Aukosh S. Jagannath

Course: Math 154 - Probability theory

Section: M-W 9-10.15, First Class: Mon. Jan 28

Room: SC 222

Office Hours: TBD

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.

Prerequisites: Calculus and linear algebra, some familiarity with proofs and elementary combinatorics (i.e., permutations and combinations). Recommended: A previous mathematics course at the level of Mathematics 19ab, 21ab, or a higher number. For students from 19ab or 21ab, previous or concurrent enrollment in Math 101 or 102 or 112 may be helpful. Freshmen who did well in Math 22a, 23a, 25a or 55a fall term are also welcome to take the course.

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

Also recommended:
Bertsekas and Tsitsiklis, "Introduction to Probability" (2nd Ed)
Feller, Intro. to Probability Vol 1
Williams, Probability with Martingales