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Lectures on Clifford Geometric Algebrasby Rafal Ablamowicz
Synopses & Reviews
The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts underlying the mathematical theories of linear and multilinear algebra, projective and affine geometries, and differential geometry. This bird's-eye view of Clifford (geometric) algebras and their applications is presented by six of the world's leading experts in the field.
Key topics and features of this systematic exposition:
* An Introductory chapter on Clifford Algebras by Pertti Lounesto* Ian Porteous (Chapter 2) reveals the mathematical structure of Clifford algebras in terms of the classical groups* John Ryan (Chapter 3) introduces the basic concepts of Clifford analysis, which extends the well-known complex analysis of the plane to three and higher dimensions* William Baylis (Chapter 4) investigates some of the extensive applications that have been made in mathematical physics, including the basic ideas of electromagnetism and special relativity* John Selig (Chapter 5) explores the successes that Clifford algebras, especially quaternions and bi-quaternions, have found in computer vision and robotics* Tom Branson (Chapter 6) discusses some of the deepest results that Clifford algebras have made possible in our understanding of differential geometry
* Editors (Appendix) give an extensive review of various software packages for computations with Clifford algebras including standalone programs, on-line calculators, special purpose numeric software, and symbolic add-ons to computer algebra systems
This text will serve beginning graduate students and researchers in diverse areas---mathematics, physics, computer science and engineering; it will be useful both for newcomers who have little prior knowledge of the subject and established professionals who wish to keep abreast of the latest applications.
This text, written by established mathematicians and physicists, provides a systematic, unified exposition of Clifford (geometric) algebras. Beginning with an introductory chapter, the book covers the mathematical structure of Clifford algebras and the basic concepts of Clifford analysis, and then provides a detailed examination of the many applications of Clifford algebras to differential geometry, physics, computer vision and robotics. No prior knowledge of the subject is assumed. The book 's breadth will appeal to graduate students and researchers in mathematics, physics, and engineering.Contents: P. Lounesto, Introduction to Clifford Algebras; I. Porteous, Mathematical Structure of Clifford Algebras; J. Ryan, Clifford Analysis; W. Baylis, Applications of Clifford Algebras in Physics; J. Selig, Clifford Algebras in Engineering; T. Branson, Clifford Bundles and Clifford Algebras; R. Ablamowicz and G. Sobczyk, Appendix: Software for Clifford (Geometric) Algebras
The subject of Clifford (geometric) algebras offers a unified algebraic framework for the direct expression of the geometric concepts in algebra, geometry, and physics. This bird's-eye view of the discipline is presented by six of the world's leading experts in the field; it features an introductory chapter on Clifford algebras, followed by extensive explorations of their applications to physics, computer science, and differential geometry. The book is ideal for graduate students in mathematics, physics, and computer science; it is appropriate both for newcomers who have little prior knowledge of the field and professionals who wish to keep abreast of the latest applications.
Table of Contents
Preface (Rafal Ablamowicz and Garrett Sobczyk) * Lecture 1: Introduction to Clifford Algebras (Pertti Lounesto) * Lecture 2: Mathematical Structure of Clifford Algebras (Ian Porteous) * Lecture 3: Clifford Analysis (John Ryan) * Lecture 4: Applications of Clifford Algebras in Physics (William E. Baylis) * Lecture 5: Clifford Algebras in Engineering (J.M. Selig) * Lecture 6: Clifford Bundles and Clifford Algebras (Thomas Branson) * Appendix (Rafal Ablamowicz and Garrett Sobczyk) * Index
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