe the basic methods for manufacturing parts and processing their surfaces, their advantages and disadvantages.
+
+
+**Section 2**
+
+
+
+1. Describe the different types of gears, their advantages and disadvantages.
+2. Describe the method of selecting the type of gears.
+3. Describe the main problems of structural, kinematic and dynamic analysis of mechanisms.
+4. Describe the methods of kinematic and dynamic analysis on the example of a given mechanism.
+5. Describe the methods of balancing mechanisms
+
+
+**Section 3**
+
+
+
+1. Describe the fundamental principles and basic laws of strength of materials.
+2. Describe the calculation method for strength and stiffness in cases of stretching/compression, shift, torsion and bending.
+3. Describe the method of selecting the shape of the machine part, depending on the type of loading.
+4. Describe methods for evaluating the durability and reliability of machine parts.
+
+
+### The retake exam
+
+
+**Section 1**
+
+
+**Section 2**
+
+
+**Section 3**
+
+
+
+
+
+
+
+
+
+
+