This course is an introduction to probabilistic modeling, including random processes and the basic elements of statistical inference. The ability to think probabilistically is a fundamental component of scientific literacy. You will learn the relevant models, skills, and tools that are the keys to analyzing data and making scientifically sound predictions under uncertainty. We emphasize the basic concepts and methodologies, and include dozens of examples and applications.
Probabilistic Systems Analysis has been offered and continuously refined at MIT for more than fifty years. The class is offered through the Electrical Engineering Department and has, over time, served multiple constituencies from engineering, operations research, and the sciences. Unlike traditional mathematics classes, it aims to develop the skills and intuition that are most useful to practicing engineers and scientists. On campus, it is taken by a large number of students with diverse backgrounds and a broad range of interests. They span the entire spectrum from freshman to beginning graduate students, and from the Engineering School to the School of Management.
Although this is not a mathematics course, it does rely on the language and some tools from mathematics. It requires a level of comfort with mathematical reasoning, familiarity with sequences, limits, infinite series, and the chain rule, as well as the ability to work with ordinary or multiple integrals.
Until quite recently, scientific literacy meant knowing calculus, some physics, and some chemistry. Even with the introduction of computers and computation, this was all that you needed to know in order to make sense of the world. But these days, you cannot understand what is going on around you if you do not understand the uncertainty attached to nearly every phenomenon. This is why probability is now a central component of scientific literacy.
What is it that has changed and has caused this shift? There are two main factors:
If these arguments sound a bit abstract, just think of any scientific field, and you quickly realize that pretty much everything is subject to uncertainty and calls for probabilistic models. For example:
The message is clear: most phenomena of interest involve significant randomness, and the only reason we collect and manipulate data is because we want to fight this randomness as much as we can. The first step in fighting an enemy like randomness is to study and understand it.
The text for this course is:
Bertsekas, Dimitri, and John Tsitsiklis. Introduction to Probability. 2nd ed. Athena Scientific, 2008. ISBN: 9781886529236.
This OCW Scholar course, designed for independent study, is closely modeled on the course taught on the MIT campus. The on-campus course has three types of class sessions: lectures, recitations, and tutorials. The lectures and recitations each meet twice a week, and the optional tutorial meets once a week.
MIT students who take the corresponding residential class typically report an average of 11-12 hours spent each week, including lectures, recitations, readings, homework, and exams.
The OCW Scholar course combines content previously published on the Fall 2010 OCW site 6.041 Probabilistic Systems Analysis and Applied Probability with 51 new videos recorded in 2013 by MIT Teaching Assistants. The Scholar course has four major learning units. Each unit has been divided into a sequence of lecture sessions that include
Most sessions also include:
To help guide your learning, some of these problems have an accompanying Help Video where an MIT Teaching Assistant solves the same problem.
In addition to the Recitation and Tutorial Problems, the course also has Problem Sets and Exams with Solutions.
It's difficult to estimate how long it will take you to complete the course, but you can probably expect to spend several hours working through each individual lecture session.
This OCW Scholar course was developed by John Tsitsiklis, Professor of Electrical Engineering, with the Department of Electrical Engineering and Computer Science (EECS) at MIT. The Help Session Videos were developed by MIT Teaching Assistants Qing He, Jimmy Li, Jagdish Ramakrishnan, Katie Szeto, and Kuang Xu. To learn more, visit the Meet the Team page.