Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Computer Science
- Code
- dimate1u0um17gm
- Title
- Discrete mathematics (p)
- Usual semester
- Autumn
- ECTS
- 3
- Language
- en
- Learning outcomes
- Knowledge: getting familiar with the main notions of discrete mathematics Ability: to apply the learned algorithms for solving complex problems Attitude: the need to deepen the applied mathematical knowledge, to gain new applied mathematical skills, to develop competencies. Aspiration to apply the mathematical knowledge for a wide range of problems Autonomy and Responsibility: based on the gained knowledge within discrete mathematics, the students are able to decide which tools are the most suitable to solve applied problems
- Course content
- Graph theory: colorings of graphs and hypergraphs. Matching Theory. Connectivity. Strongly regular graphs, the integrality condition and its applications. Block systems. Finite fields, error-correcting codes, perfect codes. Extremal graphs, Bondy-Simonovits theorem. Regularity lemma. Planarity, Kuratowski's theorem, drawing graphs on surfaces, minors, Robertson-Seymour theory. Generator functions, inversion formulas on partially ordered sets, recursions. Classical enumeration problems on graphs, number of spanning trees. Probabilistic methods, expected value method. Random graphs. Applications of fields: the linear algebraic method. Combinatorial Nullstellensatz
- Assessment method
- term grade
- Bibliography
- lecture notes