Day	Topic	Reference	Homework
1/17	Overview; Cell complexes	P. 1-8
1/22	The fundamental group	P. 21-28
1/24	Fundamental group of the circle	P. 29-31	Homework 1, due 1/31
1/29	Brouwer & Borsuk-Ulam theorems	P. 31-34
1/31	Induced homomorphisms	P. 34-37	Homework 2, Due 2/7
2/5	Van Kampen's theorem: setup	P. 40-44
2/7	Van Kampen's theorem: proof	P. 44-46	Homework 3, Due 2/14
2/12	Fundamental groups of cell complexes	P. 46-52; extra page
2/14	Fundamental groups of manifolds	Conway's ZIP Proof	Homework 4, Due 2/21
2/19	Intro to covering spaces	P. 56-61
2/21	The universal cover	P. 63-65	Homework 5, due Wednesday 2/28
2/26	Group actions; cloassification of covers	P. 67-68
2/28	Deck transformations	P. 70-74
3/12	Intro to homology	P. 97-101.
3/14	Simplicial homology	P. 102-107	Homework 6, Due Friday 3/23.
3/19	Singular homology: definitions	P. 108-110
3/21	No class (snow day)
3/26	Homotopy invariance, exact sequences	P. 110-114	P. 132 #11, 14, 16, 17, 22. Due 4/4
3/28	Relation between H1 and π1	P. 166-168
3/30	Long exact sequence of a pair	P. 114-117
4/2	Excision (in a nutshell)	P. 117-124
4/4	Simplicial = singular homology	P. 125-130	Homework 8, due Wednesday 4/11
4/9	Orientations, π1, and homology	Lee, p. 393-396
4/11	Degrees of maps	P. 134-136	Homework 9, due Wednesday 4/18
4/16	Degrees from smooth theory	P. 136, Lee, p. 457-459
4/18	Euler characteristic; Mayer-Vietoris sequence	P. 146-151	Homework 10, due Wednesday 4/25
4/23	Intro to cohomology; de Rham cohomology	P. 441-443.
4/25	The de Rham homomorphism	Lee, p. 467-483 (skipping a lot).
4/30	The de Rham theorem, Poincaré duality	Lee, p. 484-487; Wikipedia	Homework 11, due Monday 5/7