MAT/STA 235B: Probability Theory (Winter 2020) (CRN 62834/74820)
     TR 10:30-11:50 AM, 80 Social Science and Humanities 113 Hoagland (Note the room change!)

http://www.math.ucdavis.edu/~gravner/MAT235B/


INSTRUCTOR:

TA:

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:

  • conditional expectation;
  • martingales;
  • Markov chains; and
  • time permitting: applications to optimal stopping, and financial mathematics in discrete time.
  • 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.