1. komponenta

Lecture type	Total
Lectures	45

COURSE AIMS AND OBJECTIVES: Introducing students to combinatorial and discrete structures and objects. This course is important for theoretical mathematics and computer science and especially in analysis of algorithms, because it deals with fundamental mathematical techniques with many concrete examples (I.M. Gelfand: The older I get, the more I believe that at the bottom of most deep mathematical problems there is a combinatorial problem.)

COURSE DESCRIPTION AND SYLLABUS (by weeks):
1. Combinatorial enumeration (by many examples);
2. Recursive problems;
3. Computing sums - discrete calculus;
4. Binomial and q-binomial 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, 2022.
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. Combinatorial mathematics, D. B. West, Cambridge University Press, 2021.
8. Generatingfunctionology, H. S. Wilf, Academic Press, Inc., 1994.

Izborni računarski predmet 1, 2 - Regular study - Mathematics and Computer Science Education

Izborni računarski predmet 1, 2 - Regular study - Mathematics and Computer Science Education