Topic in Number Theory (Math
Instructor: Professor Dorothy Wallace
This course explores the relationship of number theory to graph
theory. The study of the integers mod N and the study of finite
graphs both involve many of the same tools and ask parallel sorts of
questions. Often one area of study informs the other. In
this course you will exercise your algebra and your linear algebra, and
review your Fourier analysis (or learn it for the first time).
Some of the basic ideas of Math 25 will appear here but it is not
necessary to have taken that course first. This topic is a good
source of open questions, research projects, and applications in
various corners of applied math.
Grades will be based on homework (presented in class) and a project.
Undergraduates will submit a paper about their project at the end
of the course. Graduate students may opt to do an oral
presentation instead. The format of the class will be as a
seminar. Everyone will have a chance to present material.
quarter we meet MWF 11:15-12:20 and T 12-1. I expect to use the
x-hour most weeks in addition to or in place of the Friday class
will be using Fourier Analysis on Finite Groups and Applications, by
Terras. Terras is noted for her problem sets, which complete the
gaps in the text, fill in background information, and are occasionally
sneaky open questions. Professor Wallace knows a lot of number
theory and some graph theory,
but she doesn't know everything in this book. We will be learning
Office hours: Wallace's office:
Kemeny 204. Office hours: M 1-2, W 2-3, Th 12-2 and by
appointment. Note that I am also teaching Math 4/27 this term,
and these hours are for both classes. If you have a long
question, I suggest making an appointment.
Honor principle: All authors must personally write any paper
with their name on it. All sources must be appropriately cited.
Any suspicion of plagiarism will be forwarded to the
Religious observance: Some students may wish to take part
in religious observances that occur during this academic term. If you
have a religious observance that conflicts with your participation in
the course, please meet with me before the end of the second week of
the term to discuss appropriate accommodations.