Klasické kombinatorické úlohy
| Thesis title in Czech: | Klasické kombinatorické úlohy |
|---|---|
| Thesis title in English: | Classic problems in combinatorics |
| Key words: | úloha o zajatcích, hanojské věže, úloha o hostech, hlasovací problém, úloha o školačkách |
| English key words: | Josephus problem, Tower of Hanoi, ménage problem, ballot problem, Kirkman's schoolgirl problem |
| Academic year of topic announcement: | 2009/2010 |
| Thesis type: | diploma thesis |
| Thesis language: | čeština |
| Department: | Department of Mathematics Education (32-KDM) |
| Supervisor: | doc. RNDr. Antonín Slavík, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 15.10.2009 |
| Date of assignment: | 15.10.2009 |
| Date and time of defence: | 21.05.2012 08:30 |
| Date of electronic submission: | 12.04.2012 |
| Date of submission of printed version: | 13.04.2012 |
| Date of proceeded defence: | 21.05.2012 |
| Opponents: | doc. RNDr. Emil Calda, CSc. |
| Guidelines |
| Práce bude zaměřena na vybrané klasické úlohy z kombinatoriky. Cílem je srozumitelně vysvětlit zadání úloh, uvést různé způsoby jejich řešení, zmínit historii úloh a jejich případná zobecnění. |
| References |
| R. L. Graham, D. E. Knuth, O. Patashnik: Concrete Mathematics. Addison Wesley, 1990
M. Gardner: Hexaflagons and Other Mathematical Diversions. The University of Chicago Press, 1988 M. Gardner: Knotted doughnuts and other mathematical entertainments. W. H. Freeman and Company, 1986 Časopisecké články, např.: David G. Poole: The Towers and Triangles of Professor Claus (or, Pascal Knows Hanoi). Mathematics Magazine, Vol. 67, No. 5 (1994), 323-344 Marc Renault: Four Proofs of the Ballot Theorem. Mathematics Magazine, Vol. 80, No. 5 (2007), 345-352 Marc Renault: Lost (and Found) in Translation: André's Actual Method and Its Application to the Generalized Ballot Problem. American Mathematical Monthly, Vol. 115 (2008), 358-363 Peter Schumer: The Josephus Problem: Once More around. Mathematics Magazine, Vol. 75, No. 1 (2002), 12-17 Ch. Groër: The Mathematics of Survival: From Antiquity to the Playground. The American Mathematical Monthly, Vol. 110, No. 9 (2003), 812-825 Kenneth P. Bogart and Peter G. Doyle: Non-Sexist Solution of the Menage Problem. The American Mathematical Monthly, Vol. 93, No. 7 (1986), 514-518 L. Holst: On the 'probléme des ménages' from a probabilistic viewpoint. Statistics & Probability Letters, Vol. 11, Issue 3, March 1991, 225-231 |