6.041x: 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

*Note - This is an Archived course*

This is a past/archived course. At this time, you can only explore this course in a self-paced fashion. Certain features of this course may not be active, but many people enjoy watching the videos and working with the materials. Make sure to check for reruns of 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.

Course Staff

  • John Tsitsiklis

    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

    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

    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

    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

    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

    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

    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

    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.

  • 2014年2月04日, 15 星期
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  • 语言: 英语 Gb



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