Mathematics for gifted students *

There are no prerequisites.

Preparation of more demanding mathematical topics for gifted students. Use of computer tools for preparing lecture materials.

Handling tasks from mathematical competitions (e.g. national mathematics competition, recreational mathematics competition, logic competition, the International Mathematical Olympiad). Preparation of a maths circle for gifted students.

Lectures by external experts, e.g. on the specifics of working with gifted students, on preparing for mathematical competitions... Conversation with high school professors about their experiences.

Use of TeX and a program for drawing mathematical figures and preparation of an article suitable for publication in the popular science journal Presek.

1. B. Burn, A. Chetwynd: A cascade of numbers : an introduction to number theory, London : Arnold, cop. 1996.
2. J. R. Silvester: Geometry : ancient and modern, Oxford : Oxford University Press, 2001.
3. A. M. Yaglom, I. M. Yaglom: Challenging mathematical problems with elementary solutions. Vol. 1, Combinatorial analysis and probability theory, San Francisco : Holden-Day, 1964.
4. A. M. Yaglom, I. M. Yaglom: Challenging mathematical problems with elementary solutions. Vol. 2, San Francisco : Holden-Day, cop. 1967.

Acquired understanding and skills to work with gifted students on demanding problems.

Knowledge and understanding of advanced elementary high school mathematical contents.

Problem solving, lectures, exercise sesions, homework, consultations. Students work with high school students.

Homework, project work, class performances.
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Damjan Kobal:
KOBAL, Damjan. Technology and simple math ideas inspire teaching. V: ICME - 12 : the 12th International Congress on Mathematical Education, July 8-15, 2012, COEX, Seul, Korea. Cheongju: Korea National University of Education, 2012, 7 str. [COBISS-SI-ID 17151577]
KOBAL, Damjan, et al. Integrating algebra and geometry with complex numbers. V: International Seminar in Mathematics Education 2011. Park City: Park City Mathematics Institute - Institute for Advanced Study, cop. 2013, 9 str. [COBISS-SI-ID 17152345]
KOBAL, Damjan. Inner product space and circle power. Publicationes mathematicae, ISSN 0033-3883, 2012, vol. 81, fasc. 1-2, str. 1-9. [COBISS-SI-ID 16336473]
KOBAL, Damjan. Bijections preserving invertibility of differences of matrices on H [sub] n. Acta mathematica Sinica, English series, ISSN 1439-8516, 2008, vol. 24, no. 10, str. 1651-1654. [COBISS-SI-ID 15588441]
Matjaž Konvalinka:
KONVALINKA, Matjaž, Seminar "Moderni izzivi poučevanja matematike", Fakulteta za matematiko in fiziko, Ljubljana, 20.-21.september 2013. Catalanova števila. Ljubljana, 21. 9. 2013. [COBISS-SI-ID 17227353]
KONVALINKA, Matjaž, FMF seminar za učitelje matematike, Fakulteta za matematiko in fiziko, Ljubljana, 21. - 22. september 2018. Gessel-Viennotova lema in determinante v kombinatoriki : Ljubljana, 22. 9. 2018. [COBISS-SI-ID 18576473]
ZAJC, Gal. Prostornine pravilnih politopov : matematika. Ljubljana: Gimnazija Bežigrad, 2019. 54 str., ilustr., mentorica Jasna Kos, somentor Matjaž Konvalinka [COBISS-SI-ID 2057090]
FISCHER, Ilse, KONVALINKA, Matjaž. The mysterious story of square ice, piles of cubes, and bijections. Proceedings of the National Academy of Sciences of the United States of America. Sep. 2020, vol. 117, no. 38, str. 23460-23466, ilustr. [COBISS-SI-ID 27280643]