MATH 131C: Topics in Analysis

• Course description: This is the third quarter of a sequence on Analysis, completing the honors sequence as well as the regular Math 131AB.
We will review the Riemann integral in Rn and then discuss Lebesgue measure, the Lebesgue integral, several convergence theorems, the relation of Lebesgue integration with Riemann integration, and finally differentiation theory. We will cover most of the first three chapters of the Stein-Shakarchi textbook. Proofs will be important, and the best attitude to bring to this class is not to believe any theorem that you don't know how to prove.

Instructor: Burt Totaro.
E-mail: totaro@math.ucla.edu.
Office Hours: 3-3:50 M and 2-2:50 F, in my office MS 6136.

TA: Dimitrios Ntalampekos (dimitrisnt@g.ucla.edu).
TA office hour: 2:30-3:30 Th in MS 3975.

• Lecture: MWF 11-11:50, MS 6229. Discussion: Tu 11-11:50, MS 6229.

• Textbook: E. M. Stein and R. Shakarchi, Real Analysis, Princeton University Press (2005), ISBN 0-691-11386-6.

• Prerequisite: Math 131B or 131BH is required.

Midterm Exams: We will have two midterm exams. The dates are Monday, April 18 and Monday, May 16. There will be no makeup exams.
Final Exam: The final exam is on Tuesday, June 7, 2016 from 11:30 AM to 2:30 PM in the lecture room, MS 6229. You must take the final to pass the class! If you have a documented reason that you are unable to take the final, you will receive an Incomplete.

Evaluation:
• Every exam will include at least one problem taken from the homework, possibly with minor variations.
• It is your responsibility to know how to do the problems. Practicing that is an essential part of studying for the exams.
• A grade of 'F' will be assigned to any student who misses the final. Incompletes are reserved for those who have completed all of the work for the class, including both midterms, but who, for a legitimate, documented reason, miss the final.
• Exams (or copies) will be returned, but I will keep copies (or originals) of the exams, as required by the math department.
• Grading: Grades will be assigned based on the higher of the following two schemes:
10% homework + 25% first midterm + 25% second midterm + 40% final
10% homework + 35% (best of two midterms) + 55% final
• 4/18 - First midterm exam.
• 5/16 - Second midterm exam.
• 5/30 - Memorial Day holiday. No class.
• 6/7 - Final exam. The final will be from 11:30 AM to 2:30 AM on Tuesday, June 7.
• Course web page: http://www.math.ucla.edu/~totaro/131c.1.16s/index.html

Review for Midterm 1.
Review for Midterm 2.

• Homework 1 (due April 5, 2016): page 37, exercises 2, 4, 5, 6, 7.

• Homework 2 (due April 12, 2016): page 37, exercises 8, 9, 11, 12. Page 46, problem 1.

• Homework 3 (due April 26, 2016): page 37, exercises 13, 16, 18, 22, 29. Page 46, problem 5.

• Homework 4 (due May 3, 2016): page 37, exercise 28. Page 89, exercises 6, 8, 10, 11, 15.

• UPDATED Homework 5 (due May 10, 2016): page 89, exercises 23, 24. Page 95, problem 2.

• Homework 6 (due May 24, 2016): page 144, exercises 2, 3, 4, 10, 11, 13.

• Homework 7 (due May 31, 2016): page 193, exercises 1, 2, 4, 5, 6, 9.

Tentative schedule of lectures, in terms of sections in the book:
3/28: Intro. 3/30: 1.1. 4/1: 1.2.
4/4: 1.2. 4/6: 1.3. 4/8: 1.3
4/11: 1.3. 4/13: 1.4. 4/15: 1.4.
4/18: Midterm 1. 4/20: 1.4. 4/22: 2.1.
4/25: 2.1. 4/27: 2.1. 4/29: 2.2.
5/2: 2.2. 5/4: 2.3. 5/6: 2.3.
5/9: 2.3. 5/11: 2.4. 5/13: 3.1.
5/16: Midterm 2. 5/18: 3.1. 5/20: 3.3.
5/23: 3.3. 5/25: 3.3. 5/27: 4.1.
5/30: Memorial Day holiday. 6/1: 4.2. 6/3: Review.