President, Mathematical Association of America
Department of Mathematics, Statistics, and Computer Science
St. Olaf College
1520 St. Olaf Avenue
Northfield, Minnesota 55057-1098
Office: Regents Hall of Mathematical Sciences 508
Revisiting Familiar Places: What I Learned at the Magazine
Abstract: Among the perks of editing Mathematics Magazine, as I did from 1995 to 2000, was the chance to see and learn an enormous variety of mathematics. Much of it was familiar, but a surprising amount was new, or different. Can there possibly be anything new to learn about cubic polynomials? Countable sets? Equilateral triangles? Bijective functions? The short answer is yes, and I'll give some examples that worked for me. The Magazine and other MAA journals are rich sources of novel --- and often surprising --- views of supposedly familiar and thoroughly understood topics from undergraduate mathematics. That such examples exist testifies to the depth and richness of our subject, including at the undergraduate level. PDF version
Abstract: "Thinking in pictures" is standard operating procedure in teaching and learning geometry, graph theory, elementary calculus, and other visually rich areas of mathematics. Less obvious, but no less valuable, are visual insights into key ideas and theorems from real and complex analysis. It's one thing to know what, say, differentiability and integrability mean, but how do they look? How do poles and essential singularities of complex functions look in color? Can countability be seen? I'll give examples and suggest implications for better teaching, learning, and understanding.
Abstract: There is more to elementary calculus than may first meet the eye, especially to those of us who teach it again and again. Well-worn calculus techniques and topics---polynomials, optimization, root-finding, methods of integration, and more---often point to deeper, more general, more interesting, and sometimes surprising mathematical ideas and techniques. I'll illustrate my thesis with figures, examples, and calculation, and give references to MAA publications and resources that can support taking elementary calculus to its extremes.