I received my B.A. from Kalamazoo College and my M.A. and Ph.D. from the University of Michigan. I began my career at Texas Tech University, but I came to Wabash in 1989 after deciding I would rather spend my career at a quality, small liberal arts college. 

My primary research area is geometry, specifically differential and integral geometry, and generalizing results from Euclidean geometry to spherical and hyperbolic geometries. I have also done work in several complex variables and control theory. Some of my research projects in spherical and hyperbolic geometries include pendulum dynamics, perimeter formulas for convex regions, how volume is generated by a moving surface, isoperimetric inequalities, and a favorite ongoing topic, how planimeters work. For details, please see my personal web page and vita.

For fun I play trumpet in the Wabash College Brass Ensemble and the Montgomery County Civic Band, I bicycle the county roads near Crawfordsville, and I make bowls and ornamental objects on my wood lathe.

Ph.D., Mathematics, University of Michigan, April 1983
        Dissertation: Curvature Estimates for Monge-Amèpre Foliations
        Thesis Advisor: Daniel M. Burns Jr.
M.A., Mathematics, University of Michigan, April 1978
B.A., Mathematics, Kalamazoo College, June 1976
        Magna cum Laude with Honors in Mathematics, Phi Beta Kappa
        Heyl Science Scholarship

MAT 106: Topics in contemporary mathematics with an emphasis in geometry, a.k.a. “Symmetry,   
                 Shape, and Space”
MAT 111 & 112: Calculus I & II
MAT 221: Geometry
MAT 223: Linear algebra
MAT 225: Multivariable calculus
MAT 333: Functions of a real variable, a.k.a. real analysis

The courses I enjoy teaching the most are the two geometry courses and multivariable calculus, since they are the most geometric-oriented of the courses we have. When I teach MAT 221, I take an approach that develops Euclidean, spherical, and hyperbolic geometries in parallel. MAT 106 is a “hands-on” course. Students work in groups and frequently explore geometric topics using linkages, mirrors, compasses & straightedges, and Styrofoam spheres and string. Multivariable calculus is a combination of calculus, linear algebra, and geometry that is the foundation of differential geometry, much of applied mathematics, and the mathematics used in science, engineering, and economics. I have also occasionally taught an upper-level topics course in computational geometry, which is the mathematics behind computer animation and graphics.

“How Pendulums Work in Spherical and Hyperbolic Geometry,” colloquium talk, Wabash College, November 2003.

“The Poincarè Conjecture,” colloquium talk, Wabash College, Sept. 2004.

“3 ≤ π ≤ 4,” colloquium talk, Wabash College, April 2006.

“The Circumference of a Convex Region,” colloquium talk, Wabash College, Nov. 2006.

“Computational Geometry: The Mathematics of Computer Graphics, Animation, and Robotics; or Linear Algebra meets Doom 3,” with Kaikai Wang, March 2008.

“Bill Swift’s Continuous, Nowhere-Differentiable Function and Area-Filling Curve,”colloquium talk, Wabash College, December 2009.

“Integral-Geometric Formulas for Perimeter in S², H² and Hilbert Planes,” with R. Alexander and I. D. Berg, Rocky Mountain Journal of Mathematics, 35 (2005) 1825–1860.

“The Volume Swept Out by a Moving Planar Region,” Mathematics Magazine, 79 (2006) 289–297.

“Area Without Integration: Make Your Own Planimeter,” with Ed Sandifer, in Hands-On History: A Resource for Teaching Mathematics, Amy Shell-Gellasch, ed., MAA Notes Series

#72, The Mathematical Association of America, Washington, D.C., 2007, pp. 71–88.

“The Dynamics of Pendulums on Surfaces of Constant Curvature,” with Patrick Coulton and Gregory Galperin, Mathematical Physics, Analysis and Geometry, 12 (2009), 97–107.

“Infinitesimal Isometries along Curves and Generalized Jacobi Equations,” with C.K. Han and J.W. Oh, to appear in J. Geometric Analysis.