*Instructor:* Dr. Károly Böröczky

*Text*: Allen Hatcher: Algebraic Topology, Chapters 0 and 2, handouts

*Prerequisite*: Some introductory topology (say a real analysis
class), and some introductory algebra (essentially the notion of
Abelian group)

**Course description: **We start with a short course on the point
set topology, which is an essential part of modern analysis, to be ready
for algebraic topology, which is one of the most dramatic topic of modern
geometry. Level depends on the background of the class.

**Topics:**

- Notion of homotopy and homotopy type
- Simplicial complexes and Cell complexes
- Homotopy extension property
- Simplicial homology
- Singular homology
- Exact sequences and Excision
- Degree
- Axioms for Homology Theory
- Mayer Vietoris Sequences
- Brouwer fixed point theorem
- No wind theorem
- Borsuk-Ulam theorem
- Invariance of domains