[IMAGE]                             Remarks on 6.436
  • Intended audience: 6.436/15.083, Fundamentals of Probabilty, is geared towards 1st or 2nd year graduate students who need to use probability in their research at a reasonably sophisticated level, e.g., to be able to read the research literature in machine learning, statistics, communications, stochastic control, queueing, etc., and to carry out research involving precise mathematical statements and proofs. One of the objectives of the course is the development of mathematical maturity.

  • Scope and relation to 6.041/6.431: 6.436 covers all of the topics in 6.041/6.431 (sample space, random variables, expectations, Bernoulli and Poisson processes, finite Markov chains, limit theorems) but at a faster pace and in much more depth. There are also a number of additional topics such as: language, terminology, and key results from measure theory; interchange of limits and expectations; moment generating and characteristic functions; multivariate normal distributions; deeper understanding of conditional distributions and expectations.

  • Background and prerequisites:

    • The only formal prerequisite is 18.02 (multivariate calculus).

    • The material is presented in a self-contained manner, not assuming a prior exposure to probability or analysis.
      Any facts from analysis that are used are introduced from sratch.

    • Nevertheless, a familiarity with elementary undergraduate probability is definitely helpful.
      In addition, a fair amount of mathematical maturity is expected, and so a course in analysis is also useful.