1. komponenta

Lecture type	Total
Lectures	45

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES:
Getting acquainted with techniques of operating with combinatorial and discrete structures and objects. The course is important for theoretical mathematics and computing, especially in the analysis of algorithms, because it deals with a number of fundamental mathematical techniques with many concrete examples.

COURSE DESCRIPTION AND SYLLABUS:
1. Combinatorial enumeration (by many examples).
2. Recursive problems.
3. Computing sums - discrete calculus.
4. Binomial and multinomial coefficients.
5. Partial ordered sets and Moebius inversion.
6. Ordinary and exponential generating functions.
7. Recursions and generating functions.
8. Formal languages and symbolic methods.
9. Lagrange's inversion formula.
10. Hypergeometric series. Gosper's algorithm.
11. Asymptotics of some important combinatorial sequences.
12. Some theorems in extremal combinatorics (Sperner's, Turan's theorem etc.).
13. Elements of algebraic graph theory.
14. Elements of geometric combinatorics.
15. Probabilistic methods.

1. Kombinatorika, skripta, V. Krčadinac, Sveučilište u Zagrebu, 2024.
2. Combinatorics: topics, techniques, algorithms, P. J. Cameron, Cambridge University Press, 1996.
3. Algebraic combinatorics, C. D. Godsil, CRC Press, 1993.
4. Concrete mathematics. A foundation for computer science, R. Graham, D. Knuth, O. Patashnik, Addison-Wesley, 1994.
5. Bijective combinatorics, N. A. Loehr, CRC Press, 2011.
6. Kombinatorna i diskretna matematika, D. Veljan, Algoritam, Zagreb, 2001.
7. Generatingfunctionology, H. S. Wilf, Academic Press, Inc., 1994.

Ostali izborni predmeti - Regular study - Computer Science and Mathematics

Ostali izborni predmeti - Regular study - Computer Science and Mathematics