Explaining the foundations of math

From: William Elliot (marsh_at_privacy.net)
Date: 09/03/04 

Date: Fri, 3 Sep 2004 02:33:00 -0700

From: Herman Rubin <hrubin@odds.stat.purdue.edu>
Newsgroups: sci.math
Subject: Re: Explaining the foundations of math

William Elliot <marsh@privacy.net> wrote:
>On Mon, 30 Aug 2004, Will Twentyman wrote:

>>> When I was in an honors section of Calc I in college, our
>>> professor made us write a paper explaining how the definition of
>>> the limit corresponds to the intuitive notion of a limit.
>>> Realizing that this class was about 50% math majors, it took most
>>> of us 3-4 tries before we generated a version that he considered
>>> acceptable. If this is a particularly difficult concept to
>>> internalize for math majors, I suspect it is even more difficult
>>> for non-math major, non-honor students to absorb.

>>> I suspect some of the authors have realized this, and decided that
>>> the students efforts are better directed at being able to *do*
>>> calculus rather than being able to understand a somewhat obscure
>>> looking definition.

>>Sigh, more watering down of education.

>It is worse than that. We are fooling people into thinking
>that doing calculus is even of much importance, except for
>researchers who have to try lots of alternatives.

Sigh, and with it US national security more and more dependent upon
technology and technological innovation. Yet, by the same principle, it's
more important to willy nilly use technology than to design and understand
proper uses for technology.

>It is FAR more important that an engineer or biologist or
>economist or whatever know what a derivative means than to
>be able to do all the computations in the universe.

I rather an engineer know how to properly use a derivative than
calculate a derivative which may be misapplied.

>I have had students tell me that the biggest problem they had with
>general topology is that they had previously had metric topology.

I've found metric space theory annoying, especially when laboriously
establishing simple topological basics.

>Knowing how to calculate does not imply any kind of understanding
>of anything except how to carry out formal calculations.

It's an intellectual dead end. 

----

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