Math 103 Home Page
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.
Expectations/Grading
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.
- Read Section 2.4
- In Section 2.3: 23 (Solution posted 11/28/2008)
- In Section 2.4: 44
- In Section 2.5: 46, 48 and 49.
- Prove Proposition 82 from lecture.
- FINAL: Due Wednesday, December 10, 2008. (By popular demand.)