Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Computer Science
- Code
- velstr1u0um20em
- Title
- Random structures and applications
- Usual semester
- Spring
- ECTS
- 3
- Language
- Learning outcomes
- Knowledge: getting familiar with the main notions and applications of random structures Ability: to understand and use mathematical models based on random structures 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 random structures, the students are able to decide which tools are the most suitable to solve applied problems
- Course content
- Method of first and second moments. Deterministic improvement of a random object. Constructing a graph with large chromatic number not containing small cycles. Random graphs, threshold function, evolution around p=logn/n. Local lemma and its applications. Correlation inequalities: 4 functions theorem and FKG-inequality, Poisson paradigm: Brun-sieve and Janson-inequalities. Martingales. Applications of entropy.
- Assessment method
- exam
- Bibliography
- lecture notes