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Title of discipline

Discrete mathematics and graph theory

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Year of study

1, Specialty “Mathematics (scientific and design activities)”

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Semester of study

2

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Number of credits

2

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Full name of lecturer

Doctor of physical and mathematical sciences, Professor Emelichev Vladimir Alekseevich

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Objectives of studying the discipline

Acquaintance with the problems and methods of discrete mathematics. Forming the skills of discrete mathematical thinking and the ability to apply it in solving specific problems.
As a result of the study, the student should be able to:
– formulate the main statements from the considered sections of discrete mathematics;
– apply the main statements to solve typical problems.

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Prerequisites

Initial information from the theory of mappings, set theory and linear algebra

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Content of discipline

Samples, cube, permutations. Subsets, Boolean. Binomial theorem and consequences. Method of mathematical induction. Inclusion and exclusion method, Eratosthenes sieve. The number of disorders, Euler’s formula. Recurrence relations, the Binet formula. Generating functions. Elements of the theory of coding.

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Recommended literature

1. Vilenkin N.Ya. Combinatorics. – Moscow: Nauka, 1969. (in Russian)
2. Zuev Yu.A. On the ocean of discrete mathematics: From enumerative combinatorics to modern cryptography. In 2 volumes. – Moscow: Book House “Librokom”, 2012. (in Russian)
3. Yablonsky S.V. Introduction to discrete mathematics. – Moscow: Nauka, 1986. (in Russian)

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Teaching methods

Reproductive (passive), visual, comparative, dialog-heuristic, problem, research

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Language of study

Russian

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Current test activities

Theoretical colloquium, written test work

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Type of current certification

Test