CS795/895 Probability Theory

Fall 2007

Instructor: Prof. Stephan Olariu
Phone: 683-3915

Course Description:

This graduate course, targeted at a Computer Science audience, proposes to take a look at fundamental issues in Probability Theory in view of their applications. I fully realize that probability theory cannot be taught without a solid grounding in measure theory, Bore sets, Stieltjes integrals, etc. However, I am not planning to get bogged down in excessive formalism: this class is geared towards the CS graduate student who needs Probability Theory in their day-to-day scholarly activities, yet do not wish to study in detail measure theory, sigma algebras and the like. The material is grouped into a set of modules -- most of them still under construction at this time. It has become clear that the computer science graduate student needs a good dose of exposure to probabilistic thinking, randomized algorithm and stochastic processes relevant to CS applications. The course is also providing coverage of certain topics suitable for graduate CS courses that are usually not seen in undergraduate probability theory courses.

The course material is organized around the following broad themes:

• Review of elementary combinatorics
• Review of elementary probability
• Random walks -- a first look
• Random variables -- review of basic results
• Random variables -- concentration results
• Stochastic processes
  • branching processes
  • random walks
  • Markovian processes
  • birth-death processes
• Applications to computer science
• Hands-on experience with probabilistic reasoning

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 35%
• Final 35%
• Class presentation 30%

Office Hours: to be arranged

Back to Dr. Olariu's Home Page