Math 410-01, Topics in Computational Mathematics Spring, 2008

Instructors:

Day, Lewis, Li (coordinator), Shi, Torczon, Stathopoulos

Course description:

In the first two-three weeks, instructors will introduce different topics of computational mathematics arising from subjects such as numerical linear algebra, quantum computing, optimization, dynamical systems, and mathematical biology. Students will select topics; then study and present the material under the guidance of instructors. Students will then write short surveys (or papers if there are new discoveries) on the topics.

The class projects may lead to undergraduate research opportunity supported by NSF CSUMS program at William and Mary.

Here are the proposed topics:

Quantum information and quantum computation (Li)
Li and students will be presentations on issues and problems in this highly active interdisciplinary research topic.
References:
[1] M. Hirvensalo, Quantum computing, Springer, 2001.
[2] J. Preskill, Lecture notes on quantum computation, http://www.theory.caltech.edu/~preskill/ph229#lecture.
Numerical Linear Algebra and data mining (Stathopoulos) Stathopoulos and students will explore some problems and algorithms stemming from various data mining topics.
References:
[1] Google's Pagerank and Beyond: The Science of Search Engine Rankings Amy N. Langville, Carl D. Meyer. Publisher: Princeton University Press.
[2] Matrix Computations, Golub and vanLoan, Publisher: John Hopkins Press.
Numerical calculation of solutions of elliptic systems (Shi and Day)
Optimization problems in distance geometry, graph algorithms, quantum computing (Troczon and Lewis).

Final grade will be based on (tentative):

     Class participation                                    25%
     Homework and evaluations                               25%
     Two presentations                                      30%
     Class project (Due: May 2)                             20%

Presentation schedule

Jan 17. Faculty - Li: Introduction
Jan 22. Faculty - Day and Shi: PDE and Dynamics
Jan 24. Faculty - Day and Shi: PDE and Dynamics
Jan 29. Faculty - Torczon: Nonlinear optimization
Jan 31. Faculty - Stathopoulos: Numerical linear algebra
Feb 5. Fauculty - Li: Quantum computing: an overview.
Feb 7. Students - Ashwin Rastogi / Jennifer Mahle - Quantum computing.
Feb 12. Students - Sean Clark / Tanner Crowder - Quantum algorithm.
Feb 14. Students 5/6 Benjamin Strahs - PasswordAgent: Secure Passwords Through Enhanced Hashing
Tim Brewster - Chemical emission: a computational approach.
Feb 19. Students 7/8. Kassie Archer/Brian Paljug: Symbolic Dynamics.
Feb 21. Students 9/10. Chris Silkworth: Symbolic dynamics.
Katie Williams: Optimization.
Feb 26. Students 11/12. Mutell: Data Mining and Its Applications in Finance.
Feb 28. Faculty
Mar 4/6. Spring break.
Mar 11. Ashwin Rastogi: Mathematical background of quantum computing
Mar 13. Tanner Crowder: Quantum Fourier Transforms
Mar 18. Sean Clark: Mathematical background of hidden subgroup algorithm
Mar 20. Phillips (William and Mary, Columbia University)
Mar 25. Jennifer Mahle: Quantum gates.
Mar 27. Tim Brewster
Apr 1. Kassie Archer
Apr 3. Brian Paljug
Apr 8. Chris Silkworth
Apr 10. Katie Williams
Apr 15. Billy Mutell
Apr 17. Benjamin Strahs
Apr 22. Faculty
Apr 24. Laura Sheppardson (University of Mississippi)