Lectures On The Number Theory Of Quaternions PDF Download
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Author | : Nicola Oswald |
Publisher | : European Mathematical Society |
Total Pages | : 0 |
Release | : 2023-05-15 |
Genre | : Mathematics |
ISBN | : 3985470111 |
Download Hurwitz’s Lectures on the Number Theory of Quaternions Book in PDF, ePub and Kindle
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).
Author | : Nicola Oswald |
Publisher | : |
Total Pages | : 0 |
Release | : 2023 |
Genre | : |
ISBN | : 9783985475117 |
Download Hurwitz's Lectures on the Number Theory of Quaternions Book in PDF, ePub and Kindle
Author | : Adolf Hurwitz |
Publisher | : |
Total Pages | : 62 |
Release | : 1994 |
Genre | : Number theory |
ISBN | : |
Download Lectures on the Number Theory of Quaternions Book in PDF, ePub and Kindle
Author | : Ron Goldman |
Publisher | : Morgan & Claypool Publishers |
Total Pages | : 177 |
Release | : 2010 |
Genre | : Computers |
ISBN | : 1608454207 |
Download Rethinking Quaternions Book in PDF, ePub and Kindle
In addition to these theoretical issues, we also address some computational questions. We develop straightforward formulas for converting back and forth between quaternion and matrix representations for rotations, reflections, and perspective projections, and we discuss the relative advantages and disadvantages of the quaternion and matrix representations for these transformations. Moreover, we show how to avoid distortions due to floating point computations with rotations by using unit quaternions to represent rotations. We also derive the formula for spherical linear interpolation, and we explain how to apply this formula to interpolate between two rotations for key frame animation. Finally, we explain the role of quaternions in low-dimensional Clifford algebras, and we show how to apply the Clifford algebra for R3 to model rotations, reflections, and perspective projections. To help the reader understand the concepts and formulas presented here, we have incorporated many exercises in order to clarify and elaborate some of the key points in the text."--P. 4 of cover.
Author | : Arthur S. Hathaway |
Publisher | : Prabhat Prakashan |
Total Pages | : 77 |
Release | : 1896-01-01 |
Genre | : Mathematics |
ISBN | : |
Download A Primer of Quaternions Book in PDF, ePub and Kindle
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.
Author | : Sir William Rowan Hamilton |
Publisher | : |
Total Pages | : 886 |
Release | : 1853 |
Genre | : Quaternions |
ISBN | : |
Download Lectures on Quaternions Book in PDF, ePub and Kindle
Author | : J.P. Ward |
Publisher | : Springer Science & Business Media |
Total Pages | : 256 |
Release | : 1997-04-30 |
Genre | : Mathematics |
ISBN | : 9780792345138 |
Download Quaternions and Cayley Numbers Book in PDF, ePub and Kindle
In essence, this text is written as a challenge to others, to discover significant uses for Cayley number algebra in physics. I freely admit that though the reading of some sections would benefit from previous experience of certain topics in physics - particularly relativity and electromagnetism - generally the mathematics is not sophisticated. In fact, the mathematically sophisticated reader, may well find that in many places, the rather deliberate progress too slow for their liking. This text had its origin in a 90-minute lecture on complex numbers given by the author to prospective university students in 1994. In my attempt to develop a novel approach to the subject matter I looked at complex numbers from an entirely geometric perspective and, no doubt in line with innumerable other mathematicians, re-traced steps first taken by Hamilton and others in the early years of the nineteenth century. I even enquired into the possibility of using an alternative multiplication rule for complex numbers (in which argzlz2 = argzl- argz2) other than the one which is normally accepted (argzlz2 = argzl + argz2). Of course, my alternative was rejected because it didn't lead to a 'product' which had properties that we now accept as fundamental (i. e.
Author | : Jürg Kramer |
Publisher | : Springer |
Total Pages | : 288 |
Release | : 2017-11-15 |
Genre | : Mathematics |
ISBN | : 3319694294 |
Download From Natural Numbers to Quaternions Book in PDF, ePub and Kindle
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.
Author | : Arthur Lefevre |
Publisher | : |
Total Pages | : 242 |
Release | : 1896 |
Genre | : Algebra |
ISBN | : |
Download Number and Its Algebra Book in PDF, ePub and Kindle
Author | : Sir William Rowan Hamilton |
Publisher | : |
Total Pages | : 882 |
Release | : 1853 |
Genre | : |
ISBN | : |
Download Lectures on Quaternions: Containing a Systematic Statement of a New Mathematical Method; ... with Numerous Illustrative Diagrams, and ... Geometrical and Physical Applications Book in PDF, ePub and Kindle