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
I have chosen to only present material that I consider beautiful.
My other goals are to present material that is useful and to introduce
The obvious prerequisites for this course are knowledge of linear
algebra and exposure to graph theory.
The less obvious requirement are "mathematical maturity" and
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
A few that I will use are:
I will teach a lot of linear algebra during this course.
You could think of this as a graduate course in linear algebra.
- 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.
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
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
You should take this course if you
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.
- like pretty math,
- anticipate needing to prove theorems later in your life, or
- want to understand eigenvalues and eigenvectors.
You can find the list of lectures I anticipate teaching
on the course homepage.
For More Information
See the notes from the first lecture.