**Math 261C**

**Randomized Algorithms**

Winter 2014

**Course: ** Math 261C: Probabilistic Algorithms and Combinatorics

**Dates:** Spring 2014 quarter, Monday-Wednesday-Fridays 12:00-12:50

**Room:** APM 7421

**Instructor:** Sam Buss

Email: sbuss@math.ucsd.edu

Office: APM 6210.

Office phone: 858-534-6455.

Voice mail: 858-792-9674.

Mobile phone: 442-2877 (same area code).

**Office hours:**
By appointment, or Monday 1:00-1:30 and Friday 1:00-1:30.

**Overview:**
This course will cover topics in randomized algorithms and
derandomization, with an emphasis on combinatorial problems
and techniques.

There are no particular prerequisites beyond a certain level of mathematical maturity. It is aimed at graduate students in mathematics, computer science and related areas. Math 261A and 261B are not prerequisites for this course.

Some students have been unable to enroll online. If this happens to you, please see the instructor for permission to enroll.

- March 31, 2014. QuickSort and QuickSelect for median and k-th element. Scribe notes by Michelle Bodnar.
- April 2, 2014. Floyd-Rivest Select for median and k-th element. Scribe notes by Marco Carmosino.
- April 4, 2014. WalkSat, part I. Scribe notes by James Aisenberg.
- April 7, 2014. WalkSat, part II; Lovász Local Lemma, part I. Scribe notes by Christian Woods.
- April 9, 2014. Lovász Local Lemma, part II. Scribe notes by Jay Cummings.
- April 11, 2014. Lovász Local Lemma, part III. Scribe notes by Sittipong (Kuang) Thamrongpairoj.
- April 14, 2014. Lovász Local Lemma, wrapup. PPSZ, part I. Scribe notes by Udbhav Singh.
- April 16, 2014. PPSZ, part II. Scribe notes by Radheshyam Balasundaram.
- April 18, 2014. PPSZ, part III. Scribe notes by James Aisenberg.
- April 21, 2014. FKG_inequality. Scribe notes by Christian Woods.
- April 23, 2014. Number theory, Pratt certificates. Scribe notes by Marco Carmosino.
- April 25, 2014. Quadratic Residues. Scribe notes by Michelle Bodnar.
- April 28, 2014. Factorization: Square Roots, RSA, Totient Function. Scribe notes by Sittipong (Kuang) Thamrongpairoj.
- April 30, 2014. Factoring univariate polynomials mod p. Scribe notes by Christian Woods.
- May 2, 2014. Solovay-Strassen primality testing. Scribe notes by Marco Carmosino.
- May 5, 2014. Quadratic Reciprocity. Scribe notes by James Aisenberg.
- May 7, 2014. Miller-Rabin algorithm, complexity classes (petting zoo). Scribe notes by Michelle Bodnar.
- May 9, 2014. Monte Carlo, FPRAS, DNF Counting (I). Scribe notes by Sittipong (Kuang) Thamrongpairoj.
- May 12, 2014. DNF Counting (II), Freiwald's Method. Scribe notes by Michelle Bodnar.
- May 14, 2014. Polynomial Identity Testing. Scribe notes by Udbhav Singh.
- May 16, 2014. Interactive Proofs (IP) for Graph Nonisomorphism; Arthur-Merlin (AM) Games. Scribe notes by Christian Woods.
- May 19, 2014. AM[2] Algorithm for Graph Non-Isomorphism. Scribe notes by Marco Carmosino.
- May 28, 2014. #P is in IP. Scribe notes by James Aisenberg.
- June 2, 2014. PCP Theorem - Introduction. Scribe notes by Udbhav Singh.
- June 4, 2014. Proof of PCP Theorem, part I. Scribe notes by Sittipong (Kuang) Thamrongpairoj.
- June 6, 2014. Proof of PCP Theorem, part II. Scribe notes by Udbhav Singh.

Here is the link for Homework Problems.

Latex source files for the PDF files are available online, by manually changing the filename extension in the URL from "pdf" to "tex".

**Course resources**.
There is no textbook for the course, but a couple of books for useful background reading
include:

- R. Matwani and P. Raghavan, "Randomized Algorithms", Cambridge Unversity Press, 1995. This is the standard graduate textbook giving an introduction to this subject. It is available on Kindle.
- M. Mitzenmacher and E. Upfal, "Probability and Computing: Randomized Algorithms and Probabilistic Analysis", Cambridge University Press, 2005. This is an undergraduate text, but it is very accessible and has a number of advanced topics, and with complete proofs. (Recommended for background reading.) This one is available on Kindle too.

These notes are very rough, and for Sam's archival storage. Not likely to be useful for anyone else. Click here.