Selected problems in discrete mathematics 1000-2M07MD
1. Combinatorial designs.
2. Dilworth's theorem and extremal set theory.
3. Generating functions and their applications.
4. Counting: inversion formulas.
5. Ramsey's theory. Extremal graphs.
6. Algebraic methods in graph theory.
7. The probabilistic method.
8. Randomness in graphs.
Type of course
Course coordinators
Learning outcomes
Knowledge
1. Extended knowledge in combinatorics and graph theory (K_W01).
2. Knowledge of basic applications of probabilistic and algebraic methods in discrete mathematics (K_W02).
3. Understanding of the role and importance of mathematical reasonings (K_W01, K_W02).
Skills
1. Ability to analyze and solve medium complexity problems in discrete mathematics (K_U01).
2. Ability to understand and apply a formal description of mathematical objects (K_U01, K_U03).
Competence
1. Awareness of own limitations and the need for further education (K_K01).
2. Ability to precisely formulate questions to deepen the understanding of given subject or to find missing elements of reasoning (K_K02).
3. Ability to self-dependently search for information in literature, also in foreign languages (K_K04).
Assessment criteria
Written exam (test), also non obligatory oral exam.
In the case of completing the course by a doctoral student, the student will present a selected issue in the class.
Bibliography
1. N. Alon, J. Spencer, 'The probabilistic method'
2. R. Diestel, 'Graph Theory'
3. J.H. van Lint, R.M. Wilson, 'A course in combinatorics'
4. H.S. Wilf, 'generatingfunctionology'
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
- Bachelor's degree, first cycle programme, Computer Science
- Master's degree, second cycle programme, Computer Science
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: