| Week | Topics | Reading | Homework | Due |
Week 1
Aug 18 & 20 |
Introduction |
1.1: Euler's Theorem
1.2: Topological equivalence
1.3: Surfaces
1.4: Abstract spaces |
Ch 1: #1, 3, 6, 7, 10, 12. |
Aug 27 |
Week 2
Aug 25 & 27 |
Topological spaces |
2.1: Open and closed sets |
Ch 1: #19; Ch 2: #1abe, 3. |
Sep 3 |
Week 3
Sep 3 |
Continuity |
2.2: Continuous functions |
Ch 2: #12, 13, 16, 17. |
Sep 10 |
Week 4
Sep 8 & 10 |
Compactness in En |
3.2: Heine-Borel Theorem |
Ch 3: #1, 3. |
Sep 17 |
Week 5
Sep 15 & 17 |
Compactness |
3.3: Compact spaces |
Ch 3: #8, 11, 17. |
Sep 24 |
Week 6
Sep 22 & 24 |
Connectedness |
3.5: Connectedness
3.6: Joining points by paths |
Ch 3: #30, 31, 33, 37, 44. |
Oct 1 |
Week 7
Sep 29 & Oct 1 |
One-Manifolds |
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Week 8
Oct 6 & 8 |
Catch-Up |
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Week 9
Oct 13 & 15 |
Midterm |
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Week 10
Oct 20 & 22 |
Product Spaces, Quotient Spaces |
3.4: Product Spaces
4.2: Identification spaces |
Ch 3: #22, 25, 39; Ch 4: #5, 7. |
Oct 29 |
Week 11
Oct 27 & 29 |
Quotient Spaces |
4.2: Identification Spaces |
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Nov 5 |
Week 12
Nov 3 & 5 |
Classification of Surfaces |
7.1: Classification
Handout |
Ch 4: #1 (show only that (a) and (c) give the same space), 2, 8 (first part), 10. |
Nov 12 |
Week 13
Nov 10 & 12 |
Classification & Homotopy |
5.1: Homotopic Maps
Hatcher, Ch 0 |
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Nov 19 |
Week 14
Nov 17 & 19 |
Fixed Points & FTA |
5.5: Brouwer Fixed-Point Theorem |
Ch 5: 1, 2, 25 (pictures will suffice); Hatcher #10. |
Nov 24 |
Week 15
Nov 24 |
Presentations |
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Week 16
Dec 1 |
Presentations |
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Week 17
Dec 8 |
Midterm (take-home due by 4pm on 12/8) |
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