Professor Jeffrey S. Rosenthal,
Department of Statistics, University of Toronto
Sidney Smith Hall, room 6024; phone (416) 978-4594; http://probability.ca/jeff/;
Time: Wednesdays, 11-2. First class Sept 10. Last class Dec 3.
Place: Lash Miller Chemistry Labs, room 158.
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. (See errata.)
Further Reading (to be held on reserve in math/stat library and/or 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 previous exposure to undergraduate-level probability theory is also recommended.
Evaluation: See separate sheet.
Note: To avoid conflict of interest, the instructor will refund $2 (his approximate royalties) to each student who purchases the textbook.