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

 Messages: [ Previous | Next ]
 Daniel Grubb Posts: 526 Registered: 12/10/04
Re: Failing Linear Algebra:
Posted: Apr 24, 2004 11:02 AM

>>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

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