Syllabus
Instructor: David Kerr
Office: Milner 121
Office hours: MT 1:30-3:00; week of May 2: MTWRF 1:30-3:00
Lectures: MWF 9:10-10:00, Milner 216
Course description: Topological spaces, continuity, Urysohn's lemma, Tietze extension theorem, nets, compact spaces, locally compact space, 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
Assignment #1 (due February 2):  4.1: 1, 2, 3, 8, 10;  4.2: 15, 16
Assignment #2 (due February 9):  4.3: 30, 31, 36;  4.4: 37, 38, 40;  optional: 4.5: 51
Assignment #3 (due February 16):  4.5: 48, 54, 56;  4.6: 58, 59, 60, 64
Assignment #4 (due February 23):  4.6: 63;  4.7: 68, 69, 70, 71
Assignment #5 (due March 2):  5.1: 3, 6, 7, 12, 13;  5.2: 18, 19, 25
Assignment #6 (not to be handed in):  5.2: 20, 21, 22;  5.3: 27, 28, 29, 30, 32, 35, 36, 37, 39, 40
Assignment #7 (due March 23):  5.3: 36, 37, 38, 39, 41;  5.4: 44, 47, 48, 51, 53
Assignment #8 (due March 30):  5.5: 54, 55, 56, 57, 58, 59, 63, 67
Assignment #9 (due April 6):  5.5: 65, 66;  6.1: 3, 4, 5, 11, 12
Assignment #10 (due April 13):  6.1: 13, 14;  6.2: 19, 20, 21, 22
Assignment #11 (due April 20):  7.1: 1, 2, 3, 4, 5, 6
Assignment #12 (due April 27):  7.2: 8, 10, 11, 12
Assignment #13 (not to be handed in):  7.3: 17, 20, 22, 24, 25
[Selected solutions]
Exams
Midterm exam: in class March 9; covers 4.1-4.7 and 5.1-5.3.
[Midterm solutions]
Final exam: May 9, 8:00-10:00 am, in Milner 216; covers the whole course.
Theorems you might be asked to state: Urysohn's lemma, Tietze's extension theorem, Tychonoff's theorem, Arzelà-Ascoli theorem, Stone-Weierstrass theorem, Hahn-Banach theorem, Baire category theorem, open mapping theorem, closed graph theorem, uniform boundedness principle, Alaoglu's theorem, Schwarz inequality, Parseval's identity, Hölder's inequality, Riesz representation theorems, Lusin's theorem.