Mathematical Methods in Theoretical Computer Science (CS286a)
Office: Jorgensen 286
Times: Tu/Th 1:00-2:25 in Jorgensen 262
Office hours: email me
- Presentations will be 40 minutes apiece; they will be on Dec 2 (Tues),
4 (Thurs), 8 (Mon), and 11 (Thurs) starting at 1pm. I'd like everyone
who is in town to attend. There WILL be food.
- Talk schedule:
- Tuesday Dec. 2 at 1pm: 1. Chris 2. Bill
- Thursday Dec. 4 at 1pm: 1. Raga 2. Brian
- Monday Dec. 8 at 1pm: 1. Dave 2. Euiwoong
- Thursday Dec. 11 at 1pm: 1. Shankar 2. Hwan-seung 3. Arda
- Lecture 1: introduction and algebra review
- Lecture 2: nearly-linear time algorithms for polynomials (FFT and multiplication)
- Lecture 3: nearly-linear time algorithms for polynomials
(multiplication continued, division with remainder, multipoint evaluation, interpolation, GCD)
- Lecture 4: integer multiplication (De et al. 2008).
- Lecture 5: integer multiplication continued; matrix multiplication (Cohn et al. 2005)
- Lecture 6: matrix multiplication continued
- Lecture 7: matrix multiplication continued; quantum factoring algorithm (Shor)
- Lecture 8: quantum factoring algorithm continued
- Lecture 9: cancelled due to FOCS
- Lecture 10: Fourier analysis on the Boolean cube and
constant-depth circuits (Linial et al.)
- Lecture 11: LMN continued; Bazzi's Theorem (Razborov 2008)
- Lecture 12: Bazzi's Theorem continued; PRGs against constant
degree polynomials (Viola 2008)
- Lecture 13: PRGs against constant
degree polynomials, continued
- Lecture 14: polynomial factorization and modular composition
- Lecture 15: polynomial factorization and modular composition,
- Lecture 16: finishing up modular composition; PV codes
(please read Parvaresh/Vardy 2005)
- Lecture 17: PV codes continued; Folded Reed-Solomon codes
(please read Guruswami/Rudra 2006)
- A. De, P. Kurur, C. Saha, R. Saptharishi. Fast Integer
Multiplication using Modular Arithmetic. 2008.
- H. Cohn, R. Kleinberg, B. Szegedy, C. Umans. Group-theoretic algorithms for matrix multiplication.
- P. Shor. Polynomial-Time Algorithms for Prime
Factorization and Discrete Logarithms on a Quantum Computer.
- N. Linial, Y. Mansour, N. Nisan. Constant depth
circuits, Fourier transform, and learnability. 1993.
- A. Razborov. A
simple proof of Bazzi's theorem. 2008.
- D. Moshkovitz, R. Raz. Sub-constant
error low-degree test of almost-linear size (Section
- J. Hastad. Some optimal
inapproximability results. 1997.
- E. Viola. The sum of d
small-bias generators fools polynomials of degree d. 2008.
- K. Kedlaya, C. Umans. Fast polynomial factorization and
modular composition. 2008.
- F. Parvaresh, A. Vardy. Correcting
errors beyond the Guruswami-Sudan radius in polynomial time.
- V. Guruswami, A. Rudra. Explicit codes achieving list decoding capacity: Error-correction with
- V. Guruswami, C. Umans, S. Vadhan. Unbalanced
Expanders and Randomness Extractors from Parvaresh-Vardy Codes.
- C. Umans. Pseudo-random
Generators for All Hardnesses.
- E. Ben-Sasson, S. Kopparty, J. Radhakrishnan. Subspace
Polynomials and List Decoding of Reed-Solomon Codes.
- A. Ta-Shma, C. Umans. Better
Lossless Condensers Through Derandomized Curve Samplers.
Useful online resources:
Possible papers for presentation: