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

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 Guest
Re: Failing Linear Algebra:
Posted: Apr 27, 2004 3:42 PM

grubb@lola.math.niu.edu (Daniel Grubb) wrote in message news:<c6bars\$ejg\$1@news.math.niu.edu>...
> >>a significant role. They often stumble because (among other problems)
> >>they don't realize they need to _memorize_ definitions _precisely_.

>
> >Memorize? I can't remember ever memorizing anything. Better just to
> >practice until you understand. Discuss, ask questions, apply. That way
> >you memorize, of course, but that's just a side-effect.

>
> No, for proof classes, which linear algebra is in many places,
> it is crucial to *memorize* the definitions. This holds for
> all the proof classes at higher levels also. There is simply no
> way of giving rigorous proofs if you don't know the actual
> definitions. All too often, students have some very vague ideas
> of what is going on and then can't even get started on a proof
> because they don't know the *exact* definiton used in the course.
>

> >>So you can do a little self-assessment here to figure out whether
> >>what you're missing is bits of topics or the core idea: can you,
> >>right this minute, define what a vector space is?

>
> >Hopefully not just as a one-to-one rendition of phrases from a
> >textbook...

>
> The student should be able to give a rendition that is at least
> equivalent to the one given in the book and that uses precise language.
> If you can't say that a basis is an independent spanning set
> then you don't know what a basis is. If you can't give the quantifiers
> for the definition of independence, you won't be able to do a
> proof using independence.
>
> --Dan Grubb

Let me try that one...independence means a group of vectors (in
homogenous form???) such that if they all equal the zero vector, then
the only possible way for that is the each coefficient of every vector
has to equal 0 too.

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