Math 727- Probability theory
TR 11:00--12:15 SNOW 301
Terry Soo, Snow 610
Office hours: Tuesdays 4-5. Wednesday 2.30-3.50.
This is a pre-measure theoretic introduction to probability
theory. We do not assume any knowledge of measure-theory, but
we will develop necessary background as needed.
Highlights will include the law of large numbers and the central
Undergraduate degree in mathematics. This is a
graduate course. Proofs will be an important part of the
course. Students should be comfortable with reading and
course will help students who are preparing for the Probability and
Statistics qualifying examination, and requires a high level of
Subject to revision
Midterm 1: 20% September 21.
Midterm 2: 20% November 2.
Final examination 40% December 12. 10.30-1 PM.
Registrar Final exam schedule
Textbook and lecture notes:
No textbook is required. I will post lecture notes online.
Other suitable references are:
Probability and random processes. Grimmett and Stirzaker
Knowing the odds: An introduction to the probability. John
Statistical inference. Casella and Berger
Probability: Theory and examples. Durrett
Foundations of modern probability. Kallenberg
Real analysis and probability. Dudley
Uncountable probability spaces
Random variables I
Random variables II
Convergence of RV I
Convergence of RV II
Some problems of a computational nature
Cauchy-Schwarz and Jensen's inequalties
Conditional distributions and expectations
Homework--to be submitted at the beginning of class
HW1: Due Tuesday September 5.
HW2: Due Tuesday September 12.
HW3: Due Tuesday September 19.
HW4: Due Thursday October 5.
HW5: Due Thursday October 12
HW5 partial sol
HW6: Due Thursday October 26
HW7: Due Thursday November 16
HW7 partial sol
HW8: Due Thursday November 30