Re: Latin and other irrelevant topics

[Brian Rogoff <bpr@shell5.ba.best.com>]

On 27 Jan 2001, Florian Weimer wrote:
> Brian Rogoff <bpr@shell5.ba.best.com> writes:
> > I think that there is quite a bit of modern mathematics that could
> > be brought to the high school student and the undergraduate (even
> > the ones who aren't majoring in mathematics) that is highly
> > relevant.
> 
> Many things are relevant, but the interest in mathematics is generally
> low among the students in engineering and computer science (at least
> that's my impression).  As a result, most lecturers here seem to focus
> on the basic stuff and present it in a rigorous manner.

I'd be happy with less rigor for CS/engineering types and more of what 
physicists call "galley proofs". Many (most?) people can't memorize
formulae so having an idea as to how to derive a formula or theorem, even
if it isn't completely rigorous, is probably better pedagogy. 

> > Non-standard analysis, differential forms (can be introduced with
> > multivariable calculus), category theory (a high school level
> > approach in the book by Lawvere and Schanuel, linear programming,
> > really the list is pretty long.
> 
> To be honest, I don't think non-standard analysis and differential
> forms are really important (compared to the Lebesgue integral, which
> is relatively old and not often taught to undergrads),

I have the opposite view. Mastery of differential forms allows the student
to get more quickly to advanced physics. Non-standard analysis is easier 
to understand than the theory of limits, at least for me. Real analysis, 
the course where you'd meet Lebesgue integration, is not necessary for 
undergraduate engineers at all. 

> exposure to category theory is probably a good idea (after you have
> seen a bunch of algebraic structures, of course).  But it's probably a
> bad idea to discuss such things with me because I'm heavily biased

I agree about the category theory, but I love talking with others who love
maths, even if they love different parts ;-).

> (I'm hardly interested in calculus and applied mathematics, but I'll
> admit that's the part which is relevant for most students).

Gasp! Understanding the infinitesimal calculus is the "pons asinorum" of 
engineering mathematics. Well, now I expect Robert Dewar to tell me that 
I've used "pons asinorum" incorrectly; just trying to keep this
irrelevant, off topic thread on topic.

> > Personally, I'd much rather spend time studying math than studying Latin; 
> > the latter seems a waste of time, like being forced to read Shakespeare. 
> 
> The way I learned Latin at school was a bit similar to real
> mathematics, in fact more than math itself (we were taught the Latin
> grammar in a rather formal way, and math mostly consisted of very
> technical symbolic manipulations).

I have a very strong continuous applied math background, and almost no
Latin background whatsoever. Sounds like you were taught math by reading 
the reference manual rather than the rationale. 

-- Brian