Here is the syllabus for the course.
Check out the Probability Seminar for talks on topics that might interest you.
This course will cover the basics of measure theory with some probabilistic flavor. Measure theory is the modern way of doing integration. It is a core part of mathematics and used in many applied sciences, such as statistics and economics.
Two basic goals for the course:
(1) We will cover carefully the central parts of measure and integration theory. These also form the mathematical foundation of probability theory. Consequently Math 629 will be valuable preparation for example for courses in stochastic processes and theoretical statistics, including our graduate probability course Math 831. For students considering graduate studies in mathematics, Math 629 would be good preparation for graduate analysis.
(2) As we cover measure theory we will introduce the parallel notions from probability theory, beginning with how random experiments are modeled with measure spaces that are then called probability spaces. Probabilistic examples and applications of the theory are a perfect complement to abstract measure theory.
This should make an enjoyable and interesting course for advanced undergraduate students and graduate students. A good background for 629 is an ability to do rigorous analysis, for example at the level of UW Math 421 or 521 (sequences, series, convergence, lim inf and lim sup, Riemann integration). Parts of this background can be reviewed or covered in the beginning of 629. Prerequisites in probability are not necessary.
I will gladly answer further inquiries.
Timo Seppalainen, Mathematics, email < seppalai@math.wisc.edu > .