Students should understand the topics listed in the minimal learning outcomes on the Math 543 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.

Probability spaces

Random variables

Independence

Expectation

Conditioning

Probability measures on product spaces

Generating functions

Discrete Markov chains