Below is an approximate schedule of topics to be covered in the course.
| Week of | Topics | Rudin sections |
|---|---|---|
| Aug 24 | Ordered sets | 1.1, 1.2 |
| Aug 31 | Bounds, extrema, fields, $\R$, the Archimedean Property, density of $\Q$ | 1.2-1.4 |
| Sep 7 | Existence of roots, metric spaces | 1.4, 2.2 |
| Sep 14 | Open, closed, and compact sets | 2.2, 2.3 |
| Sep 21 | Compact sets, compact intervals | 2.3 |
| Sep 28 | The Heine-Borel Theorem, sequences, convergence | 2.3, 3.1 |
| Oct 5 | Properties of limits, subsequences, Cauchy sequences, completeness | 3.1-3.3 |
| Oct 12 | Limits superior and inferior, limits of functions, continuity | 3.4, 4.1, 4.2 |
| Oct 19 | Review, midterm, continuity and open sets | 4.2, 4.3 |
| Oct 26 | Uniform continuity, connected sets, limits and infinity, directional limits | 4.3-4.5, 4.7 |
| Nov 2 | Derivatives, local extrema, mean value theorem | 5.1, 5.2 |
| Nov 9 | Riemann sums, integrals, the Fundamental Theorem of Calculus | 6.1-6.3 |
| Nov 16 | Sequences of functions; Thanksgiving | 7.1, 7.2 |
| Nov 23 | Uniform convergence | 7.3 |
| Nov 30 | The Stone-Weierstrass Theorem, review | 7.4, 7.7 |
| Dec 7 | RRR Week | |
| Dec 14 | Exam Week |
Last updated: February 24, 2025.