| Lecture |
Date |
Section |
Topic |
Homework |
| 1 |
1/13 |
|
No Class |
|
| 2 |
1/15 |
|
No Class
|
|
| 3 |
1/18 |
1.1 |
Equivalence
|
1.1# 3, 9, 10, 11*; 1.2# 1, 2, 5* |
| 4 |
1/20 |
1.2 |
Bijections
|
1.2# 5, 9, 13, 14* |
| 5 |
1/22 |
1.3 |
Continuous Functions
|
|
| 6 |
1/25 |
1.3 |
Continuous Functions
|
1.3# 7, 9, 11 |
| 7 |
1/27 |
1.4 |
Topological Equivalence
|
1.4# 2, 10, 11, 15* |
| 8 |
1/29 |
1.5 |
Topological Invariants
|
1.5# 7, 8* |
| 9 |
2/1 |
1.5 |
Topological Invariants
|
1.5# 8 |
| 10 |
2/3 |
1.6 |
Isotopy
|
1.4# 3, 11 |
| 11 |
2/5 |
2.1 |
Knots, Links, and Equivalences
|
|
| 12 |
2/8 |
2.2 |
Knot Diagrams
|
1.6# 7, 10; 2.1# 2, 3 |
| 13 |
2/10 |
2.3 |
Reidemeister Moves
|
2.2# 5, 6, 15, 8* |
| 14 |
2/12 |
2.3 |
Reidemeister Moves
|
2.3# 3, 4, 11, 9* |
| 15 |
2/15 |
2.4 |
Colorings
|
2.4# 1, 2, 4* |
| 16 |
2/17 |
2.4 |
Colorings
|
2.4# 5*, 6, 7, 10 |
| 17 |
2/19 |
2.5 |
The Alexander Polynomial (definition and examples only)
|
2.5# 3, 4, 7, 8* |
| 18 |
2/22 |
2.5 |
The Alexander Polynomial (definition and examples only)
|
|
| 19 |
2/24 |
2.6 |
Skein Relations
|
|
| 20 |
2/26 |
2.6 |
Skein Relations
|
|
| 21 |
3/1 |
2.7 |
Midterm 1
|
|
| 22 |
3/3 |
2.7 |
The Jones Polynomial
|
|
| 23 |
3/5 |
3.1 |
Definitions and Examples of Surfaces
|
2.7# 2, 3, 4, 5 |
| 24 |
3/15 |
3.2 |
Cut-and-Paste Techniques
|
3.1# 1, 3, 8, 9* |
| 25 |
3/17 |
3.3 |
The Euler Characteristic and Orientability
|
|
| 26 |
3/19 |
3.3 |
The Euler Characteristic and Orientability
|
3.2# 1, 2, 6, 7 |
| 27 |
3/22 |
3.4 |
Classification of Surfaces
|
3.3# 3, 4 |
| 28 |
3/24 |
3.4 |
Classification of Surfaces
|
3.3# 8 |
| 29 |
3/26 |
5.1 |
Continuous Functions on Closed Bounded Intervals
|
3.4# 1, 2, 3, 10*, 13 |
| 30 |
3/29 |
5.3 |
Sperner's Lemma
|
3.3# 8; 3.4# 1, 2, 3, 6, 13 |
| 31 |
3/31 |
5.4 |
Brouwer Fixed-point Theorem for a Disk
|
|
| 32 |
4/2 |
|
Midterm 2
|
|
| 33 |
4/5 |
7.1 |
Metric Spaces
|
5.1# 1, 5, 8, 9 |
| 34 |
4/7 |
7.1 |
Metric Spaces
|
5.2# 1, 2, 7 |
| 35 |
4/9 |
7.2 |
Topological Spaces
|
5.4# 1 |
| 36 |
4/12 |
7.2 |
Topological Spaces
|
|
| 37 |
4/14 |
7.3 |
Connectedness
|
|
| 38 |
4/16 |
7.3 |
Connectedness
|
|
| 39 |
4/19 |
7.4 |
Compactness
|
|
| 40 |
4/21 |
7.4 |
Compactness
|
|
| 41 |
4/23 |
7.5 |
Quotient Spaces
|
7.2# 1, 4, 6, 12 |
| 42 |
4/26 |
|
|
|