Recent Publications

· Even order regular magic squares are singular, The American Mathematical Monthly 107 (2000) 777-782.

I receive a couple of emails each year 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/

· Linearly Dependent Sets of Polynomials, Fallacies, Flaws and Flimflam #249, College Mathematics Journal 37 (March 2006), p. 122.

This item contains 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).

· 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 website:

http://dimacs.rutgers.edu/Publications/Modules/moduleslist.html

· An Elementary Derivation of the Method of Least Squares, New York State Mathematics Teachers’ Journal, Vol. 57, No. 3 (2007).

This paper describes a way to explain the method of least squares using only material found in a typical college algebra course.