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