This is a copy of the original website for this course, which I taught at UCLA in 2014. All of the contact information below is out of date.

Math 131B-1: Real Analysis, Lecture 1

Winter 2014

Instructor: Kristen Hendricks
Office: 6617D Math Sciences Building
Office Hours: M 12:30-2:00 W 1:00-2:30 [Priority to this class on W.]
E-Mail: hendricks at math .ucla .edu
TA: Geoffrey Iyer
Office: 6160 Math Sciences Building
Office Hours: R 12:00-1:30
E-Mail: gsiyer at math .ucla .edu
A printable copy of the syllabus is here.

Location and Time

MWF 9-9:50, MS 5137. TA Discussion Section Thursday, 9-9:50, MS 5147.

Content

This course is a continuation of Math 131A. The goal is a rigorous treatment of topics in analysis, going beyond those topics already familiar from calculus. We will study metric spaces and basic point-set topology, function spaces and notions of convergence of sequences of functions, power series and analytic functions, and basic Fourier analysis. We will continue to emphasize learning how to formulate and prove mathematical statements. Correspondingly, homework will be an extremely important part of this course.

Textbook

Apostol, Mathematical Analysis. Addison (1974). Second Edition.

Prerequisites

Math 115A, Math 131A.

Homework

Homework will be assigned weekly and (usually) due at the beginning of lecture on Friday. Homework must be stapled and contain your name, the assignment number, and "Math 131B" on the first page, or it will not be accepted. Do not submit homework by e-mail. No late homework will be accepted. However, your lowest homework score will be dropped when computing your grade.


You are encouraged to work in groups on your homework; this is generally beneficial to your understanding and helps you learn how to communicate clearly about mathematics. However, you must write up all solutions yourself. Moreover, since crediting your collaborators is an important element of academic ethics, you should write down with whom you worked at the top of each assignment.

Exams

There will be two in-class midterms, tentatively scheduled for Wednesday, January 29 and Friday, February 28. There will also be a final exam Tuesday, March 18, 11:30 a.m.-2:30 p.m. Make-up exams are strongly discouraged, and should not be needed given the grading system. If you feel you have extraordinary circumstances, please talk to me about them as soon as possible, preferably at least a week before the exam.

Grading

Your grade will be computed according to one of the following schemes (whichever is higher):

Homework: 25%, Midterms 1 & 2: 20% each, Final: 35%
OR
Homework 25%, Highest Midterm: 20%, Final: 55%

A reasonable curve compatible with the department guidelines will be applied to the final scores; the average will probably be a B or B-, but since this is a small class, circumstances may affect it in either direction. We will use the myUCLA gradebook facility to record grades during the quarter.

Schedule

We will approximately follow the official schedule of topics here. However, note that the chapter numbers listed there are for a different textbook; our course will cover portions of Chapters 3, 4, 9,11, and 12. (There may also be an additional reference posted online for the material of Chapter 11.) The exact reading will be posted as the quarter progresses.

Homeworks

Homework 1 (Due January 13th).

Homework 2 (Due January 17th).

Homework 3 (Due January 24th).

Homework 4 (Due February 3rd).

Homework 5 (Due February 10th).

Homework 6 (Due February 19th).

Homework 7 (Due February 26th).

Homework 8 (Due March 7th).

Homework 9 (Due March 14th).

Optional Homework 10 (Not for collection; this is purely to help you study.).