Courses:

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 6.431 (sample space, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains, limit theorems) but at a faster pace and in more depth. There will also be a number of 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.

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

While the only formal prerequisite is 18.02, the course will assume some familiarity with elementary undergraduate probability and mathematical maturity. A course in analysis would be helpful but is not required.

• There will be 10, more or less equally spaced, homework sets. Together with the TA's feedback, they will count for 20% of the final grade. Homework solutions will be handed out on the day that the homework is due. Late homework will be heavily discounted.
• There will be a 2-hour evening quiz, which will count for 35% of the grade.
• There will be a comprehensive final exam, during final's week, which will count for 45% of the final grade.

• You may interact with fellow students when preparing your homework solutions. However, at the end, you must write up solutions on your own. Duplicating a solution that someone else has written (verbatim or edited), or providing solutions for a fellow-student to copy is not acceptable. If you do collaborate on homework, you must cite, in your written solution, your collaborators. Also, if you use sources other than assigned readings in one of your solutions, e.g., an "expert" consultant, or another text, be sure to cite the source.
• In general, we expect students to adhere to basic, common sense concepts of academic honesty. Presenting somebody else's work as if it were your own, or cheating in exams, will not be tolerated, and MIT procedures will be followed.