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Fundamentals of Probability

Graduate · Historical course

Fall 2018

This is a course on the fundamentals of probability geared towards first or second-year graduate students who are interested in a rigorous development of the subject. The course covers sample space, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains, and limit theorems. There is also a number of additional topics such as: language, terminology, and key results from measure theory; interchange of limits and expectations; multivariate Gaussian distributions; and deeper understanding of conditional distributions and expectations.

Readings

  • M. Adams and V. Guillemin. Measure Theory and Probability. Birkhauser, 1996. ISBN: 9780817638849.
    Listed reading
  • P. Billingsley. Probability and Measure. 3rd Edition, Wiley, 1995. ISBN: 9780471007104.
    Listed reading
  • R. Durrett. Probability: Theory and Examples. 3rd Edition, Duxbury Press, 2004, ISBN: 9789534424411.
    Listed reading
  • [GS] G. R. Grimmett and D. R. Stirzaker. Probability and Random Processes. Oxford University Press, 3rd edition, 2001. ISBN: 9780198572220.
    Listed reading
  • [C] E. Çinlar. Probability and Stochastics. Springer, 2011. ISBN: 9780387878584.
    Listed reading
  • [W] D. Williams. Probability with Martingales. Cambridge University Press, 1991. ISBN: 9780521406055.
    Listed reading
  • [BT] D. P. Bertsekas and J. N. Tsitsiklis. Introduction to Probability. 2nd Ed., Athena Scientific, 2008. ISBN: 9781886529236. Chapter 1 is available online. ↗
    Listed reading
  • Week #: 1 · Readings: No readings assigned.
    Reading assignment
  • [W] Chapter 1
    Listed reading
  • [BT] Go through the last section of Chapter 1 for background on counting.
    Listed reading
  • [GS] Chapter 3
    Listed reading
  • Week #: 8 · Readings: No readings assigned.
    Reading assignment
  • [C] Chapter 4
    Listed reading
  • Week #: 11 · Readings: No readings assigned.
    Reading assignment
  • [C] Chapter 3
    Listed reading
  • Week #: 14 · Readings: Notes from Lecture 21 (PDF) and Lecture 22 (PDF) . ↗
    Reading assignment
  • Week #: 16 · Readings: No readings assigned.
    Reading assignment
Sources