### Math 2210: Real Analysis

#### Professor Richard Kenyon Tel. 863-6406 rkenyon -at- math dot brown dot edu office: Kassar 305 Office hours: Thursdays 2-4pm

Text: Folland, Real Analysis, 2nd ed. (isbn 0-471-31716-0)

## The take-home final is HERE and due by 5:00pm Dec 21.

(slide it under my door if I am not in my office).

Course outline: We'll cover much of the material in chapters 1-6: measures, integration, Banach spaces, Hilbert spaces, L^p spaces.

Chapter 4: We won't cover this material in class. However please read/review sections 4.1,4.2,4.4,4.5.
Ideally you should be comfortable or at least capable of doing the following exercises from this chapter:
8,10,11,13,16,18,19,50,51,52,54,64.
Also some important results from this chapter are 4.15, 4.16, 4.42.

Midterm solutions

Grading: there will be one midterm, one final, and biweekly homework.
Your final grade will be weighted as follows: Homework 25% Midterm 25% Final 50%.

Homework 1 (due Oct 1.)
Prove that [0,1] has the Bolzano-Weierstrass property: every sequence has a convergent subsequence.
Page 24: #3,4.
Page 27: #9,10,12
Page 32: #23

Homework 2 (due Oct 15.)
here

Homework 3 (due Nov 5.)
Page 48: 3,5,9
Page 59: 22,25
Page 63: 32,33,34,38,42
Page 77: 55,59.
solutions

Homework 4 (due Nov 19.)
Page 88: #4,6
Page 92. #9,10,13,17
Page 154: #2,4,5,7,11.
solutions

Homework 5 (due Dec 8.)
Page 155: #9
Page 159: #18,20,22
Page 164: #30,41,42

Homework 6 (do not turn in)
Page 177: #55,56,57,59,65.
Page 186. #1,6,12.