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Апрель

# Algebra and Analysis

2021/2022
Учебный год
ENG
Обучение ведется на английском языке
6
Кредиты
Статус:
Курс обязательный
Когда читается:
1-й курс, 1, 2 модуль

### Course Syllabus

#### Abstract

The course of Algebra and Analysis is intended for beginners. Its goal is to introduce the students to the language of mathematics and basic ideas of graphs, vectors, matrices, derivation, and integration. These are indispensable tools of any domain of science using data analysis. 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

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

#### Course Contents

• "Set theory. Logic. Combinatorics. Graphs."
• “Linear Algebra”
• "Analytic geometry"
• ''Mathematical Analysis''

#### Assessment Elements

At the seminars that pass online, all students must keep their cameras switched on.
• 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 online exam.
• Average of all Mini-tests
This mark is constructed as an average of 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 knowlege and understanding. The rounding to the nearest integer is used. At the tests that pass online, the students must switch on theirs cameras.
• 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 the course. If a student was absent at the tests without legitimate reasons he/she gets 0 for this test. In case of online test, 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 teacher.
• 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 the course. If a student was absent at the tests without legitimate reasons he/she gets 0 for this test. In case of online test, 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 teacher.
• Self-study report
The goal of this task is independent work with mathematical literature, extraction the main ideas from a given mathematical book chapter. After the work with the given literature, the student should present the material to the 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.
• Individual Home Test
For this test students can use any resourses they could find, including internet sites, internet calculators, and programming

#### Interim Assessment

• 2021/2022 2nd module
0.15 * Test 2 + 0.1 * Individual Home Test + 0.1 * Self-study report + 0.25 * Exam + 0.15 * Test 1 + 0.1 * Activity grade + 0.15 * Average of all Mini-tests

#### Recommended Core Bibliography

• F. Aleskerov, H. Ersel, D. Piontkovski. Linear Algebra for Economists. Springer, 2011
• Williams, G. (2019). Linear Algebra with Applications (Vol. Ninth edition). Burlington, MA: Jones & Bartlett Learning. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1708709