Day	Topic	Reference	Homework
1/15	Overview; Cell complexes	P. 1-8
1/17	The fundamental group	P. 21-28
1/22	Fundamental group of the circle	P. 29-31	Homework 1, due 1/31
1/24	Brouwer & Borsuk-Ulam theorems	P. 31-34
1/29	Induced homomorphisms	P. 34-37
1/31	Van Kampen's theorem	P. 40-46	Homework 2, Due 2/7
2/5	Fundamental groups of cell complexes	P. 46-52; extra page
2/7	Fundamental groups of manifolds	Conway's ZIP Proof	Homework 3, Due 2/14
2/12	No class
2/14	Intro to covering spaces	P. 56-61	Homework 4, due Thursday 2/21
2/19	The universal cover	P. 63-65
2/21	Group actions; cloassification of covers	P. 67-68	Homework 5, due Thursday 2/28
2/28	Deck transformations	P. 70-74
3/12	Intro to homology; simplicial homology	P. 97-105.
3/14	Singular homology: definitions	P. 106-109	Homework 6, Due Thursday 3/21.
3/19	Properties of singular homology	P. 109-114
3/21	Relation between H1 and π1; exact sequences	P. 113-114, 166-168	P. 132 #11, 14, 16, 17. Due 3/28.
3/26	Long exact sequence of a pair	P. 114-117
3/28	Excision (in a nutshell)	P. 117-124	Homework 8, due Thursday 4/4
4/2	Simplicial = singular homology	P. 125-130
4/4	5-Lemma; Mayer-Vietoris Sequence	P. 129, 149-51	Homework 9, due Thursday 4/11
4/9	Euler characteristic; Orientations and homology	P. 146-147
4/11	Degrees of maps	P. 134-136	Homework 10, due Thursday 4/18
4/16	Degrees from smooth theory	P. 136, Lee, p. 457-459
4/18	Intro to cohomology	P. 441-443.
4/23	The de Rham homomorphism	Lee, p. 467-483 (skipping a lot).	Homework 11, not due
4/25	The de Rham theorem	Lee, p. 484-487
4/30	Poincaré duality	P. 241-248; Wikipedia