Rick (Frederick J.) Wicklin,

Assistant Professor of Mathematics, School of Mathematics, and Postdoctoral Fellow, The Geometry Center

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Educational Interests

Rick develops labs that use numerical, symbolic, and graphical software to better communicate the ideas of calculus, and to demonstrate how mathematics may be used to understand problems arising in the physical and biological sciences. You can read a summary of the labs, or if you are mathematically inclined, go to the real labs themselves: For those hardcore algebraic geometers out there (go ahead, admit it!), Rick is also co-author of the world-famous Nephroid Lab, source of the wildly popular joke:
A man walks into a diner and orders a cup of coffee. Upon being served he turns to the waiter and says "Waiter, there's a nephroid in my cup." The waiter looks into the cup and says, "That's not a nephroid, that's the singular fold curve of an algebraic variety."
(Okay, so it's not widely popular.... :-)

Rick is also interested in educational issues at the K-12 level, and in the exposition of mathematics to the general public (for example, see Rick's article in MAA FOCUS and his article on engineering education). He sees geometry and interactive graphical software as an important component of both of these areas. During the summer of 1994, Rick developed curriculum for a summer enrichment program for 6-8th grade students from populations that are traditionally underrepresented in mathematics. As part of this summer program, the students constructed the world's largest icosahedron. Rick has created an on-line teacher's guide that describes how to build a Platonic solid as a classroom project.

Research Interests

Recent Publications

Description of Research Areas

A portion of Rick's research time is devoted to developing Pisces: a Platform for Implicit Surface and Curves and the Exploration of Singularities. He is interested in computing and visualizing geometric structures which arise in dynamical systems: bifurcation surfaces, invariant manifolds, and (un)stable manifolds of fixed points. Pisces provides a common interface to a variety of continuation algorithms and serves as a platform for algorithmic development.

With Jesús de Loera, Rick has used Pisces as a platform for implementing an algorithm (due to O. Ya. Viro) that constructs combinatorial models of algebraic curves. They are using this tool to explore the topology of algebraic curves (Hilbert's sixteenth problem).

A related interest is the mathematical modeling of gravitational lensing. Rick is currently trying to understand (with A. Petters, Princeton) the geometry of gravitational lensing when there are several lensing objects between the source and the observer.

Rick is one of the authors of DsTool, a widely-used interactive toolkit for the exploration of dynamical systems. He recently (Oct, 1996) organized a Workshop on Issues in the Computation of Bifurcations and Singularities in Dynamical Systems; this workshop was attended by 50 of the top researchers in computational bifurcation theory.

For a complete list of Rick's research publications, see his curriculum vita.

Miscellany

Rick Wicklin graduated from Cornell University in 1993 with a degree in Applied Mathematics. His main interest is the development of technology-based modules and laboratory materials for the undergraduate calculus curriculum.

In his spare time, Rick likes to climb mountains and go cross-country skiing with his wife, Nancy. He wishes that Minnesota had more mountains, but at least the ski trails are good! He finds it interesting that God never received tenure in a university. Blue Ribbon


Rick Wicklin  <fjw@geom.umn.edu>
The Geometry Center
1300 South Second Street
Minneapolis, MN 55454
(612) 626-8308
Last modified: Mon Jun 30 13:42:46 1997
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