| Call number: | 64818 | |
| Room/Time: | MW 1:10pm--2:25pm, 203 Math | |
| Instructor: | Mikhail Khovanov | |
| Office: | 620 Math | |
| Office hours: | Monday 2:30-3:30pm, Wednesday 12-1pm | |
| E-mail: | | |
| Teaching Assistant: | Kat Christianson | |
| TA office hours: | Monday 4:30-5:30, Tuesday 11:30-12:30 in Help Room, 406 Math | |
| Midterm : | Wednesday, October 21 | |
| Review Session: | Friday, December 18, 5:30-7pm, Math 507 | |
| Final: | Monday, December 21, 1:10-4pm, 203 Math | |
| Webpage: | www.math.columbia.edu/~khovanov/topology2015 | |
--> Prerequisites The first semester of "Introduction to Modern Algebra" (Math W4041) or equivalent is required, since we'll be using group theory in the second half of the course. You also need to be familiar with how to write proofs. Familiarity with analysis (Math V1208 or W4061) is recommended as well.
Textbook Topology, by James R. Munkres, second edition. Available on Amazon or Barnes and Noble. Columbia University bookstore should have it. We are using the more expensive Pearson edition. Much cheaper (and probably identical except for the paper quality) Prentice-Hall edition is listed as out of stock.
Syllabus:
Topological spaces and continuous maps. Examples of topologies.
Closed sets, interior, limit points. Hausdorff spaces.
Product topology.
Connectedness and path-connectedness.
Compactness.
Metric spaces and their topology.
Countability and separation axioms
Normal spaces, the Uryson lemma.
Homotopic maps.
The fundamental group. Examples.
Retraction and homotopy equivalence.
Groups via generators and relations.
Free groups and amalgamated products.
The van Kampen theorem and its applications.
Surfaces and their classification.
If time allows: Knots, their fundamental group and other invariants.
Homework: Homework
will be assigned on Wednesdays, due Wednesday the next week before class.
The first problem set is due September 16. The lowest homework score
will be dropped.
The numerical grade for the course will be the following linear combination:
35% homework, 25% midterm, 40% final.
Homework 1 Due September 16.
Homework 2 Due September 23.
Homework 3 Due September 30.
Homework 4 Due October 7.
Homework 5 Due October 14.
Homework 6 Due October 21.
Homework 7 Due November 4.
Homework 8 Due November 11.
Homework 9 Due November 18.
Homework 10 Due December 2.
Homework 11 Due December 9.