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Students' competitions in mathematics

Code: 133310
ECTS: 3.0
Lecturers in charge: doc. dr. sc. Matija Bašić - Lectures
izv. prof. dr. sc. Ilja Gogić - Lectures
izv. prof. dr. sc. Vjekoslav Kovač - Lectures
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.
Load:

1. komponenta

Lecture typeTotal
Lectures 30
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES: The main aim of the course is preparing students for international competitions in mathematics. In addition to reviewing the undergraduate material, the participants will gain familiarity with a variety of techniques, ideas and certain tricks for solving original mathematical problems. Other objectives of the course are: promoting the general mathematical culture to interested students, introducing better students to the scientific research, and encouraging students for self-guided study and practice.

COURSE DESCRIPTION AND SYLLABUS: The actual topics vary from year to year, depending on the structure and interests of the audience and the actuality of the topics themselves.
1. The minimal polynomial and other tricks from linear algebra
2. Divide and conquer, project and conquer
3. Quadratic residues
4. Algebraic combinatorics
5. Iterative dynamical systems
6. The probabilistic method in combinatorics and graph theory
7. The classification of two-dimensional manifolds
8. Group actions and Burnside's lemma
9. The Riemann zeta function
10. Estimation and the asymptotic calculus in mathematical analysis
11. Elliptic curves
12. Applications of the Fourier analysis on finite abelian groups
13. The Hamel bases and applications
14. Introduction to algebraic topology
15. Ultrametric spaces
16. The Baire category theorem
17. Partially ordered sets
18. Tilings and the Gröbner bases
Literature:
  1. R. Gelca, T. Andreescu: Putnam and beyond
  2. G. J. Szekely: Contests in Higher Mathematics: Miklos Schweitzer Competitions 1962-1991
2. semester
Fakultativni kolegiji - Regular study - Applied Mathematics
Fakultativni kolegiji - Regular study - Computer Science and Mathematics
Fakultativni kolegiji - Regular study - Financial and Business Mathematics
Fakultativni kolegiji - Regular study - Mathematical Statistics
Fakultativni kolegij - Regular study - Mathematics
Fakultativni kolegij - Regular study - Mathematics and Computer Science Education
Fakultativni kolegij - Regular study - Mathematics and Physics Education
Fakultativni kolegij - Regular study - Mathematics Education
Fakultativni kolegij - Regular study - Mathematics Education
Fakultativni kolegiji - Regular study - Theoretical Mathematics

4. semester
Fakultativni kolegiji - Regular study - Applied Mathematics
Fakultativni kolegiji - Regular study - Computer Science and Mathematics
Fakultativni kolegiji - Regular study - Financial and Business Mathematics
Fakultativni kolegiji - Regular study - Mathematical Statistics
Fakultativni kolegij - Regular study - Mathematics
Fakultativni kolegij - Regular study - Mathematics and Computer Science Education
Fakultativni kolegij - Regular study - Mathematics and Physics Education
Fakultativni kolegij - Regular study - Mathematics Education
Fakultativni kolegij - Regular study - Mathematics Education
Fakultativni kolegiji - Regular study - Theoretical Mathematics

6. semester
Fakultativni kolegij - Regular study - Mathematics
Fakultativni kolegij - Regular study - Mathematics and Physics Education
Fakultativni kolegij - Regular study - Mathematics Education

8. semester
Fakultativni kolegij - Regular study - Mathematics and Physics Education

10. semester
Fakultativni kolegij - Regular study - Mathematics and Physics Education
Consultations schedule:

Content

Link to the course web page: https://www.pmf.unizg.hr/math/predmet/snim_a