Math 410-01, Topics in Computational Mathematics
Day, Lewis, Li (coordinator), Shi, Torczon, Stathopoulos
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
NSF CSUMS program at William and
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.
 M. Hirvensalo, Quantum computing, Springer, 2001.
 J. Preskill, Lecture notes on quantum computation,
- Numerical Linear Algebra and data mining (Stathopoulos)
Stathopoulos and students will explore some problems and algorithms
stemming from various data mining topics.
 Google's Pagerank and Beyond: The Science of Search Engine Rankings
Amy N. Langville, Carl D. Meyer. Publisher: Princeton
 Matrix Computations, Golub and vanLoan, Publisher: John Hopkins
- 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
- 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)