Math 523-Probability (Fall 2026)

Instructor: Xia Chen

Office: Ayres 318.

Email: xchen3@tennessee.edu

Website: https://web.math.utk.edu/~xchen3

Class: MWF 1:50 pm. -2:40 pm. (Ayres 121)

Office Hours: MWF 10:00 am.- 11:00 am.

Text Book: Probability: A graduate course, 2nd edition (by Allan Gut).

Course Description:
This is the first half of a year-long graduate course series (the second half is Math 524 in the Spring 2027) in probability. In this semester, we will provide a rigorous treatment of the materials such as probability space, random variable (expectation, independence, etc.), convergence theorems, zero-one laws, Borel-Canttelli lemma and distribution theory. In the Spring of 2027, we will continue on the same book with more advanced and special topics such as inequalities in probability, characteristic functions, convergences of random variables law of large numbers, Central limit theorem and martingales.
I will give planty of examples to help understanding a variety of concepts introduced during the course. I plan to keep this course self contained, and will not assume material other than what is covered in the first course of probability and in advanced calculus. In particular, I will not assume results from measure theory, which will be developed as part of the course.

Homework:

Homework will be asingned but not collected. Sixty percent of the exam problems (in midterms and in final) comes directly from assigned homework.

Tests:

We will have three midterm exams and one final exam. Sixty percent of the exam problems comes directly from assigned homework and other fourty percent is relevant to the assigned homework and to the the lecture

Grading: Final Exam 30%; Midterm 60% (20% for each)

Letters will be assigned as follows (subject to change): A:90-100%, B:80-89%, C:70-79%, D:60-70%, F:59% or below.

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