PREREQUISITES: A solid working knowledge of advanced calculus. Measure theory will be reviewed at the beginning of the course, but some additional reading would be advisable if you've never seen it before. Here are the topics from measure theory: measurable spaces, Lebesgue integral, Lebesgue measure in Rd, monotone and dominant convergence theorems, Fubini's theorem, Radon-Nikodym theorem. Also, knowledge of basic combinatorics, such as permutations, combinations, selections with and without replacement.
TEXTBOOK:
The required textbook is
R. Durrett, Probability: Theory and Examples
(5th edition, Cambridge University Press, 2019. Free online version is available from the author.
Sections 1.1-1.7, 2.1-2.6, 3.2-3.4, 3.6 will be covered
in this part of the course. There are many other books that cover this material, e.g.,
L. Breiman, Probability (1968),
D. Williams, Probability With Martingales (1991),
J. Jacod, P. Protter, Probability Essentials (2000).
The last two books are similar in scope
(covering most of 235AB) and
easiest to read, thus
suitable as gentler supplements to Durrett.
TOPICS:
GRADE:
Course grade will be based on the following:
ADDITIONAL POLICIES:
Homework will be assigned about once a week, with due date and time. You will have about
7 days to complete each assignment. Although you can discuss homework
problems with me and other students from the class,
everything you turn in should be your work. Copying another person's work or solutions found elsewhere
(say, in books or on the internet) is cheating.
Late submissions will not be accepted for any assignment.
The final exam will be take-home.
On this exam you must work
alone and use only your notes from this class.
Your solutions will be graded not only on correctness, but also on clarity, organization, and
quality of writing.
There are free resources available on
the web. A good example are the Probability Tutorials. Some other sites
are listed on
The Probability Web
(click on
Teaching Resources).
You may also use my undergraduate
lecture notes to brush up on elementary probability.