John McDonald Title: Postdoctoral Fellow Dates: January 1, 1997 -- present Office: Geometry Center, Room 434 Phone: (612) 626-8308 E-mail: johnmcd@geom.umn.edu Personal Homepage: http://www.geom.umn.edu/~johnmcd/

Research Activities at the Geometry Center

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 Zelevinskii.

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.
GeometryWindow.java
GeometryWindow.class

I have created a sample PlaneGeometry applet.

Education

Ph.D in mathematics, 1996
Northwestern University, Evanston, IL
Dissertation: "Fractional Power Series Expansions and Resultants"
Dissertation Advisor: Dr. Mikhail Kapranov

M.A in mathematics, 1993
Northwestern University, Evanston, IL

B.S in mathematics, 1991
The University of Michigan, Ann Arbor, MI
Honors Thesis (joint work with Michelle French): "On the Growth of Algebras"

Professional Experience

Employment

• 1997 - present: Assistant Professor
  School of Mathematics
  University of Minnesota, Minneapolis, MN
  
  
• 1997 - present: Postdoctoral Fellow
  The Geometry Center
  University of Minnesota, Minneapolis, MN
  
  
• 1996: Postdoctoral Fellow
  Department of Mathematics
  University of California at Berkeley, Berkeley, CA
  
  
• 1990 - 1991: Instructor
  The University College
  Northwestern University, Evanston, IL
  
  
• 1990: Visiting Instructor
  Department of Mathematics
  Oakton Community College, Skokie, IL
  
  
• 1991 -- 1996: Graduate Teaching and Research Assistant
  Department of Mathematics
  Northwestern University, Evanston, IL
  
  

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John McDonald <johnmcd@geom.umn.edu>
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

<johnmcd@math.umn.edu>
School of Mathematics
University of Minnesota
420 Vincent Hall
206 Church St. S.E
Minneapolis MN 55455
(612) 625-5099

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The Geometry Center Home Page

Comments to: webmaster@geom.umn.edu
Created: Nov 19 1995 --- Last modified: September 16 1997