Day	Topic	Reference	Homework
1/11	Overview; Cell complexes	P. 1-8
1/13	The fundamental group	P. 21-28	Homework 1, due Thursday 1/20
1/18	Fundamental group of the circle	P. 28-30
1/20	Fund. group of circle, Brouwer fixed pt theorem	P. 30-32	Homework 2, due Thursday 1/27
1/25	Borsuk-Ulam theorem, simply connected spheres	P. 32-35
1/27	Induced homomorphisms	P. 34-37
2/1	Van Kampen's theorem	P. 40-44	Homework 3, due Thursday 2/10
2/3	Proof of van Kampen; graphs and trees	P. 44-46
2/8	Fundamental groups of cell complexes	P. 46-52; extra page
2/10	Fundamental groups of manifolds	Conway's ZIP Proof	Homework 4, due Thursday 2/17
2/15	Intro to covering spaces	P. 56-61
2/17	The universal cover	P. 63-65	Homework 5, due Thursday 2/24
2/22	Group actions; classification of covers	P. 67-68
2/24	Deck transformations	P. 70-72	Homework 6, due Thursday 3/10.
3/8	Intro to homology	P. 97-101
3/10	Simplicial homology	P. 101-106	Homework 7, due Thursday 3/17.
3/15	Singular homology: definitions	P. 106-109
3/17	Properties of singular homology	P. 109-114
3/22	Relation between H1 and π1; homology groups of spheres	P. 114-115, 166-168	P. 132 #11, 14, 16, 17. Due 3/31.
3/24	Long exact sequence of a pair	P. 114-117
3/29	Excision (in a nutshell)	P. 117-124
3/31	Simplicial = singular homology; Five-Lemma	P. 125-130	Homework 9, due Thursday 4/7
4/5	Mayer-Vietoris Sequence	P. 149-51
4/12	Euler characteristic; Orientations and homology	P. 146-147
4/14	Degrees of maps	P. 134-136	Homework 10, due Thursday 4/21
4/15	Decrees from smooth theory; homology with coefficients	P. 136; Lee, p. 457-459
4/19	Intro to cohomology	P. 185-189
4/21	de Rham cohomology	Lee, p. 467-483 (skipping a lot).	Homework 11, not due