Study program: 122 Computer Science

Degree: Bachelor

Type of module: lectures, seminars

Lecturer: Prof. Dmytro Sytnikov

Language: English

Credit Points: 4 ECTS

Descrpition:

A compulsory discipline of the professional and practical training. It has the next content modules: Topic 1. Relations and operations with them. Cartesian product. Definition of relations. Binary and n-ary relations. Domains. Ways of relation construction. Operations with relations. Topic 2. Properties of binary relations. Reflexivity, antireflexivity, symmetricity, antisymmetrisity, asymmeticity, transitivity. Classes of binary relations. Equivalence relations. Order relations. Tolerance relations. Topic 3. Functional relations. Domains. Functions and mappings. Types of mappings: surjections, injection, bijections. Topic 4. Combinatorics definition. Models of typical combinatorial configurations. r-samples. General rules and problems of combinatorics. Rules of sum and product. Permutations, allocations, combinations (with and without repetition). Topic 5. Problems of objects allocation. Allocation of similar objects. Allocation of different objects. Stirling numbers, Morgan numbers, Bell numbers. Compositions. Topic 6. General concepts of graph theory. Typical problems of graph theory. Topic 7. Graph definition. Types of graphs. Non-oriented and oriented graphs. Basic terminology. Geometric interpretation of graphs. Graph matrices. Number of edges and vertices. Topic 8. Graph operations.