18.175 Theory of Probability: Fall, 2012

Lectures: MWF 1-2, 2-142

Office hours: Friday 2-4, 2-180

Assignments: 7 term problem sets (worth 10% of grade) and 1 final problem set (worth 30% of grade).

Official course description: Sums of independent random variables, central limit phenomena, infinitely divisible laws, Levy processes, Brownian motion, conditioning, and martingales.

Texts: There are many excellent textbooks and sets of lecture notes that cover the material of this course, several written by people right here at MIT. The course material is contained in the union of the following online texts for first-year graduate probability courses:

A gentler introduction to some of the material in the course appears in David Gamarnik's notes. For a more general analysis reference, there is also the online text Applied Analysis by Hunter and Nachtergaele.

Other excellent graduate probability books (that I don't think have been posted online, at least not by the authors) include (but are obviously not limited to) Patrick Billingsley's book , Richard Dudley's book , Dan Stroock's book and David Williams' book. There's a lot of overlap between these books, but you'll develop strong opinions if you spend much time with them. Here is one person's rated list of graduate probability books. (You probably won't agree with the list author's opinions, but it's still a nice list.) This course will more or less follow Durrett's treatment, with supplemental material and perspectives in lectures. Most of the material in the slides is lifted pretty directly from Durrett or from one of the other online sources listed above. I use the same notation as Durrett whenever possible.

Stellar course web site