Mathematical Interests

My interests are broad - extending from most areas of the undergraduate mathematics currriculum into new or little known related topics, as well as the history of mathematics.  I am also interested in aspects of mathematics education, primarily curriculum development and use of technology.  But most of my scholarship is in the area of expository mathematics.

Some recent and current projects include:

  • Marden's Theorem.  Developed both for its intrinsic interest and also as a proof of concept for coordinating articles in MAA journals serving different audiences.  Specifically, I developed a traditional journal article for the MAA's math faculty audience, a briefer overview article for the student audience of Math Horizons, and an on-line expanded treatment featuring extensive hypertext, color and animated graphics,  and other presentation elements impossible to realize in a print journal.   See Ivars Peterson's commentary on this project.
  • Leveling with Lagrange.  A discussion of the Lagrangian function approach to Lagrange multipliers.  Shows that a traditional heuristic justification for this approach is misleading, and provides a new alternative.  Also reports on the history of Lagrange's formulation of the technique. 
  • Running in the Rain.  Joint work with Bruce Torrence, Randolph-Macon College.  Analyzes strategies for staying as dry as possible running in the rain, modeling the runner as a rectangular prism, sphere, ellipsoid, and other shapes.   An overview was published in Math Horizons.
  • Uncommon Excursions in Three Mathematical Realms.  This is a book I recently finished.  See my books page for more information.
  • Summing the reciprocal square integers using generating functions.  Joint work with Mark McKinzie, St. John Fisher College.  Many proofs have been given for Euler's discovery that the sum of the reciprocal square integers is  pi2/6.  In this project we show how an obvious strategy using generating functions leads to a function called dilog, and what appears to be a road block.  There is a path around the road block using two key facts -- both discovered by Euler.  So, although this eventually provides a different proof than the ones Euler published, you still need Euler's help to make it work.   (in progress).