Applications of algebraic geometry in mathematical contests
| Thesis title in Czech: | Aplikace algebraické geometrie v matematických soutěžích |
|---|---|
| Thesis title in English: | Applications of algebraic geometry in mathematical contests |
| Key words: | Animace|Desarguesova involuce|kružnice|kuželosečky|resultant|algebraická geometrie|projektivní geometrie|eliptická křivka |
| English key words: | Animation|Desargues Involution|circles|conics|resultants|algebraic geometry|projective geometry|elliptic curve |
| Academic year of topic announcement: | 2021/2022 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | angličtina |
| Department: | Department of Algebra (32-KA) |
| Supervisor: | doc. RNDr. Jan Šťovíček, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 21.12.2021 |
| Date of assignment: | 21.12.2021 |
| Confirmed by Study dept. on: | 31.01.2022 |
| Date and time of defence: | 23.06.2022 09:00 |
| Date of electronic submission: | 12.05.2022 |
| Date of submission of printed version: | 12.05.2022 |
| Date of proceeded defence: | 23.06.2022 |
| Opponents: | Sebastian Opper, Ph.D. |
| Guidelines |
| Student se seznámí se základy algebraické geometrie, např. ze zdrojů [1,2,3] a zaměří se na aplikace těchto (vysokoškolských) metod na úlohy v matematických soutěžích, např. v matematické olympiádě. Konkrétně se pokusí takto popsat např. Desarguesovu involuci [4] a tzv. metodu animace [5]. |
| References |
| [1] W. Fulton, Algebraic Curves (An Introduction to Algebraic Geometry), http://www.math.lsa.umich.edu/~wfulton/CurveBook.pdf, 2008.
[2] D. Cox, J. Little, D. O'Shea, Ideals, varieties, and algorithms, Second Edition, Springer, New York, 2005. [3] A. Gathmann, Algebraic geometry, skripta kurzu z Kaiserslautern, https://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2002/alggeom-2002.pdf, 2002/2003. [4] N. Phat Nguyen, A Generalization of Desargues' Involution Theorem, https://arxiv.org/abs/1912.12200, 2019. [5] Z. Chroman, G. K. Goel, A. Mudgal, The Method of Animation, https://artofproblemsolving.com/community/c6h1952595p13480666, 2019. |