# MATH 403

## MTH 403: Probability

### Overview

Measure-theoretic foundations of probability. The Radon-Nikodym theorem and conditional expectation. Infinite products and Kolmogorov’s extension theorem. Random variables, modes of convergence, independence, and the monotone class theorem. Laws of large numbers. Characteristic functions and the central limit theorem. Martingales, inequalities, the optional sampling theorem.

## Instructor

Arjun Krishnan

• Lectures: M W 09:00–10:15 pm in Hylan 1106A
• Office: Hylan 817
• Office Hours: 11 - 12pm Mondays and Wednesdays in my office, or by appointment.
• E-mail: rochester at shirleyarjun dot net

## Textbook

I plan to follow Davar Khoshnevisan’s textbook: Probability.

In addition to this, I will occasionally refer to:

1. Durrett’s book on probability. It’s also available for free online on Rick Durrett’s website. I’m using version 5a from 2017. Version 4.0 was published by cambridge university press. I will use this for discrete-time Markov chains.
2. Varadhan’s Probability. This is a bit sparse.
3. Williams Probability with Martingales. Will use it for Monotone class theorem, $$\pi-\lambda$$ theorem and some elementary material on Martingales.

Grading will be based on Homework and a Final.

 Homework 50% Final 50%

Final: TBA

## Homework

• Will be assigned on the homework page almost every week.
• It will be due the following Wednesday 11:59pm through gradescope. You must access gradescope through blackboard.
• You have one extra day to submit late homework (with a late penalty), and your lowest homework score will be dropped.
• In this class, you may freely discuss homework with each other. You may pair up with one other person and submit homework together. If you do collaborate, you must tell me that you’re collaborating.

## Disability Support

The University of Rochester respects and welcomes students of all backgrounds and abilities. In the event you encounter any barrier(s) to full participation in this course due to the impact of disability, please contact the Office of Disability Resources. The access coordinators in the Office of Disability Resources can meet with you to discuss the barriers you are experiencing and explain the eligibility process for establishing academic accommodations. You can reach the Office of Disability Resources at: (585)275-9049; 1-154 Dewey Hall. Or, visit Center for Excellence in Teaching and Learning.

To be granted alternate testing accommodations, you must fill out forms with CETL at least seven days before each and every exam. These forms are not sent automatically.

### Homework

You may collaborate on homework with one other person, but you must state that you did, and both you will get the same grade.

Exams must be your own. No online resources allowed. You can use any of the textbooks stated on the syllabus.

### Math Dept policy on unauthorized online resources:

Any usage whatsoever of online solution sets or paid online resources (chegg.com or similar) is considered an academic honesty violation and will be reported to the Board on Academic Honesty. In particular, any assignment found to contain content which originated from such sources is subject to a minimum penalty of zero on the assignment and a full letter grade reduction at the end of the semester (e.g. a B would be reduced to a C). Depending on the circumstances, this may apply even if the unauthorized content was obtained through indirect means (through a friend for instance) and/or the student is seemingly unaware that the content originated from such sources. If you have any questions about whether resources are acceptable, please check with your instructor.