Робоча програма навчальної дисципліни «Дискретна математика (англійська мова навчання)» #

Course study program — Discrete Mathematics (English language of instruction)

Course components / Навігація #

1. Study course description #

2. The aim of the course and the expected results #

2.1 Aim of the course #

The aim of the course is to give students a rigorous foundation in the discrete structures and methods that underpin computer science and software engineering: sets and their algebra, relations and functions, Boolean algebra and propositional logic, methods of mathematical proof, elementary number theory, graph theory, combinatorics and probability, and the theory of finite automata. The course develops the ability to state a problem in precise mathematical language, to reason about it rigorously, and to apply discrete-mathematical models and algorithms to practical computing tasks — data representation, logic design, algorithm analysis, and formal specification. It provides the mathematical background required by Algorithms and Data Structures and later programming courses.

2.2 Expected study results #

As a result of studying the course, the student should

know:

• the basic notions of set theory and set algebra, relations and functions, and their properties;
• the laws of Boolean algebra and propositional logic, the canonical normal forms (DNF/CNF, ANF) and methods of minimization (Karnaugh maps, Quine–McCluskey);
• the principal methods of proof — direct, contrapositive, contradiction, mathematical induction, and well-ordering;
• the fundamentals of number theory: divisibility, the Euclidean algorithm, congruences, and Euler’s and Fermat’s theorems;
• the basic concepts of graph theory, combinatorics and probability;
• the models of finite automata and regular languages;

be able to:

• operate on sets, relations and functions and represent them formally (matrices, graphs, characteristic functions);
• construct and minimize Boolean functions and design simple logic circuits;
• construct and verify rigorous mathematical proofs;
• solve problems on divisibility, congruences and modular arithmetic;
• model applied problems with graphs and apply graph algorithms (traversal, shortest paths, spanning trees, colouring, matching);
• solve combinatorial and probabilistic problems;
• design finite automata and regular expressions for a given language.

2.3 Prerequisite courses #

None.

3. Course plan #

15 lecture slots; lectures 9 and 15 are tests (module and final control). The two content modules are aligned to the test placement. Number theory is taught at Lecture 8 (after Proof methods), so the module test falls on Lecture 9 and the graph, probability and automata chapters occupy Lectures 10–14.

Legend. — — not scheduled. ↑ Lab N / ↑ P N — the cell is merged with the row above: one work covers several topics (Lab 1 → L01–L02, Lab 5 → L07–L08, Practical 1 → L01–L02). A work listed on two separate rows spans both topics (Practical 3 appears on L04 and L06 — truth tables and normal forms).

Content module 1 (lectures 1–9) #

Content module 2 (lectures 10–15) #

4. Control methods and course rating grading #

The course is graded on a 100-point scale, split between two written tests, the laboratory works, and the practical assignments.

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