MAT 235A: Probability (Fall 2017) (CRN 48653)
     TR 10:30-11:50 AM, 1344 Storer

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


INSTRUCTOR:

TA:

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 (4th edition, Cambridge University Press, 2010, list of corrections). Free online version is also available. 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.
  • 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.