Mathematics for gifted students *

Mathematics Education
4 ali 5 year
Hours per week – 1. semester:
Content (Syllabus outline)

Different mathematical problems and challenges that emphasize understanding and independent problem solving are presented. Problems we work on are independent and consist of classical geometry problems, number theory problems, linear algebra problems, topology, game theory and other problems. We deal with classical problems from mathematical competitions. All the sesions are designed as problem solving sessions. Students also work very practically with gifted high school students for 15 school hours.


Zbirke domačih in mednarodnih tekmovanj
Sprotna matematična tekmovanja
J.H. Silvester, Geometry: Ancient and Modern
A.M.Yaglom, I.M. Yaglom, Challenging mathematical problems with elementary solutions, Dover Publications 1987.
R.P. Burn, A. Chetwynd: A Cascade of Numbers, An Introduction to number theory, Arnold 1996.

Objectives and competences

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

Intended learning outcomes

Knowledge and understanding of advanced elementary high school mathematical contents.

Learning and teaching methods

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)

Lecturer's references

Seminar "Moderni izzivi poučevanja matematike", Fakulteta za matematiko in fiziko, Ljubljana, 29. in 30. september 2006, ŠEMRL, Peter. Dve temi za matematični krožek. Ljubljana, 30. 9. 2006. [COBISS-SI-ID 17317209]
Seminar "Moderni izzivi poučevanja matematike", Fakulteta za matematiko in fiziko, Ljubljana, 24. in 25. september 2004, ŠEMRL, Peter. Pi. Ljubljana, 24. 9. 2004. [COBISS-SI-ID 17357913]
ŠEMRL, Peter. Maps on matrix spaces. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 2006, vol. 413, no. 2-3, str. 364-393. [COBISS-SI-ID 13906009]
ŠEMRL, Peter. Orthogonality preserving transformations on the set of n-dimensional subspaces of a Hilbert space. Illinois journal of mathematics, ISSN 0019-2082, 2005, vol. 48, no. 3, str. 567-573. [COBISS-SI-ID 13404249]
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]