Title: Postdoctoral Fellow
Dates: January 1, 1997 -- present
Office: Geometry Center, Room 434
Phone: (612) 626-8308
My current research interests center around several topics. First, the
connections between the combinatorics of convex polytopes and
computational geometry. In this direction I have contributed two papers
on algorithms for building series expansions using the combinatorics
of related Newton Polytopes. Secondly, I am interested in generalizations
of the discriminants and resultants studied by Gelfand, Kapranov and
I am also highly involved in extensive on-going work with Prof. Robert Welland of Northwestern University in mathematical modeling and simulations of physical systems. As a graduate student, I collaborated in the design of Northwestern's Experimental Mathematics Program. For information on this work and our course, see our website at http://www.kildare.math.nwu.edu.
For sample images of a fascinating fractal associated with my research into mass-spring systems click here.
Additionally, I am interested in many areas of software design. My current projects
include the WindowsNT(TM) version of the Geometry Center's popular visualization
package Geomview. Interests in this direction include 3D-graphics using OpenGL
and Microsoft's Direct3D(TM), Microsoft's Component Object Model and ActiveX(TM)
specifications, and interface design under WindowsNT(TM). I am currently
conducting a seminar at The Geometry Center on COM and ActiveX.
This spring I will be teaching a course entitled "Technology in the Geometry Classroom." This course is designed for high-school geometry teachers, and will instruct participants in the use of software tools, videos, and WWW-based lessons while they study modern and classical geometry problems. Course projects help them to learn techniques and develop examples that can be incorporated into their own classes. The materials are divided into four self-contained parts: Internet Skills, Classical Geometry, Dynamical Systems, and Symmetries and Patterns. For more detailed information on this course visit the course website at http://www.geom.umn.edu/education/math5337/.
For students of the Java section of this course, here are the links to
the class file and java file for the GeometryWindow object.
I have created a sample PlaneGeometry applet.
John McDonald <email@example.com> The Geometry Center University of Minnesota 400 Lind Hall 207 Church St. S.E. Minneapolis, MN 55455 (612) 626-8308 John can also be reached at <firstname.lastname@example.org> School of Mathematics University of Minnesota 420 Vincent Hall 206 Church St. S.E Minneapolis MN 55455 (612) 625-5099
Created: Nov 19 1995 --- Last modified: September 16 1997