FOM: Berkeley and nonstandard analysis....Teaching Calculus and Analysis using infintesimals

[Matt Insall]

In reply to Professor Davis
Re:  Friday, January 28, 2000 10:32 AM

Here at UMR, my colleague, Rob Roe, used Stroyan's text, with Mathematica,
for the honors calculus one year.  He seemed to think it was going well.
(Unfortunately, we don't have very many honors students here, and not long
after, the system was rearranged so that honors students no longer take a
separate course, but arrange with their individual instructors to do extra
work for their honors credit.  I see what I think are pros and cons for the
new system.)  Anyway, in the regular sequence, the calculus text is chosen
by committee, and that makes it difficult to do anything new.  When we did
try something along the lines of a ``reform calculus'' book, we got burned.
Nobody liked the book, and it was abandoned after one semester.  It seems to
me that it is probably to soon to suggest another experiment in calculus
here.


Last year, I went through parts of Bell's new (1998) little book on
``nil-square'' infinitesimal analysis, called ``A Primer of Infinitesimal
Analysis'', in a seminar with a few of my colleagues.  For a while, it
seemed we had some good ideas for making infinitesimal analysis easy for
freshman, and my colleagues seemed happy, but the ``nil-square'' feature is
actually eventually a bit difficult to use with a reasonable geometric
intuition, so that fizzled.  Last semester, I taught Logic from Enderton's
(1972) book, ``A Mathematical Introduction to Logic'', and made it to the
end of chapter 2, where nonstandard analysis is surveyed.  The students
(mostly mathematics graduate students, with one mechanical engineering
graduate student) seemed to enjoy the course, and especially commented
positively on the nonstandard analysis.


 Name: Matt Insall
 Position: Associate Professor of Mathematics
 Institution: University of Missouri - Rolla
 Research interest: Foundations of Mathematics
 More information: http://www.umr.edu/~insall