This calendar is subject to change, but should give a general idea of when we will cover certain topics.

**The final exam will be held 12-2:30pm in Room 6417 on December 16th.**

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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 |