Caltech CS 150 Probability and Algorithms, Fall 2018

Leonard J. Schulman

My office hours are by appointment at the beginning of the term, after that I'll fix a regular time (but appointments will still be fine). Starting Oct 12: my OH on Fridays at 11:00. Preliminary Syllabus

TA: Jenish Mehta,

Added December 17: Revised and collected lecture notes for the whole term.

Lecture Notes: I usually wind up revising my lecture notes after teaching, so they will be gradually posted here, as we go.
  1. Lecture 1. Appetizers
  2. Lecture 2. Some basics: measure; measurable functions, random variables and events
  3. Lecture 3. Linearity of expectation, union bound, existence theorems: the probabilistic method, union bound, Ramsey theory
  4. Lecture 4. Upper and lower bounds: Bonferroni, tail events, Borel-Cantelli
  5. Lecture 5. Kolmogorov 0-1 law, random walk, percolation
  6. Lecture 6. Markov and Chebyshev inequalities, power mean inequality; deletion method
  7. Lecture 7. Conditional expectations, FKG inequality
  8. Lecture 8. Method of conditional expectations: MAX3SAT. Algebraic fingerprinting: Freivalds
  9. Lecture 9. Algebraic fingerprinting: testing associativity
  10. Lecture 10. Perfect matchings, polynomial identity testing
  11. Lecture 11. Perfect matchings in general graphs. Parallel computation. Isolating lemma
  12. Lecture 12. Isolating lemma. Find a perfect matching in parallel
  13. Lecture 13. Independent rvs, Chernoff bound, applications
  14. Lecture 14. Stronger Chernoff bound, applications
  15. Lecture 15. Application of large deviation bounds: Shannon's coding theorem. Central limit theorem
  16. Lecture 16. Application of CLT to Gale-Berlekamp. Khintchine-Kahane. Moment generating functions
  17. Lecture 17. Johnson-Lindenstrauss embedding
  18. Lecture 18. Cont. JL embedding; Bourgain embedding
  19. Lecture 19. Cont. Bourgain embedding
  20. Lecture 20. Pairwise independence, Shannon coding theorem again, second moment inequality
  21. Lecture 21. G(n,p) thresholds
  22. Lecture 22. Concentration of the number of prime factors; begin Khintchine-Kahane for 4-wise independence
  23. Lecture 23. Cont. Khintchine-Kahane for 4-wise independence; begin MIS in NC
  24. Lecture 24. Cont. MIS, begin derandomization from small sample spaces
  25. Lecture 25. Limited linear independence, limited statistical independence, error correcting codes
  26. Lecture 26. Lovasz local lemma
  27. Lecture 27. Applications and further versions of the local lemma
  28. Lecture 28. Moser-Tardos branching process algorithm for the local lemma
Problem Sets:
  1. PS1
  2. PS2
  3. PS3
  4. PS4
  5. PS5
TA Office Hours: weeks that an assignment is due: M 7:00pm Ann 121; off weeks: W 7:00pm Ann 107. Problem sets are due to Jenish's mailbox by W 6:00pm. Here is the class calendar, and you should be able to add it to your own calendar through the link at the bottom-right.

Library course reserve page. One of the books, Motwani and Raghavan, is available there as an e-book.