The Grassmann Algebra Book

Grassmann Algebra: Exploring extended vector algebra with Mathematica

The chapters:  1. Introduction  ||  2. The Exterior Product  ||  3. The Regressive Product  ||  4. Geometric Interpretations  ||  5. The Complement  ||  6. The Interior Product  ||  7. Exploring Screw Algebra  ||  8. Exploring Mechanics  ||  9. Exploring Grassmann Algebra  ||  10. Exploring the Generalized Grassmann Product  ||  11. Exploring Hypercomplex Algebra  ||  12. Exploring Clifford Algebra  ||  13. Exploring Grassmann Matrix Algebra  ||  A Guide to GrassmannAlgebra  ||  A Brief Biography of Grassmann  ||  Notation  ||  Glossary  ||  Bibliography  ||  Index

  Download the detailed Table of Contents:  Table Of Contents.pdf  [19 pages]

The primary purpose of this book is to provide a readable account in modern notation of Grassmann's major algebraic contributions to mathematics and science. I would like it to be accessible to scientists and engineers, students and professionals alike. Consequently I have tried to avoid all mathematical terminology which does not make an essential contribution to understanding the basic concepts. The only assumption I have made about the reader's background is that they have some familiarity with basic vector algebra.

The secondary purpose of this book is to provide an environment for exploring Grassmann algebra. For general applications in higher dimensional spaces, computations by hand in any algebra become tedious, indeed limiting, thus restricting the hypotheses that can be explored. For this reason, the book is accompanied by a package for exploring the algebra written in a computer algebra system (Mathematica). You can read the book without using the package, or you can use the package to extend the examples in the text, experiment with hypotheses, or explore your own interests. You will need Mathematica to run the package.

  Download the Grassmann Algebra book:  Grassmann Algebra Book.pdf  [759 pages]

File format  The book opens in your browser or downloads as a Portable Document Format (.pdf) file, and provided your browser is enabled with Adobe Acrobat Reader or your computer is running Mac OS X, you should be able to read it on screen and print it if you wish. Please see the Book and Package Versions page for further information on the draft status of the book.

Copyright agreement  The book is protected by copyright. It is a condition of your downloading it that you agree to use it for your own individual private study only. Parts of the book may not otherwise be copied or distributed in any way in whole or in part without the permission of the author. You may reference or quote small sections of the work as long as due acknowledgment is made.

Precedence claims  Publication on the web establishes precedence for any new or original previously unpublished results. Any reference to elements of this work should follow standard journal publication practice.

John Browne,
Sep 3, 2009, 9:50 PM
John Browne,
Sep 3, 2009, 5:00 PM