Algebra and Analysis

2024/2025

Учебный год

ENG

Обучение ведется на английском языке

6

Кредиты

Кто читает:

Департамент математики

Статус:

Курс по выбору

Когда читается:

1-й курс, 1, 2 модуль

Преподаватель

Элияшев Юрий Валерьевич

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 their 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

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

Course Contents

• 1. Set theory. Logic. Combinatorics. Graphs.
• 2. Linear Algebra
• 3. Analytic geometry
• 4. Mathematical Analysis

Assessment Elements

• Activity grade
• Exam
• Test 2
• Average of all mini 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.
• Test 1

Interim Assessment

• 2024/2025 2nd module
  0.1 * Activity grade + 0.16 * Average of all mini tests + 0.3 * Exam + 0.22 * Test 1 + 0.22 * Test 2

Bibliography

Recommended Core Bibliography

• Ford, W. (2015). Numerical Linear Algebra with Applications : Using MATLAB (Vol. First edition). London: Academic Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=485990
• 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

Recommended Additional Bibliography

• Бинарные отношения, графы и коллективные решения. Примеры и задачи : учебное пособие для вузов / Ф. Т. Алескеров, Э. Л. Хабина, Д. А. Шварц, Л. Г. Егорова. — Москва : Издательство Юрайт, 2021. — 458 с. — (Высшее образование). — ISBN 978-5-534-14489-5. — Текст : электронный // Образовательная платформа Юрайт [сайт]. — URL: https://urait.ru/bcode/477702 (дата обращения: 27.08.2024).

Authors

• BRODSKAYA NATALYA NIKOLAEVNA