Lecturer: Christian Bär
Content:
What are the Euler and Betti numbers, what are homotopy and homology groups? In algebraic topology one tries to understand the shape of spaces by assigning algebraic invariants to them.
The lecture course will provide a thorough introduction to these concepts. The structures under consideration are fundamental for many geometric disciplines (differential and algebraic geometry) to global analysis and mathematical physics.
As applications of the calculus we will treat some classical theorems from topology such as the Jordan curve theorem, the theorem of Borsuk-Ulam and the ham-sandwich theorem.
Lectures:
TBA
Exercise class:
TBA
Moodle link:
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Module numbers:
MAT-AM-D221, MAT-VM-D611, MAT-VM-D612
MAT-VM-D811, MAT-VM-D812
Prerequisites:
A Bachelor degree in mathematics or physics is more than sufficient. Ambitious Bachelor students from second year can attend the course.
Literature:
Lecture notes will be provided in the moodle which contain further hints to the literature.