STA 2111F: Graduate Probability I (Fall, 2005)

STA 2111F is a course designed for Master's and Ph.D. level students in statistics, mathematics, and other departments, who are interested in a rigorous, mathematical treatment of probability theory using measure theory.

Instructor: Professor Jeffrey S. Rosenthal, Department of Statistics, University of Toronto. Sidney Smith Hall, room 6024; phone (416) 978-4594; http://probability.ca/jeff/;

Time: Tuesdays, 2-5. First class Sept 13. Last class Dec 6.

Textbook: Rosenthal, J.S. (2000), A First Look at Rigorous Probability Theory. Singapore: World Scientific Publishing. Available at U of T Bookstore or from www.wspc.com.

Important Note About the Textbook: If you have the first printing of the textbook (the version without any writing on the back), then be sure to check the errata, in compressed postscript or PDF.

Further Reading (available on short-term loan in the math/stat library):

• P. Billingsley (1995), Probability and measure (3rd ed.). John Wiley & Sons.
• R. Durrett (1996), Probability: theory and examples (2nd ed.). Duxbury Press.
• B. Fristedt and L. Gray (1997), A modern approach to probability theory.

Content: We will follow the textbook fairly closely, covering approximately the first half. Specific topics to be covered include: probability measures, the extension theorem, random variables, distributions, expectations, laws of large numbers, Markov chains. (The follow-up course, STA 2211S, will then cover the rest of the textbook, including weak convergence, characteristic functions, central limit theorems, Radon-Nykodym Theorem and Lebesgue Decomposition, conditional probability and expectation, martingales, and Kolmogorov's Existence Theorem.)

Prerequisites: Students should have a strong undergraduate background in Real Analysis, including calculus, sequences and series, elementary set theory, and epsilon-delta proofs, at the level of (say) "Elementary Classical Analysis" by Jerrold E. Marsden (W.F. Freeman and Co., 1974); or "Real Analysis with Real Applications" by K.R. Davidson and A.P. Donsig (Prentice-Hall, 2002). Some previous exposure to undergraduate-level probability theory is also recommended.

Note: To avoid conflict of interest, the instructor will refund \$2 (his approximate royalties) to each student who purchases the textbook.

This document is available at http://probability.ca/jeff/teaching/0506/sta2111/