Math 6210

Instructor: Ken Bromberg
Office: JWB 303
Phone: 581-7916

Math 6210 is a standard graduate course in real analysis. The material we will cover will prepare you for the real analysis half of the analysis prelim. More importantly this is standard material (along with 6310-20 and 6510-20) which forms the basis for a doing research in any area of pure mathematics.

Book:

The text for the class is "Real and Complex Analysis" by Walter Rudin. The text is available at the bookstore. There is also an international paperback version which should be considerably cheaper and can be found online at Amazon. I plan to follow the book fairly closely. In particular most of the homework problems will come from Rudin's book. I will attempt to cover the first nine chapters. This is a lot of material so we may spend more time on some topics than others.

Another excellent book is "Introductory Real Analysis" by Kolmogrov and Fomin. This book is not required but it is published by Dover so you should be able to find an inexpensive copy (check Amazon).

Homework:

Homework will be assigned regularly. It and a final exam will be the basis for your grade. I will not accept late homework (unless you have a very good excuse).

I encourage you to work together on the homework. Everyone will still be required to individually write up each problem. You should indicate who you worked with at top of your homework.

Problem Session:

There will be a problem session once a week. It will take place Mondays at 3 in LCB 225. Everyone will get a chance at the board!

Office hours:

You can come by my office anytime. I should be around all day on Tuesday and Thursday and in the afternoon on Monday, Wednesday and Friday. If you want to make sure that I am in you should make an appointment either after class or via email.

I strongly encourage you to come by my office. This can be a very difficult class and it is important to not fall behind.

Final:

The final exam is December 13 from 8:30 - 10 AM. It will be a replica of the analysis half of the prelim (which is why it is only 1 1/2 hours instead of 2).

Assignments:

Homework 1

Homework 2:     Rudin, Chapter 1, #3,5,6 plus extra problems
                            Due 9/15 at 4 PM (An outline for problem 1 was added on 12/11)

Homework 3:      Rudin, Chapter 2, #3,4,8,9,11
                            Chapter 3, #14,16 (You can assume all functions are real. For 16 only do the first part, the proof of Egoroff's Theorem.)
                            Due 10/4 at 4PM

Homework 4:      Rudin, Chapter 4, #1, 2, 3, 6
                            Due 10/27 at 4PM

Homework 5:      Rudin, Chapter 5, #1, 2, 3, 4, 5 plus extra problems
                            Due 11/10 at 4PM