Day	Topic	Pages from Hatcher or other reference	Homework
1/18	Overview; Cell complexes	P. 1-8
1/20	The fundamental group	P. 21-28	Homework 1, due Thursday 1/27
1/25	Fundamental group of the circle	P. 29-31
1/27	Brouwer & Borsuk-Ulam theorems	P. 31-34
2/1	Induced homomorphisms	P. 34-37	P. 38-39, #8, 9, 10, 16. Due Tuesday 2/8
2/3	Van Kampen's theorem	P. 40-46
2/8	Applications of van Kampen	P. 46-52; extra page
2/10	Fundamental groups of manifolds	Conway's ZIP Proof, Mapping class group	Homework 3, due Thursday 2/17
2/15	Intro to covering spaces	P. 56-61
2/17	The universal cover	P. 63-65	Homework 4, due Thursday 2/24
2/22	Group actions	P. 70-74
2/24	Classification of covering spaces	P. 61-62, 66-68.	Homework 5, due Tuesday 3/15.
3/1	Intro to homology	P. 97-101.
3/3	Simplicial homology	P. 102-107.
3/15	Singular homology: definitions	P. 108-110.	P. 131-132 #4, 5, 8, 10, 11. Due Thursday 3/24
3/17	Properties of singular homology	P. 110-113.
3/22	Exact sequences, H1 vs. π1	P. 113-114, 166-168.
3/24	Long exact sequence of a pair	P. 114-117.	P. 123 #14, 16, 17. P. 53 #9 (easier using homology!) Due 3/31
3/29	Excision (in a nutshell)	P. 117-124
3/31	Simplicial = singular homology	P. 125-130
4/5	Orientations, π1, and homology	Lee, p. 329-334	Homework 8, due 4/14
4/7	Degrees of maps	P. 134-135
4/12	Degrees from smooth theory	P. 136, Wikipedia
4/14	Mayer-Vietoris sequence	P. 149-153	Homework 9, due 4/21
4/19	Intro to cohomology	P. 186-189.
4/21	De Rham cohomology	Lee, p. 388-399 (skipping a lot).
4/26	The de Rham theorem	Lee, p. 425-430.	Homework 10, due 5/5
4/28	Poincaré duality	P. 241-248; Lee, p. 432; Wikipedia