Algebra and Analysis

2022/2023

Academic Year

ENG

Instruction in English

6

ECTS credits

Delivered at:

Department of Mathematics

Course type:

Compulsory course

When:

1 year, 1, 2 module

Instructor

Shmileva, Elena

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

• Activity grade
  At the seminars that pass online, all students must keep their cameras turned on.
• 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 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 online exam.
• 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 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 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 professor.
• 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 professor.

Interim Assessment

• 2022/2023 2nd module
  0.3 * Exam + 0.1 * Self-study report + 0.05 * Activity grade + 0.15 * Test 1 + 0.2 * Average of all Mini-tests + 0.15 * Test 2

Bibliography

Recommended Core Bibliography

• Gareth Williams. (2012). Linear Algebra with Applications. [N.p.]: Jones & Bartlett Learning. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=459020

Recommended Additional Bibliography

• Fuad Aleskerov, Hasan Ersel, & Dmitri Piontkovski. (2011). Linear Algebra for Economists. Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.spr.sptbec.978.3.642.20570.5
• Алескеров, Ф. Т. Бинарные отношения, графы и коллективные решения : учебное пособие / Ф. Т. Алескеров, Э. Л. Хабина, Д. А. Шварц. — 2-е изд. — Москва : ФИЗМАТЛИТ, 2012. — 344 с. — ISBN 978-5-9221-1363-2. — Текст : электронный // Лань : электронно-библиотечная система. — URL: https://e.lanbook.com/book/59762 (дата обращения: 00.00.0000). — Режим доступа: для авториз. пользователей.