240C Homework Assignments
Only hand in the problems with (*) after them. However,
you should make sure that you are able to do all of the problems.
Warning: Numbering is from the most
current version of the notes.

Due Monday, April 5, 2004.
Chapter 23. 23.6*, 23.16*, 23.17, 23.18, 23.19, 23.20*, 23.21*

Due Friday, April 9, 2004.
Chapter 24. 24.1, 24.2*, 24.3*, 24.4*, 24.5*, 24.6, 24.10*, 24.13*

Due Monday, April 19, 2004.
Chapter 25. 25.1, 25.2*, 25.3*, 25.4, 25.5*, 25.7*, 25.13*, 25.14*,
Chapter 16. 16.1*, 16.2*.

Due Monday, April 26, 2004.
Chapter 25. 25.16*, 25.19*, 25.20*(see below), 25.24*, 25.26*, 25.29*, 25.34*, 25.35

Due Monday, May 3, 2004. (Note: the lecture notes have just
been updated on 4/26/04.)
Chapter 28. 28.4, 28.6, 28.8*, 28.9*, 28.10*, 28.11*, 28.13*(see below),
28.15, 28.16, 28.17
Chapter 29. 29.1, 29.2*, 29.3*

Due Monday, May 12, 2004. (Last Assignment.)
Chapter 29: 29.7*, 29.8*, 29.9*, 29.10*, 29.11 (Numbering
from Previous Version of the notes.)
Chapter 33: 33.4*, 33.8*, 33.9*
Below are the same problems (but numbered differently) form the
current version of the notes.
240A Homework Assignments
Only hand in the problems with (*) after them. However,
you should make sure that you are able to do all of the problems.
Warning: For old assignments, the numbers below in the
HTML file may no
longer correspond to the correct problem because of changes to the notes.
Sorry!! However click here
for a PDF file of the assigned problems with the correct numbering for the
current version of the notes.

Homework #1 is Due Monday, October 6, 2003.
Read Pages 521 in Part I of the
lecture notes and do the following Exercises in those notes:
2.1*, 2.2, 2.3*, 2.4*, 2.5
3.1, 3.2, 3.3*, 3.8*
4.5*, 4.6, 4.7*, 4.8*

Homework #2 is Due Monday, October 13, 2003. The
following problems are from
Part II: Metric and Banach Space Basics:
4.3, 4.9, 4.10* (Hint: use 4.9), 4.11*, 4.12*, 4.13, 4.14, 4.15*
6.2*, 6.3*, 6.4*, 6.7, 6.8, 6.11*, 6.12, 6.13*, 6.15* (Hint: use the dominated
convergence theorem.)

Homework #3 is Due Wednesday, October 22, 2003. The
following problems are from
Part II: Metric and Banach Space Basics:
6.10* (definitely do this problem), 6.14
7.1*, 7.2*, 7.3*, 7.4, 7.5, 7.6*, 7.7*, 7.10*

Homework #4 is Due
Wednesday, October 29, 2003.
Friday October 31, 2003.
From Part II: Metric
and Banach Space Basics:
8.1, 8.3*, 8.6*, 8.9*, 8.10*, 8.11, 8.14, 8.16*, 8.17*
[and perhaps 8.4, 8.5* if
we reach these in class].

Homework #5 is Due
Friday, November 7, 2003 Monday, November 10, 2003.
From: Part II: Metric
and Banach Space Basics: 8.4*, 8.5*
From: Part III: Topological
Spaces I.: 10.1, 10.2*, 10.3, 10.4*, 10.7*
From: Lebesgue Integration
Theory Notes: 18.1*, 18.2, 18.3*, 18.4*

Homework #6 is Due Wednesday, November 19, 2003.
From: Part III: Topological
Spaces I.: 10.5, 10.6*, 10.20*, 10.21*, 10.24*
From: Lebesgue Integration
Theory Notes: Read Proposition 18.33: 18.5, 18.6*, 18.9*, 18.10*,
18.11*, 18.12

Homework #7 is Due Friday December 5, 2003.
(Please use the
problems from the most current version of the notes when doing the
homework problems.)
From: Lebesgue Integration
Theory Notes: 19.1, 19.2*, 19.3*, 19.4*, 19.5*, 19.6*, 19.7*, 19.8, 19.10*(Hint:
"Fatou times two."), 19.14*, 19.16*
From: Folland p. 60: (# 2.31b,e)*.
(In part b the answer is off by a "" sign and the sum is on
k.
In part e, s=a. You may also freely use the Taylor series expansion for
(1z)^(1/2) which is convergent for z<1.)
240B Homework Assignments
Only hand in the problems with (*) after them. However,
you should make sure that you are able to do all of the problems.
Warning: For old assignments, the numbers below in the
HTML file may no
longer correspond to the correct problem because of changes to the notes.
Sorry!!

