Hurwitz S Lectures On The Number Theory Of Quaternions
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Hurwitz S Lectures On The Number Theory Of Quaternions
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Author : Nicola Oswald
language : en
Publisher: European Mathematical Society
Release Date : 2023-05-15
Hurwitz S Lectures On The Number Theory Of Quaternions written by Nicola Oswald and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-15 with Mathematics categories.
Quaternions are non-commutative generalizations of the complex numbers, invented by William Rowan Hamilton in 1843. Their number-theoretical aspects were first investigated by Rudolf Lipschitz in the 1880s, and, in a streamlined form, by Adolf Hurwitz in 1896. This book contains an English translation of Hurwitz's 1919 textbook on this topic as well as his famous 1-2-3-4 theorem on composition algebras. In addition, the reader can find commentaries that shed historical light on the development of this number theory of quaternions, for example, the classical preparatory works of Fermat, Euler, Lagrange and Gauss, to name but a few, the different notions of quaternion integers in the works of Lipschitz and Hurwitz, analogies to the theory of algebraic numbers, and the further development (including Dickson's work in particular). The authors have implemented parts of the book in stand-alone courses, and they believe that the present book can also complement a course on algebraic number theory (with respect to a noncommutative extension of the rational numbers).
Hurwitz S Lectures On The Number Theory Of Quaternions
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Author : Nicola Oswald
language : en
Publisher:
Release Date : 2023
Hurwitz S Lectures On The Number Theory Of Quaternions written by Nicola Oswald and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.
Lectures On The Number Theory Of Quaternions
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Author : Adolf Hurwitz
language : en
Publisher:
Release Date : 1994
Lectures On The Number Theory Of Quaternions written by Adolf Hurwitz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Number theory categories.
Quaternion Algebras
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Author : John Voight
language : en
Publisher: Springer Nature
Release Date : 2021-06-28
Quaternion Algebras written by John Voight and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-28 with Mathematics categories.
This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.
Number Theory Of Quaternions
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Author : Thomas A. Matthews
language : en
Publisher:
Release Date : 1964
Number Theory Of Quaternions written by Thomas A. Matthews and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Quaternions categories.
A Primer Of Quaternions
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Author : Arthur S Hathaway
language : en
Publisher: Independently Published
Release Date : 2019-05-03
A Primer Of Quaternions written by Arthur S Hathaway and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-03 with categories.
The Theory of Quaternions is due to Sir William Rowan Hamilton, Royal Astronomer of Ireland, who presented his first paper on the subject to the Royal Irish Academy in 1843. His Lectures on Quaternions were published in 1853, and his Elements, in 1866, shortly after his death. "The Elements of Quaternions" by Tait is the accepted text-book for advanced students.The following development of the theory is prepared for average students with a thorough knowledge of the elements of algebra and geometry, and is believed to be a simple and elementary treatment founded directly upon the fundamental ideas of the subject. This theory is applied in the more advanced examples to develop the principal formulas of trigonometry and solid analytical geometry, and the general properties and classification of surfaces of second order.In the endeavour to bring out the number idea of Quaternions, and at the same time retain the established nomenclature of the analysis, I have found it necessary to abandon the term "vector" for a directed length. I adopt instead Clifford's suggestive name of "step," leaving to "vector" the sole meaning of "right quaternion." This brings out clearly the relations of this number and line, and emphasizes the fact that Quaternions is a natural extension of our fundamental ideas of number, that is subject to ordinary principles of geometric representation, rather than an artificial species of geometrical algebra.The physical conceptions and the breadth of idea that the subject of Quaternions will develop are, of themselves, sufficient reward for its study. At the same time, the power, directness, and simplicity of its analysis cannot fail to prove useful in all physical and geometrical investigations, to those who have thoroughly grasped its principles....
Fundamental Number Theory With Applications
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Author : Richard A. Mollin
language : en
Publisher: CRC Press
Release Date : 2008-02-21
Fundamental Number Theory With Applications written by Richard A. Mollin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-21 with Mathematics categories.
An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition • Removal of all advanced material to be even more accessible in scope • New fundamental material, including partition theory, generating functions, and combinatorial number theory • Expanded coverage of random number generation, Diophantine analysis, and additive number theory • More applications to cryptography, primality testing, and factoring • An appendix on the recently discovered unconditional deterministic polynomial-time algorithm for primality testing Taking a truly elementary approach to number theory, this text supplies the essential material for a first course on the subject. Placed in highlighted boxes to reduce distraction from the main text, nearly 70 biographies focus on major contributors to the field. The presentation of over 1,300 entries in the index maximizes cross-referencing so students can find data with ease.
Modular Forms And Related Topics In Number Theory
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Author : B. Ramakrishnan
language : en
Publisher: Springer Nature
Release Date : 2020-11-24
Modular Forms And Related Topics In Number Theory written by B. Ramakrishnan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-24 with Mathematics categories.
This book collects the papers presented at the Conference on Number Theory, held at the Kerala School of Mathematics, Kozhikode, Kerala, India, from December 10–14, 2018. The conference aimed at bringing the active number theorists and researchers in automorphic forms and allied areas to demonstrate their current research works. This book benefits young research scholars, postdoctoral fellows, and young faculty members working in these areas of research.
Number Theory
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Author : W.A. Coppel
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-03
Number Theory written by W.A. Coppel 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 2009-10-03 with Mathematics categories.
Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study.
International Symposium On Mathematics Quantum Theory And Cryptography
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Author : Tsuyoshi Takagi
language : en
Publisher: Springer Nature
Release Date : 2020-10-22
International Symposium On Mathematics Quantum Theory And Cryptography written by Tsuyoshi Takagi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-22 with Technology & Engineering categories.
This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography.