New Foundations in Mathematics
The Geometric Concept of Number
Authors: Sobczyk, Garret
Free Preview Geometric algebra, the central topic of the book, provides a unique way to unify, streamline, and simplify teaching and applying many different areas of mathematics
 Presents and casts new light on an impressively broad range of math from elementary level
 Features many exercises and problems to enhance the reader's skills and understanding
 Topics and applications selected to encourage further, more specific research by both graduates and undergraduates
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 About this Textbook

The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner.
New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.
 Reviews

From the book reviews:
“This book is suitable for graduate students and researchers interested in learning how W. K. Clifford’s geometric algebras provide a common, geometrically wellinterpreted algebraic language for linear algebra, vector calculus, linear operators, forms, relativity, symmetry, differential geometry, nonEuclidean and projective geometry as well as Lie algebras. Every section is followed by an appropriate set of exercises, deepening and consolidating the section’s content.” (Eckhard M. S. Hitzer, Mathematical Reviews, July, 2014)
 Table of contents (18 chapters)


Modular Number Systems
Pages 121

Complex and Hyperbolic Numbers
Pages 2342

Geometric Algebra
Pages 4366

Vector Spaces and Matrices
Pages 6783

Outer Product and Determinants
Pages 8593

Table of contents (18 chapters)
 Download Preface 1 PDF (66.4 KB)
 Download Sample pages 1 PDF (504.2 KB)
 Download Table of contents PDF (117.1 KB)
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Bibliographic Information
 Bibliographic Information

 Book Title
 New Foundations in Mathematics
 Book Subtitle
 The Geometric Concept of Number
 Authors

 Garret Sobczyk
 Copyright
 2013
 Publisher
 Birkhäuser Basel
 Copyright Holder
 Springer Science+Business Media New York
 eBook ISBN
 9780817683856
 DOI
 10.1007/9780817683856
 Hardcover ISBN
 9780817683849
 Edition Number
 1
 Number of Pages
 XIV, 370
 Number of Illustrations
 23 b/w illustrations, 32 illustrations in colour
 Topics