Tentative Calendar for Math 70100: Functions of a Real Variable (Fall 2019)

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

The final exam will be held 12-2:30pm in Room 6417 on December 16th.
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Last modified on December 2, 2019.
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