College-level calculus (single-variable and multivariable). Although this is not a mathematics course, it does rely on the language and some tools from mathematics. It requires a level of comfort...see more...
Introduction to Probability - The Science of Uncertainty
An introduction to probabilistic models, including random processes and the basic elements of statistical inference.
About this Course
The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications. The world is also full of data. Probabilistic modeling and the related field of statistical inference are the keys to analyzing data and making scientifically sound predictions.
Probabilistic models use the language of mathematics. But instead of relying on the traditional "theorem - proof" format, we develop the material in an intuitive -- but still rigorous and mathematically precise -- manner. Furthermore, while the applications are multiple and evident, we emphasize the basic concepts and methodologies that are universally applicable.
The course covers all of the basic probability concepts, including:
- multiple discrete or continuous random variables, expectations, and conditional distributions
- laws of large numbers
- the main tools of Bayesian inference methods
- an introduction to random processes (Poisson processes and Markov chains)
The contents of this course are essentially the same as those of the corresponding MIT class (Probabilistic Systems Analysis and Applied Probability) -- a course that has been offered and continuously refined over more than 50 years. It is a challenging class, but it will enable you to apply the tools of probability theory to real-world applications or your research.
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John Tsitsiklis is a Professor with the Department of Electrical Engineering and Computer Science, and a member of the National Academy of Engineering. He obtained his PhD from MIT and joined the faculty in 1984. His research focuses on the analysis and control of stochastic systems, including applications in various domains, from computer networks to finance. He has been teaching probability for over 15 years.
Patrick Jaillet is a Professor of Electrical Engineering and Computer Science and Co-Director of the MIT Operations Research Center. He obtained his PhD in Operations Research at MIT. His research interests deal with optimization and decision making under uncertainty as applied to transportation and the internet economy. Professor Jaillet’s teaching includes subjects such as algorithms, optimization, and probability.
Dimitri Bertsekas is a Professor with the Department of Electrical Engineering and Computer Science, and a member of the National Academy of Engineering. He obtained his PhD from MIT and joined the faculty in 1979. His research focuses on optimization theory and algorithms, with an emphasis on stochastic systems and their applications in various domains, such as data networks, transportation, and power systems. He has been teaching probability for over 15 years.
Qing He is a graduate student in the MIT Department of Electrical Engineering & Computer Science. Her research interests include inference, signal processing, and wireless communications -- all of which rely on the fundamental concepts taught in 6.041x. Qing has taken several probability classes at MIT, and has been a teaching assistant for this course for two semesters.
Jimmy Li is a graduate student in MIT's Department of Electrical Engineering & Computer Science. His research focuses on applying the tools taught in this and related courses to problems in marketing. He took 6.041 as an undergraduate and has also been a TA for the course three times.
Jagdish Ramakrishnan recently received his PhD at MIT’s Department of Electrical Engineering and Computer Science. His dissertation focused on optimizing the delivery of radiation therapy cancer treatments dynamically over time. His general research interests include systems modeling, optimization, and resource allocation. He was a teaching assistant for this course twice while at MIT.
Katie Szeto is a member of the Business Operations team at Dropbox. She received her Bachelor and Master of Engineering degrees from MIT. Her Master’s thesis explored applications of probabilistic rank aggregation algorithms. Katie took 6.041 with Professor Tsitsiklis when she was a sophomore at MIT. Later, as a graduate student, she was a teaching assistant for the class.
Kuang Xu is a graduate student in the Department of Electrical Engineering & Computer Science at MIT. His research focuses on the design and performance analysis of large-scale networks, such as data centers and the Internet, which involve a significant amount of uncertainties and randomness. Kuang took his first probability course in his junior year, and served as a teaching assistant for 6.041 in 2012.
College-level calculus (single-variable and multivariable). 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, the chain rule, as well as the ability to work with ordinary or multiple integrals.
Nothing! The course is free.
You can register at any time, but you will not get credit for any assignments that are past due.
The course starts on Tuesday, February 4, 2014 and ends on the due date of the final exam, on Tuesday, May 20, 2014.
The course material is organized along units that are aligned with the chapters of the textbook. Each unit contains between one and three lecture sequences. Each lecture sequence consists of short video clips, interleaved with short problems to test your understanding. Each unit also contains a wealth of supplementary material, including videos that go through the solution of various problems.
The class follows closely the text Introduction to Probability by Bertsekas and Tsitsiklis; see the publisher's website or Amazon for a description and reviews. The publisher is generously providing a free online-only version of the textbook, which will be linked to the course materials. The publisher will also provide a substantial discount for purchasing a printed version. Details on how to obtain this discount will be provided on the course site, before the start date of the course.
Video lectures as well as worked problems will be available and you can watch these at your own convenience. Homework assignments and exams, however, will have due dates.
Yes, we will provide transcripts of all clips (lectures, worked problems, etc.) that are synched to the videos.
Grades (Pass or Not Pass) are based on a combination of scores on the weekly homework assignments (11 total), two midterm exams, and a final exam.
This is an ambitious class in that it covers a lot of material in substantial depth. Furthermore, the only way of mastering the subject is by actually solving on your own a fair number of problems. 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.