[IMAGE]                             Remarks on 6.041
6.041, Introduction to Probability, is a comprehensive introduction to probabilistic models.

It is complemented by substantial online resources, including a full set of EdX videos for the class Introduction to Probability - The Science of Uncertainty (archival version is permanently available), as well as more traditional videotaped lectures under OCW.

Depending on personal learning styles, different students rely on these resources to a larger or smaller extent.

  • The two half-courses: As of the Fall of 2016, 6.041 is offered as a sequence of two 6-unit courses (6.041A and 6.041B). Taking this sequence will be essentially the same as taking the original 12-unit course.

  • The first half (6.041A) covers the basic elements of probabilistic models, including discrete and continuous distributions, multiple random variables, means and variances, conditioning, Bayes formulas, and limit theorems. As such, it provides a solid foundation for taking other classes that rely on probabilistic reasoning.

  • EECS requirements: The first half (6.041A) can be used to satisfy the Probability Grounding requirement in EECS.

  • Prerequisite for later courses. 6.041A is a formal prerequisite for certain classes such as 6.011. Even though it is not currently a formal prerequisite for classes such as 6.008 or 6.036, it does provide useful and relevant background, allowing for clearer understanding of the topics in such classes.

  • The second half (6.041B) has three main components:

    • Additional topics in basic probability: functions of random variables, and a deeper view of conditional expectations.

    • A thorough introduction into Bayesian inference in discrete continuous, and mixed settings (posterior distributions, maximum a posteriori probability estimation, linear and general least mean squares estimation, Beta distributions, linear normal models).

    • An introduction to stochastic processes (probabilistic models that evolve in time) focused on the Bernoulli and Poisson processes and finite-state Markov chains.

    6.041B is important for those who will be making substantial use of probabilistic models later on.