Math 6040: Fall 2002
Mathematical Probability

Reading/Homework
Why Graduate
Training in
Probability? 		Have a look at the findings of a recent advisory panel to the National Science Foundation here. (For html buffs, the NSF's general URL is http://www.nsf.gov.)
Instructor Davar Khoshnevisan (JWB 102)
Office Hours M 2:40-3:30 p.m.
Email davar@math.utah.edu
Web http://www.math.utah.edu/~davar/math6040/2002
Lectures MWF 10:45-11:35 a.m. (NS 202)
Prerequisites At least concurrent enrollment in Real Analysis (Math 6210).
Texts
  • D. Williams, Probability with Martingales, Cambridge University Press, 2001. (Required)

  • R. Durrett, Probability: Theory and Examples, Duxbury Press, Second Edition, 1996. (Recommended)

  • My lecture notes (clickable when available. Each section is posted after the relevant lecture. Continually updated.)
Information This is a first-year Ph.D. course in mathematical probability. The prerequisite is a Ph.D. course in measure theory/analysis, and so we will spend some but very little time developing this material. This course is not a natural continuation of undergraduate probability (Math 5010).

Extra-special emphasis is paid to:
  • Developing a solid theoretical foundation for probability.
  • Preparing, in one semester, enough material so that the student will then be ready to go on to learn about various special topics such as:
    • Stochastic calculus (math. finance), stochastic differential equations, etc.
    • Stochastic analysis, applications to mathematical physics, PDEs, etc.
    • Ergodic theory, and information theory.
    • Discrete probability (applications in combinatorics, graph theory, theoretical computer science, etc.)
Topics
  • Measure theory (primer)
  • Independence
  • Weak Convergence
  • Martingales
  • Discrete Markov Chains
  • Brownian Motion
  • Elements of Stochastic Differential Equations (New)
Intended Audience
  • Probability theory, PDEs, and real and harmonic analysis (or related areas)
  • Theoretical computer science (or related areas)
  • Mathematical physics (or related areas)
  • Mathematical finance (or related areas; emphasis on mathematical here)
Grade Weekly homeworks (80%) and a take-home final (20%). This is a prelim course, so grading is taken very seriously.
Other Information
  • See the listings of the probability/harmonic analysis seminar for activity in these areas. You may wish to attend the first few weeks of this seminar where general/related results on analysis and Fourier series are introduced.


Disclaimer
© 2002 by the Dept of Math. University of Utah