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Math 7800/7810: Probability I/II

2024 Fall/2025 Spring, Auburn University

Contacts

Lecture Instructor Dr. Le Chen lzc0090@auburn.edu
Class Time and Room TR, 2:00 PM -- 3:15 PM Parker Hall 252
Office hours TR, 1:00 PM -- 1:50 PM Parker Hall 203

Course description

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. It has been widely used in areas of study such as statistics, finance, artificial intelligence, machine learning, game theory, mathematical physics, etc.

This course is the first course of the two-semester sequential courses -- Math 7800 and Math 7810. In Math 7800 -- Probability I, we will cover the standard materials for the measure-based probability theory, including measure theory, laws of large numbers, and central limit theorems. While in Math 7810 -- Probability II, we will cover some more advanced topics such as martingale theory, Brownian motion, stochastic differential equations, random matrices, etc. These topics may vary from year to year.

Textbook

Coverage

Math 7800 will cover topics such as measure-theoretical probability theory, including strong and week laws of large numbers, characteristic functions, central limit theorems. We will follow mostly most parts of the first three chapters of the text book:

Math 7810 will cover more advanced topics, including convergence of distributions, conditional probability/expectations, and martingale theory. Depending on the request, we may also cover some materials from random matrices.

Prerequisite

Students obligations and tips

This is a demanding course and it requires a great deal of work from your side. In order to successfully master the material and complete the course, you are expected to


Note: The syllabus was created in April 2024, and it is subject to changes during the semester.


Homework

Test and exam

Attendance

Assessment


Tentative schedule and slides


Gradescope


Honor code

Accessibility

Your success in this class is important to me. We will all need accommodations because we all learn differently. If there are aspects of this course that prevent you from learning or exclude you, please let me know as soon as possible. Together we will develop strategies to meet both your needs and the requirements of the course.

I encourage you to visit the Office of Accessibility to determine how you could improve your learning as well. You can register and make a request for services from the Office of Accessibility. In this case, please do inform me of such requests. See the following link for more information:

Harassment and Discrimination


Acknowledgment

  1. Logo image is generated by ChatPGT 4.

© Le Chen, Math 7800/7810 -- Probability I/II, Auburn, 2024 Fall/2025 Spring