Academic priorities 243

Circa 1900 High School curricula were set without much input from "math professors", the people teaching, and those taking, high school mathematics were more interested in those math skills that could actually be applied in business, technical fields and everyday life.

I got an S.B. in Theoretical Mathematics and three advanced degrees in EE and I've taught basic calc and ordinary differential equations to *engineering* students. What the math. department wants to teach them and what they actually need are orthogonal (to within practically measureable accuracy). I have come to the conclusion that anyone who even *thinks* of going through epsilon-delta proofs in a first calculus course should be sent back to Mars. And since the late 1960's, when the hyper-real number system and non standard analysis were first expostulated, there is no need to demonize non-zero infinitesimals in order to maintain mathematical rigo(u)r!

The "if it has a practical application it is contaminated, let's do something else" mentality of modern theoretical mathematics professors is one of the banes of modern mathematics education at all levels.

Yes, I can count to infinity (constructive proof with non-finite induction) and distinguish countable and uncountable infinities. I know why thinking of dx-dt as a ratio of infinitesimals is meaningless in standard analysis and why it is not only rigorously defineable in non-standard analysis, but it is also pedagogically quite useful and more comprehensible to most of the students than the older analytical rigorous forms (e.g., epsilon-delta formulations).

Anybody who thinks the current practictioners of modern theoretical mathematics know beans about computation are truly not paying attention. Some of the *applied* mathematics people do, but they are looked down upon (if considered at all) by the theoreticians. (OK, there may be a few rare exceptions, but ...)

Kevin (don't get me started) Rhoads