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, jenishc@gmail.com.

Lecture Notes: I usually wind up revising my lecture notes after teaching, so they will be gradually posted here, as we go. The entire lecture notes from two years ago are also posted, at the end of this page, but since they are buggy and I'm making lots of changes, I suggest you use the current notes when possible.
  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
Problem Sets:
  1. PS1
  2. PS2
  3. PS3
  4. PS4
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.

All 18 lectures of 2016 compiled
(Contact me if you want material from lectures in earlier years.)