Day	Topic	Reference	Homework
1/23	Overview; Cell complexes	P. 1-8
1/28	The fundamental group	P. 21-28
1/30	Fundamental group of the circle	P. 29-31	Homework 1, due 2/6
2/4	Brouwer & Borsuk-Ulam theorems	P. 31-34
2/6	Induced homomorphisms	P. 34-37	P. 38-39, #8, 10, 16. Due 2/13
2/11	Van Kampen's theorem	P. 40-46
2/13	Applications of van Kampen	P. 46-52; extra page
2/18	Fundamental groups of manifolds	Conway's ZIP Proof
2/20	Intro to covering spaces	P. 56-61	Homework 3, due Wednesday 2/27
2/25	The universal cover	P. 63-65
2/27	Group actions; cloassification of covers	P. 67-68	Homework 4, due Wednesday 3/6
3/4	Deck transformations	P. 70-74
3/6	Intro to homology	P. 97-101.
3/18	Simplicial homology	P. 102-107.
3/20	Singular homology: definitions	P. 108-110.	P. 131-132 #4, 5, 8, 10, 11. Due Wednesday 3/27.
3/25	Homotopy invariance, H1 vs. π1	P. 110-113, 166-168.
3/27	Long exact sequence of a pair	P. 114-117.
4/1	Excision (in a nutshell)	P. 117-124
4/3	Simplicial = singular homology	P. 125-130	P. 132 #14, 16, 17, 22. P. 53 #9 (easier using homology!) Due 4/10
4/8	Formal viewpoint; Mayer-Vietoris sequence	P. 149-153, 160-162
4/10	Orientations, π1, and homology	Lee, p. 329-334	Homework 7, due 4/14
4/15	Degrees of maps	P. 134-135
4/17	Degrees from smooth theory	P. 136, Wikipedia
4/22	Intro to cohomology	P. 186-189.
4/24	De Rham cohomology	Lee, p. 388-399 (skipping a lot).	Homework 8, due 5/3
4/29	The de Rham theorem, Poincaré duality	Lee, p. 425-430; Wikipedia
5/3	Poincaré duality	P. 241-248; Lee, p. 406-407, 432