Lec. | Date | Chapter | Topic |
---|---|---|---|
1 | 8/21 | 2 | Countable and uncountable sets. |
2 | 8/23 | 2 | Cantor set and Cantor function. |
3 | 8/25 | 1, 2 | Monotone functions. More on Cantor function. |
4 | 8/28 | 3 | Metric spaces. |
5 | 8/30 | 3 | More on metrics. Bounded sets. |
6 | 9/1 | 3 | Normed vector spaces. |
- | 9/4 | - | Labor Day - No Classes |
7 | 9/6 | 3 | Limits in metric spaces. |
8 | 9/8 | 3 | Cauchy sequences. "Coordinatewise" convergence. |
9 | 9/11 | 4 | Open sets. |
10 | 9/13 | 4 | Closed sets. |
11 | 9/15 | 4 | Interior and closure. Dense sets. |
12 | 9/18 | 4, 5 | Relative metric. Continuous functions. |
13 | 9/20 | 5 | Continuous functions. |
14 | 9/22 | 5 | Homeomorphisms. |
15 | 9/25 | 5 | Isometries. Distance to a set. |
16 | 9/27 | 5 | Continuous real-valued functions. |
17 | 9/29 | Problems pdf | |
18 | 10/2 | Exam 1 covering Chapters 2-5. Study guide pdf | |
19 | 10/4 | 6 | Connectedness. |
20 | 10/6 | 6 | Connectedness. |
21 | 10/9 | 7 |
Review: Continuous functions on [a,b]. Boundedness vs total boundedness. |
22 | 10/11 | 7 | Total boundedness. |
23 | 10/13 | 7 | Completeness. |
24 | 10/16 | 7 | Nested closed sets. Contractions. |
25 | 10/18 | 7 | Completions. |
26 | 10/20 | 7, 8 | More on completions. Compactness. |
27 | 10/23 | 8 | Continuous functions on compact metric spaces. |
28 | 10/25 | 8 | Compactness via open covers. |
29 | 10/27 | 8 | Uniform continuity. |
30 | 10/30 | 8 | Properties of uniformly continuous functions. |
31 | 11/1 | Uniform continuity — problems pdf | |
32 | 11/3 | Chapter 8 — problems pdf | |
33 | 11/6 | Exam 2 covering Chapters 6-8. Study guide pdf | |
34 | 11/8 | 9 | Exam 2 discussion. Open dense sets. |
35 | 11/10 | 9 | Baire Category Theorem. |
36 | 11/13 | 10 | Pointwise and uniform convergence. |
37 | 11/15 | 10 | Consequences of uniform convergence. |
38 | 11/17 | 10 | Uniform convergence of derivatives. Spaces of bounded and continuous functions. |
11/19-25 | Thanksgiving Holiday - no classes | ||
39 | 11/27 | 10 | Weierstrass M-test. Power series. |
40 | 11/29 | 11 | Equicontinuity. |
41 | 12/1 | 11 | The Arzela-Ascoli Theorem. |
42 | 12/4 | 12 | The Stone-Weierstrass Theorem. |
43 | 12/6 | 9,11 | Discontinuities. |
44 | 12/8 | Chapters 9,10,11 — problems pdf |
The Final Exam will be on Monday, Dec. 11, 4:40-6:30 p.m. in 107 Willard.