Recent
Research Projects
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A Markov Method
for Ranking College Football Conferences (with A. Murphy) Mathematics Awareness Month
website, April 2010. (www.mathaware.org/mam/2010/essays/Mattingly.pdf) This is an undergraduate research project
completed by Amber Murphy, a 2009 graduate of SUNY Cortland’s Adolescence
Education—Mathematics program. This study explored the use of Markov chains
to develop rankings of Division I college football teams, from which rankings
of conferences were then derived. Amber’s participation was supported by a
2008 Summer Research Fellowship awarded by the SUNY Cortland
Undergraduate Research Council. Our final paper was included as a theme
essay on the 2010 Mathematics Awareness Month website.
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An Elementary Derivation
of the Method of Least Squares, New York State
Mathematics Teachers’ Journal, Vol. 57, No. 3 (2007), pp. 94-98. This paper describes a way to explain the method of
least squares using only material found in a typical college algebra course.
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Some
Problems are NP-Harder Than Others, (with S. Cockburn, B. Coleman and K. Somers)
DIMACS Educational Module Series 06-1, Center for Discrete Mathematics &
Theoretical Computer Science, Rutgers University, May 2006. This educational module
is intended for use as a supplement in an undergraduate course in graph
theory, linear programming, analysis of algorithms, or independent study. It
discusses two graph theory problems: the Vertex Cover problem and the
Dominating Set problem. The module may be freely downloaded from the DIMACS
Educational Module Series website.
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Linearly Dependent Sets
of Polynomials, Fallacies, Flaws and
Flimflam #249, College Mathematics Journal 37 (March 2006), p. 122. This short item describes
an interesting question that came up some years ago in my linear algebra
course. Unfortunately, there were some typographical errors: In the statement
of the theorem and in the preceding paragraph, the phrase “linearly
independent” should be “linearly dependent.” Also in the statement of the
theorem, “vector spaces” should be “vector space.” Ed Barbeau, the editor of
the FFF column, published a correction in the November 2006 issue (p. 384).
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Even order regular magic squares are singular, The American
Mathematical Monthly 107 (2000), pp. 777-782. I continue to receive occasional emails
about this paper, which contains a conjecture that odd order regular magic
squares are nonsingular. However, Peter Loly and his colleagues have
discovered that this is false! You can access much of his work at his
website: http://home.cc.umanitoba.ca/~loly/
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