CS795/895 Probability Theory for Computer Science

Fall 2009

Instructor: Prof. Stephan Olariu
Phone: 683-3915

Course Description:

In undergraduate computer science courses, even in the most advanced ones, computer science phenomena are being looked at either deterministically or, at best, from a simplistic ``average case'' perspective. This approach flies in the face of the fact that virtually all phenomena underlying computer science are stochastic in nature. It follows that the student walks away with an incomplete and often distorted understanding of many fundamental computer science concepts. And yet, the analysis of a good many of these phenomena is within reach, assuming a reasonable exposure to probability theory, stochastic processes and queueing theory. To the best of this instructor's knowledge, no undergraduate course in probability theory covers all the topics above with the needs of a computer science student in mind There is a huge body of knowledge concerning probability theory, stochastic processes and queueing theory. The main challenge and stated goal is to select those topics that will equip the participants with the basic tools necessary for the investigation of computer science phenomena. We will start with a review of basic probability theory results and build up to a level at which stochastic processes and queueuing theory concepts become accessible. Specifically, the menu includes:

• basic probability theory
• random variables and their moments
• basic stochastic processes
• basic queueing phenomena <\ul>

  Intended audience: graduate students in computer science, engineering, mathematics, economics, etc. While the contents is intended to be mathematically correct, rigor is occasionally sacrificed in favor of simplicity: this is to say, proofs that rely on measure-theoretic concepts will be systematically omitted and/or replaced by ``intuitively satisfying'' arguments In an ideal world, the students taking this class should have been exposed to

  • advanced calculus at a suitable level
  • probability theory at advanced undergraduate level
  • stochastic processes at the level of a first course <\ul>

    In a less-than-perfect world, the students often lack proficiency in one or more of the above areas. With this in mind, I will spend the first part of the course (roughly, four weeks) to review relevant topics in probability theory

    Topical coverage: The material is grouped into a set of modules in what seems to me a ``natural'' order.

    • Module-0: Introduction to probability
    • Module-I: Review of probability theory -- some important probability distributions
    • Module-II: Transforms and their applications -- generating functions and the Laplace transform
    • Module-III: Review of stochastic processes
      • Poisson processes
      • Markov chains
      • Random walks
    • Module-IV: Birth-and Death queueing models
    • Module-V: Queueing networks
    • Module-VI: Applications to modeling and performance analysis of computer science phenomena -- selected topics presented by students in the form of guest lectures

    Prerequisites: graduate standing in Computer Science, Computer Engineering, or Electrical Engineering.

    Text: no formal text; a number of relevant papers from recent journal publications and conference proceedings will be discussed in class.

    Grading Scheme:

    • Midterm 30%
    • Class participation 35%
    • Two formal class presentations 40%

    Office Hours: to be arranged

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