# Mathematics 411 MATHEMATICAL ANALYSIS FALL 2006

### FINAL EXAM

The final exam will be HELD Wednesday, December 20, 8:00–11:00 AM, in ARC 333.
• I will hold office hours in Hill 520 Friday, 12/15, 11:00–12:00AM, Monday, 12/18, 10:00–11:30 AM and Tuesday, 12/19, 3:30–5:00 PM.

### ANNOUNCEMENT: EXAM COVERAGE

Exam 2 will be held Thursday, November 16. The exam will cover through the material of the previous week, that is, Chapter 3 and Chapter 4 through the section on "continuity and compactness" which ends in the middle of page 93.

### ANNOUNCEMENT: CLASS POSTPONED

Math 411 will not meet Thursday, November 9. We will replace this class by meeting Wednesday, November 15, from 5:00 to 6:20, in Hill Center 124. Homework assignment 7 will be due Tuesday, November 14.

### Homework assignments. Turn in starred problems only:

• Assignment 9, due Tuesday 12/12: Rudin Chapter 5, problems 21, *22, 24, *26, 27; Rudin Chapter 6, problems *2, *3, 4
• Assignment 8, due Thursday 11/30: Rudin Chapter 4, problems *10, *11, 15; Rudin Chapter 5, problems 1, *2, *6, 13
• Assignment 7, due Tuesday 11/14: Rudin Chapter 3, problems 21, 22, *24; Rudin Chapter 4, problems 1, *2, *4, 5, *7.
Solutions to Assignment 7.
• Assignment 6, due Tuesday 10/31: Rudin Chapter 3, problems *8, 9, *11, 13, *14, *16, 19.
Solutions to Assignment 6.
• Assignment 5, due Tuesday 10/24: Rudin Chapter 3, problems 1, *2, *3, 4, *5, 6, *7.
Solutions to Assignment 5.
• Assignment 4, due Tuesday 10/10: Rudin Chapter 2, problems *12, *15, 17, *19, 20, 21, *22. Extra credit: 18. I recommend that you look over problems 23--30; I may assign a few later, but in any case these give some interesting topological results.
• Assignment 3, due Tuesday 10/3: Rudin Chapter 2, problems *2, 5, *6, *7, 8, *9. In solving problem 2 you may use without proof the fact that a polynomial of degree n has at most n complex roots.
Some solutions to Assignment 3. In fact, so far a solution only to Rudin 2.2, since no one expressed interest in any other problem. If you want some other solutions, email me or come in to discuss the problems.
• Assignment 2, due 9/21: Rudin Chapter 1, problems 13, *15, *16, 17, *20; Supplementary problems *2. Problem 16 may be tricky and it is not very important; don't spend a lot of time on it.
Glance at supplementary problems 3–5 and, if you like, do 5 for extra credit.
Some solutions to Assignment 2.
• Assignment 1, due 9/14: Rudin Chapter 1, problems 1, 3, *5, *6, 8, *9
Some solutions to Assignment 1.