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Topic: Failing Linear Algebra:
Replies: 54   Last Post: Jan 10, 2007 12:47 PM

 Messages: [ Previous | Next ]
 Thomas Nordhaus Posts: 433 Registered: 12/13/04
Re: Failing Linear Algebra:
Posted: Apr 27, 2004 3:32 PM

Anonymous schrieb:

>rusin@vesuvius.math.niu.edu (Dave Rusin) wrote in message news:<c69sdb\$oi7\$1@news.math.niu.edu>...

>> Our students "do well on the very first exam" because that's the part
>> of the course where we warm up with techniques for solving linear
>> systems of equations and such topics. But our LA course is also our
>> students' first course in which abstractions, axioms, and proofs play
>> a significant role. They often stumble because (among other problems)
>> they don't realize they need to _memorize_ definitions _precisely_.
>> 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?
>>
>> dave

>
>Dave, this may be my problem. I did decent on the first exam because,
>like you said, it was solving linear systems, echelon form, linear
>dependences--easier stuff like that. I've always been a little
>confused with the concepts, but I think I may finally be getting a
>grip on what a vector space is:

<Just some philosophizing:>

That's familiar: You feel comfortable with specific examples but can't
see the abstraction, the "structure" behind. In German there is a
saying meaning roughly: "You can't see the forest because of all the
trees"... As mathematics is the "science of structures", you will have
to get to this point. But it's a worthwhile goal to pursue because
it's really uplifting if you finally reach that point - As the old
greeks said: "Heureka!" I finally found!

Thomas

Date Subject Author
4/22/04 Guest
4/22/04 Michael N. Christoff
1/10/07 Gerry Myerson
1/10/07 Jonathan Miller
1/10/07 Guest
1/10/07 David C. Ullrich
1/10/07 Acid Pooh
1/10/07 Guest
4/23/04 Brian Borchers
4/27/04 Guest
1/10/07 maky m.
4/26/04 David Ames
1/10/07 Guest
1/10/07 Michael Stemper
1/10/07 maky m.
4/23/04 Porker899
4/27/04 Guest
1/10/07 Abraham Buckingham
1/10/07 Mitch Harris
1/10/07 Guest
1/10/07 Grey Knight
1/10/07 Guest
1/10/07 Toni Lassila
1/10/07 Thomas Nordhaus
1/10/07 George Cox
4/28/04 Dave Rusin
4/28/04 George Cox
4/28/04 George Cox
4/29/04 Marc Olschok
4/29/04 Mitch Harris
4/29/04 Robert Israel
4/28/04 Guest
4/29/04 Guest
1/10/07 Dave Rusin