Load:

1. komponenta
Lecture type  Total 
Lectures 
30 
Exercises 
15 
* Load is given in academic hour (1 academic hour = 45 minutes)

Description:

COURSE AIMS AND OBJECTIVES: Introduce 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 qbinomial 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.

Literature:

 D. Veljan: Kombinatorna i diskretna matematika
 R. Graham, D. Knuth, O. Patashnik: Concrete Mathematics. A Foundation for Computer Science
 D. Knuth: Selected Papers on Discrete Mathematics, CSLI Lecture Notes No. 106
 J. van Lint, R. Wilson: A Course in Combinatorics
 K. Rosen (Ed.): Handbook of Discrete and Combinatorial Mathematics
 S. K. Lando: Lectures on Generating Functions
 R. P. Stanley: Enumerative Combinatorics, Vol. I & II
