6.436J/15.085J Fundamentals of Probability

Fall 2017
Lectures Monday, Wednesday 2:30–4:00 PM in Room E51-345
Recitations (1) Friday 11:00 AM–12:00 noon, (2) 12:00 noon–1:00 PM in Room 4-145
First lecture: Wednesday, September 6
First recitation: Friday, September 8

Instructor:
  Professor Tamara Broderick
  Office Hours: Monday, 4–5 PM, 32-G498
  Email:

TAs:
  Martín Zubeldía
  Email:

  Tianheng Wang
  Email:

  TA Office Hours (starting Tues 9/12): Tuesday, 4–5 PM, 56-154


Description

This is a course on the fundamentals of probability geared towards first or second-year graduate students who are interested in a rigorous development of the subject. The course covers most of the topics in 6.041/6.431 (sample space, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains, limit theorems) but at a faster pace and in a lot more depth. There are also many additional topics such as: language, terminology, and key results from measure theory; interchange of limits and expectations; multivariate Gaussian distributions; deeper understanding of conditional distributions and expectations.

Piazza Site

Our course Piazza page is here: https://piazza.com/mit/fall2017/6436

Intended audience

The course is geared towards students who need to use probability in their research at a fairly sophisticated level, e.g., to be able to read the research literature in communications, stochastic control, machine learning, queueing, etc., and to carry out research involving precise mathematical statements and proofs. One of the objectives of the course is the development of mathematical maturity.

Prerequisites

While the only formal prerequisite is 18.02, the course will assume some familiarity with elementary undergraduate probability and some mathematical maturity. A course in analysis will be helpful. It is not required, but be prepared to work harder if you have not had it.