Instructor: Dr. Miklós ABÉRT
Prerequisites: basic algebra and basic linear algebra
Spectral theory is a powerful, general tool in mathematics. We use it when we try to understand a mathematical object from the eigenvalues and eigenvectors of some natural linear operator acting on the object. For instance, the behavior of the random walk on a graph (or a group) can be effectively understood using the eigenvalues of the adjacency operator. The self-connectivity of a finite graph (which measures how fast information spreads in the corresponding network) is also controlled spectrally.
In the course, we will reach a new understanding of finite and infinite groups and graphs using spectral methods.
Inquiry based mathematics means that the students discover most of the material by themselves, with help from the teacher and each other. When it works, the course is more effective (and much more fun) than a traditional class. It also strongly enhances presentation skills.
For a detailed description of what traditional inquiry based learning is, see:
The course will be a substantial modification of what is written there. Abert has taught IBL courses at the University of Chicago, both as regular undergraduate courses and in the REU program.