This talk of Clifford Algebra has me really excited, and I would like to recommend a book that has taught me a lot about the geometric aspects of vectors. It's Geometrical Vectors by Gabriel Weinreich (U. of Chicago Press, 1998). ISBN 0-226-89048-1 (pbk). I got my copy from amazon.com early this summer and it's a great read. I don't understand all of it yet, but it's the only book that clearly describes the conceptual differences between covariant and contravariant vectors. It also discusses the properties of bivectors and related entities.
I also have a copy of Hestenes' book New Foundations for Classical Mechanics (second edition) and it's equally fascinating but much more in depth.
The thought of incorporating geometric algebra into an introductory physics text would be another truly landmark innovation and should be seriously considered!
Cheers,
Joe Heafner - Instructional Astronomy and Physics
Home Page http://users.vnet.net/heafnerj/index.html
I'll never be able to afford a Lexus, but I do have a Mac. Same thing.
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