Probability and Algorithms, Caltech CS150, Winter 2005

Leonard J. Schulman

Office hours by appointment; send me an email.
TA: Xiaojie Gao. Office hours: Tuesday 8:30-10:00pm.
Lectures: MW 10:30-12:00. Location: Steele 125.

Catalog listing:

Elementary randomized algorithms and algebraic bounds in communication, hashing, and identity testing. Game tree evaluation. Topics may include randomized parallel computation; independence, k-wise independence and derandomization; rapidly mixing Markov chains; expander graphs and their applications; clustering algorithms.

Some useful books:

  1. Adams and Guillemin, Measure theory and probability
  2. Motwani & Raghavan, Randomized Algorithms (open reserve, SFL)
  3. Alon & Spencer, The Probabilistic Method (open reserve, SFL)
  4. Feller, Probability Theory
  5. Cover & Thomas, Information Theory
  6. Grimmett & Stirzaker, Probability and Random Processes. This is also the source of the following two quotes. The first says something instructive about probability: "To understand the theory of chance thoroughly, requires a great knowledge of numbers, and a pretty competent one of Algebra." (John Arbuthnot, An essay on the usefulness of mathematical learning, 25 November 1700.) The second quote is taken totally out of context and provides dubious instruction about probabilists: "Besides gambling, many probabilists have been interested in reproduction." (G & S p. 171.)
  7. Artin, Algebra
  8. Herstein, Topics in Algebra

Problem sets:

Links:

The page for the previous offering of this class is here.