Ergodic theory studies the probabilistic behavior of dynamical systems as they evolve through time.
This course will be an introduction to the basic notions in ergodic theory. Then we will cover ergodic, weak mixing, mixing, and Bernoulli transformations, and transformations admitting and not admitting an invariant measure. There will be an emphasis on specific examples such as group rotations, the binary odometer transformations, and rank-one constructions. Evaluation will be based on homework and exams.