#### 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.

- Lecture 1. Appetizers
- Lecture 2. Some basics: measure; measurable functions, random variables and events
- Lecture 3. Linearity of expectation, union bound, existence
theorems: the probabilistic method, union bound, Ramsey theory
- Lecture 4. Upper and lower bounds: Bonferroni, tail events, Borel-Cantelli
- Lecture 5. Kolmogorov 0-1 law, random walk, percolation
- Lecture 6. Markov and Chebyshev inequalities, power mean inequality; deletion method
- Lecture 7. Conditional expectations, FKG inequality
- Lecture 8. Method of conditional expectations: MAX3SAT. Algebraic fingerprinting: Freivalds
- Lecture 9. Algebraic fingerprinting: testing associativity
- Lecture 10. Perfect matchings, polynomial identity testing
- Lecture 11. Perfect matchings in general graphs. Parallel computation. Isolating lemma
- Lecture 12. Isolating lemma. Find a perfect matching in parallel
- Lecture 13. Independent rvs, Chernoff bound, applications
- Lecture 14. Stronger Chernoff bound, applications
- Lecture 15. Application of large deviation bounds:
Shannon's coding theorem. Central limit theorem
- Lecture 16. Application of CLT to Gale-Berlekamp. Khintchine-Kahane. Moment generating functions
- Lecture 17. Johnson-Lindenstrauss embedding
- Lecture 18. Cont. JL embedding; Bourgain embedding
- Lecture 19. Cont. Bourgain embedding
- Lecture 20. Pairwise independence, Shannon coding theorem again, second moment inequality
- Lecture 21. G(n,p) thresholds

Problem Sets:
- PS1
- PS2
- PS3
- 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.)