This schedule is tentative, and will be updated infrequently.
The homework page will always be up to date.
| Date |
Section |
Topics |
| Th
8/29 |
No class. |
|
| Tu
9/3 |
Overview: point-set versus algebraic topology, Brouwer Fixed-Point Theorem | |
| Th
9/5 |
Ch 2.12-13 | Topological spaces, Basis for a topology |
| Tu
9/10 |
Ch 2.14-15 | Order topology, product topology on XxY |
| Th
9/12 |
Ch 2.16-17 | Subspace topology, closed sets |
| Tu
9/17 |
Ch 2.17-18 | Limit points, Hausdorff spaces, continuous functions |
| Th
9/19 |
Ch 2.19-20 | Product topology, Metric Topology |
| Tu
9/24 |
Ch 2.21-22 | Metric Topology, Quotient topology |
| Th
9/26 |
Ch 3.23-24 | Connected subspaces |
| Tu
10/1 |
In-class exam |
|
| Th
10/3 |
Ch 3.26-27 (return to 25 later) | Compact subspaces |
| Drop
period ends 10/4 |
||
| Tu
10/8 |
Ch 3.28-29 | Limit point compactness, local compactness |
| Th
10/10 |
Fall
Break |
|
| Tu
10/15 |
Ch 4.30-31 |
Countability axioms, separation axioms |
| Th
10/17 |
Ch 4.32-33 |
Normal spaces, Urysohn Lemma |
| Tu
10/22 |
Ch 4.34 |
Urysohn Metrization Theorem |
| Th
10/24 |
Ch 4.35 |
Tietze Extension Theorem |
| Tu
10/29 |
Ch 5; Take-home exam out |
Tychonoff Theorem |
| Th
10/31 |
Ch 9.51-52 |
Homotopy of paths, fundamental group |
| Tu
11/5 |
Ch 9.53; Take-home exam due |
Covering spaces |
| Th
11/7 |
Ch 9.54 |
Fundamental group of the circle |
| Deadline
to withdraw 11/8 |
||
| Tu
11/12 |
Ch 9.55, 57 |
Retractions and fixed points, Borsuk-Ulam Theorem |
| Th
11/14 |
Ch 9.58 |
Deformation retracts and homotopy type |
| Tu
11/19 |
Ch 9.59 |
Fundamental group of S^n |
| Th
11/21 |
Ch 9.60 |
Fundamental groups of some surfaces |
| Tu
11/26 |
Ch 11.68-69 |
Direct products and free products of groups |
| Th
11/28 |
Thanksgiving |
|
| Tu
12/3 |
Ch 11.70-71 |
Seifert-van Kampen Theorem, Fundamental group of a wedge of circles |
| Th
12/5 |
Ch 11.72-73 |
Adjoining a 2-cell, Fundamental group of the torus and dunce cap |
| Tu
12/10 |
-- |
Extra day for catch-up |
| Final
Exam |
||