2008 March 5 / E-Mail Me

Schedule

Topology, Carleton College Math 354, Winter 2008, Prof. Joshua R. Davis

We largely follow the textbook (Munkres, Topology, 2nd edition), but we cover only a few chapters (perhaps 2, 3, 9, 11, 12, depending on students' background and interests). Remember to read the day's sections before class, and to do the problems promptly after class rather than waiting for their due date.

Day	Date	Topic	Reading	Problems	Hand-In Day
1	F 1/4	overview	Vector Fields
2	M 1/7	spaces, bases	12, 13	13 #1, 4, 5, 8	4
3	W 1/9	metrics, norms, inner products	20 until 20.3, Inequalities	20 #1b, 9	6
4	F 1/11	products, subspaces	15, 16 until order topology	16 #1, 4, 6	6
5	M 1/14	closed sets, Hausdorffness	17	17 #7, 8, 11, 12, 13, 19	9
6	W 1/16	continuity	18	18 #3, 10, 11	9
7	F 1/18	homeomorphisms, manifolds	21	21 #2	9
8	M 1/21	quotients	22	22 #3, 4	12
9	W 1/23	connectedness	23, skim 24, skim 25 Connectedness	23 #11 24 #1c, 2, 3, 8c	12
10	F 1/25	exam 1
11	M 1/28	compactness, Heine-Borel	26, skim 27	26 #4b, 5, 8 27 #2b	14
12	W 1/30	Urysohn lemma	32.3, 33.1, 36	grade 22#3, 24#3
13	F 2/1	embedding manifolds	36	none
	M 2/4	midterm break
14	W 2/6	homotopy, isotopy	Groups, 51, 52	51 #1, 3	17
15	F 2/8	fundamental group, covering spaces	52, 53	52 #3, 4, 6 53 #3, 6b	17
16	M 2/11	liftings	54	54 #3, 6	20
17	W 2/13	retractions, Brouwer fixed-point	55	55 #1, 2	20
18	F 2/15	catch up		none
19	M 2/18	Borsuk-Ulam, ham sandwich	57	none
20	W 2/20	homotopy equivalence	58	none (exam)
21	F 2/22	catch-up		none
22	M 2/25	intro Seifert-van Kampen	59	none
23	W 2/27	free groups, Seifert-van Kampen	skim (67, 68, 69), 70	none
24	F 2/29	fundamental group examples	70, 73	none
25	M 3/3	fundamental groups of surfaces	73, 74
26	W 3/5	surgery on surfaces	75, 76
27	F 3/7	classification of surfaces	77, 78	(exam)
28	M 3/10	what's next?