NetNews Usenet Archive 1992 #30/NN_1992_30.iso/spool/sci/math/16954

Internet Message Format | 1992-12-15 | 3.5 KB

Xref: sparky sci.math:16954 sci.edu:1236
Newsgroups: sci.math,sci.edu
Path: sparky!uunet!usc!rpi!utcsri!helios.physics.utoronto.ca!alchemy.chem.utoronto.ca!mroussel
From: [e-mail] (Marc Roussel)
Subject: Re: Student attitudes
Message-ID: <[e-mail]>
Followup-To: sci.edu
Organization: Department of Chemistry, University of Toronto
References: <[e-mail]> <[e-mail]>
Date: Tue, 15 Dec 1992 15:19:23 GMT
Lines: 53

In article <[e-mail]> [e-mail] (Michael Branton)
writes:
>I would agree that physicists could teach calculus and algebra. "As well as
>any mathematician could..." is, of course, a statement whose truth relies at
>least upon what concepts and viewpoint is desired. My experience has been that
>the emphasis within physics is usually on manipulations and cookbook
>techniques (so that one can get down to the real work at hand.)

     Then your experience has been different from mine.  Most of my physics
professors have emphasized correct and careful mathematics.  Cookbook
methods have been taught to me at least as often by mathematicians as by
physicists.  It's easier to teach math that way, so there will always be
some faculty, regardless of department, who will follow this path of least
resistance.

>That you claim
>it could be done to any degree of rigour required, I take as prima facie
>evidence that you suffer from a narrow viewpoint as to what calculus might be
>about, the ways in which the ideas can be presented and thus what role
>mathematics should play in a student's education.

     Interesting viewpoint...  Perhaps you would care to expand on it.
There are certainly bits of mathematics best left to the mathematicians,
but introductory applied mathematics courses (calculus, linear algebra, etc.)
are not among them.  Every physicist worthy of the name knows these
subjects at least as well as most mathematicians.  Since the math
departments don't guarantee that these courses will be taught by experts
(only that they will be taught by departmental staff), I don't see what
we would lose by having physicists teach them.  It is clear what we
would gain however:  a satisfying synergy between the mathematical and
physical content of the courses.  There is currently no such synergy
since the mathematicians only get around to teaching the material months
or years after it was learned in the physics class.
     Physicists already teach advanced mathematics courses.  (These
courses are often either called "mathematical physics" or they are
disguised as "advanced classical mechanics" or "general relativity" or
something like that.)  For that matter, chemists often offer more
satisfying group theory courses than the mathematicians do.  The level
of rigour is high.  Complete proofs of relevant theorems are provided.
The principal difference is the pace and topic selection.
     Note that we're not talking about breadth requirement courses.  To
a physicist, calculus is no less a part of the curriculum than
mechanics.  Physicists (mostly) don't learn calculus for cultural reasons.
Why should we treat the core mathematical subjects differently from the
advanced mathematical topics covered in senior "physics" courses?

                Marc R. Roussel
                                [e-mail]


P.S.:  I have redirected followups to sci.edu since that is where, in my
       opinion, this discussion belongs.  If you disagree, you'll have
       to manually edit the newsgroups line of the header.