4/29: I will hand out take-home exam tomorrow in class. It will be due on Monday May11, 11:00am.
1/21: See below for Week 1 reading assignment. Try to read at least part of it before first class.
1/7: The first meeting is on Tuesday January 27.
Lecture Schedule and Assignment
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| Week | Topics | Section Numbers | Homework Problems |
|
Week 1 |
Set theory and Logic. | Reading: sections 1-7 | HW1 (Due Feb 5) |
|
Week 2 |
Continue on set theory and logic, Topological space, Basis for topology |
Reading: sections 8-10, 12-13 | HW2 (Due Feb 12) |
|
Week 3 |
Order topology, Product topology, Subspace topology, Closed sets and closure | Reading: sections 14-17 | HW3 (Due Feb 19) |
|
Week 4 |
Limit points, Hausdorff Spaces, Continuous functions, Product Topology | Reading: section 17-19 | HW4 (Due Feb 26) |
|
Week 5 |
Metric topology, Quotient topology | Reading: sections 20-22 | HW5 (Due Mar 5) |
|
Week 6 |
Connectedness, Connected subspaces of the real line, Components and local connectedness | Reading: sections 23-25 | HW6 (Due Mar 12) |
|
Week 7 |
Compactness, Compact subspaces of the real line, Local compactness | Reading: sections 26-27, 29 | HW7 (Due Mar 26) |
|
3/16-3/20 |
Spring Break (No Class) | กก | กก |
|
Week 8 |
Countability axioms, Separation axioms, Normal spaces | Reading: sections 30-32 | HW8 (Due Apr 2) |
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Week 9 |
Urysohn Lemma, Urysohn Metrization Theorem | Reading: sections 33-34, 36 | HW9 (Due Apr 9) |
|
Week 10 |
Homotopy of paths, Fundamental group, Covering Spaces | Reading: sections 51-53 | HW10 (Due Apr 16) |
|
Week 11 |
Covering Spaces, The fundamental group of the circle, Retractions and fixed points | Reading: sections 53-55 | HW11 (Due Apr 23) |
|
Week 12 |
The fundamental theorem of algebra, Borsuk-Ulam theorem, Deformation retracts and homotopy type | Reading: sections 56-58 | No HW (see next week for final assignment) |
|
Week 13 |
Fundamental group of Sn and some surfaces | Reading: sections 59-60 | Final homework handout |
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