MATH 608
Real Variables II
Spring 2019
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
Exams
Midterm exam: in class March 6; covers 4.1-4.7 and 5.1-5.3
Final exam: May 3, 8:00 to 10:00 a.m.; covers the whole course
Theorems you might be asked to state: Urysohn's lemma, Tietze's extension theorem, Tychonoff's theorem, Stone-Weierstrass theorem, Hahn-Banach theorem, Baire category theorem, open mapping theorem, closed graph theorem, uniform boundedness principle, Alaoglu's theorem, Schwarz inequality, Hölder's inequality, Riesz representation theorems, Lusin's theorem.