| Date | Tentative class plan: |
| Fri, Aug 30 | The real number system (Following Chapter 1 of Rudin) |
| Mon, Sep 2 | Graduate Center is closed. |
| Thu, Sep 5 | We have class (day follows a Monday schedule). Cardinality |
| Fri, Sep 6 | Topological spaces |
| Mon, Sep 9 | Topological spaces (completing § 4.1 of Folland) |
| Fri, Sep 13 | Sequences (roughly following Chapter 3 of Rudin) |
| Mon, Sep 16 | Continuity following § 4.2 of Folland |
| Fri, Sep 20 | Continuity |
| Mon, Sep 23 | Finish Continuity. Discuss connected sets. |
| Fri, Sep 27 | Nets following § 4.3 of Folland), Compact sets (loosely) following § 4.4 of Folland and Chapter 2 of Rudin (for metric spaces). |
| Mon, Sep 30 | No classes scheduled. |
| Fri, Oct 4 | Finish Compact sets |
| Mon, Oct 7 | Tychonoff's Theorem (appears in Folland § 4.6) Locally compact Hausdorff spaces (roughly following Folland § 4.5) |
| Fri, Oct 11 | Finish Locally compact Hausdorff spaces |
| Mon, Oct 14 | No classes scheduled. |
| Wed, Oct 16 | We have class (day follows a Monday schedule). The Arzela-Ascoli Theorem (roughly following Folland § 4.6) |
| Fri, Oct 18 | The Stone-Weierstrass Theorem (roughly following Folland § 4.7) |
| Mon, Oct 21 | Review for the midterm |
| Fri, Oct 25 | Midterm Exam |
| Mon, Oct 28 | Review of differentiation in R^n (Following Chapter 5 of Pugh) |
| Fri, Nov 1 | Implicit and Inverse Function Theorems (Following Chapter 5 of Pugh) |
| Mon, Nov 4 | Implicit and Inverse Function Theorems |
| Fri, Nov 8 | Finish Implicit and Inverse Function Theorems. Normed Vector Spaces (Following Folland § 5.1) |
| Mon, Nov 11 | Sequence spaces The Hahn-Banach Theorem (Following Folland § 5.2) |
| Fri, Nov 15 | More on The Hahn-Banach Theorem.
Banach limits. |
| Mon, Nov 18 | The Baire Category Theorem (Folland § 5.3 and additional applications) |
| Fri, Nov 22 | The Baire Category Theorem |
| Mon, Nov 25 | Hilbert Spaces (Following Folland § 5.5) |
| Fri, Nov 29 | College is closed. |
| Mon, Dec 2 | Hilbert Spaces, Discussion of closest point projections (following Einseidler-Ward, Functional Analysis, Spectral Theory, and Applications, § 3.1.2) |
| Fri, Dec 6 | Finish discussion of Hilbert Spaces Brief discussion of Strong and Weak topologies. |
| Mon, Dec 9 | Special Topics |