This course is an introduction to the theory of stochastic processes. The course begins with a review of probability theory and then covers Poisson processes, discrete-time Markov chains, martingales, continuous-time Markov chains, and renewal processes. The course also focuses on applications in operations research, finance, and engineering. No prior knowledge of measure theory is required. However, the focus of the course is on the mathematics and proofs are emphasized. Prerequisites: at least a one-semester calculus-based course in probability (MATH340/STAT230 or equivalent). A background in real analysis is helpful. Instructor consent is required. Instructor: Arlotto