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

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George Cox

Posts: 868
Registered: 12/6/04
Re: Failing Linear Algebra:
Posted: Apr 28, 2004 2:44 PM
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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
addition;
(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
Read Failing Linear Algebra:
Guest
4/22/04
Read Re: Failing Linear Algebra:
Michael N. Christoff
1/10/07
Read Re: Failing Linear Algebra:
Gerry Myerson
1/10/07
Read Re: Failing Linear Algebra:
Jonathan Miller
1/10/07
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
David C. Ullrich
1/10/07
Read Re: Failing Linear Algebra:
Acid Pooh
1/10/07
Read Re: Failing Linear Algebra:
Guest
4/23/04
Read Re: Failing Linear Algebra:
Russell Blackadar
4/23/04
Read Re: Failing Linear Algebra:
Brian Borchers
4/27/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
maky m.
4/26/04
Read Re: Failing Linear Algebra:
David Ames
1/10/07
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Michael Stemper
1/10/07
Read Re: Failing Linear Algebra:
maky m.
4/23/04
Read Re: Failing Linear Algebra:
Porker899
4/27/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Abraham Buckingham
1/10/07
Read Re: Failing Linear Algebra:
Mitch Harris
1/10/07
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Grey Knight
1/10/07
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Toni Lassila
1/10/07
Read Re: Failing Linear Algebra:
Thomas Nordhaus
1/10/07
Read Re: Failing Linear Algebra:
George Cox
4/28/04
Read Re: Failing Linear Algebra:
Dave Rusin
4/28/04
Read Re: Failing Linear Algebra:
George Cox
4/28/04
Read Re: Failing Linear Algebra:
George Cox
4/29/04
Read Re: Failing Linear Algebra:
Marc Olschok
4/29/04
Read Re: Failing Linear Algebra:
Mitch Harris
4/29/04
Read Re: Failing Linear Algebra:
Robert Israel
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
4/28/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
4/29/04
Read Re: Failing Linear Algebra:
Russell Blackadar
4/29/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
5/1/04
Read Re: Failing Linear Algebra:
Russell Blackadar
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
1/10/07
Read Re: Failing Linear Algebra:
Dave Rusin
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
4/30/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
David C. Ullrich
4/27/04
Read Re: Failing Linear Algebra:
Guest
4/27/04
Read Re: Failing Linear Algebra:
Guest
4/28/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Law Hiu Chung
4/30/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
David C. Ullrich

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