## MAT/STA 235A: Probability Theory (Fall 2019) (CRN 48875/61071)      TR 10:30-11:50 AM, 1130 Bainer

http://www.math.ucdavis.edu/~gravner/MAT235A/

Grades were submitted on Dec. 13. Have nice holidays!

INSTRUCTOR:
Janko Gravner
3210 MSB (Mathematical Sciences Build.), 752-0825, gravner[at]math[dot]ucdavis[dot]edu.
Please only use email in an emergency, e.g., if you are sick and you cannot reach me by phone. I will not reply to emails with questions about class material, etc.
Office Hours: Mon. 10-11am, Tue. 12-1pm, Wed. 10-11am.

TA:
Kyle Johnson
3229 MSB, email: kyljohnson[at]ucdavis[dot]edu
Office Hours: Wed., 2-3pm.

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:

• introduction: probability measures, random variables, expected values, independence;
• strong and weak laws of large numbers;
• weak convergence and central limit theorem; and,
• time permitting: Poisson convergence, large deviations.