Associate Professor of Mathematics and the MathCEP Director of Educational Programs and UMTYMP.

Also see (now in its fifth year): the Minnesota Journal of Undergraduate Mathematics.

Current / Recent Courses

Math 8001, Math 5251 and other courses can be found on Moodle (older courses) or Canvas.

UMTYMP students can find links to their Canvas sites and WebWork server on the main MathCEP website.

MathCEP Programs

Contact Info
Vincent Hall 4

Mailing Address
127 Vincent Hall
206 Church St SE
Minneapolis, MN 55455


I always enjoy sharing the beauty of mathematics with others, whether K-12 students, undergraduates, MAA meetings or public lectures. Recently the most commonly requested talks have been Spherical Cats and Ham Sandwiches, a visual introduction to topology which can be modified for all audiences, and a behind-the-scenes look at Möbius Transformations Revealed (see below).


I have a long-standing interest in mathematical visualization and its use in the classroom. Links to various projects:

Student Projects

I frequently supervise CLA senior projects, usually (but not always) with students who have taken a class with me and with whom I share some mathematical and/or educational interests. Students can always contact me to discuss potential projects.

I also lead research projects with students, particularly UMTYMP students and alumni. See this paper for an example.

Möbius Transformations Revealed

Möbius Transformations Revealed is an award-winning short film by Doug Arnold and myself which has been viewed nearly 2 million times on YouTube alone. We originally created it for the 2007 Science and Engineering Visualization Challenge, sponsored by the NSF and Science Magazine. It has been featured in a number of articles and websites, including:

A short clip of the movie is included in the film Achieving the Unachievable, a documentary about M.C. Escher's Print Gallery.

Go to the movie download page to watch the film and for more links to press coverage.

Möbius Transformations Revealed is a wonderful video clarifying a deep topic. This is amazing work by Douglas Arnold and Jonathan Rogness of the University of Minnesota. Edward Tufte

Selected Publications and Presentations

  1. Mathematical Visualization
    Journal of Math Education at Teachers College, 2011
    [ Link to Journal Page ], [ Direct PDF Link ]
    See also this followup blog post.
  2. Möbius Transformations Revealed. (With Doug Arnold)
    Notices of the AMS, Nov 2008
    [PDF ]
  3. Historical Perspectives on a Program for Mathematically Talented Students (With Harvey Keynes)
    11th International Congress on Mathematical Education, 2008
    [PDF ]
  4. Constructing Mathlets Quickly using LiveGraphics3D (With Martin Kraus)
    Journal of Online Mathematics and its Applications (Now Loci), 2006
    [web ]