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# Algebra and Analysis

2023/2024
ENG
Instruction in English
6
ECTS credits
Course type:
Elective course
When:
1 year, 1, 2 module

### Course Syllabus

#### Abstract

The course of Algebra and Analysis (modules 1, 2) is intended for beginners. Its goal is to introduce the students to the language of mathematics and basic ideas of vectors, matrices, derivation, and integration. These are indispensable tools of any domain of science using data. Special attention will be devoted to applications. This course will help you to gain a higher level of mathematical maturity necessary in subsequent courses.

#### Learning Objectives

• The goals of the course are to introduce the students to basic ideas of graphs, vectors, matrices, derivation, and integration
• to accustom students to the language of mathematics, to develop theirs abilities to communicate with mathematical symbols and logic quantifiers
• to develop the ability of students to prove theorems or/and formulas by themself and to demonstrate the importance of rigorous proofs
• to overcome fear to read math books and articles
• to make a habit of mathematical rigor in scientific discussions

#### Expected Learning Outcomes

• The student applies basic facts from graph theory in simple social networks
• The student uses the mathematical induction for proofs
• analyzes functions by construction of their plots
• applies the matrix transformations and decompositions
• performs actions with vectors in a linear space, explains geometric meaning of the operations
• uses equations of the line and the plane to compute distances
• performs computations with matrices, vectors, linear systems

#### Course Contents

• Set theory. Logic. Combinatorics. Graphs.
• Linear Algebra
• Analytic geometry
• Mathematical Analysis

#### Assessment Elements

• Test 1
All students must write the Tests and Mini-tests at the time that the teacher announced in advance. Those, who are absent at the Tests by legitimate reasons (medical reasons confirmed by the corresponding medical documents), will have an opportunity to write the test at the end of the course. If a student was absent at the tests without legitimate reasons he/she gets 0 for this test. In the case of online tests, all students must keep cameras turned on and must stay clearly visible by the cameras. Otherwise, the professor has a right to put 0. It is forbidden to use the internet resources, internet calculators, and social networks for this test. It is forbidden to communicate with anybody during this test. Otherwise, the professor has a right to put 0. The results and personal mistakes are discussed at the consultations with the professor.
• Self-study report
The goal of this task is independent work with mathematical literature, extracting the main ideas from a given mathematical book chapter. After the work with the given literature, the student should present the material to a teacher (or a teacher assistant) keeping the structure: introduction, the main results, conclusion. The part "main results" should contain the most important formulas, ideas, theorems clearly explained. The teacher (teacher assistant) has a right to ask additional questions or/and give additional tasks connected with the subject of the given material.
• Test 2
All students must write the Tests and Mini-tests at the time that the teacher announced in advance. Those, who are absent at the Tests by legitimate reasons (medical reasons confirmed by the corresponding medical documents), will have an opportunity to write the test at the end of the course. If a student was absent at the tests without legitimate reasons he/she gets 0 for this test. In the case of online tests, all students must keep cameras turned on and must stay clearly visible by the cameras. Otherwise, the professor has a right to put 0. It is forbidden to use the internet resources, internet calculators, and social networks for this test. It is forbidden to communicate with anybody during this test. Otherwise, the professor has a right to put 0. The results and personal mistakes are discussed at the consultations with the professor.
• Average of all tests
This mark is constructed as an average of all mini-tests. The duration of each mini-test is 30 minutes. Mini-tests are given more frequently than usual tests. They are used for more regular control of students' knowledge and understanding. The rounding to the nearest integer is used. At the tests that pass online, the students must turn on theirs cameras.
• Exam
At the exam, it is forbidden to use any notes and any copybooks, as well as any gadget with internet. The students who violate these rules will get a warning, if they violate the rules twice they will get 0. All students must turn on cameras on their computers and must stay clearly visible by the cameras during the exam, if the exam is online. Otherwise, the mark will be 0. It is forbidden to use internet calculators, and social networks for the exam. It is forbidden to communicate with anybody during the exam. Otherwise, the professor has a right to put 0. It is highly recommended to upload the solutions in .pdf format in case of an online exam.

#### Interim Assessment

• 2023/2024 2nd module
0.1 * Activity grade + 0.2 * Average of all tests + 0.3 * Exam + 0.1 * Self-study report + 0.15 * Test 1 + 0.15 * Test 2