
S. M. C.  
Department of
Mathematics
Saint Michael's
College
Winooski Park
Colchester,
VT 05439


phone: 802 654 2660


fax: 802 654 2610  
email: jellismonaghan@smcvt.edu  
Click here for alter ego.  
Jo EllisMonaghan  
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.
Calc III (Fall 03) MA 211A meets MWF 9:3010:20 in STE 270, Th 8:5010:50 in JEM 373
Abstract Algebra (Fall 03) MA 406 A meets MWF 10:3011:35 in JEM 389.
Some classes from prior semesters
Combinatorics MA 216 (Spring 03)
Finite Math MA 101 (Fall 02)
Calc I MA 109 ( Fall 02)
Calc I I MA 109 (Spring 03)
Calc II MA 111 (Spring 00)
Calc III MA 211 (Spring 00)
Student Research: Here are some recent presentations (mostly PowerPoint) by past and current studentstalks 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 industrydriven 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 Hopfalgebras 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 lineclick 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 designPowerPoint]
A Hopfalgebraic structure for generalized transition polynomials. Special Session on Combinatorial Hopf Algebras at the AMS meetings in Montreal, QC, 5/5/2002 [abstract and ps file583 KB]
Independent Studies with Industry Partnership. MathFest 2002, Burlington VT. [PowerPoint461 KB]
Practical Applications and the Universality of the Tutte Polynomial. UVM Colloqium Talk, 2/15/2002. [Links]
Relations for SkeinType Graph Polynomials. South Eastern, Baton Rouge, 2/26/2001. [Abstract] [Click here for postscript file866 KB].
The Circuit Partition Polynomial and Integer Evaluations of the Tutte Polynomial. CoNE, Smith College, 2/10/2001. [Click here for postscript file1550 KB] (sorry so large26 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 lineclick here to go to the site.
Identities
for the circuit partition polynomials, with applications to the diagonal
Tutte polynomial, to appear
in Advances in Applied Mathematics.
[Click here for postscript file305 KB].
Graph
Theoretical Problems in Next Generation Chip Design
(with P. Gutwin), to appear in Congressus Numerantium. [click
here for postscript file810 KB]
Generalized
transition polynomials (with I. Sarmiento), Congressus Numerantium
155 (2002) 5769.[click
here for postscript file491 KB].
Medial
graphs and the Penrose polynomial (with I. Sarmiento), Congressus
Numerantium 150 (2001),
211–222.[click
here for postscript file2 files]
Home
sweet home: A financial incentive for the lower level mathematics course
(with George Ashline), PRIMUS XI, no. 1 (2001), 16–26.
Differentiating the Martin
polynomial.
Congressus Numerantium 142 (2000), 173–83.[click here for postscript file449
KB]
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, McGrawHill
Primis, 1999, pp. 42–80.
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 1^{st} editions of Manuel Molles’
text Ecology: Concepts and
Applications. WCB McGrawHill, New York, 1999.
Interdisciplinary
population projects in a first semester calculus course (with George
Ashline), PRIMUS IX (March 1999), 39–55.
Microcosm
to macrocosm: Population models in biology and demography (with George
Ashline), Tools for Teaching, UMAP unit 777
(1999), 39–80
Martin
polynomial miscellanea. Congressus
Numerantium 137 (1999), 19–31. [click here for postscript file481 KB]
New results for the Martin polynomial. Journal of Combinatorial Theory, series B 74 (1998), 326–52. [click here for postscript file4 files]
Some
remarks on domination (with D. Archdeacon, D. Froncek, P. C. B.
Lam, B. Wei, and R. Yuster), submitted.
Exploring
the TutteMartin connection, submitted.
[click
here for postscript file799 KB]
Financing
your dream home (with George Ashline), submitted.
Water
rockets in flight (with George Ashline), submitted.
Water
rockets in flight: Calculus in action (with George Ashline and Alain Brizard), submitted.
For more information, you may want to check out these.
Maple Home Page Very, very cool Maple stuffincluding 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 mathematiciansa 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:
Did you ever wonder what made your teacher get so excited about some topic in Mathematics? On this page, we will try to collect items about Mathematics one of which hopefully may explain this wierd behavior.
http://www.ams.org/careers/mcbb.html Check out this web site for lots of people doing cool (mathrelated) 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. 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.