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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
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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 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 Russell Blackadar
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
1/10/07 Russell Blackadar
4/28/04 Guest
1/10/07 Russell Blackadar
4/29/04 Russell Blackadar
4/29/04 Guest
1/10/07 Russell Blackadar
1/10/07 Russell Blackadar
5/1/04 Russell Blackadar
1/10/07 Russell Blackadar
1/10/07 Dave Rusin
1/10/07 Russell Blackadar
4/30/04 Guest
1/10/07 Guest
1/10/07 David C. Ullrich
4/27/04 Guest
4/27/04 Guest
4/28/04 Guest
1/10/07 Law Hiu Chung
4/30/04 Guest
1/10/07 David C. Ullrich

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