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

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Robert Israel

Posts: 11,902
Registered: 12/6/04
Re: Failing Linear Algebra:
Posted: Apr 29, 2004 6:57 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


In article <c6rt4c$f602h$1@uni-berlin.de>,
Mitch Harris <harrisq@tcs.inf.tu-dresden.de> wrote:
>Dave Rusin <rusin@vesuvius.math.niu.edu> wrote:

>>Yeah, sure. A vector space is a module over a field. That's absolutely
>>true and probably given that way in Bourbaki somewhere, but even in
>>selective institutions I can't believe students learn about modules
>>before vector spaces. Is there really a source anywhere that pretends to
>>_introduce_ vector spaces in terms of abelian groups?


>Er.. yeah. MacLane and Birkhoff, Algebra, 3rd ed. 1988.

>Chapter 5 Modules "An R-module is an additive abelian group together
> with a function..."


>Chapter 6 Vector Spaces "A vector space is a module over a field F."

>I don't know if teachers actually use this as a textbook for an undergrad
>class though.


It has happened. I first learned linear algebra from Herstein (himself,
as well as his text "Topics in Algebra") at U of Chicago in 1969-70:
"A nonempty set V is said to be a vector space over a field F if
V is an abelian group ..."

Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia
Vancouver, BC, Canada V6T 1Z2



Date Subject Author
4/22/04
Read Failing Linear Algebra:
Guest
4/22/04
Read Re: Failing Linear Algebra:
Michael N. Christoff
1/10/07
Read Re: Failing Linear Algebra:
Gerry Myerson
1/10/07
Read Re: Failing Linear Algebra:
Jonathan Miller
1/10/07
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
David C. Ullrich
1/10/07
Read Re: Failing Linear Algebra:
Acid Pooh
1/10/07
Read Re: Failing Linear Algebra:
Guest
4/23/04
Read Re: Failing Linear Algebra:
Russell Blackadar
4/23/04
Read Re: Failing Linear Algebra:
Brian Borchers
4/27/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
maky m.
4/26/04
Read Re: Failing Linear Algebra:
David Ames
1/10/07
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Michael Stemper
1/10/07
Read Re: Failing Linear Algebra:
maky m.
4/23/04
Read Re: Failing Linear Algebra:
Porker899
4/27/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Abraham Buckingham
1/10/07
Read Re: Failing Linear Algebra:
Mitch Harris
1/10/07
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Grey Knight
1/10/07
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Toni Lassila
1/10/07
Read Re: Failing Linear Algebra:
Thomas Nordhaus
1/10/07
Read Re: Failing Linear Algebra:
George Cox
4/28/04
Read Re: Failing Linear Algebra:
Dave Rusin
4/28/04
Read Re: Failing Linear Algebra:
George Cox
4/28/04
Read Re: Failing Linear Algebra:
George Cox
4/29/04
Read Re: Failing Linear Algebra:
Marc Olschok
4/29/04
Read Re: Failing Linear Algebra:
Mitch Harris
4/29/04
Read Re: Failing Linear Algebra:
Robert Israel
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
4/28/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
4/29/04
Read Re: Failing Linear Algebra:
Russell Blackadar
4/29/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
5/1/04
Read Re: Failing Linear Algebra:
Russell Blackadar
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
1/10/07
Read Re: Failing Linear Algebra:
Dave Rusin
1/10/07
Read Re: Failing Linear Algebra:
Russell Blackadar
4/30/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
David C. Ullrich
4/27/04
Read Re: Failing Linear Algebra:
Guest
4/27/04
Read Re: Failing Linear Algebra:
Guest
4/28/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
Law Hiu Chung
4/30/04
Read Re: Failing Linear Algebra:
Guest
1/10/07
Read Re: Failing Linear Algebra:
David C. Ullrich

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