[BUG] a reading list

[Martin Jackson]

All,

At the end of my multivariate course, I give students a list of 
things to read for their own interest.  I've included it below with 
the hope that some of you can add suggestions.  Of the items on the 
list, Weinreich's Geometrical Vectors was new to me this semester.  I 
haven't finished reading this because I showed to my physics 
colleague with whom I am team-teaching and he was so interested that 
he hasn't yet returned it.

Martin



Harry M. Schey, Div, Grad, Curl, and All That, 3rd ed.  (details at
http://www.amazon.com/exec/obidos/ASIN/0393969975). Schey's goal is to
develop strong physical/geometric intuition for vector calculus.  The
approach is similar to how we have done vector calculus.  This book should
be accessible to you now.  You can get something out of it from a casual
read and a lot of out it from careful study.

Gabriel Weinreich, Geometrical Vectors (details at
http://www.amazon.com/exec/obidos/ASIN/0226890481).  Weinreich carefully
distinguishes among various "flavors" of vector.  He gives specific
physical and geometric interpretations for each flavor.  This book should
be accessible to you now.  You can get something out of it from a casual
read and a lot of out it from careful study.


Michael Spivak, Calculus on Manifolds (details at
http://www.amazon.com/exec/obidos/ASIN/0805390219).  This book is at a
higher level than Div, Grad, Curl and All That and Geometrical Vectors and
requires careful study.  There are parts that require some linear algebra.
The book culminates in the general version of Stokes' Theorem I mentioned
in class.

Michael J. Crowe, A History of Vector Analysis (details at
http://www.amazon.com/exec/obidos/ASIN/0486679101).  This is a
straightforward and clearly written history of the subject.  The book gives
a great sense of how this particular part of mathematics evolved in
connection with the physics of electricity and magnetism.  This history
includes some interesting battles among people advocating particular points
of view.  The main conflicts are between those favoring a quarternion
approach and those who want to extract what we now think of as a vector
approach.  The book has lots of quotable material from the writings of
the relevant players.

Victor Katz, "The History of Stokes' Theorem" Mathematics Magazine, Vol.
52, No.3, May 1979 (available through the JSTOR journal archive at
http://links.jstor.org/sici?sici=0025-570X%28197905%2952%3A3%3C146%3ATHOST%3E2.0.CO%3B2-O">
if you have access).  This article gives a quick history of the Divergence
Theorem, Green's Theorem, and Stokes' Theorem.  Each theorem was first
stated in "pre-vector" language, then restated in vector language, and
later generalized in the language of differential forms.  Part of this
story is related to the full history given in Crowe.  The article ends with
a (very quick) discussion of the general version of Stokes' Theorem that is
the culmination of Spivak's text.