Re: math programs
- From: "guylesmith@xxxxxxxxx" <guylesmith@xxxxxxxxx>
- Date: 7 Sep 2006 16:24:54 -0700
Calculus is interesting in that much of it could be taught after high
school algebra with additional material added as one learns about other
forms and functions (e.g., geometric shapes, trig functions, logs,
etc.) and how the basic ideas of Calculus apply to each. In the
university scheme of things, the first 2-3 courses in Calculus are
considered lower division or even college prep at places like MIT. In
the world of upper division mathematics, Calculus is the beginning of
Analysis, wherein you prove the operations you learned to take for
granted in Calculus. In conjunction with Vector Calculus and Advanced
Calculus, you need to understand, or at least know how to work with, a
fair amount of Linear Algebra, which itself is a bridge from
computation to learning how to do proofs, at least that was typically
one's first exposure to proofs in the old days. These days lower
division math and engineering students generally have to take a course
in Discrete Mathematics and/or some sort of Intro To Mathematical
Proofs before moving on to Linear Algebra or a first course in Analysis
or Abstract Algebra. If you make it that far, congratulations, you're
now officially a geek, not just in appearance! ;^) However, many
enegineering students forego Analysis and Abstract Algebra entirely and
go from Calculus and Linear Algebra right into Differential Geometry
(which only took Einstein 10 years to master, but it's easier now)
and/or Differential Equations, and/or Complex Variables, where you'll
learn Calculus all over again, but for complex numbers. I could go on,
but if you get that far, you'll probably have read numerous course
descriptions for upper division, MA, MS, and PhD mathematics programs
by then.
studylogic06@xxxxxxxxx wrote:
I'm developing an interest in studying mathematics, and I notice that a
lot of university math departments list their main areas in the
pure-math program as "algebra, analysis, and geometry/topology"...
where does calculus fit into this bunch? Is it not considered a "big"
area? or is it not considered an area of pure math? or is it simply
considered a part of one of the areas already mentioned, and if so
which one?
thanks
.
- References:
- math programs
- From: studylogic06@xxxxxxxxx
- math programs
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