Infopaket

Discrete Mathematics

ОК.13

Обов’язкова дисципліна для ОП

First

2021/2022

3 Semester

6

The student must know: the basic concepts of discrete mathematics such as: Finite sets, operations on sets, n-ary relations and their properties; Methods default Boolean functions and their analytical account, statement of the problem of minimizing Boolean functions in the analytical and geometric forms, techniques to minimize (analytical and geometrical), methods of combinational logic synthesis schemes; Basic concepts of graph theory, the main types of graphs isomorphic isomorphism and graph embedding; Finite automata, methods of their setting, automatons first and second kind, machines Mealy and Moore, algebra of regular events, key objectives and methods of abstract and structural analysis and synthesis of finite automatons, basic principles of computational theory.

Full-time form

The discipline "Discrete Mathematics" is based on a series of disciplines of professional and practical training, in particular, "Mathematical Analysis", "Programming", "Fundamentals of Computer Hardware and Software".

Fundamentals of set theory and set theory and algebraic operations on them. Unary, binary and ternary relations: properties, methods of assignment and operations on them. Injective, surjective and bijective mappings, their properties. The concept of algebra and polybasic algebra, their examples. Boolean functions: tabular and analytical tasks, incompletely defined functions. The problem of minimizing Boolean functions and basic methods. Methodology of logical synthesis of combinational schemes. Exchange graphs and the main methods of their task. Properties and isomorphism of graphs. Finite automata and basic methods of their task. Automata are deterministic and nondeterministic, equivalence theorem. Computational theory.

1. Погорілий С.Д. Програмне конструювання. Підручник за редакцією академіка АПН України Третяка О.В., видання 2-е. Київ : ВПЦ "Київський університет", Київ, 2007. 2. Погорілий С.Д. Дискретна математика. Київ : ВПЦ “Київський університет”, 1996. 3. Погорілий С.Д. “Автоматизація наукових досліджень. Основоположні математичні відомості. Програмне забезпечення” за редакцією академіка АПН України Третяка О. В. Київ: ВПЦ “Київський університет”, 2002. 4. A.V. Anisimov, S.D. Pogorilyy, D.Yu. Vitel. About the Issue of Algorithms formalized Design for Parallel Computer Architectures. Applied and Computational Mathematics, vol. 12, №2, 2013, p.p. 140-151.

Lectures, seminars, individual independent work.

Semester assessment: The semester includes 3 forms of reporting: participation in seminars (for each of the 4 possible solutions to the task in the boards from 0 to 5 points, a total of 0 to 20 points); for control work from 0 to 20 points; for passing the colloquium - from 0 to 20 points. Final assessment (in the form of an exam): the form of the exam is written-oral. The exam ticket consists of 2 questions and tasks. Each question is evaluated from 0 to 13 points, the solution of the problem - from 0 to 14 points. In total, you can get from 0 to 40 points for the exam. The condition for achieving a positive grade for the discipline is to obtain at least 60 points, while the grade for the exam can’t be less than 25 points. Conditions for admission to the exam: student receives a total of not less than 35 points per semester

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