Delivered at:: Department of Mathematics

Course type:: Elective course

When:: 1 year, 1, 2 module

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

Bachelor’s Programme 'Sociology and Social Informatics'

Coronavirus Live

Algebra and Analysis

Course Syllabus