**Instructor:**
Professor Jeffrey S. Rosenthal,
Department of Statistics, University of Toronto

Sidney Smith Hall, room 6024; phone (416) 978-4594; contact me;
http://probability.ca/jeff/

**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 www.wspc.com (U.S. $24).
(See errata.)

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

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

**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.

This document is available at http://probability.ca/jeff/courses/sta2111-02a.html.