The following is a tentative syllabus for the course and will be updated as necessary. All associated assignments may be found on the homework page.
Week | Lectures | Sections in Text | Brief Description |
---|---|---|---|
1 | 6/24 | §1, 5 | Course introduction, set theory |
6/25 (Sa) | §2, 6, 7 | Special Class (10:40-11:45am) Functions, cardinality of sets, and LaTeX |
|
2 | 6/27 | §12 | Topological spaces |
6/28 (x) | §13 | Bases | |
6/29 | §3, 14 | Orders and the order topology | |
7/1 | §15, 16 | The product and subspace topologies | |
3 | 7/4 | Independence Day (no class) | |
7/5 (x) | §16, 17 | Subspace topology (ctd.), position of a point in a set, closed sets |
|
7/6 | §17 | Closure, limit points | |
7/8 | §17 | Limit points and Hausdorff spaces | |
4 | 7/11 | §18 | Continuous functions |
7/12 (x) | §18 | Homeomorphisms and topological properties | |
7/13 | Midterm Exam | Material through §17 | |
7/15 | DF Away (no class) | ||
5 | 7/18-22 | DF Away (no class) | |
6 | 7/25 | §20 | Metric spaces |
7/26 (x) | §21 | Properties of metric spaces | |
7/27 | §19 | The infinite product topology | |
7/29 | §23 | Connected sets | |
7 | 8/1 | §23, 24 | Products of connected sets, IVT, path connected sets |
8/2 (x) | §3, 25 | Equivalence relations, connected components, local connectedness |
|
8/3 | §26 | Compact spaces | |
8/5 | §26, 27 | More on compactness | |
8 | 8/8 | §27, 31-35 | Heine--Borel Theorem, separation axioms, Urysohn's Lemma |
8/10 | §30, NIB | Manifolds | |
8/12 | §22 | Quotient topology | |
9 | 8/15 | Classification of manifolds | |
8/17 | Classification of manifolds (cont.) | ||
8/19 | §51 | Homotopies and path homotopies | |
10 | 8/22 | §52 | Fundamental group |
8/24 | Results in algebraic topology | ||
8/27 | Final Exam | 3-6pm, Kemeny 105 |