Re: Calculus texts

["Edwin R. Schweber" <edschweb@ix.netcom.com>]

JACK L. URETSKY (C) 1996; HEP DIV., ARGONNE NATIONAL LAB, ARGONNE, IL
60439 wrote:
> Hi all-
>         I've come to the conclusion that there are no calculus texts
> the hew, even approximately, to the pedagogical lines laid out by Arons
> for the teaching of introductory physics. 
>           
Jack and all:

    I think the problem applies to all H.S. math texts. There seems to
be a
tendency to assume that using pseudo-mathematical language is a
substitute
for explaining a concept. This semester, besides physics, I am teaching
trig to some of our lowest level seniors. The text introduces the
concept 
of radian measure without any attempt at explaining why it is a more
natural measure than degreees or without explaining why taking the
ratio of arc length to the radius of a circle inscribed around the
angle is independent of the circle's radius.

   In past years I have used books that start off with "circular
functions" rather than with the right triangle trig that would
seem (to me anyway) to form the proper motivation for generalizing
the definition of the trig functions to non-accute angles.

    When I was in grad school one of the math professors was
expressing admiration for a colleague who had a solid reputation
in algebraic topology; much of which stemmed for his Ph.D
thesis. However, the proof given in the thesis had errors which had
to be corrected by others. Why then was this work the basis of
a solid reputation. According to the professor I was talking to
it was because this other mathematician was the first one to
intuit that the result should be true.

   That the construction of a rigorous logical proof is the last
step in the elucidation of a mathematical concept, which comes
only aftera good deal of intuition is precisely what seems to
elude many writers of math textbooks.

Ed Schweber (edschweb@ix.netcom.com)
Physics Teacher
Solomon Schechter Day School
West Orange, NJ