# Fall 2008

 Meets MWF 1:45 -- 2:50 X-Hour Th 1:00 -- 1:50 Where 028 Haldeman Instructor Dana Williams Office 305 Kemeny Hall Hours Tu 1-2, W 9-10, Th 10-11

Course Description and sample analysis certification questions.

## Complex X-hour

As something of an experiment/bonus, Matt Mahoney will be runing a mini-course in complex analysis during our x-hour.  This component of the course is optional for undergraduates.  The idea is that complex analysis is a significant part of the analysis certification exam, but it is not usually covered in any of the graduate offerings here at Dartmouth.  This means you'll get a chance to see some complex analysis, but at the expense of some additional work.  Matt and I will definitely want your feedback on how this works for you.

There will be homework which will be collected every week or two.  In addition, there will be a "take-home" mid-term and final.

## Homework

Written work should be done on one side only of 8.5''x11'' paper with smooth edges. Each problem should begin a new page.
• GENERAL PREPARATION (i.e., nothing to be turned in):    Read chapter 0 in the text.  Also review the theory of the Riemann integral and compare what you've studied in the past with the treatment in either Goldberg's Methods of Real Analysis sections 7.2--7.4 or Rudin's Principles of Mathematical Analysis chapter 6 (and Theorem 11.33).
• ASSIGNMENT ONE: Due Wednesday, October 1st.
• ASSIGNMENT TWO: Read sections 1.1--1.6.  Also, Due Monday, October 20th.
• FIRST COMPLEX ASSIGNMENT: Due, Thursday, October 23rd.
• OPTIONAL ASSIGNMENT: How many Borel sets are there?  (You are free to ask me about this, but you shouldn't turn in anything.  Here are some solutions to the Borel set problem.)
• ASSIGNMENT THREE: (Due November 7th)
• Read Sections 2.1, 2.2 and 2.3.
• In Section 2.1: 2, 4 and 9.
• In Section 2.2: 14.
• In Section 2.3: 19 and 20.
• For problem 9 in section 2.1, recall that a continuous bijection from a compact space into a Hausdorff space is necessarily a homeomorphism.  Also, the Cantor function is defined on page 39 and is constant on the intervals in [0,1] deleted from the Cantor set.  You can assume the result from exercise 29 in Chapter 1 without proving it.
• MIDTERM: Due FRIDAY, November 14th. (Problem 8 fixed now). Brief solutions for 1-7.
• ASSIGNMENT FOUR: Due, Monday, November 24th.