PřF:M5210 How to use topology - Course Information
M5210 How to use topology
Faculty of Scienceautumn 2017
- Extent and Intensity
- 0/2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: z (credit).
- Teacher(s)
- Mgr. Marek Filakovský, Ph.D. (lecturer)
Mgr. Pavel Paták, Ph.D. (lecturer) - Guaranteed by
- doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 18. 9. to Fri 15. 12. Thu 15:00–16:50 MS1,01016
- Prerequisites
- Basic notions from algebra and calculus
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Algebra and Discrete Mathematics (programme PřF, N-MA)
- Geometry (programme PřF, N-MA)
- Mathematical Analysis (programme PřF, N-MA)
- Mathematics (programme PřF, B-MA)
- Course objectives
- Students will understand the Borsuk-Ulam theorem including its proof and will be able to apply it to various problems.
- Learning outcomes
- Students will be able to understand basic research articles in the field of discrete topology and geometry
- Syllabus
- 1. Motivation
- 2. Basic constructions
- 3. Borsuk-Ulam theorem I
- 3. Borsuk-Ulamova theorem II - geometric proof
- 5. Abstract simplicial complexes
- 6. Multicolored partitions and necklaces
- 7. Algebraic topology - basic constructions
- 8. Embeddability
- 9. Interesting questions I
- 10. Interesting questions II
- 11. Interesting questions III
- Literature
- recommended literature
- Matoušek, Jiří. Using the Borsuk-Ulam Theorem, Springer 2003
- Hatcher, Allen. Algebraic topology I. http://math.cornell.edu/~hatcher
- Teaching methods
- Lectures, exercises and homeworks
- Assessment methods
- A "passed" mark will be given based on the homeworks of the participant
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught only once. - Teacher's information
- http://www.math.muni.cz/~filakovsky
- Enrolment Statistics (recent)
- Permalink: https://is.muni.cz/course/sci/autumn2017/M5210