STA 2111F: Graduate Probability I (Fall, 2002)

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; contact me;

Time and Place: Wednesdays 11:10-2:00, in Bahen Centre room B024.

Textbook: Rosenthal, J.S. (2000), A First Look at Rigorous Probability Theory. Singapore: World Scientific Publishing. Available at U of T Bookstore ($36.80) or from (U.S. $24). (See errata.)

Further Reading (first one to be held on reserve in math/stat library, last two at Gerstein):

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 exposure to undergraduate-level probability theory is recommended but not essential.

Evaluation: Homework assignments 40%; in-class quizzes 40%; attendance and class participation 20%.

Tentative Schedule: Quizzes: four, each 20 min long, at beginning of class on Oct 2, Oct 23, Nov 13, and Dec 4. Homework: three, each assigned in class, then due on a Friday at 4:00 pm; (1) assigned Sept 25, due Oct 11; (2) assigned Oct 23, due Nov 8; (3) assigned Nov 20, due Dec 6.

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

See Homework #1, Homework #2, Homework #3.

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