Кто читает:: Департамент больших данных и информационного поиска

Статус:: Курс обязательный

Когда читается:: 1-й курс, 1 модуль

Преподаватель

Правдивец Николай Александрович

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Abstract

This course in discrete mathematics includes elements of set theory, logic algebra, combinatorics, binary relations, and graph theory. In addition to familiarization with the basic concepts, it is supposed to teach basic skills in self-creation of models of logical, combinatorial, graph problems and their solutions. The course is taught in a distance format, provided by 12 hours of lectures, 12 hours of seminars, 22 hours of independent work and an exam.

Learning Objectives

- to introduce the basics of set algebra;
- to teach the basics of logic algebra, to teach how to work with logical expressions, propositions, predicates;
- provide the skill of self-formalization of tasks in the language of logic and predicates;
- teach the basics of combinatorics and solving basic combinatorial problems;
- to introduce the basic concepts of binary relations, their properties and operations on them;
- to teach the basics of graph theory, the use of basic algorithms for working with graphs;
- teach students to work with formal mathematical concepts, including rigorous proof of simple statements;
- provide skills in applying discrete mathematics methods to solve applied problems.

Expected Learning Outcomes

knowledge of basic concepts of set theory, logic, combinatorics, binary relations and graph theory;
the ability to apply the ideas and methods of discrete mathematics to solve applied problems;
understanding how mathematics works;
the ability to distinguish rigorous reasoning from plausible reasoning and to conduct rigorous reasoning independently.

Course Contents

Binary relationships (2 hours of lectures, 2 hours of seminars, 4 hours of independent work)
Graph theory (4 hours of lectures, 4 hours of seminars, 8 hours of independent work)
Sets (2 hours of lectures, 2 hours of seminars, 2 hours of independent work)
Logic (2 hours of lectures, 2 hours of seminars, 4 hours of independent work)
Combinatorics (2 hours of lectures, 2 hours of seminars, 4 hours of independent work)

Assessment Elements

Homework
Exam

Interim Assessment

2024/2025 2nd module
0.6 * Exam + 0.4 * Homework

Bibliography

Recommended Core Bibliography

Lovász, L., Pelikán, J., & Vsztergombi, K. (2003). Discrete Mathematics : Elementary and Beyond. New York: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=108108
Бинарные отношения, графы и коллективные решения : учеб. пособие для вузов, Алескеров, Ф. Т., 2017
Задачи по теории множеств, математической логике и теории алгоритмов, Лавров, И. А., 2009
Комбинаторика, Виленкин, Н. Я., 2013
Лекции по дискретной математике : учебник / М. Н. Вялый, В. В. Подольский, А. А. Рубцов [и др.]. — Москва : Высшая школа экономики, 2021. — 496 с. — ISBN 978-5-7598-2212-7. — Текст : электронный // Лань : электронно-библиотечная система. — URL: https://e.lanbook.com/book/199883 (дата обращения: 00.00.0000). — Режим доступа: для авториз. пользователей.
Теория графов, Оре, О., 2009
Хаггарти, Р. Дискретная математика для программистов / Р. Хаггарти. — 2-е изд., испр. — Москва : Техносфера, 2012. — 40 с. — ISBN 978-5-94836-303-5. — Текст : электронный // Лань : электронно-библиотечная система. — URL: https://e.lanbook.com/book/73011 (дата обращения: 00.00.0000). — Режим доступа: для авториз. пользователей.

Recommended Additional Bibliography

Дискретная математика для инженера : [учеб. пособие], Кузнецов О.П., 2009
Лекции по дискретной математике / Нац . исслед . ун-т «Высшая школа экономики».-2-е изд., пересмотр. - 978-5-7598-2880-8 - Вялый М.Н., Подольский В.В., Рубцов А.А., Шварц Д.А., Шень А. - 2023 - Москва: ВШЭ - https://ibooks.ru/bookshelf/392827 - 392827 - iBOOKS

Authors

Ахмедова Гюнай Интигам кызы

Магистерская программа «Магистр по наукам о данных»

Discrete Mathematics