Topic in Number Theory (Math
75)

Spring 2012

Instructor: Professor Dorothy Wallace

Spring 2012

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.

Grading: 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.

Attendance: This 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 meeting.

Text: We 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 new things together.

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 COS.

**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.