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 rigorous mathematical introduction to probability theory. It will be proof-based, will be at a substantially higher level than Stat 230, and much faster paced. We should be covering (not exhaustive): random variables (discrete, continuous, multi-dimensional distributions, etc.), conditional probability, characteristic and moment generating functions, the law of large numbers and central limit theorem, random walks, Poisson Processes, Markov chains, function spaces, and random graphs.

Coreq: MATH 138 or 148.

Antireq: STAT 220, 230

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