#### 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.

**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.

- 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
- Lecture 22. Concentration of the number of prime factors; begin Khintchine-Kahane for 4-wise independence
- Lecture 23. Cont. Khintchine-Kahane for 4-wise independence; begin MIS in NC
- Lecture 24. Cont. MIS, begin derandomization from small sample spaces
- Lecture 25. Limited linear independence, limited statistical independence, error correcting codes
- Lecture 26. Lovasz local lemma
- Lecture 27. Applications and further versions of the local lemma
- Lecture 28. Moser-Tardos branching process algorithm for the local lemma

Problem Sets:
- PS1
- PS2
- PS3
- PS4
- 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.