|S. M. C.|
Department of Mathematics
Saint Michael's College
Colchester, VT 05439
phone: 802 654 2660
|fax: 802 654 2610|
|Click here for alter ego.|
|Contact me||On Campus||Courses||Advising||St. Mike's Links|
|Student Research||My Research||Papers||Talks||Other Stuff|
SMC Office: STE 217A. Fall 2003 Office Hours: MW 12:15 - 1:15, Th 10:00 - 11:00 and by appointment.
Fall 2003 Classes
Calc III (Fall 03) MA 211A meets MWF 9:30-10:20 in STE 270, Th 8:50-10:50 in JEM 373
Abstract Algebra (Fall 03) MA 406 A meets MWF 10:30-11:35 in JEM 389.
Some classes from prior semesters
Student Research: Here are some recent presentations (mostly PowerPoint) by past and current students--talks from Senior Seminars, Hudson River, Parents' Weekend, and some Independent Study results. Note: The mathematics in some of the presentations requires MathType to be viewed properly.
Fighting the Plane Patti Fogarty, '00, an SMC alum. This is part of her UVM master's thesis, given as a talk here at SMC in Spring '03.
The Instant Insanity Game Sarah Graham, '06, for Parents' weekend Spring '03.
Origin of The Euler Cycle The Seven Bridges of Konigsberg Whitney Sherman, '04, for Parents' weekend, Spring '03.
Graphic Tool for Computer Chip Layout Laura McLane, '02, a Spring '03 Hudson River Talk about her work on an industry-driven independent study project.
Error Detection and Correction Colin Kriwox, '02, a Senior Seminar Talk in Spring '03.
Island Networks Aaron Derochers, '04, a Spring '03 Hudson River talk about an application of graph theory to anthropology.
Doctorate in Mathematics: University of North Carolina, Chapel Hill, NC. fall 1995. Advisor: James D. Stasheff.
Areas of Research : Algebra and Combinatorics.I am interested in both graph theory and abstract algebra, particularly in using algebraic techniques to achieve graph theoretic results. My recent work has been primarily with graph polynomials, constructing them and embedding them in algebraic structures sufficiently rich to extract new information from them. I have been able to use Hopf-algebras to derive new identities for the Martin polynomials of both oriented and unoriented Eulerian graphs, as well as for the Tutte polynomial along the diagonal y = x. Currently, I am considering two problems. One is developing a new graph polynomial that might lead to some insights into the cycle double cover conjecture. The other is constructing a generalization of the Penrose polynomial to address graph coloring questions.
Talks with available overheads:
Postscript files are available for the overheads for some of my talks. They can be viewed and printed using Ghostview, which is available on line--click here to go to the site. The mathematics in some of the PowerPoint presentations requires MathType to be viewed properly.
Graph Theoretical Problems in Next Generation Chip Design. South Eastern, Boca Raton, 3/3/03. [Graphs in chip design--PowerPoint]
A Hopf-algebraic structure for generalized transition polynomials. Special Session on Combinatorial Hopf Algebras at the AMS meetings in Montreal, QC, 5/5/2002 [abstract and ps file--583 KB]
Independent Studies with Industry Partnership. MathFest 2002, Burlington VT. [PowerPoint--461 KB]
Practical Applications and the Universality of the Tutte Polynomial. UVM Colloqium Talk, 2/15/2002. [Links]
Relations for Skein-Type Graph Polynomials. South Eastern, Baton Rouge, 2/26/2001. [Abstract] [Click here for postscript file--866 KB].
The Circuit Partition Polynomial and Integer Evaluations of the Tutte Polynomial. CoNE, Smith College, 2/10/2001. [Click here for postscript file--1550 KB] (sorry so large--26 color slides done in Word take up a lot of space....) Proofs for much of what was covered in this talk can be found in Identities for the Circuit Partition Polynomials... below.Papers
Postscript files are available for several of these papers. They can be viewed and printed using Ghostview, which is available on line--click here to go to the site.
for the circuit partition polynomials, with applications to the diagonal
Tutte polynomial, to appear
in Advances in Applied Mathematics.
[Click here for postscript file--305 KB].
Theoretical Problems in Next Generation Chip Design
(with P. Gutwin), to appear in Congressus Numerantium. [click
here for postscript file--810 KB]
transition polynomials (with I. Sarmiento), Congressus Numerantium
155 (2002) 57-69.[click
here for postscript file--491 KB].
graphs and the Penrose polynomial (with I. Sarmiento), Congressus
Numerantium 150 (2001),
here for postscript file--2 files]
sweet home: A financial incentive for the lower level mathematics course
(with George Ashline), PRIMUS XI, no. 1 (2001), 16–26.
Differentiating the Martin
Congressus Numerantium 142 (2000), 173–83.[click here for postscript file--449
many people are in your future? Elementary models of population growth
(with George Ashline), in Making
meaning: Integrating science through the case study approach to teaching and
learning, ed. S. Kuntz et al, McGraw-Hill
Primis, 1999, pp. 42–80.
many people are in your future? Elementary models of population growth
(with George Ashline) (updated version), Case studies in ecology, ed. S.
Kuntz et al., accompanying the 1st editions of Manuel Molles’
text Ecology: Concepts and
Applications. WCB McGraw-Hill, New York, 1999.
population projects in a first semester calculus course (with George
Ashline), PRIMUS IX (March 1999), 39–55.
to macrocosm: Population models in biology and demography (with George
Ashline), Tools for Teaching, UMAP unit 777
polynomial miscellanea. Congressus
Numerantium 137 (1999), 19–31. [click here for postscript file--481 KB]
New results for the Martin polynomial. Journal of Combinatorial Theory, series B 74 (1998), 326–52. [click here for postscript file--4 files]
remarks on domination (with D. Archdeacon, D. Froncek, P. C. B.
Lam, B. Wei, and R. Yuster), submitted.
the Tutte-Martin connection, submitted.
here for postscript file--799 KB]
your dream home (with George Ashline), submitted.
rockets in flight (with George Ashline), submitted.
rockets in flight: Calculus in action (with George Ashline and Alain Brizard), submitted.
Saint Michael's-related links
For more information, you may want to check out these.
Maple Home Page Very, very cool Maple stuff--including lots of demos for understanding calculus concepts for example. Check out the Maple Applications and the Student pages.
MathSciNet This is the foremost research tool for mathematicians--a searchable index, with reviews, to current mathematical articles.
http://birrell.org/andrew/knotwork/ Very cool applet for generating celtic knots
UVM/SMC Joint Combinatorics Seminar Biweekly speakers from academia and industry using and developing combinatorial techniques.Graph Theory Resources This site has links to people, problems, journals, etc. involved with graph theory.
Math Archives This is a huge archive of all kinds of math related resources, from teaching resources to CAS (eg Maple) support, from graphing calculators to electronic journals.POPMathematics What is POP Mathematics? From the site creators:
Actuarial Careers Here are some links providing information about actuarial careers.
The following website has some great explainations and good Java applets for a wide range of mathematical concepts. http://www.math.montana.edu/~frankw/ccp/Java/Overview.htm
The wallpaper on this page was modified from wallpaper taken from http://www.eccentrics.com/scruffypup/ where there are lots of other very lyrical wallpapers.
Family only, please.