3 semester

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Title of discipline

Discrete mathematics and graph theory

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Year of study

2, Specialty “Mathematics and information technologies” (Specialization “Web-programming and Internet Technologies”)

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Semester of study

3

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Number of credits

4

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Full name of lecturer

Candidate of physical and mathematical sciences, Associate Professor Metelsky Yury Mikhailovich

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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

Logical rules of combinatorics. Arrangements and combinations. Binomial and polynomial theorems. Method of inclusion and exclusion. Recurrence relations. Generating functions. Combinatorics of partitions. Ways for specifying Boolean functions. Basic logical equivalences. Shannon’s decomposition. The duality principle. Closed classes of Boolean functions. Completeness of the system of Boolean functions.

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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 colloquiums, written test works

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Type of current certification

Exam