**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:** Thursdays, 12-3. First class Sept 9. Last
class Dec 2.

**Place:** Wilson Hall (New College), room 523.
(Building "WI" on
campus map.)

**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.

**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.

This document is available at http://probability.ca/jeff/teaching/0405/sta2111/