**Instructor: **David Kerr
**Office:** Blocker 525K

**Office hours:** T 10:00-11:30, or by appointment

**Lectures:** MWF 9:10-10:00, BLOC 161

**Course description:**
Topological spaces, continuity, Urysohn's lemma, Tietze extension theorem,
nets, compact spaces, locally compact spaces, Tychonoff's theorem,
Ascoli-Arzelà theorem, Stone-Weierstrass theorem, normed vector spaces,
Banach spaces, linear operators, linear functionals,
Hahn-Banach theorem, Baire category theorem, open mapping theorem,
closed graph theorem, uniform boundedness principle, topological vector spaces,
weak and weak* topologies, Alaoglu's theorem, Hilbert spaces,

Lp spaces,
Hölder's inequality, Minkowski's inequality, dual of

Lp, Radon measures,
Riesz representation theorem, Lusin's theorem,
dual of

C0(

X).
Prerequisite: MATH 607.

**Textbook:** G. B. Folland.

*Real Analysis. Modern Techniques and Their Applications*.
Second edition. Published by John Wiley & Sons, New York, 1999.

**Assignments** (due Wednesdays in class):

*Assignment #1* (due January 23): **4.1:** 1, 2, 3, 8, 10; **4.2:** 15, 16

*Assignment #2* (due January 30): **4.2:** 17, 20, 24; **4.3:** 30, 31, 32, 36

*Assignment #3* (due February 6): **4.4:** 37, 38, 40; **4.5:** 51, 54, 56; **4.6:** 58, 59

*Assignment #4* (due February 13): **4.6:** 63; **4.7:** 68, 69, 70, 71

*Assignment #5* (due February 20): **5.1:** 3, 6, 7, 12, 13; **5.2:** 18, 19, 25

*Assignment #6* (due February 27): **5.3:** 27, 29, 32, 37, 39, 40, 41

*Assignment #7* (due March 20): **5.4:** 44, 47, 48, 51, 53; **5.5:** 54, 55, 56, 57, 58

*Assignment #9* (due March 27): **5.5:** 59, 63, 67; **6.1:** 3, 4, 5, 11, 12, 13

*Assignment #10* (due April 3): **6.2:** 19, 20, 21, 22

*Assignment #10* (due April 10): **7.1:** 1, 2, 3, 4, 5, 6

*Assignment #10* (due April 17): **7.2:** 8, 10, 11, 12

*Assignment #11* (due April 24): **7.3:** 17, 22, 25