- point-set topology: compactness, connectedness, etc.
- theory and classification of surfaces
- triangulations
- fundamental group and covering spaces
- homology; fixed point theorems

I'll cover much of the material in Chapters 1-8, but not all of it.

Sometimes I will supplement the text with my own notes.

assigned each Tuesday and collected the following Tuesday. There is no late HW.

Click here for the assignments.

HW: 35%

Midterm: 30 %

Final: 35 %

- Sample Proofs
- A Note on Bases
- Construction of the Reals
- Cauchy Sequences of Functions
- Compactness proof of the fundamental thm of alg.
- Sperner's Lemma
- Polygonal Jordan Curve Theorem
- General Jordan Curve Theorem
- Examples of Manifolds
- Hairy Sphere Theorem
- Classification of (Triangulated) Surfaces
- Differential Forms and Cohomology