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Topic: Failing Linear Algebra:
Replies: 91   Last Post: Jan 10, 2007 12:56 PM

 Messages: [ Previous | Next ]
 Marc Olschok Posts: 409 Registered: 12/6/04
Re: Failing Linear Algebra:
Posted: Apr 29, 2004 8:38 AM

Anonymous wrote:
> George:
>

>>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!
>>

>
> I think you just made me remember what an abelian group is.
> It's closed under its operation, it's associative, commutative,
> it's got an inverse, and it's got the identity element in it.
> There may be some other condition, since aren't
> all the above needed for any group?
> I remember something about an abelian group forming a table
> with a diagonal, or something....

To remarks:

(1) too many "It's", referring to different things.

(2) this would be an excellent time, to grab a textbook or your notes and
_lookup_ the definition of "group" and "abelian group".

>
> So, basically, "abelian group" is just an easier way of
> saying "vector space".

No.

> Rather than listing all 8 conditions. But, that assumes the student *knows*
> what an abelian group is.

Not really. One can list all the conditions; but it would be nice at least
to group the conditions in a coherent way and to mention those conditions
that correspond to the axioms for an abelian group.
Those students who have met "abelian groups" before would benefit and
the others would not be hurt.

Marc

Date Subject Author
4/24/04 Daniel Grubb
4/24/04 Marc Olschok
4/24/04 Daniel Grubb
4/24/04 Marc Olschok
4/24/04 Daniel Grubb
4/24/04 Thomas Nordhaus
4/24/04 Dave Rusin
4/25/04 Jonathan Miller
4/25/04 Felix Goldberg
4/24/04 Daniel Grubb
4/28/04 Tim Mellor
4/28/04 James Dolan
4/28/04 Daniel Grubb
4/28/04 James Dolan
4/28/04 Daniel Grubb
4/28/04 gersh@bialer.com
4/29/04 Daniel Grubb
4/29/04 Dave Rusin
4/28/04 Guest
4/29/04 Guest
4/28/04 Guest
1/10/07 David C. Ullrich
4/29/04 Dave Rusin
4/28/04 Guest
1/10/07 Law Hiu Chung
1/10/07 Dave Seaman
1/10/07 Marc Olschok
1/10/07 George Cox
4/28/04 Guest
1/10/07 Dave Rusin
4/28/04 Lee Rudolph
4/28/04 Guest
4/28/04 Guest
1/10/07 Marc Olschok
1/10/07 Toni Lassila
4/29/04 Guest
1/10/07 M L
1/10/07 Thomas Nordhaus
4/30/04 Guest
1/10/07 David C. Ullrich
1/10/07 Toni Lassila
4/30/04 Guest
1/10/07 George Cox
1/10/07 Marc Olschok
4/30/04 Guest
4/30/04 Guest
4/27/04 Guest
1/10/07 Thomas Nordhaus
1/10/07 David C. Ullrich
1/10/07 Dave Rusin
1/10/07 David C. Ullrich
5/9/04 James Dolan
5/10/04 David C. Ullrich
5/10/04 James Dolan
5/10/04 David C. Ullrich
5/10/04 Marc Olschok
5/10/04 David C. Ullrich
4/27/04 Guest
1/10/07 Thomas Nordhaus
4/27/04 Guest
1/10/07 magidin@math.berkeley.edu
1/10/07 David C. Ullrich
1/10/07 Marc Olschok
1/10/07 David C. Ullrich
1/10/07 Tim Mellor
4/28/04 Daniel Grubb
4/28/04 Daniel Grubb
4/27/04 Guest
1/10/07 David C. Ullrich
4/28/04 Dave Rusin
4/28/04 Daniel Grubb
4/27/04 Guest
1/10/07 Marc Olschok
4/24/04 Wayne Brown
4/24/04 Thomas Nordhaus
4/24/04 David Ames