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

 Messages: [ Previous | Next ]
 gersh@bialer.com Posts: 12 Registered: 12/13/04
Re: Failing Linear Algebra:
Posted: Apr 28, 2004 11:35 PM

grubb@lola.math.niu.edu (Daniel Grubb) wrote in message news:<c6or0b\$3tn\$1@news.math.niu.edu>...
> >|It is certainly reasonable for a linear algebra exam to
> >|have a student show that a certain structure is a vector space!

>
> >how do you manage to memorize mathematical definitions when you don't
> >even seem to be able to remember the issue under discussion in a
> >newsgroup thread? the issue was whether there is any reason to
> >memorize definitions by rote instead of just using a piece of paper or
> >computer to memorize them for you, so your comment is entirely
> >irrelevant.

>
> No, I did remember the context. I *do* think it is reasonable
> for a student to show a certain structure is a vector space
> without having a machine or piece of paper with the definition
> on it. If they cannot show that, say, the collection of anti-symmetric
> matrices is a vector space without any computer or other pieces of
> paper, then they don't understand what a vector space is. I would
> say the same thing in an abstract algebra course with the definition
> of a group, or a ring, or a module over a ring, etc. If you cannot give
> a definition that is logically equivalent to the one in the book, you
> don't know the subject. You have to have such in order to show a structure
> is a group, or a ring, or a module, etc. You certainly need one in order
> to prove anything about them.
>
> --Dan Grubb

You don't have to remember the defintion. You just have to remember a
bunch of examples. For vector spaces, I just think of R^n, and then
generalize. It relates to algebra to it has to have something to do
with operations. So, vectors have to be additive, and scalars have to
be nice. The definition is pretty obvious. Memorization is only really
needed for geometry.

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