This course examines the construction and analysis of stochastic processes which are used as mathematical models of systems that appear to vary or fluctuate randomly. A stochastic process is a set of random variables indexed by time or space. They have applications in many fields, including biology, chemistry, neuroscience, physics, information theory, and finance. This course introduces the basics of stochastic processes and their applications with an emphasis on problem-solving. This class will first review probability theory with a concentration on conditional expectations and distributions. Then it will cover topics such as discrete and continuous time Markov chains, branching processes, Poisson processes, birth-and-death processes, and related subjects along with applied examples using a professional software package.
Prerequisites: MATH 211 and, either MATH 214 or 261