Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Computer Science
- Code
- extkom1u0um20em
- Title
- Extremal combinatorics
- Usual semester
- Spring
- ECTS
- 3
- Language
- Learning outcomes
- Knowledge: getting familiar with the main notions of extremal combinatorics Ability: to understand and use extremal combinatorics 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 in extremal combinatorics, the students are able to decide which tools are the most suitable to solve applied problems
- Course content
- Excluded non-bipartite subgraphs: theorems of Erdős-Stone-Simonovits and Dirac. Excluded bipartite subgraphs: paths and the Turán-number of K(p,q). Finite geometric and algebraic constructions. Szemerédi regularity theorem and its applications. Turán-Ramsey type theorems. Extremal set families: Sperner and Erdős-Ko-Rado theorems, generalizations. Ray-Chaudhury theorem.
- Assessment method
- exam