M5210 How to use topology

Faculty of Science
autumn 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
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