A New Approach To Differential Geometry Using Clifford S Geometric Algebra
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A New Approach To Differential Geometry Using Clifford S Geometric Algebra
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Author : John Snygg
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-09
A New Approach To Differential Geometry Using Clifford S Geometric Algebra written by John Snygg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-09 with Mathematics categories.
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. 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, beginning-level graduate students, and researchers in the algebra and physics communities.
A New Approach To Differential Geometry Using Clifford S Geometric Algebra
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Author :
language : en
Publisher:
Release Date : 2011-12-01
A New Approach To Differential Geometry Using Clifford S Geometric Algebra written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-01 with categories.
Clifford Algebra To Geometric Calculus
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Author : David Hestenes
language : en
Publisher: Springer Science & Business Media
Release Date : 1984
Clifford Algebra To Geometric Calculus written by David Hestenes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.
Real Spinorial Groups
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Author : Sebastià Xambó-Descamps
language : en
Publisher: Springer
Release Date : 2018-11-22
Real Spinorial Groups written by Sebastià Xambó-Descamps and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-22 with Mathematics categories.
This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry. After a concise mathematical introduction, it offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions), it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. Lastly, the book provides pointers to major applications, an extensive bibliography and an alphabetic index. Combining the characteristics of a self-contained research monograph and a state-of-the-art survey, this book is a valuable foundation reference resource on applications for both undergraduate and graduate students.
Topological And Statistical Methods For Complex Data
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Author : Janine Bennett
language : en
Publisher: Springer
Release Date : 2014-11-19
Topological And Statistical Methods For Complex Data written by Janine Bennett and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-19 with Mathematics categories.
This book contains papers presented at the Workshop on the Analysis of Large-scale, High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013. It features the work of some of the most prominent and recognized leaders in the field who examine challenges as well as detail solutions to the analysis of extreme scale data. The book presents new methods that leverage the mutual strengths of both topological and statistical techniques to support the management, analysis, and visualization of complex data. It covers both theory and application and provides readers with an overview of important key concepts and the latest research trends. Coverage in the book includes multi-variate and/or high-dimensional analysis techniques, feature-based statistical methods, combinatorial algorithms, scalable statistics algorithms, scalar and vector field topology, and multi-scale representations. In addition, the book details algorithms that are broadly applicable and can be used by application scientists to glean insight from a wide range of complex data sets.
The Renaissance Of General Relativity In Context
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Author : Alexander S. Blum
language : en
Publisher: Springer Nature
Release Date : 2020-11-12
The Renaissance Of General Relativity In Context written by Alexander S. Blum and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-12 with Mathematics categories.
This contributed volume explores the renaissance of general relativity after World War II, when it transformed from a marginal theory into a cornerstone of modern physics. Chapters explore key historical processes related to the theory of general relativity, in addition to presenting a thorough treatment of the relevant science behind these episodes. A broad historiographical framework is introduced first, thus providing the broad context in which the given computational approaches and case studies occurred. Written by an international and interdisciplinary group of expert authors, these chapters will bring readers to a more complete understanding of Einstein’s theory. Specific topics include: Social and citation networks The Fock-Infeld dispute Wheeler’s turn to gravitation theory The position of general relativity in theories of fundamental interactions The pursuit of a quantum theory of gravity The emergence of dark matter in relation to cosmological models Institutional frameworks for gravitational wave search in Europe The Renaissance of General Relativity in Context is ideal for historians, philosophers, and sociologists of science. Students and researchers in physics will also be interested in the topics explored.
Geometric Algebra For Computer Science
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Author : Leo Dorst
language : en
Publisher: Elsevier
Release Date : 2010-07-26
Geometric Algebra For Computer Science written by Leo Dorst and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-26 with Computers categories.
Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhancing way to represent the geometry of 3D objects in computer programs. In this book you will find an introduction to GA that will give you a strong grasp of its relationship to linear algebra and its significance for your work. You will learn how to use GA to represent objects and perform geometric operations on them. And you will begin mastering proven techniques for making GA an integral part of your applications in a way that simplifies your code without slowing it down. * The first book on Geometric Algebra for programmers in computer graphics and entertainment computing* Written by leaders in the field providing essential information on this new technique for 3D graphics* This full colour book includes a website with GAViewer, a program to experiment with GA
A Student S Guide To General Relativity
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Author : Norman Gray
language : en
Publisher: Cambridge University Press
Release Date : 2019-01-03
A Student S Guide To General Relativity written by Norman Gray and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-03 with Science categories.
Vectors, tensors and functions -- Manifolds, vectors and differentiation -- Energy, momentum and Einstein's equations
A Crack In Everything
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Author : Marcus Chown
language : en
Publisher: Bloomsbury Publishing
Release Date : 2024-06-06
A Crack In Everything written by Marcus Chown and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-06 with Science categories.
What is space? What is time? Where did the universe come from? The answers to mankind's most enduring questions may lie in science's greatest enigma: black holes. A black hole is a region of space where gravity is so strong that nothing, not even light, can escape. This can occur when a star approaches the end of its life. Unable to generate enough heat to maintain its outer layers, it shrinks catastrophically down to an infinitely dense point. When this phenomenon was first proposed in 1916, it defied scientific understanding so much that Albert Einstein dismissed it as too ridiculous to be true. But scientists have since proven otherwise. In 1971, Paul Murdin and Louise Webster discovered the first black hole: Cygnus X-1. Later, in the 1990s, astronomers using NASA's Hubble Space Telescope found that not only do black holes exist, supermassive black holes lie at the heart of almost every galaxy, including our own. It would take another three decades to confirm this phenomenon. On 10 April 2019, a team of astronomers made history by producing the first image of a black hole. A Crack in Everything is the story of how black holes came in from the cold and took cosmic centre stage. As a journalist, Marcus Chown interviews many of the scientists who made the key discoveries, and, as a former physicist, he translates the most esoteric of science into everyday language. The result is a uniquely engaging page-turner that tells one of the great untold stories in modern science.
Geometric Algebra For Physicists
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Author : Chris Doran
language : en
Publisher: Cambridge University Press
Release Date : 2007-11-22
Geometric Algebra For Physicists written by Chris Doran and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-22 with Science categories.
Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with early chapters providing a self-contained introduction to geometric algebra. Topics covered include new techniques for handling rotations in arbitrary dimensions, and the links between rotations, bivectors and the structure of the Lie groups. Following chapters extend the concept of a complex analytic function theory to arbitrary dimensions, with applications in quantum theory and electromagnetism. Later chapters cover advanced topics such as non-Euclidean geometry, quantum entanglement, and gauge theories. Applications such as black holes and cosmic strings are also explored. It can be used as a graduate text for courses on the physical applications of geometric algebra and is also suitable for researchers working in the fields of relativity and quantum theory.