Top 10 Algorithms of 20th and 21st Century

MATH 595 (Section TTA)

Fall 2014

TR 2:00 pm - 3:20 pm, Room 341 Altgeld Hall
University of Illinois at Urbana-Champaign, Department of Mathematics

Instructors : Yuliy Baryshnikov and Anil N. Hirani

Schedule:
In bold below are the main algorithm lectures. Other lectures are reports on applications/extensions/related topics and algorithms.
08/26 Introduction
08/28 Metropolis
09/02 Integer relations detection
09/04 Simplex algorithm for linear programming
09/09 LU decomposition for solving linear systems
09/11 Quicksort
09/16 Metropolis application to physical problem
09/18 QR decomposition and least squares
09/23 ...
09/25 Conjugate gradients
09/30 LP duality, image segmentation using LP
10/02 Kalman filter
10/07 Interior point methods, max-flow, other LP applications
10/09 Kalman filter contd.
10/14 Particle filters; Bloom filter
10/16 Bloom filter contd.; LLL basis reduction
10/21 LLL basis reduction contd.
10/23 Iterative linear solvers
10/28 QR iteration for eigenvalue computation
10/30 Fast Fourier Transform
11/04 Multi-pivot quicksort
11/06 Metropolis applications
11/11 ...
11/13 FFT applications
11/18 Isospectral domains and spectrum computation
11/20 FFT applications
11/25 [Fall break]
11/27 [Fall break]
12/02 Introduction to parallel algorithms
12/04 Fast multipole method
12/09 Bloom filter applications

Description: In January 2000, Computing in Science and Engineering magazine published a list of 10 algorithms which (in their words) had the "greatest influence on the development and practice of science and engineering in the 20th century". With an eye towards the future we have prepared a slightly modified list of Top 10 algorithms which we will study in this class.

There will be approximately 2-3 sessions (lecture/discussion) on each algorithm. The first session for each algorithm will be a lecture by the instructors. In it we will give an overview of the algorithm and its applications and provide the relevant reading list and programming suggestions. Later sessions on that algorithm will largely be student-led and moderated by the instructors. For each algorithm there will be a team of 3 students working with the instructors : a historian, a programmer and a scribe.

The historian will have primary responsibility for leading the survey of the literature, the programmer will do the computer experiments, and scribe will record the material collected and presented by that team.

List of algorithms:

Metropolis algorithm for Monte Carlo (with Gibbs sampler)
Integer relation detection (PSLQ, LLL and related algorithms)
Simplex method for linear programming (with interior point methods)
Matrix factorization algorithms for solving linear systems and least squares
Quicksort
Conjugate gradients and Krylov subspace methods for solving linear systems
Bloom filter
QR algorithm for eigen computations
Fast Fourier transform
Fast multipole method

Readings: Reading material is available on U of I Box. You will need a U of I Box account. (This is different from a general Box account that you might have signed up for directly with Box.) Once you have a U of I box account you can download the readings.

Grading: Grading will be based on class participation and project.

Computing environment: The programmer in each team of 3 will have to do some programming. For a course like this we prefer Python (and occasionally MATLAB). Sage is basically Python so that works too. Any code we provide will be in Python (and perhaps sometimes in MATLAB). Students are free to use any programming environment. In addition to or instead of Python/Sage, students are free to use MATLAB/Octave, C/C++, Java, Fortran, Mathematica or any other programming environment.

Prerequisite: Calculus and linear algebra. Programming is not a prerequisite for everyone (we need about a third of the students to know some programming).

Announcements: will be posted on Compass.

Contacts:
Anil N. Hirani, email
375 Altgeld Hall

Yuliy Baryshnikov, email
302 Altgeld Hall