Introduction to Stochastic Processes

This course is designed to introduce the undergraduate to the fundamental ideas of stochastic (or random) processes. Such processes are used in the study of mathematical models where there are elements of uncertainty and hence probabilistic quantities are introduced into the model. These models are found in fields such as the analysis of algorithms, the theory of queues, the pricing of stock options, financial mathematics, econometrics, linear programming, and biomathematics. The courses will cover the topics of Markov chains (discrete and continuous time), renewal theory, queuing theory, Brownian motion, and stationary processes. Applications of the various topics will also be discussed.