| Lec. | Date | Topics | Chapter |
|---|---|---|---|
| 1 | 8/20 | Real numbers. | 1 |
| 2 | 8/23 | Finite, countable, and uncountable sets. | 2 |
| 3 | 8/27 | Cantor set. Metric spaces. | 2 |
| 4 | 8/29 | Open and closed sets, limit points, etc. | 2 |
| - | 9/3 | -- Labor Day -- | |
| 5 | 9/5 | Unions and intersections. Closure and interior. | 2 |
| 6 | 9/10 | Perfect sets. Connected and separated sets. | 2 |
| 7 | 9/12 | Compact sets. | 2 |
| 8 | 9/17 | Compact sets. | 2 |
| 9 | 9/19 | Compact sets. | 2 |
| 10 | 9/24 | Convergent sequences. | 3 |
| 11 | 9/26 | Convergent sequences. Cauchy sequences. | 3 |
| 12 | 10/1 | Complete metric spaces. | 3 |
| 13 | 10/3 | Subsequences. Lim inf and lim sup. | 3 |
| 14 | 10/7 | Series. Series of non-negative terms. The number e. | 3 |
| 15 | 10/10 | Absolute convergence. Root and ratio tests. | 3 |
| 16 | 10/15 | Homework discussion, etc. | |
| 17 | 10/17 | Midterm Exam | |
| 18 | 10/22 | Power series. Alternating series. | 3 |
| 19 | 10/24 | Sums and products of series. Rearrangements. | 3 |
| 20 | 10/29 | Limits of functions. | 4 |
| 21 | 10/31 | Continuity. | 4 |
| 22 | 11/5 | Continuity and compactness. | 4 |
| 23 | 11/7 | Continuity of the inverse function. Uniform continuity. Continuity and connectedness. |
4 |
| 24 | 11/12 | Discontinuities. Monotonic functions. | 4 |
| 25 | 11/14 | Differentiation. | 5 |
| 26 | 11/19 | Differentiation. | 5 |
| - | 11/21-25 | -- Thanksgiving Holidays -- | |
| 27 | 11/26 | Riemann integral and Riemann-Stieltjes integral. | 6 |
| 28 | 11/28 | Integrable functions. | 6 |
| 29 | 12/3 | Properties of the Riemann-Stieltjes integral. Integration and differentiation. |
6 |