| Wk | Date | Topics and activities | Assignments |
| 1 | 08/28 | Rational numbers | A construction of $\mathbf{Z}$ Note on fields |
| 08/30 | Ordered fields | Homework 1 and a solution | |
| 2 | 09/02 | The least upper bound property | |
| 09/04 | The field of real numbers | ||
| 09/06 | No Class (Dorian) | ||
| 3 | 09/09 | Cardinality, Euclidean structure of $\mathbf{R}^n$ | Note on $\mathbf{R}^n$ |
| 09/11 | Metric spaces | Note on metric topology | |
| 09/13 | Basic topology | Homework 2 and a solution | |
| 4 | 09/16 | Compactness | |
| 09/18 | Compactness in $\mathbb{R}^n$ | ||
| 09/20 | Connectedness | Homework 3 and a solution | |
| 5 | 09/23 | Sequences | |
| 09/25 | Limits | Homework 4 and a solution | |
| 09/27 | Subsequences and compactness | ||
| 6 | 09/30 | Cauchy sequences and completeness | |
| 10/02 | Comparison, relative rates | ||
| 10/04 | Monotonicity, infinite limits | ||
| 7 | 10/07 | Midterm 1 | Solution |
| 10/09 | Superior and inferior limits, series | Homework 5 and a solution | |
| 10/11 | Series of positive terms | ||
| 8 | 10/14 | Fall break | |
| 10/16 | The Root and Ratio tests | Homework 6 and a solution | |
| 10/18 | Operations on series | Euler's number $e$ | |
| 9 | 10/21 | Conditional convergence, rearrangement | |
| 10/23 | Limits of functions | ||
| 10/25 | Continuous functions | ||
| 10 | 10/28 | Continuity and compactness | Homework 7 and a solution |
| 10/30 | Continuity and connectednessThe Intermediate Value Theorem | ||
| 11/01 | Differentiability | ||
| 11 | 11/04 | The Chain Rule, local extrema | |
| 11/06 | Mean value theorems | ||
| 11/08 | Midterm 2 | Solution | |
| 12 | 11/11 | Taylor approximations | Homework 8 and a solution |
| 11/13 | Local behavior | Note on comparison relations | |
| 11/15 | Power series | Note on sequences of functions | |
| 13 | 11/18 | Analytic functions | |
| 11/20 | Riemann sums | ||
| 11/22 | Riemann integrals | ||
| 14 | 11/25 | Integrable functions | Homework 9 and a solution |
| 11/27 | Thanksgiving Break | ||
| 11/29 | Thanksgiving Break | ||
| 15 | 12/02 | Properties of the integral | Note on the properties of the Riemann integral |
| 12/04 | The Fundamental Theorem of Calculus | ||
| 12/06 | The exponential and logarithmic functions |