**Instructor: ** Professor Jeffrey Rosenthal
(contact me,
Sid Smith room 6024, phone (416) 978-4594)

**Time:** Tuesdays, 1:00 to 4:00 pm, Mechanical
Engineering room 254.

**Textbook:** "Probability and Measure", 3rd ed., by Patrick
Billingsley.
(John Wiley & Sons, 1995.
Available at U of T Bookstore, $90.95.)

**Content: **
We will largely follow the textbook, though the order
of certain topics will be changed. A rough outline is that Chapters 1
and 4 will be covered, with necessary measure-theoretic material from
Chapters 2 and 3 introduced as needed.
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 chapters 5, 6, and 7,
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).

**Evaluation: **
Homework assignments 65%;
attendance and class participation 35%.

Course homework assignments -- tentative.