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New Foundations in Mathematics: The Geometric Concept of Number Hardcover – October 28, 2012

ISBN-13: 978-0817683849 ISBN-10: 0817683844 Edition: 2013th

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New Foundations in Mathematics: The Geometric Concept of Number + Grassmann Algebra Volume 1: Foundations: Exploring extended vector algebra with Mathematica + Vector and Geometric Calculus
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Product Details

  • Hardcover: 370 pages
  • Publisher: Birkhäuser; 2013 edition (October 28, 2012)
  • Language: English
  • ISBN-10: 0817683844
  • ISBN-13: 978-0817683849
  • Product Dimensions: 9.1 x 5.9 x 1.2 inches
  • Shipping Weight: 1.4 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #1,432,924 in Books (See Top 100 in Books)

Editorial Reviews

From the Back Cover

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.

The book begins with a discussion of modular numbers (clock arithmetic) and modular polynomials. This leads to the idea of a spectral basis, the complex and hyperbolic numbers, and finally to geometric algebra, which lays the groundwork for the remainder of the text. Many topics are presented in a new
light, including:

* vector spaces and matrices;
* structure of linear operators and quadratic forms;
* Hermitian inner product spaces;
* geometry of moving planes;
* spacetime of special relativity;
* classical integration theorems;
* differential geometry of curves and smooth surfaces;
* projective geometry;
* Lie groups and Lie algebras.

Exercises with selected solutions are provided, and chapter summaries are included to reinforce concepts as they are covered. Links to relevant websites are often given, and supplementary material is available on the author’s website.
 
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.

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Most Helpful Customer Reviews

By DN on May 21, 2014
Format: Hardcover Verified Purchase
I enjoyed and am glad I purchased this book, the second of Dr. Sobczyk's that I own since I bought his "Clifford Algebra to Geometric Calculus". The sections on spectral bases alone make it worth reading.
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