4 semester

1

Название

дисциплины

Discrete Mathematics and Mathematical Logic-2

2

Курс обучения

2, Mathematics and Information Technologies

3

Семестр обучения

4

4

Количество кредитов

4

5

Ф.И.О. лектора

Candidate of Sciences in Psychics and Mathematics , Associate professor

Kirill Kuzmin

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Цели изучения

дисциплины

This course serves as a gateway to modern mathematics; its aim is to introduce some basic ideas and methods used in discrete mathematics. The course contributes to three main goals. Firstly, students are exposed to the notation as well as a number of important theorems and techniques in Combinatorics, Boolean Functions, Logic and Graph Theory. Secondly, this course provides an insight into different aspects of mathematics which have found important applications in computer science and related areas. Finally, it provides a treatment of discrete mathematics for students planning to study such areas of advanced mathematics and Computer Science as, Operations Research, Design and Analysis of Algorithms, Bioinformatics, Machine Learning.

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Пререквизиты

Discrete Mathematics and Mathematical Logic-1.

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Содержание

дисциплины

Topics covered are selected from the following list: Boolean Functions including normal forms, minimization in DNF classes, characterizations of closed classes of Boolean functions, E. Post theorem; Graph Theory including graph isomorphism, connectivity, shortest path problem, trees, Eulerian and Hamiltonian circuits, graph colourings and bipartite matchings, planar graphs, extremal graph theory.

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Рекомендуемая

литература

1. Selezneva S. N. The basics of discrete mathematics – Moscow: MAX Press, 2010. (in Russian)

2. Shen A. Mathematical induction – Moscow: Moscow Center for Continuous Mathematical Education, 2007. (in Russian)

3. Shen A., Vyaliy M., Podolskii V., Rubtcov A., Shvartc D. Lectures on discrete mathematics – Moscow: Moscow Centre for Continuous Mathematical Education, 2017. (in Russian)

4. Conradie W., Goranko V. Logic and discrete mathematics: a concise introduction – Chichester: Wiley, 2015.

5. Emelichev V. A., Melnikov O. I., Sarvanov V. I., Tyshkevich R. I. Letures on graph theory – Moscow: Libkorom, 2015. (in Russian)

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Методы преподавания

Lectures,

Seminars and Tutorials,

Independent Study,

Problem-based learning,

Learning through research.

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Язык обучения

Russian

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Условия (требования),

текущий контроль

The final mark for each was determined in a way that takes into account two marks: final examination test (60%), participation in seminars and mid-semester tests (40%).

One must obtain a grade of 4 (out of 10) or better to fulfil the programme requirements. 

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Форма текущей

аттестации

Examination