PREREQUISITES: A solid working knowledge of advanced calculus and basic combinatorics. Working knowledge of measure theory: measurable spaces, sigma-algebras, Lebesgue integral and Lebesgue measure, monotone and dominant convergence theorems, Fubini's theorem, and independence. Material from 235A: strong and weak convergence of random variables and laws of large numbers, convergence in distribution (i.e., weak convergence of measures), and central limit theory.
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.
Chapters 4 and 5 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 (2004).
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. You may discuss homework
problems with me and other students from the class. You may award
yourself a point for every homework problem which you essentially solve,
by your own judgment. You will be asked to report your total
number of homework points as part of your final exam submission.
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.
You may also use my undergraduate
lecture notes to brush up on elementary probability.