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
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
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
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