Math 727- Probability theory
Fall 2017
TR 11:00--12:15 SNOW 301

Terry Soo, Snow 610
Office hours: Tuesdays 4-5. Wednesday 2.30-3.50.

Course description.
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 limit theorem. 

Prerequisites.
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 writing proofs.

Qualifying examination
This course will help students who are preparing for the Probability and Statistics qualifying examination, and requires a high level of mathematical maturity.

Grading
Subject to revision

Homework:  20%
Midterm 1:   20% September 21. M1Q M1S
Midterm 2:   20% November 2. M2S
Final examination 40% December 12. 10.30-1 PM. Registrar Final exam schedule
Final Exam

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 Walsh
Probability.  Karr
Statistical inference.  Casella and Berger

More advanced:

Probability: Theory and examples.  Durrett
Foundations of modern probability.  Kallenberg
Real analysis and probability.  Dudley

Notes:


Probability Spaces
Uncountable probability spaces
Counting
Conditional probability
Random variables I
Random variables II
Expectation I
Expectation II
Variance
Convergence of RV I
Convergence of RV II
Characteristic functions
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. HW1 solutions
HW2: Due Tuesday September 12. HW2 solutions
HW3: Due Tuesday September 19. HW3 solutions
HW4: Due Thursday October 5. HW4 solutions
HW5: Due Thursday October 12 HW5 partial sol
HW6: Due Thursday October 26 HW6 sol
HW7: Due Thursday November 16 HW7 partial sol
HW8: Due Thursday November 30 HW8 sol