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### Combinatorics

 Code: 45679 ECTS: 5.0 Lecturers in charge: prof. dr. sc. Vedran Krčadinac - Lectures Lecturers: prof. dr. sc. Vedran Krčadinac - Exercises English level: 1,0,0 All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

### 1. komponenta

Lecture typeTotal
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 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.
Literature:
1. D. Veljan: Kombinatorna i diskretna matematika
2. R. Graham, D. Knuth, O. Patashnik: Concrete Mathematics. A Foundation for Computer Science
3. D. Knuth: Selected Papers on Discrete Mathematics, CSLI Lecture Notes No. 106
4. J. van Lint, R. Wilson: A Course in Combinatorics
5. K. Rosen (Ed.): Handbook of Discrete and Combinatorial Mathematics
6. S. K. Lando: Lectures on Generating Functions
7. R. P. Stanley: Enumerative Combinatorics, Vol. I & II
 1. semester Izborni predmet 1, 2, 3, 4 - Regular study - Mathematical Statistics 2. semester Izborni predmet 1, 2, 3, 4 - Regular study - Mathematical Statistics 3. semester Izborni predmeti 5, 6, 7 - Regular study - Mathematical Statistics 4. semester Izborni predmeti 5, 6, 7 - Regular study - Mathematical Statistics
Consultations schedule: