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]
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