990 Lincoln Place
Boulder, CO 80302
(970) 302-6315 (cell)
I live in Boulder, Colorado, and teach
at the University of Northern Colorado. My research is in
geometry, logic, and formal reasoning with diagrams;
you can find some of the papers that I've written here.
Ph.D. in Mathematics, Cornell University, May 2001
M.S. in Computer Science, Cornell University, August 1999
A.B. in Mathematics, Princeton University, June 1994
Current Research Activities:
Reasoning with Geometric Diagrams - It has long been assumed in
mathematical communities that diagrams can be properly used only as aids
to human intuition which have no place in formal proofs, reducing diagrams
to second-class citizens of the mathematical world. My research aims
to show that diagrams can be used rigorously and fruitfully in formal mathematics,
and, indeed, that the formal proofs that one gets using diagrams are more
understandable and correspond better to normal informal proofs (of
the kind that one finds in Euclid's Elements, for example) than
traditional linguistic formal proofs. You can find some of my work here.
- The Teaching and Learning of Mathematics using Inquiry-Based Methods - Most of my teaching is done using inquiry-based methods, and I have had several publications and presentations in this area. You can find some of them here.
(Pictures: climbing Longs Peak, July 2007; playing the cello, Jan.
2000; and sitting in my garden, Summer 1997.)
Last updated: 11/8/17