Probability theory nominally concerns phenomena with uncertain outcomes. While its origins can be traced back to gambling rooms and insurance programs, it now plays a central role in many branches of the sciences and engineering, from biology and physics, to signal processing and data science. During this course we will learn how to construct and analyze probabilistic models as well as understand and prove universal properties of such models.

This course will be a (moderately rigorous) introduction probability theory. We should be covering (not exhaustive): random variables (discrete, continuous, multi-dimensional distributions, etc.), conditional probability, characteristic and generating functions, the law of large numbers and central limit theorem, random walks, Markov chains, martingales, high dimensional and geometric probability, and entropy.

Grimmett and Stirzaker, "Probability and Random Processes" (3rd Ed)

Bertsekas and Tsitsiklis, "Introduction to Probability" (2nd Ed)

Feller, Intro. to Probability Vol 1

Williams, Probability with Martingales