Math 103 Home Page
Fall 2008
Meets 
MWF 1:45  2:50

XHour 
Th 1:00  1:50 
Where

028 Haldeman

Instructor

Dana Williams

Office

305 Kemeny Hall

Hours

Tu 12, W 910,
Th 1011

Course Description and sample
analysis certification questions.
Complex Xhour
As something of an experiment/bonus, Matt Mahoney will be runing a
minicourse in complex analysis during our xhour. 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 "takehome" midterm 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 7.27.4 or Rudin's
Principles of Mathematical Analysis chapter 6 (and Theorem
11.33).
 ASSIGNMENT ONE: Due
Wednesday, October 1st.
 ASSIGNMENT TWO: Read sections 1.11.6. 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 17.
 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.)