STA 2111F: Graduate Probability I (Fall, 1998)

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 Rosenthal (contact me, Sid Smith room 6024, phone (416) 978-4594)

Time: Tuesdays, 1:00 to 4:00 pm, Sidney Smith Hall room 2128.

Textbook: The main reference will be the instructor's lecture notes. In addition, several reference books will be kept on reserve in university libraries; click here for details.

Content: We will follow the lecture notes fairly closely. 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 notes, 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%.

See the official course announcement, Homework #1, Homework #2 (in compressed postscript format).