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

 Messages: [ Previous | Next ]
 Brian Borchers Posts: 148 Registered: 12/6/04
Re: Failing Linear Algebra:
Posted: Apr 23, 2004 11:55 AM

I've also taught introductory linear algebra many times. David
Ullrich's advice is correct as far as it goes. I have a few

Suppose that you have a definition like:

A <frotz> is a <mumble> that has the properties
1. <foo>
2. <bar>
3. <plugh>

and theorems like:

In any <frotz>, <x> happens.

You'll find that lots of exercises are of the form:

Consider <plover>. Is <plover> a <frotz>?

When you solve such a problem it may be that your grader will accept a
"yes" or "no" answer, and it's likely that the answer in the back of
the book will be a simple "yes" or "no". Do not be tempted by this.
because <plover> has properties <foo>, <bar>, and <plugh>", followed
by work that shows this. On the other hand, if the answer is "no",
then your answer should be something like, "No, because <plover> does not
satisfy <bar>", followed by work that shows this.

The important point here is that mathematics is not simply a guessing game.

You should also take time after memorizing the definition and the
theorem to come up with examples and counterexamples related to this
definition. Start by coming up with a <frotz>, verifying that is has
properties <foo>, <bar> and <plugh>, and that <x> happens. Then
construct something that is almost a <frotz> but doesn't satisfy
property <foo>. Does <x> happen? If it doesn't, then you can see one
reason why the property <foo> is part of the definition of a <frotz>.

In general, you need to explore each of the parts of the definition, and
understand what "goes wrong" when one of the required properties is not
satisfied.

--
Brian Borchers borchers@nmt.edu
Department of Mathematics http://www.nmt.edu/~borchers/
New Mexico Tech Phone: 505-835-5813
Socorro, NM 87801 FAX: 505-835-5366

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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