Students should understand the topics outlined in the minimal learning outcomes on the Math 544 Wiki page. As evidence of that understanding, students should be able to demonstrate mastery of all relevant vocabulary, familiarity with common examples and counterexamples, knowledge of the content of the major theorems, understanding of the ideas in their proofs, and ability to make direct application of those results to related problems.

Convergence of random variables

Laws of Large Numbers

Stochastic processes

Ergodic theory

Martingales

Brownian motion

Itô integral