Here's an idea for teaching the epsilon-delta definition of the limit. Instead of starting with limits, start with continuity. It's easier because, first of all, people have some natural intuition of what continuity is. And the actual definition is easier to remember: |x-a| and |f(x)-f(a)| are related in a way that |x-a| and |f(x)-b| are not. Also, the asymmetric condition 0<|x-a| is not an issue. So there aren't as many distractions for the student encountering the epsilon-delta technique for the first time. Once there is some level of comfort with the rigorous definition of continuity, limits can be introduced by considering how it is that functions can fail to be continuous, and whether a given discontinuity could be removed by changing the value at one point.

My most recent book, Linearity, Symmetry, and Prediction in the Hydrogen Atom, is a textbook for an undergraduate course for math, physics and physical chemistry majors, explaining how the mathematical study of representation theory (known to physicists and chemists as group theory) can be used to predict some of the structure of the hydrogen atom without using the Schroedinger equation. For more information and reviews, please click on the yellow book image on the left.

My first book,Symmetry in Mechanics: A Gentle, Modern Introduction"was published in March 2001 by Birkhauser Boston. The book received some enthusiastic reviews! One is in the January 2002 issue of Physics Today, on page 57. One is in the May 2002 issue of Current Science (Vol. 82, No. 9, p. 1170. ) Yet another is in the April, 2003 issue of the American Mathematical Monthly. Still another is at Amazon.com. For more information, or to purchase the book, please click on the cover image on the left.

George Mackey, representation theorist and father of one of my best friends, passed away in 2006. When I was a sophomore in college, wavering between mathematics and physics, he was kind enough to write me two long letters (one and two). He also sent me the text of a speech he had given, entitled What Do Mathematicians Do?.