Math/Stat 521: Advanced Probability I
Instructor: Zhen-Qing Chen
Phone: (206) 543-1907 (Office)
Fax: (206) 543-0397
Office: Padelford Hall, Room C-341
Office hours: Mondays 1:30-2:20 pm.
and Wednesday 2:30-3:20 pm. at Padelford C-341.
Lectures: MWF: 11:30 am.-12:20 pm. at LOW 113.
Textbook: Probability: Theory and Examples
by Richard Durrett,
Fourth edition, Cambridge University Press, 2010.
K.L. Chung: A Course in Probability Theory, third edition. 2001.
I plan to cover, approximately, the first five chapters of the textbook
in this course. That is:
Probability sample spaces, random variables, distribution functions;
Expectation and moments;
Weak and strong laws of Large Numbers,
Weak convergence, characteristic functions;
Central Limit Theorems;
Infinitely Divisible and Stable Distributions;
Random Walks, stopping times, transience and recurrence.
There will be biweekly homework assignments
throughout the quarter for your own practice. The most important
function of homework is that it helps you to internalize concepts
and to develop problem solving skills. There will be two in class
exams given on Friday November 3, 2017 and
Friday December 8, 2017.
The home work will count for 20% and the two exams will count for 40% each towards
your course grade.
Students are assumed to be familiar with measure theory
and Lebesgue integration,
such as covered in Real Analysis courses
or Math 426.
Chapter 1 and the appendix of the textbook provides a good review of
the results from measure theory we needed. You are encouraged to read
it for a quick review.
You are also supposed to have learned, or learn on your own, some
basic combinatorics covered in Math/Stat 394.
Here is the Course Syllabus
Read the textbook before and after each lecture.