| Lectures | Sections in Text | Brief Description |
|---|---|---|
| Day 1: 9/24 | 1.1, 1.2, 1.3, and 1.5 | Notation; Background material; Why proofs? |
| Day 2: 9/26 | 2.2 | Real numbers as infinite decimals |
| Day 3: 9/29 | 2.3, 2.4 | Limits; Basic properties |
| Day 4: 10/1 | 2.5 | Least upper bound property of R |
| Day 5: 10/3 | 2.6, 2.7 | Subsequences; Cauchy sequences |
| Day 6: 10/6 | 2.7 | More about sequences, their subsequences, lim inf and lim sup |
| Day 7: 10/8 | --- | First midterm exam |
| Day 8: 10/10 | 4.1, 4.2 | R^n as normed vector space and metric space |
| Day 9: 10/13 | 4.3 | Topology of R^n |
| Day 10: 10/15 | 4.3, 4.4 | Topology of R^n; Compact subsets and the Heine-Borel theorem |
| Day 11: 10/17 | 3.1, 3.2 | Series; Convergence tests for series |
| Day 12: 10/20 | 3.2, 3.4 | Alternating series; Absolute and conditional convergence |
| Day 13: 10/22 | 3.4 | Rearrangement of series |
| Day 14: 10/24 | 2.8 | Cardinality |
| Day 15: 10/27 | 3.3, 4.4 | The number e; The Cantor set |
| Day 16: 10/29 | 5.1, 9.1 | Limits of functions; Continuous functions on metric spaces |
| 10/29 | --- | Second midterm exam (in the evening) |
| Day 17: 10/31 | 5.3 | Properties of continuous functions |
| Day 18: 11/3 | 5.3 | Properties of continuous functions |
| Day 19: 11/5 | 5.4, 5.5 | Compactness and extreme values; Uniform continuity |
| Day 20: 11/7 | 5.6, 5.2 | Intermediate Value Theorem; Discontinuous functions |
| Day 21: 11/10 | 5.2, 5.7 | Discontinuous functions; Monotone functions |
| Day 22: 11/12 | --- | Third midterm exam |
| Day 23: 11/14 | 6.1 | Differentiable functions |
| Day 24: 11/17 | 6.2 | Mean Value Theorem |
| Day 25: 11/19 | 6.3 | Riemann integral |
| Day 26: 11/20 | 6.3 | Riemann integral |
| Day 27: 11/21 | 6.3, 6.4 | Riemann integral; Fundamental theorem of calculus |
| Day 28: 11/24 | 6.6 | Measure zero and Lebesgue's theorem |
| Day 29: 12/1 | 8.1, 8.2, 8.4 | Limits of functions; Pointwise and uniform convergence; Series of functions |
| Day 30: 12/3 | --- | Review of Chapter 6 |