Discrete-time stochastic analysis: Stochastic basis, filtration, stochastic sequences. Absolute continuity of probability measures and conditional expectations. Martingale-like and predictable stochastic sequences. Doob's decomposition. Stopping times and related properties. Uniformly integrable stochastic sequences. Transition from discrete-time to continuous-time stochastic analysis. Introduction to stochastic integration with respect to Brownian motion. Prerequisites: STAT 471 or consent of the Department.