Re: math programs
- From: "The poster formerly known as Colleyville Alan" <nospam@xxxxxxxxxx>
- Date: Thu, 07 Sep 2006 03:47:35 GMT
<studylogic06@xxxxxxxxx> wrote in message
news:1157562920.971950.98500@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Hmm, yes. As I delve more into the course descriptions and
prerequisites for the analysis classes, it does seem that they are
heavily associated with calculus.
This page has an overview of the subject. http://www.math-atlas.org/
Click on the "Take a tour" link to get an introduction and "start the tour"
when you get to the next page.
Yes, calculus is subsumed under the category of analysis, so it may not be
mentioned separately.
So I guess it is safe to say that 'calculus' does not merit its own
mention as a major area in the programs because it is considered part
of the early development of the 'analysis' area (I see there is an
opinion against this in the thread,
Herman is rather outspoken about the idea that one should learn concepts and
only then proceed to computation. Since I just finished Calculus I a few
weeks agon, I happen to agree with him that too much emphasis is placed on
doing calculations without understanding the concepts. That was less of a
problem in differential calculus, but seems to be more pronounced in the
study of integration. The last part of Calc I touched on integration and
now my Calculus II class is reviewing that little bit and moving on from
there. Unfortunately, it seems to me like it is all technique at this
point.
Herman has decades of teaching experience and has seen the results of this
kind of teaching. Other professors here disagree with him as to the order
in which topics should be presented. I think it is somewhat moot since the
universities specify the order in which the classes are taught.
but by "early development" I mean
the usual order that the material is presented in for teaching purposes
in most schools)...
similar in the way that 'arithmetic' wouldn't be
listed since it is well covered under the algebra area (not saying that
we don't utilize arithmetic in the other areas, just that it is mostly
taught within a sequence that leads to higher algebras)
so in general, at least in the typical way that material is taught, the
main areas and what they include could be...
ALGEBRA - includes arithmetic, basic number theory, pre-algebra,
college algebra, linear algebra, and some more...
ANALYSIS - includes various levels of basic and advanced calculus,
functions, infinity, proofs, and more...
GEOMETRY/TOPO - trigonometry, geometry (Euclidean and non-E), topology,
spaces...
Though it would be an interesting Philosophy of Mathematics question to
discuss how arbitrary or real the above divisions are... but of course,
we have to have some way of dividing up the material for pedagogical
purposes... or do we? I wonder what interesting material and theorems
other societies might come up with if they were spoon-fed the material
in different patterns or with no divisions at all.
.
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