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Topic: Failing Linear Algebra:
Replies: 54   Last Post: Jan 10, 2007 12:47 PM

 Messages: [ Previous | Next ]
 George Cox Posts: 868 Registered: 12/6/04
Re: Failing Linear Algebra:
Posted: Apr 28, 2004 2:44 PM

Dave Rusin wrote:
>
> In article <408EC9A3.DB73D12C@SPAMbtinternet.com.invalid>,
> George Cox <george_coxANTI@SPAMbtinternet.com.invalid> wrote:
>
> [Vector space.]
>

> >What is the precise
> >definition? If the precise definition has words like "abelian group" in
> >it, then what is the precise meaning of them? And so on.

>
> Yeah, sure. A vector space is a module over a field. That's absolutely
> true and probably given that way in Bourbaki somewhere, but even in
> selective institutions I can't believe students learn about modules
> before vector spaces. Is there really a source anywhere that pretends to
> _introduce_ vector spaces in terms of abelian groups?

I was taught (33 years ago in the University of Birmingham, UK) that a
vector space is
(1) a set of elements (the vectors) which form an abelian group under
(2) etc....
The phrase "commutative group" or "additive group" might have been used
instead of "abelian group"--you'll forgive me if I can't quite remember!

The course was the first algebra course in the first year of a BA.

How do you/US universities/today's commonly used texts define vector
space?

>
> Hmm, I suppose some here would argue that it messes up students'
> understanding of modules if they are first tainted by facts learned
> for vector spaces, which then have to be unlearned in the general case.
>
> dave

--
G.C.
Note ANTI, SPAM and invalid to be removed if you're e-mailing me.

Date Subject Author
4/22/04 Guest
4/22/04 Michael N. Christoff
1/10/07 Gerry Myerson
1/10/07 Jonathan Miller
1/10/07 Guest
1/10/07 David C. Ullrich
1/10/07 Acid Pooh
1/10/07 Guest
4/23/04 Brian Borchers
4/27/04 Guest
1/10/07 maky m.
4/26/04 David Ames
1/10/07 Guest
1/10/07 Michael Stemper
1/10/07 maky m.
4/23/04 Porker899
4/27/04 Guest
1/10/07 Abraham Buckingham
1/10/07 Mitch Harris
1/10/07 Guest
1/10/07 Grey Knight
1/10/07 Guest
1/10/07 Toni Lassila
1/10/07 Thomas Nordhaus
1/10/07 George Cox
4/28/04 Dave Rusin
4/28/04 George Cox
4/28/04 George Cox
4/29/04 Marc Olschok
4/29/04 Mitch Harris
4/29/04 Robert Israel
4/28/04 Guest
4/29/04 Guest
1/10/07 Dave Rusin