Discrete mathematics
Course: System Analysis
Structural unit: Faculty of Computer Science and Cybernetics
Title
Discrete mathematics
Code
Module type
Обов’язкова дисципліна для ОП
Educational cycle
First
Year of study when the component is delivered
2022/2023
Semester/trimester when the component is delivered
1 Semester
Number of ECTS credits allocated
7
Learning outcomes
Know the basic concepts of mathematical logic, basic mathematical models and methods used in modern computer science.
Know the basic concepts of set theory and relations. Be able to write concepts and statements using formal mathematical symbols, to conduct mathematical proofs and formal justifications of statements of varying complexity.
Know the basic concepts of combinatorics. Be able to perform calculations of various combinatorial objects, apply the acquired knowledge in practical situations.
Know the basic concepts of graph theory. Be able to conduct mathematical proofs and formal substantiation of statements of varying complexity.
Know the basic concepts of Boolean function theory. Be able to perform calculations of various combinatorial objects for Boolean functions.
Know the basic concepts of automata theory: basic models of finite automata and the relationship between them and formal languages, be able to use automatic models to construct algorithms.
Form of study
Full-time form
Prerequisites and co-requisites
1. Know the basic concepts of general algebra and elementary mathematics.
2. Be able to effectively use the specified mathematical apparatus to solve various practical problems.
Course content
The subject of the discipline "Discrete Mathematics" is the presentation of basic concepts, models, results and methods of modern discrete (computer) mathematics. The discipline considers the following sections: elements of mathematical logic, set theory and relations, combinatorics, graph theory, Boolean function theory, automaton theory.
It is taught in the 1st and 2nd semesters of the 1st year in the amount of 210 hours. 7 ECTS credits, in particular: lectures - 56 hours, practical - 44 hours, independent work - 106 hours, consultations - 4 hours. The course includes 4 tests. The discipline ends with exams in the 1st and 2nd semesters.
Recommended or required reading and other learning resources/tools
1. Trokhimchuk RM, Nikitchenko MS Discrete mathematics in examples and problems / RM Trokhimchuk. - Tutorial. - Kyiv: Ukrainian Orthodox Church "Kyiv University", 2017. - 248 p.
2. Trokhimchuk RM Discrete Mathematics / RM Trokhimchuk. - К .: Вид. House "Staff", 2010.
3. Trokhimchuk RM Collection of problems and exercises on the theory of sets and relations: textbook. way. / RM Trokhimchuk. - Kyiv: Ukrainian Orthodox Church "Kyiv University", 2012.
4. Trokhimchuk RM Boolean functions: textbook. way. / RM Trokhimchuk. - Kyiv: Ukrainian Orthodox Church "Kyiv University", 2001.
5. Trokhimchuk RM Collection of problems in the theory of Boolean functions: textbook. way. / RM Trokhimchuk. - Kyiv: Ukrainian Orthodox Church "Kyiv University", 2002.
6. Karnaukh TO, Stavrovsky AB Introduction to discrete mathematics / Karnaukh TO - Kyiv: Ukrainian Orthodox Church "Kyiv University", 2006.
7. Karnaukh TO Combinatorics / Karnaukh TO - Kyiv: Ukrainian Orthodox Church "Kyiv Universit", 2011.
Planned learning activities and teaching methods
Lecture, practical classes, independent work
Assessment methods and criteria
Test work, current assessment, exam
Language of instruction
Ukrainian
Lecturers
This discipline is taught by the following teachers
Departments
The following departments are involved in teaching the above discipline