Probability and Algorithms, Caltech CS150, Winter 2007

Leonard J. Schulman

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.

Course textbook:

• Mitzenmacher and Upfal, Probability and Computing, Cambridge 2005 (reserve, SFL)

Some useful books:

1. Adams and Guillemin, Measure theory and probability
2. Motwani & Raghavan, Randomized Algorithms (reserve, SFL)
3. Alon & Spencer, The Probabilistic Method (reserve, SFL)
4. Feller, Probability Theory
5. Cover & Thomas, Information Theory
6. Grimmett & Stirzaker, Probability and Random Processes.
7. Artin, Algebra
8. Herstein, Topics in Algebra

Problem sets:

• Problem set 1
• Problem set 2
• Problem set 3
• Problem set 4