Handouts:
632 is a survey of some important classes of stochastic processes: Markov chains in both discrete and continuous time, point processes, and renewal processes. The material is treated at a level that does not require measure theory. Consequently technical prerequisites needed for this course are light: calculus and linear algebra are sufficient. However, the material is sophisticated, so a degree of intellectual maturity and a willingness to work hard are required.
Good knowledge of undergraduate probability at the level of UW-Madison Math 431 (or an equivalent course) is required. This means familiarity with basic probability models, random variables and their probability mass functions and distributions, expectations, joint distributions, independence, conditional probabilities, the law of large numbers and the central limit theorem. The handout Probability Basics covers some of these prerequisites. If you need a thorough review of basics, the textbook A First Course in Probability by S. Ross is recommended.
In class we go through theory, examples to illuminate the theory, and techniques for solving problems. Homework exercises and exam problems are paper-and-pencil calculations with examples and special cases.
A typical advanced math course follows a strict theorem-proof format. 632 is not of this type. Mathematical theory is discussed in a precise fashion but only some results can be rigorously proved in class. This is a consequence of time limitations and the desire to leave measure theory outside the scope of this course. Interested students can find the proofs in the textbook. For a thoroughly rigorous probability course students should sign up for the graduate probability sequence 831-832.
Check out the Probability Seminar for talks on topics that might interest you.