| Date |
Topic |
Homework |
Due
date |
| WEEK 1 |
|||
| 01/20 |
Introduction |
||
| 01/22 |
1.1 Open sets and definition of a topology |
2,5,6,7,8 |
never |
| 1.2 Basis of a topology | |||
| WEEK 2 |
|||
| 01/27 |
1.2 Basis of a topology | 11,12,13,15,19 |
Thu, Feb 5 |
| 01/29 | 1.3 Closed sets | 27,28,32,34,37 | Thu, Feb 5 |
| WEEK 3 | |||
| 02/03 |
2.1 Interior and closure of sets |
|
|
| 2.2 Limit points | |||
| 02/05 |
2.3 The boundary of a set |
||
| 3.1 The subspace topology | |||
| WEEK 4 | |||
| 02/10 |
3.2 The product topology |
||
| 02/12 |
3.3 The quotient topology |
||
| 3.4 More examples of quotient spaces | |||
| WEEK 5 | |||
| 02/17 |
Review |
||
| 02/19 |
EXAM 1 |
||
| WEEK 6 | |||
| 02/24 |
4.1 Continuity | ||
| 02/26 |
4.2 Homeomorphisms | ||
| WEEK 7 |
|||
| 03/03 | 5.1 Metrics | ||
| 5.3 Properties of metric spaces | |
||
| 03/05 |
5.4 Metrizability | ||
| WEEK 8 |
|||
| 03/10 |
6.1 A first approach to connectedness | ||
| 03/12 |
6.2 Distinguishing topological spaces via connectedness | ||
| WEEK 9 |
|||
| 03/24 |
6.3 Intermediate Value Theorem | |
|
| 03/26 |
6.4 Path connectedness | ||
| WEEK 10 |
|||
| 03/31 |
Review |
|
|
| 04/02 |
EXAM 2 |
||
| WEEK 11 |
|||
| 04/07 |
7.1 Compactness | ||
| 7.2 Compactness in metric spaces | |||
| 04/09 | 7.3 The Extreme Value Theorem | ||
| 7.4 Limit point compactness | |||
| WEEK 12 |
|||
| 04/14 |
8.1 Iterating functions | ||
| 04/16 |
8.2 Stability | ||
| 8.3 Chaos | |||
| WEEK 13 | |||
| 04/21 |
9.1 Homotopy | ||
| 04/23 |
9.2 Circle functions, degree, and retractions | ||
| 10.1 The Brouwer Fixed Point Theorem | |||
| WEEK 14 |
|||
| 04/28 |
14.1 Manifolds |
||
| 14.2 Euler characteristcs and compact surfaces | |||
| 04/30 |
14.3 Three-manifolds |
||
| 14.4 The geometry of the universe | |||
| FINALS |
|||
| 05/13 |
FINAL EXAM (8:00-10:00) |
Check other important dates on the Academic
Calendar