MAT 444-01 - Senior Seminar: Ergodic Theory

4 credits (Spring)

Ergodic theory is the study of the transformations of a set that both preserve the “size” of subsets and suitably “mix” the elements. In particular, what can we say about the long-term behavior that appears after repeatedly applying such a mixing function? The techniques in the field are heavily analytic, but results from ergodic theory have recently been applied in striking ways to solve problems in combinatorics and number theory. To help understand these transformations, we will develop the fundamental properties of Lebesgue measure, which is a powerful and elegant way to assign a size to almost every subset of the real numbers.

Prerequisite: MAT 316. MAT 321 is strongly recommended.
Instructor: Mileti