Overview
- Includes chapter-by-chapter exercises
- Provides a rare undergraduate-level approach to the subject matter
- Promotes the application of Clifford algebra to differential geometry
- Presents a significant portion of general relativity without reference to such Newtonian terms as "force", "momentum", or "energy"
- Only up-to-date title of its kind
- Includes supplementary material: sn.pub/extras
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (12 chapters)
-
Front Matter
-
Back Matter
Keywords
About this book
Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space.
Â
Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, Â beginning-level graduate students, and researchers in the algebra and physics communities.
Â
Reviews
From the reviews:
“The book is written in a very pedagogical style and seems to be the mirror of the original ideas of its author in the area of mathematical physics. … The typography is excellent and the figures are beautiful. … Graduate and advanced undergraduate students in physics and even in mathematics will find in this book an understanding of the contribution of Clifford algebras to the field of differential geometry as well as motivation to continue their study.” (Pierre Anglès, Mathematical Reviews, March, 2014)
“The book under review is perfectly organized textbook for undergraduate students in mathematics and physics due to the large experience of the author. … The author provides quite interesting historical analysis … . This book is a natural continuation of the previous book of the author … .” (Milen Hristov, JGSP Journal of Geometry and Symmetry in Physics, Vol. 33, 2014)
“The author develops the differential geometry of curves and surfaces by using Clifford’s geometric algebra. … The book is enriched with several very interesting and extensive historical and biographical presentations. … it can serve as an accompanying source for someone who studies differential geometry, or for someone who wants to look at known facts from a different viewpoint. Also, it is ideal for studying geometry through historical development, and thus this book could also be useful for reading courses on certain aspects of geometry.” (A. Arvanitoyeorgos, Zentralblatt MATH, Vol. 1232, 2012)
Authors and Affiliations
Bibliographic Information
Book Title: A New Approach to Differential Geometry using Clifford's Geometric Algebra
Authors: John Snygg
DOI: https://doi.org/10.1007/978-0-8176-8283-5
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2012
Hardcover ISBN: 978-0-8176-8282-8Published: 08 December 2011
eBook ISBN: 978-0-8176-8283-5Published: 09 December 2011
Edition Number: 1
Number of Pages: XVII, 465
Number of Illustrations: 102 b/w illustrations
Topics: Differential Geometry, Mathematical Methods in Physics, Mathematical Physics, Mathematics, general, Algebra, Applications of Mathematics