Presentation: written work should be done on one side only of 8.5''x11'' paper with smooth edges. Each problem should begin a new page.
Deadlines: papers should be turned in by 12:30pm on the due date. Extensions may (and usually will) be granted if requested at least twenty-four hours before the due date. Late homework will not be accepted.
| Date | Reading | Topic | ||
| 1 | 1/17 | 1.1 - 1.4 | Rational numbers | |
| 1/19 | 1.5 - 1.11 | Ordered sets | ||
| 2 | 1/22 | 1.12 - 1.18 | Fields | |
| 1/24 | 1.19 - 1.21 | The real field | ||
| 1/26 | 1.36 - 1.37 | Euclidean spaces | ||
| 3 | 1/29 | 2.15 - 2.17 | Metric spaces | |
| 1/31 | 2.18 - 2.23 | Basic topology | ||
| 2/02 | No class | |||
| 4 | 2/05 | 2.24 - 2.28 | Basic topology | |
| 2/07 | 2.31 - 2.38 | Compactness | ||
| 2/09 | 2.39 - 2.42 | Compactness | ||
| 5 | 2/12 | Compactness in $\mathbb{R}^n$ | ||
| 2/14 | 2.45 - 2.47 | Connectedness | ||
| 2/16 | Midterm 1 | |||
| 6 | 2/19 | 3.1 - 3.2 | Sequences | |
| 2/21 | 3.3 | Limits | ||
| 2/23 | 3.4 - 3.7 | Subsequences and compactness | ||
| 7 | 2/26 | 3.8 - 3.12 | Cauchy sequences and completeness | |
| 2/28 | 3.13 - 3.14 | Monotonicity, infinite limits | ||
| 3/02 | 3.15 - 3.17 | Inferior and superior limits | ||
| 8 | 3/12 | Loose ends, review | ||
| 3/13 | Midterm 2 | |||
| $\pi$ | 3.20 | Special sequences | ||
| 3/16 | 3.21 , 3.26 | Series: vocabulary and examples | ||
| 9 | 3/19 | 3.22 - 3.25 | Cauchy's criterion, comparison theorems | |
| 3/21 | 3.27 - 3.29 | Series of non-negative terms | ||
| 3/23 | 3.30 - 3.32 | Euler's number $e$ | ||
| 10 | 3/26 | 3.33 - 3.37 | The root and ratio tests | |
| 3/28 | 3.47 - 3.51 | Sums and products of series | ||
| 3/30 | 3.43 | Alternating series | ||
| 11 | 4/02 | 3.52 - 3.55 | Conditional convergence and rearrangement | |
| 4/04 | Sequences and series: wrap-up | |||
| 4/06 | 4.1 - 4.4 | Limits of functions | ||
| 12 | 4/09 | 4.5 - 4.8 | Continuity | |
| 4/11 | 4.9 - 4.11, 4.25 - 4.26 | Continuity | ||
| 4/13 | Problem session | |||
| 13 | 4/16 | 4.13 - 4.15 | Continuity and compactnesss | |
| 4/18 | 4.16 - 4.17 | Extreme values | ||
| 4/20 | 4.22 - 4.23 | Continuity and connectedness | ||
| 14 | 4/23 | 5.1 - 5.5 | Differentiability | |
| 4/25 | 5.6 - 5.11 | Mean value results | ||
| 4/27 | 5.13 - 5.15 | L'Hospital's Rule, Taylor's expansion | ||
| 5/02 | Final examination |