403

MTH 403: Probability

Overview

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

Instructor

Arjun Krishnan

  • Lectures: 9.40-10.55 AM in Hylan 1106B
  • Office: Hylan 817
  • Office Hours: 2.00pm - 3.00pm Thursdays and 11am - 12pm on Fridays in my office, or by appointment.
  • Email: arjun.krishnan at rochester dot edu

Teaching Assistant

Roan James

  • Email: rjames15@UR.Rochester.edu
  • Office: Hylan 1103
  • Office Hours: Fridays 1.30 - 2.30pm

Course description

Class time and place

9:40am - 10.55am Tuesdays and Thursdays in Hylan 1106B.

Textbook

I will use my own notes, which will draw from the following sources:

  1. Le Gall’s textbook: Measure Theory and Probability
  2. Davar Khoshnevisan’s textbook: Probability.
  3. 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.

Prerequisites

MTH 471 or equivalent.

Grading and Exams

Grading will be based on Homework, a Midterm and a Final.

Homework 30%
Midterm 30%
Final 40%

Homework.

  • There will be weekly homework, it will be assigned on Tuesday (or Wednesday at the latest), and it will be due the following Tuesday in class.
  • The first homework will be assigned on Jan 21, and you can find it on this webpage.
  • Honesty policy: you may not look up solutions to homework problems on the internet and present them as your own. You may freely discuss homework with each other. But your work must be your own, and you may not copy someone else’s answers.

Midterm: In class, Mar 20.

Final: May 9, Room TBA.

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.

Academic Honesty

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, notes or textbooks allowed.

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.