Due Wednesday January 14, 2004.
The following problems are from
V: Lebesgue Integration Theory: Part I.
notes:
20.2, 20.5*, 20.6, 20.7*, 20.8, 20.9*, 20.10*, 20.11, 20.15*, 20.17*

Due Wednesday January 21, 2004.
The following problems are from
V: Lebesgue Integration Theory: Part I.
notes:
20.18*, 21.1*, 21.2, 21.5*, 21.6, 21.7*, 21.9*, 21.12**,
21.13**.
Hint for 21.1*: use the idea in the proof of the version
of DCT in Corollary 21.17 just above this problem.)
(The problems lined out will be on the next homework assignment. The "**"  means you should definitely do these problems and hand them in.)

Due Wednesday January 28, 2004.
(V: Lebesgue Integration Theory: Part I.
notes:)
Chapter 21. 21.2, 21.5*, 21.6, 21.7*, 21.13*
(Part III: Topological
Spaces.)
Chapter 10. 10.12*, 10.13, 10.15*, 10.16*, 10.17*  current numbering
(Chapter 10. 10.10*, 10.11, 10.13*, 10.14*, 10.15*
old numbering)

Due Wednesday February 4, 2004.
(Part III: Topological
Spaces.)
Chapter 10. 10.8*, 10.9*, 10.10*, 10.18, 10.19, 10.20*, 10.21
Chapter 11. 11.1, 11.2*, 11.3, 11.4*, 11.5*, 11.6, 11.7*, 11.8, 11.9, 11.10*,
11.11
Numbering is from the current version of the
notes.

Due
Wednesday Friday February
11
13, 2004. (Note: new due date.)
(V: Lebesgue Integration Theory: Part I.
notes:)
Chapter 21. 21.3*, 21.4
Part III: Topological
Spaces.)
Chapter 11. 11.12*, 11.13*, 11.14, 11.15*, 11.16*,
11.19*
Chapter 12. 12.1, 12.2*, 12.4*, 12.6, 12.7*,
12.8, 12.9
There is a typo in 11.13: please replace $d_A(y)
= 1$ by $d(0,y) = 1.$

Due
Wednesday Friday February
27, 2004. (Note: new due day.)
Part III: Topological
Spaces.)
Chapter 12. 12.6*, 12.7*, 12.8, 12.9 (just look at this one)
Chapter 22: Approximation
and Convolution
Chapter 22. 22.1*, 22.3, 22.9*, 22.10*, 22.11*

Due Friday March 5, 2004.
(Note, numbers have changed in Chap. 22, please refer to the newest version.)
Chapter 14: Hilbert Space Basics
Chapter 14. 14.1*, 14.2, 14.3*, 14.4, 14.5, 14.7, 14.8*
Chapter 22: Approximation
and Convolution
Chapter 22. 22.3, 22.4*, 22.8*, 22.9*, 22.10*
Chapter 23:
L^2 Hilbert Space Techniques.
Chapter 23. 23.7* (Corrected version of this exercise appears below.)

Due Friday, March 12, 2004.
Chapter 14: Hilbert Space Basics
Chapter 14. 14.6*, 14.14*
Chapter 23:
L^2 Hilbert Space Techniques.
Chapter 23. 23.1*, 23.2*, 23.3, 23.4*, 23.5*,
23.8*, 23.10*
Numbering is from the most current version of the notes.

Remarks on doing the homework.
The homework is an important part of this class. The homework
is your best chance to learn the material in this course. You may consult others
on the problems, but in the end you are responsible for understanding the
material. I suggest that you try all the problems on your own before consulting
others. Even false starts on problems will help you learn.
Here is what the TA will be looking for in your solutions.
 The solutions must be written clearly. This includes
reasonable handwriting and good English. If the TA has to struggle to read
what you have written, he will not grade the problem!
 The solutions should be complete and clear. A good rule of
thumb is: if you have some doubt about your solution it is probably wrong or
at best incomplete.
 Results that you use in your proof from undergraduate
analysis or from the text book or from the lecture notes should be stated
clearly. Here is an example of what I am looking for:
... So we have shown that f_{n} converges to f uniformly. Since each
f_{n} is
continuous and the uniform limit of continuous functions is continuous,
we know that f is continuous.
The reference to a theorem from undergraduate analysis is underlined..
