Math 245B

MATH 245B : Real Analysis

Announcements:

(Mar 24) Final solutions are available here. Final grades are available here.
(Mar 14) Steve’s office hours for this week are Mon 2-5, Wed 2-5, and for next week are Mon 2-5. My office hours are also Mon 2-5 on finals week (I won’t be around on Tuesday, and on part of Wednesday).
(Mar 9) The final will consist of seven questions, covering Chapters 4-5. Last year’s final is available here, and solutions available here.
(Mar 9) The due date of the last homework has been changed to reflect the current pace of material covered in lectures.
(Feb 8) Midterm scores are available here. Midterm solutions are available here.
(Feb 5) The fourth homework has been changed to reflect (a) the current lecture material, and (b) the topics covered in the midterm.
(Feb 4) This year’s midterm will be three questions, and cover up to Section 4.5 (locally compact Hausdorff spaces), excluding the material on nets (Section 4.3) and on the portions of 3.5 that refer to bounded variation. It will be similar in format and level to last year’s midterm.
(Jan 20) Last year’s midterm is available here, and solutions available here.

· Instructor: Terence Tao, tao@math.ucla.edu, x64844, MS 5622

· Lecture: MWF 12-12:50, MS 5138

· Quiz section: Th 12-12:50, MS 5138

· Office Hours: Tu 1-2. (Also Mon 4-5, but this is shared with my undergraduate class).

· TA: Steven O’Dell, sodell@math.ucla.edu, MS 6142

· TA Office hours: Tu 9-10, W2-3

· Textbook: Folland, Real Analysis, Second Edition, Wiley Interscience 1999, ISBN 0471317160. We will cover the last part of Chapter 3 (Sections 3.4-3.5; Lebesgue differentiation theorem) and Chapters 4-6 (Topology, function spaces, L^p spaces); some variation from this plan may develop depending on time constraints. If you were not in last quarter’s 245A class, you should read Chapter 1-3 by yourself to acquaint yourself with some background material. Note that a current list of errata to this text is maintained here (thanks to Julia Garibaldi for pointing this out).

· Prerequisite: Math 245A (or equivalent). In particular, students should be familiar with measure spaces, the Lebesgue integral, metric spaces, and various types of convergence of functions (e.g. pointwise versus uniform convergence).

· Grading: Homework (30%), Midterm (30%), Final (40%). In addition, a nominal bonus point (1%) will be awarded to each student who presents at least one homework problem at the blackboard during at least one quiz section.

· Exams: The midterm will be on Wednesday, Feb 9, with format and topics to be chosen later. The midterm is open book and open notes. The final will be on Thursday March 24, at 3:00 pm, MS 5138, with format and topics to be chosen later. The final is open book and open notes. Makeup exams will only be available by prior arrangement or by an exceptionally good excuse after the fact. Requests to reweight the exam gradings also require an exceptionally good excuse (i.e. better than “I did poorly on my midterm”).

· Reading Assignment: You should read Chapter 3 if you have not already encountered this material. Of course, you should also be reading the sections covered in lecture (and homework) concurrently with the course.

· Homework: There will be eight homework assignments, due in Quiz sections. The lowest homework score will be dropped. In each assignment, three of the homework questions, selected at random, will be graded in detail. NOTE: In your assignments you may freely use the axiom of choice.

1. First homework (Due Friday, Jan 21): Folland Chapter 3, Questions 23, 25, 37, 42; Chapter 4, Questions 1, 3, 5. Note change of date.

2. Second homework (Due Thursday, Jan 27): Folland Chapter 4, Questions 7, 8, 10, 13, 16, 17, 27.

3. Third homework (Due Thursday, Feb 3): Folland Chapter 4, Questions 24, 28, 39, 40, 43, 44, 45, 52

4. Fourth homework (Due Thursday, Feb 10): Folland Chapter 4, Questions 48, 49, 50, 54, 59, 60. Note change of problems.

5. Fifth homework (Due Thursday, Feb 17): Folland Chapter 4, Questions 63, 64, 65, 67, 68, 69

6. Sixth homework (Due Thursday, Feb 24): Folland Chapter 4, Question 71. Chapter 5, Questions 4, 6, 7, 8, 9

7. Seventh homework (Due Thursday, Mar 3): Folland Chapter 5, Questions 11, 12, 13, 14, 17, 19, 22, 25

8. Eighth homework (Due Tuesday, Mar 15): Folland Chapter 5, Questions 30, 35, 36, 47, 48, 56, 57, 59, 67. Note change of date.