Math 131B-2

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 All of the contact information below is out of date.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-2: Real Analysis, Lecture 2

Spring 2014

Instructor:	Kristen Hendricks
Office:	6617D Math Sciences Building
Office Hours:	M 4-5, W 2-3, F 9-10
E-Mail:	hendricks at math .ucla .edu

TA:	Zhiqiang Li
Office:	2344 Math Sciences Building
Office Hours:	TBD
E-Mail:	lizhiqiangfly at gmail .com

A printable copy of the syllabus is here.

Location and Time

MWF 1-1:50, Humanities 169. TA Discussion Section Thursday, 1-1:50, 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 Monday. There will probably be nine homeworks in all. 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. You should also cite any other sources other than lecture and the textbook (another book, a blog about analysis, etc) you use.

Exams

There will be two in-class midterms, tentatively scheduled for Wednesday, April 23 and Wednesday, May 21. There will also be a final exam Thursday, June 12th, 11:30 a.m.-2:30 p.m. There will not be any make-up exams except in extreme and documented circumstances, or for religious holidays.

Grading

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

Homework: 20%
Midterms 1 & 2: 20% each
Final: 40%
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 April 7th). Solutions.

Homework 2 (Due April 14th). Solutions.

Homework 3 (Due April 21st). Solutions.

Homework 4 (Due April 28th). Solutions.

Homework 5 (Due May 5th). Solutions.

Homework 6 (Due May 12th). Solutions.

Homework 7 (Due May 19th). Solutions.

Homework 8 (Due May 30th). Solutions.

Homework 9 (Due June 6th). Solutions.

Exams

Sample Midterm 1 . Solutions.