From Natural Numbers To Quaternions
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From Natural Numbers To Quaternions
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Author : Jürg Kramer
language : en
Publisher: Springer
Release Date : 2017-11-15
From Natural Numbers To Quaternions written by Jürg Kramer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-15 with Mathematics categories.
This textbook offers an invitation to modern algebra through number systems of increasing complexity, beginning with the natural numbers and culminating with Hamilton's quaternions. Along the way, the authors carefully develop the necessary concepts and methods from abstract algebra: monoids, groups, rings, fields, and skew fields. Each chapter ends with an appendix discussing related topics from algebra and number theory, including recent developments reflecting the relevance of the material to current research. The present volume is intended for undergraduate courses in abstract algebra or elementary number theory. The inclusion of exercises with solutions also makes it suitable for self-study and accessible to anyone with an interest in modern algebra and number theory.
The Concept Of Number
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Author : Benno Artmann
language : en
Publisher:
Release Date : 1988
The Concept Of Number written by Benno Artmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Quaternions For Computer Graphics
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Author : John Vince
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-11
Quaternions For Computer Graphics written by John Vince 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 2011-06-11 with Computers categories.
Sir William Rowan Hamilton was a genius, and will be remembered for his significant contributions to physics and mathematics. The Hamiltonian, which is used in quantum physics to describe the total energy of a system, would have been a major achievement for anyone, but Hamilton also invented quaternions, which paved the way for modern vector analysis. Quaternions are one of the most documented inventions in the history of mathematics, and this book is about their invention, and how they are used to rotate vectors about an arbitrary axis. Apart from introducing the reader to the features of quaternions and their associated algebra, the book provides valuable historical facts that bring the subject alive. Quaternions for Computer Graphics introduces the reader to quaternion algebra by describing concepts of sets, groups, fields and rings. It also includes chapters on imaginary quantities, complex numbers and the complex plane, which are essential to understanding quaternions. The book contains many illustrations and worked examples, which make it essential reading for students, academics, researchers and professional practitioners.
Real Quaternionic Calculus Handbook
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Author : João Pedro Morais
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-08
Real Quaternionic Calculus Handbook written by João Pedro Morais 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 2014-01-08 with Mathematics categories.
Real quaternion analysis is a multi-faceted subject. Created to describe phenomena in special relativity, electrodynamics, spin etc., it has developed into a body of material that interacts with many branches of mathematics, such as complex analysis, harmonic analysis, differential geometry, and differential equations. It is also a ubiquitous factor in the description and elucidation of problems in mathematical physics. In the meantime real quaternion analysis has become a well established branch in mathematics and has been greatly successful in many different directions. This book is based on concrete examples and exercises rather than general theorems, thus making it suitable for an introductory one- or two-semester undergraduate course on some of the major aspects of real quaternion analysis in exercises. Alternatively, it may be used for beginning graduate level courses and as a reference work. With exercises at the end of each chapter and its straightforward writing style the book addresses readers who have no prior knowledge on this subject but have a basic background in graduate mathematics courses, such as real and complex analysis, ordinary differential equations, partial differential equations, and theory of distributions.
Utility Of Quaternions In Physics
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Author : Alexander McAulay
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2017-06-18
Utility Of Quaternions In Physics written by Alexander McAulay and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-18 with categories.
In math, the quaternions are a number method that extends the complex numbers. They were originally described by the mathematician William Rowan Hamilton and applied to mechanics in space (3D). Quaternions characteristics are that multiplication of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two lines in 3D (the quotient of two vectors). Quaternions find uses in theoretical and applied mathematics, in particular for calculations involving 3D rotations such as in computer graphics, computer vision, and crystallographic texture analysis. In useful applications, they find use alongside other methods, like Euler angles and rotation matrices, depending on the application. In contemporary mathematical language, quaternions form a 4D associative normed division algebra over the real numbers, and consequently also a domain. In fact, the quaternions were the elementary noncommutative division algebra to be discovered. According to the Frobenius theorem, it is one of only two finite-dimensional dividing rings containing the real numbers as a proper subring, and the other being the complex numbers. These rings are also Euclidean Hurwitz algebras, of whichever quaternions are the largest associative algebra.
A Primer Of Quaternions
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Author : Arthur Stafford Hathaway
language : en
Publisher:
Release Date : 1896
A Primer Of Quaternions written by Arthur Stafford Hathaway and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1896 with History categories.
A Primer of Quaternions by Arthur Hathaway Stafford, first published in 1896, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it.
Numbers
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Author : Heinz-Dieter Ebbinghaus
language : en
Publisher: Springer Science & Business Media
Release Date : 1991
Numbers written by Heinz-Dieter Ebbinghaus 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 1991 with Mathematics categories.
This book is about all kinds of numbers, from rationals to octonians, reals to infinitesimals. It is a story about a major thread of mathematics over thousands of years, and it answers everything from why Hamilton was obsessed with quaternions to what the prospect was for quaternionic analysis in the 19th century. It glimpses the mystery surrounding imaginary numbers in the 17th century and views some major developments of the 20th century.
Introduction To Quaternions
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Author : Philip Kelland
language : en
Publisher:
Release Date : 1882
Introduction To Quaternions written by Philip Kelland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1882 with Quaternions categories.
Visualizing Quaternions
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Author : Andrew J. Hanson
language : en
Publisher: Elsevier
Release Date : 2006-02-06
Visualizing Quaternions written by Andrew J. Hanson and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-06 with Mathematics categories.
Introduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available. The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important—a beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions. Richly illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing. Covers both non-mathematical and mathematical approaches to quaternions.
On Quaternions And Octonions
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Author : John H. Conway
language : en
Publisher: CRC Press
Release Date : 2003-01-23
On Quaternions And Octonions written by John H. Conway and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-23 with Mathematics categories.
This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less f