New Foundations in Mathematics The Geometric Concept of Number /

• Main Author: Sobczyk, Garret (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston : Birkhäuser Boston : Imprint: Birkhäuser, 2013.
• Subjects: Mathematics.; Algebra.; Group theory.; Matrix theory.; Topological groups.; Lie groups.; Physics.; Applied mathematics.; Engineering mathematics.; Linear and Multilinear Algebras, Matrix Theory.; Topological Groups, Lie Groups.; Group Theory and Generalizations.; Mathematical Methods in Physics.; Appl.Mathematics/Computational Methods of Engineering.

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,...

Table of Contents:

• 1 Modular Number Systems
• 2 Complex and Hyperbolic Numbers
• 3 Geometric Algebra
• 4 Vector Spaces and Matrices
• 5 Outer Product and Determinants
• 6 Systems of Linear Equations
• 7 Linear Transformations on R^n
• 8 Structure of a Linear Operator
• 9 Linear and Bilinear Forms
• 10 Hermitian Inner Product Spaces
• 11 Geometry of Moving Planes
• 12 Representations of the Symmetric Group
• 13 Calculus on m-Surfaces
• 14 Differential Geometry of Curves
• 15 Differential Geometry of k-Surfaces
• 16 Mappings Between Surfaces
• 17 Non-Euclidean and Projective Geometries
• 18 Lie Groups and Lie Algebras
• References
• Symbols.