I teach one section of intermediate algebra each semester in addition to my
physics courses, and I've run into a similar evolution in mathematical
vocabulary. In "the old days", a+bi was a complex number and bi an
imaginary number; but in the text we now use for this course, a+bi is an
imaginary number and bi is a "pure" imaginary number. (Maybe this alternate
terminology has always been around, and I just never encountered it until
now.)
_______________________________________
Fred Lemmerhirt
Waubonsee Community College
Sugar Grove, Illinois
<mailto: flemmerhirt@mail.wcc.cc.il.us> http://chat.wcc.cc.il.us/~flemmerh/physics.html
-----Original Message-----
From: Edmiston, Mike [mailto:edmiston@BLUFFTON.EDU]
Sent: Friday, November 22, 2002 1:52 PM
To: PHYS-L@lists.nau.edu
Subject: Re: 2 pi i = 0
I may be getting too old. I agree that John Denker's definition of a
function is what math profs are teaching these days. But it not what=
I
learned when I went to school.
When I studied math it was possible to have a multi-valued function.
The definition of function in use today is what we used to call a
"single-valued function." Since we used to have multi-valued functio=
ns
it was sometimes necessary to specify that a function be single-value=
d.
For example, all of my quantum-mechanics books say that one of the
criteria for determining permissable wave functions is that the funct=
ion
must be single-valued. According to the current definition of functi=
on,
such a statement is meaningless.
In this regard I have a bit of a bone to pick with mathematicians. I
find that mathematicians sometimes just agree to change things withou=
t
checking (or even telling) people in fields that heavily use math. F=
or
example, the Seventh Edition of Physical Chemistry by Peter Atkins (a
very popular book) just came out in 2002. In the quantum section it
says that psi must be a single-valued function. So Atkins, like many
physicists and chemists, does not yet know that there no longer is su=
ch
a thing as a multi-valued function. I only became aware of this beca=
use
I have tried to help my son and daughter with their math assignments.
They explained to me, "No dad, the curve you just drew is a relation,
not a function, don't you even know the basics?" Well, I did once, b=
ut
the basics seem to keep changing.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu
This posting is the position of the writer, not that of SUNY-BSC, NAU or the
AAPT.
This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.