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%

- 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)