Instructor: Ken Bromberg
Office: JWB 303
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.
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 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
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.
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
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.
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).
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