Probabilistic systems analysis and applied probability

Lectures: 2 sessions / week, 1 hour / session

Recitations: 2 sessions / week, 1 hour / session

Tutorials: 1 session / week, 1 hour / session

Welcome to 6.041/6.431! This fundamental subject is concerned with the nature, formulation, and analysis of probabilistic situations. No previous experience with probability is assumed. This course is fun, but also demanding.

Students intending to take the undergraduate version of the course need to sign up for 6.041, while those intending to take the graduate version should sign up for 6.431, which includes full participation in 6.041, together with some additional homework problems, additional topics, and possibly different quiz and exam questions.

6.041/6.431 has three types of class sessions: lectures, recitations, and tutorials. The lectures and recitations each meet twice a week. In addition, there will be a tutorial once a week, which is not mandatory, but is highly recommended.

Lectures serve to introduce new concepts. They have an overview character, but also include some derivations and motivating applications. In recitation, your instructor elaborates on the theory, works through new examples with your participation, and answers your questions about them. In tutorial, you discuss and solve new examples with a little help from your classmates and your instructor. Tutorials are active sessions to help you develop confidence in thinking about probabilistic situations in real time. Tutorials are highly recommended; past students have found them to be very helpful.

The prerequisite for 6.041/6.431 is 18.02, or a year of college-level calculus for those with undergraduate degrees from other universities.

The text for this course is:

Bertsekas, Dimitri, and John Tsitsiklis. Introduction to Probability. 2nd ed. Athena Scientific, 2008. ISBN: 9781886529236.

Solutions to end-of-chapter problems are available: (PDF - 1.5MB)

A few of these problems will be covered in recitation and tutorial. The remaining ones can be used for self-study (for best results, always try to solve a problem on your own, before reading the solution).

Additionally, the following books may be useful as references. They cover many of the topics in this course, although in a different style. You may wish to consult them to get a different perspective on particular topics.

Drake, Alvin. Fundamentals of Applied Probability Theory. McGraw-Hill, 1967. ISBN: 9780070178151.

Ross, Sheldon. A First Course in Probability. 8th ed. Prentice Hall, 2009. ISBN: 9780136033134.

We grade homework, but often only a small, randomly chosen subset of the problems. We do post detailed solutions on the course Web site. Your TA is available to discuss your work with you, both before and after it is due. You may encounter difficulty figuring out where your own solution of a homework problem went astray. There are many ways to approach most probability problems. Just agreeing with our problem solutions may not explain why your approach didn't work.

Grades will be determined by your work in all aspects of this subject.

In order to get the most out of the course, it is important to not fall behind. It is also important to read the text carefully before attempting to solve the homework problems. A very good practice is to review the lecture notes before attending the next lecture or recitation; this way, recitations and tutorials will be much more informative and meaningful.

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