jopix2.jpg (12204 bytes) S. M. C.
Department of Mathematics
Saint Michael's College
Winooski Park
Colchester, VT  05439


phone: 802 654 2660
fax: 802 654 2610
WB01542_.gif (729 bytes) Click here for alter ego.
Jo Ellis-Monaghan

Contact me On Campus Courses Advising St. Mike's Links
Student Research My Research Papers Talks Other Stuff

On Campus

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.  




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.


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.

  1. Identities 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].  

  2. Graph Theoretical Problems in Next Generation Chip Design (with P. Gutwin), to appear in Congressus Numerantium. [click here for postscript file--810 KB]

  3. Generalized transition polynomials (with I. Sarmiento), Congressus Numerantium 155 (2002) 57-69.[click here for postscript file--491 KB].

  4. Medial graphs and the Penrose polynomial (with I. Sarmiento), Congressus Numerantium 150 (2001), 211–222.[click here for postscript file--2 files]

  5. Home sweet home: A financial incentive for the lower level mathematics course (with George Ashline), PRIMUS XI, no. 1 (2001), 16–26.

  6. Differentiating the Martin polynomial.   Congressus Numerantium 142 (2000), 173–83.[click here for postscript file--449 KB]

  7. How 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.

  8. How 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.

  9. Interdisciplinary population projects in a first semester calculus course (with George Ashline), PRIMUS IX (March 1999), 39–55.

  10. Microcosm to macrocosm: Population models in biology and demography (with George Ashline), Tools for Teaching, UMAP unit 777 (1999), 39–80

  11. Martin polynomial miscellanea. Congressus Numerantium 137 (1999), 19–31. [click here for postscript file--481 KB]

  12. New results for the Martin polynomial. Journal of Combinatorial Theory, series B 74 (1998), 326–52. [click here for postscript file--4 files]

  13. Some remarks on domination (with D. Archdeacon, D. Froncek, P. C. B. Lam, B. Wei, and R. Yuster), submitted.

  14. Exploring the Tutte-Martin connection, submitted. [click here for postscript file--799 KB]

  15. Financing your dream home (with George Ashline), submitted.

  16. Water rockets in flight (with George Ashline), submitted.

  17. Water 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.

Other Stuff

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.  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:   Check out this web site for lots of people doing cool (math-related) things you might be interested in too.

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.

The wallpaper on this page was modified from wallpaper taken from where there are lots of other very lyrical wallpapers.

Family only, please.


When this site was last updated:  08/30/11