Math 632– Introduction to Stochastic Processes

Course Content: The course consists of Chapters 1-4 from Durrett’s book: discrete time Markov chains, Poisson processes, renewal processes, and continuous time Markov chains.  I also hope to cover at least a portion of chapter 5, martingales. Further, I will have some extra topics such as simulation and applications to biology.  The course will begin with a review of basic probability (though this is *not* a substitute for having taken math 431 or equivalent).

Prerequisites: Calculus, linear algebra, and an introduction to probability (at the level of Math 431) are su伍cient. However, the material in this class is sophisticated, so a degree of intellectual maturity and a willingness to work hard are required.  For this reason some 500-level work in mathematics is recommended for background, preferably in analysis (521).  Students must have enough mathematical maturity to be comfortable following proofs in the textbook and in the lectures, and must also be able to construct proofs of their own on homeworks and tests.

Exams: There will be two midterm examinations and a final.  No make-up midterm exams will be given unless proof of extraordinary circumstance is provided at least one week before the exam day. According to university policy, no early final exams will be given for ANY reason.

Homework Assignments: Reading assignments and homework exercises will be given in class and posted on the course website. It is your responsibility to get this information. Some notes on homework:

● The homework problems are graded mainly on your reasoning. Part of doing good mathemat- ics is explaining your reasoning in a way that is easy to understand. It is your responsibility to provide a clear explanation to the grader.