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

 Messages: [ Previous | Next ]
 George Cox Posts: 868 Registered: 12/6/04
Re: Failing Linear Algebra:
Posted: May 1, 2004 6:42 AM

Anonymous wrote:
>
> Marc:
>

> >The first time, I spent in a linear algebra course (Kaiserslautern, 1986)
> >introduced sets, groups, rings and fields, modules and then vector spaces.
> >(in that order)

>
> Odd. We did sets and then groups in algebraic structures. We touched upon
> rings, I think, but I don't remember what they are. Have no idea about fields,

The definition of vector space will mention scalars. The scalars form a
field.

> if they're not vector fields, which someone already said they aren't. Never
> heard of modules.
>
> We did vectors, then vector spaces, then subspaces. Then spans, dependence,
> bases, matrices, determinants, then eigenvalues and vectors. It's odd because
> Schaum's Outlines does it in a different order. And Cliff's does an even
> different order.
>

> >By the time we met vector spaces, the notion of image and kernel as well
> >as the proof of the first homomorphism theorem

>
> "Homomorphism theorem"? Is this what's called "Dimension Theorem" now?

No.

>
> >But nowadays nobody needs to be afraid of modules in a linear algebra course,
> >unless it is only a MMC (Matrix Manipulation Course).
> >

>
> What are modules? And why are they related to marix manipulation? BTW, I, for

In the definition of vector space, replace "field of scalars" with
"ring".

> one, would love to have taken a linear algebra course that was all MMC. I love

An MMC wouldn't be a linear algebra course. There are vector spaces
that have nothing to do with matrices.

> the stuff!

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

Date Subject Author
4/24/04 Daniel Grubb
4/24/04 Marc Olschok
4/24/04 Daniel Grubb
4/24/04 Marc Olschok
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4/24/04 Daniel Grubb
4/28/04 Tim Mellor
4/28/04 James Dolan
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4/28/04 Daniel Grubb
4/28/04 gersh@bialer.com
4/29/04 Daniel Grubb
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4/28/04 Guest
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1/10/07 David C. Ullrich
4/29/04 Dave Rusin
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1/10/07 Law Hiu Chung
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1/10/07 Marc Olschok
1/10/07 Toni Lassila
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