Re: Explaining the foundations of math

From: Herman Rubin (hrubin_at_odds.stat.purdue.edu)
Date: 09/02/04 

Date: 2 Sep 2004 16:09:04 -0500

In article <20040830080416.Y75154@agora.rdrop.com>,
William Elliot <marsh@privacy.net> wrote:
>On Mon, 30 Aug 2004, Will Twentyman wrote:
>> Van Jacques wrote:

>> > For example, Weierstrass's main lasting contribution to math
>> > was to define the limit of f(x) at x_o as follows:

>> > For any e > 0 there exists d_o such that if 0 < d < d_o, then
>> > | f(x_o +/- d) - L | < e, then L = lim(f(x)) as x --> x_o.

>> 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.

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'm not saying that decision is correct, just that they are removing a
>> barrier to being able to do calculus that appears to be unimportant for
>> many students.

>Just wait until they have to hassle with metric spaces, spaces with norms,
>modern analysis or topology. They'll founder and flop.

I have had students tell me that the biggest problem they had
with general topology is that they had previously had metric
topology. It is easy to go from general to special, but the
other direction involves UNlearning.

        It ain't what you don't know that hurts you;
        It's what you know that ain't so.

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

>Not an approach at all helpful for math majors, graduate physics majors. 

-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558