Re: Galois Theory ok, weird lie from sci.math

From: Will Twentyman (wtwentyman_at_read.my.sig)
Date: 10/14/04 

Date: Wed, 13 Oct 2004 20:02:57 -0400

James Harris wrote:

> poespam-trap@yahoo.com (Randy Poe) wrote in message news:<df76407e.0410120655.4065dd4b@posting.google.com>...
>
>>jstevh@msn.com (James Harris) wrote in message news:<3c65f87.0410111700.16fc6823@posting.google.com>...
>>
>>>>Could one really become a mathmatician without training in that area of
>>>>algebra? I can see a mathematician *forgetting* the areas of algebra
>>>>necessary to understand the depth of JSH's errors, but I don't see how one
>>>>could avoid having been trained in them. This is all stuff from the
>>>>beginning undergraduate "intro to abstract algebra" course (e.g., Herstein,
>>>>"Topics in Algebra") that even a budding mathematician who intends to work
>>>>as far away from algebra as possible would be unable to avoid. :-)
>>>
>>>I have a B.Sc. in physics. I do know a little algebra.
>>
>>I went to grad school in physics. With the exception of a seminar
>>in group theory I sat in on, I never learned any "algebra" in
>>the sense that the mathematicians are using it.
>>
>>Note that phrase "abstract algebra". This "algebra" is not
>>what you learned in high school. It's not required for
>>a degree in physics. It's not a prerequisite to calculus,
>>which you probably also had.
>
> So now abstract algebra is supposedly different from algebra?

Yes. Abstract algebra focuses on the properties of the set and
operation(s) as a whole. Standard algebra is focused on manipulations
of elements/variables within the set. The result is a completely
different focus, and a corresponding different emphasis. The
manipulations you do are generally not that important in abstract
algebra. They are "trivial computations" that have little to do with
properties of the structure as a whole. As an excercise sometime, try
comparing a college algebra text with an abstract algebra text. Focus
just on how they discuss polynomials and rational expressions.

[snip]

> That doesn't mean I hadn't learned about them before, though I don't
> think I did, as I *have* looked over at least one abstract algebra
> text as a kid, as part of a class that bored me immensely.

[snip]

> That's one reason I'm not that impressed by those of you who think you
> know so much, when you don't *understand* mathematics.

Apparently you didn't understand what you read as a kid. 

-- 
Will Twentyman
email: wtwentyman at copper dot net
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