STA 2111F: Graduate Probability I (Fall, 2011)

STA 2111F is a course designed for Master's and Ph.D. level students in statistics and other departments, who are interested in a rigorous, mathematical treatment of probability theory using measure theory.

Instructor: Professor Jeffrey S. Rosenthal, Department of Statistics, University of Toronto. Sidney Smith Hall, room 5016B; phone (416) 978-4594;; 'jeff' at ''

Time: Mondays, 1:10 - 4:00. First class Sept 12. Last regularly-scheduled class Dec 5. Makeup class Wednesday Dec 7 (1:10 - 4:00). Final exam Dec 12 (1:10 - 4:00 in SS2106). No class Oct 10 (Thanksgiving) nor Nov 7 (Fall Break).

Location: Room 2108 of Sidney Smith Hall (building "SS" on campus map).

Textbook: A First Look at Rigorous Probability Theory, 2nd ed., by J.S. Rosenthal (World Scientific Publishing, Singapore, 2006). Available at U of T Bookstore or World Scientific or or or (See also the partial solutions manual.)

Library copies: Copies of the textbook have been placed on short-term loan at both the Mathematical Sciences Library (Bahen Centre) and the Laidlaw Library (University College).

Further Reading: See the references listed in "Appendix B" of the textbook.

Note: To avoid conflict of interest, the instructor will offer a refund of $2 (his approximate royalties) on Oct 3 to each student who has purchased the textbook (with receipt) for this course.

Course 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 be familiar with undergraduate-level probability theory, and should also have a strong background in basic undergraduate-level Real Analysis, including calculus, sequences and series, elementary set theory, and epsilon-delta proofs, as briefly summarised in e.g. "Appendix A" of the textbook. (On the other hand, students who have already studied lots of graduate-level Real Analysis might perhaps find this course too low-level and thus inappropriate for them.)

Evaluation: Midterm test [solutions] (Oct 24, 1:10pm, 60 mins, in room HA410) 20%; Homework #1 (assigned Oct 3, due Oct 31 at 1:10pm sharp) 20%; Homework #2 (assigned Nov 7, due Nov 28 at 1:10pm sharp) 20%; Final exam (Dec 12, 1:10-4:00, 150 mins, in SS2106) 40%.

Lateness policy: Homeworks are due at 1:10pm sharp. Lateness penalties are: 1-10 mins = 1 point; 11-30 mins = 2 points; 31 mins - 24 hours = 10% of total points; longer = (10% of total points) x (number of days late, rounded UP).

Regrading policy: Regrading requests should only be made for genuine grading errors, and should be initiated by writing or typing a complete explanation of your concern (together with your full name, student number, e-mail address, and telephone number) on a separate piece of paper, and giving this together with your original unaltered homework/test/exam paper to the instructor within one week of when the graded item was first available. Warning: your mark may end up going down rather than up. Further details are available here.

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