Below is an approximate schedule of topics to be covered in the course.
| Week of | Topics | Rudin sections |
|---|---|---|
| Jan 18 | Ordered sets, bounds, extrema, fields, $\R$, the Archimedean Property | 1.1-1.4 |
| Jan 25 | Density of $\Q$, existence of roots | 1.4 |
| Feb 1 | Metric spaces, open, closed, and compact sets | 2.2, 2.3 |
| Feb 8 | Compact sets, compact intervals | 2.3 |
| Feb 15 | The Heine-Borel Theorem, sequences, convergence | 2.3, 3.1 |
| Feb 22 | Properties of limits, subsequences, Cauchy sequences, completeness | 3.1-3.3 |
| Mar 1 | Limits superior and inferior, limits of functions, continuity | 3.4, 4.1-4.3 |
| Mar 8 | Review, midterm | |
| Mar 15 | Uniform continuity, connected sets, limits and infinity, directional limits | 4.3-4.5, 4.7 |
| Mar 22 | Spring recess | |
| Mar 29 | Derivatives, local extrema, mean value theorem | 5.1, 5.2 |
| Apr 5 | Riemann sums, integrals, the Fundamental Theorem of Calculus | 6.1-6.3 |
| Apr 12 | Sequences of functions | 7.1, 7.2 |
| Apr 19 | Uniform convergence | 7.3 |
| Apr 26 | The Stone-Weierstrass Theorem, review | 7.4, 7.7 |
| May 3 | RRR Week | |
| May 10 | Exam Week |
Note that Rudin does not have numbered sections within chapters, so I use, e.g., "1.4" above to refer to the fourth subsection of Chapter 1.
Last updated: February 24, 2025.