Dr. Perry's area of expertise include:
1. Problems from journals published by the MAA. These tend to be relatively easy and short term (days or weeks). Solving them requires a bit of time and creativity. The solution is usually known already, so the payoff is in the experience of solving the problem. Once you finish, you can submit it to the journal and see your name in print.
2. Mathematical problems suitable for undergraduate exploration:
* Problems in combinatorial game theory (Nim, Hackenbush, Life, etc.)
* Fixing Dodgson's method for computing determinants
* Other fraction-free methods to compute determinants
* Techniques to triangularize a sparse matrix
3. Programming projects suitable for students with some programming background in C/C++, Java, Python. Such projects will be useful either for a problem of interest to me & the larger community or for education. |
The F5 criterion revised (joint with Alberto Arri)
Journal of Symbolic Computation, vol. 46 (2011) pgs. 1017-1029, DOI 10.1016/j.jsc.2011.05.004
http://arxiv.org/abs/1012.3664
Modifying Faugère's F5 algorithm to ensure termination
(joint with Christian Eder, Justin Gash, John Perry)
ACM Communications in Computer Algebra, 2011
http://dl.acm.org/authorize?6565546
http://arxiv.org/abs/1012.3664
Signature-based algorithms to compute Gröbner bases
(joint with Christian Eder, John Edward Perry)
ISSAC '11 Proceedings of the 36th international symposium on Symbolic and algebraic computation, 2011
http://dl.acm.org/authorize?438266
http://arxiv.org/abs/1101.3589
Generalizing Dodgson's method: a "double-crossing" approach to computing determinants (joint with Deanna Leggett and Eve Torrence)
College Mathematics Journal, January 2011, vol. 42 no. 1 pgs. 43-54, DOI 10.4169/college.math.j.42.1.043
http://arxiv.org/abs/0906.3840
F5C: a variant of Faugère's F5 algorithm with reduced Gröbner bases (with Christian Eder)
Journal of Symbolic Computation, December 2010, vol. 45 issue 12 pgs. 1442-1458, DOI 10.1016/j.jsc.2010.06.019
An Extension of Buchberger's Criteria for Gröbner basis decision
London Mathematical Society Journal of Computation and Mathematics, vol. 13 (2010) pgs. 111-129, DOI 10.1112/S1461157008000193)
Are Buchberger's Criteria necessary for the chain criterion? (joint with Hoon Hong)
Journal of Symbolic Computation, July 2007, vol. 42 issue 7 pgs. 717-732, DOI 10.1016/j.jsc.2007.02.002 |
