# Spectral Graph Theory, Fall 2015

**The first lecture will be on the 3rd floor of 17 Hillhouse **

AMTH 561/CPSC 662, is a graduate
course on Spectral Graph Theory and related topics.
It will be taught in the style of a math class.
I will present a bunch of theorems, a few algorithms, and many open
problems.
I have chosen to only present material that I consider beautiful.
My other goals are to present material that is useful and to introduce
fundamental concepts.
The obvious prerequisites for this course are knowledge of linear
algebra and exposure to graph theory.
The less obvious requirement are "mathematical maturity" and
"mathematical literacy".
I will sometimes make use of concepts that every graduate student in
Mathematics should know.
I assume that students who are not familiar with these can look them
up.
A few that I will use are:
- The fact that a continuous function on a closed, bounded subset
of Euclidean space achieves its minimum.
- Brouwer's fixed point theorem.
- The field of characteristic 2.

I will teach a lot of linear algebra during this course.
You could think of this as a graduate course in linear algebra.
## Requirements

There will be 5 or 6 problem sets, and no tests or exams.
You may collaborate in small groups on the problem sets.
Some of the problems will be hard.
**The problems sets and related announcements will be distributed via Classes V2.**
I will occasionally include material in my lecture notes that I will
not have time to cover in class. You are responsible for that
material.

## Resources

I will not assign a book for this course.
Rather, I will produce notes for all the lectures.
## Should you take this course?

You can get a good feel for what this course will be like by looking
at the lecture notes from previous years.
Here are the notes from
2012,
2009, and
2004.
You should take this course if you
- like pretty math,
- anticipate needing to prove theorems later in your life, or
- want to understand eigenvalues and eigenvectors.

This course is suitable for some advanced undergraduates.
But, I warn them that it will move at a fast pace
and will not be nearly as friendly as a typical undergrad course.
You can find the list of lectures I anticipate teaching
on the course homepage.

## For More Information

See the notes from the first lecture.