Probability Courses 
Visit the Department of Mathematics
web site for current course listings. To apply for a graduate program visit the Faculty of Graduate Studies. 
Math 418419Starting Fall 2013, Math 418 will be crosslisted with Math 544, and Math 419 with Math 545. 
Probability: Math 544545 (crosslisted with Math 418419)This pair of courses provides a thorough introduction to measuretheoretic probability. No prior knowledge of probability is assumed. Results from measure theory are stated and used without proof. The focus is on discrete time and continuous time stochastic processes. Topics include: martingales, law of large numbers, central limit theorem, Brownian motion and special topics. 
Stochastic Analysis: Math 546This is a rigorous course on finite dimensional continuous stochastic
processes, focusing on Markov processes. Topics include:
stochastic integration with respect to continuous semimartingales,
Itô's formula for continuous semimartingales and applications,
stochastic differential equations, Girsanov's formula, martingale problems.

Discrete Probability: Math 548This course covers more advanced topics in discrete probability. Some probability background is needed, including Markov chains and martingales. Measure theory may be used at some points. Topics include spectral analysis of Markov chains and mixing times, electrical networks and random walks, random graphs (ErdosRenyi, random regular graphs, etc.), percolation (leading up to Smirnov's theorem on conformal invariance) and other statistical mechanics models (Ising, Potts). 
Topics in Probability: Math 608This is a topics course in probability which is offered when there is sufficient student interest. The topic of the course changes from year to year depending on the interests of students and instructor. In Fall 2013 a pilot course on Stochastic Processes and their Applications will be taught as MATH 608D. The course is intended for graduate students in applied fields with a need for Markov Chains and Monte Carlo methods, but without an advanced background in analysis. The course outline can be found here. 
Topics in Mathematical Physics: Math 609This topics course often studies a subject of interest to graduate students in probability. 