Ma/ACM/IDS 140 abc. Probability. 9 units (3-0-6); first, second, third terms, 2025-26. Prerequisites: For 140 a, Ma 108 b is strongly recommended. This course begins with an overview of measure theory, followed by topics that include random walks, the strong law of large numbers, the central limit theorem, martingales, Markov chains, characteristic functions, Poisson processes, and Brownian motion. Towards the end, some further topics may be covered, such as stochastic calculus, stochastic differential equations, Gaussian processes, random graphs, Markov chain mixing, random matrix theory, and interacting particle systems.
Instructors: Tamuz, El-Maazouz, Zhang

Ma 191 abc. Selected Topics in Mathematics. 9 units (3-0-6); first, second, third terms, 2025-26. Each term we expect to give between 0 and 6 (most often 2-3) topics courses in advanced mathematics covering an area of current research interest. These courses will be given as sections of 191. Students may register for this course multiple times even for multiple sections in a single term. The topics and instructors for each term and course descriptions will be listed on the math option website each term prior to the start of registration for that term.
Instructors: T. Yu, Pham, Zhang, Yang, Heinaevaara, Looi, Svoboda, Marcolli, El-Maazouz, Flach, Dong