From: zeleny@husc10.harvard.edu (Mikhail Zeleny)
Newsgroups: rec.arts.books,sci.math
Subject: Re: Remedial Math
Date: 21 Jan 93 23:06:46 GMT
Organization: The Phallogocentric Cabal

For the sake of continued dialogue between weenies and nerds, let us
keep this thread cross-posted.

In article <1993Jan21.145456.9200@math.ucla.edu> 
dstein@oak.math.ucla.edu (David Stein) writes:

>Mikhail Zeleny writes:

MZ:
>>To recapitulate: the best introduction to general mathematical culture,
>>as required by such disciplines as philosophy, linguistics, computer
>>programming, and so on, is to be found in the beginning courses on real
>>analysis, topology, and abstract algebra.  Another prerequisite for the
>>above is a course in formal logic and set theory.  In addition, work in
>>linguistics will call for familiarity with lattice theory and other
>>aspects of universal algebra.  I believe that all of the above should be
>>required of anyone graduating with a B.A. in these areas.

DS:
>  I second that opinion.  Though I do not think it is so important that 
>the B.A.'s go through these courses with the same rigour and exhaustiveness 
>as the math students have to; the important thing is to expose all to the 
>ideas and concepts underlying abstract mathematical thought.

I disagree.  In my experience, no beginning graduate or undergraduate
class in mathematics can be said to aim for rigor and exhaustiveness,
and it is a good thing, too.  In a UCLA philosophy class, I once sat
through the development of the combinatorial parts of ZFC, expertly
conducted with both rigor and exhaustiveness, on the level of logical
and set-theoretic primitives.  I do not believe that to be the optimal
way of learning the theory, nor even a good way of talking about it to
the cognoscenti.  On the other hand, the typical result of catering to
the liberal arts majors by attempting "to expose all to the ideas and
concepts underlying abstract mathematical thought" is bound to remain
vacuous, to the extent that if fails in teaching them to write and
understand mathematical proofs, or even avoids the attempt altogether.

DS:
>  A friend of mine was teaching some pre-Calculus class, the one where the
>university tries to undo the damage done in high school.  He started the 
>first day by showing there exist irrational numbers, and by explaining why 
>are the reals not countable.  About half of his class switched sections on 
>him.  Towards the middle of the semester he was fired, allegedly for not
>following the syllabus.  The next day he was rehired--the students stood
>by him and asked for his return.  For many of them, I suspect, this was
>the first time in years they actually cared about math.

The New York Times informs me that *all* graduates of a certain
liberal arts college are expected to have received instruction in two
languages, ancient and modern, and to have read, among other things,
Dedekind's classic essay on the nature of numbers.  I like that.

> - Debil
>
>^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>Debil, on the shores of Bohemia.
>################################
>--
>^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>Debil, on the shores of Bohemia.
>################################

cordially,
mikhail zeleny@husc.harvard.edu
"Le cul des femmes est monotone comme l'esprit des hommes."
Newsgroups: rec.arts.books