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Author: J.P. Ward Publisher: Springer Science & Business Media ISBN: 9401157685 Category : Mathematics Languages : en Pages : 252
Book Description
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: J.P. Ward Publisher: Springer Science & Business Media ISBN: 9401157685 Category : Mathematics Languages : en Pages : 252
Book Description
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: Michael E. Taylor Publisher: American Mathematical Soc. ISBN: 1470456702 Category : Education Languages : en Pages : 306
Book Description
This text develops linear algebra with the view that it is an important gateway connecting elementary mathematics to more advanced subjects, such as advanced calculus, systems of differential equations, differential geometry, and group representations. The purpose of this book is to provide a treatment of this subject in sufficient depth to prepare the reader to tackle such further material. The text starts with vector spaces, over the sets of real and complex numbers, and linear transformations between such vector spaces. Later on, this setting is extended to general fields. The reader will be in a position to appreciate the early material on this more general level with minimal effort. Notable features of the text include a treatment of determinants, which is cleaner than one often sees, and a high degree of contact with geometry and analysis, particularly in the chapter on linear algebra on inner product spaces. In addition to studying linear algebra over general fields, the text has a chapter on linear algebra over rings. There is also a chapter on special structures, such as quaternions, Clifford algebras, and octonions.
Author: Kevin McCrimmon Publisher: Springer Science & Business Media ISBN: 0387217967 Category : Mathematics Languages : en Pages : 584
Book Description
This book describes the history of Jordan algebras and describes in full mathematical detail the recent structure theory for Jordan algebras of arbitrary dimension due to Efim Zel'manov. Jordan algebras crop up in many surprising settings, and find application to a variety of mathematical areas. No knowledge is required beyond standard first-year graduate algebra courses.
Author: John H. Conway Publisher: CRC Press ISBN: 1439864187 Category : Mathematics Languages : en Pages : 172
Book Description
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
Author: Nadiya Gubareni Publisher: CRC Press ISBN: 1000209539 Category : Mathematics Languages : en Pages : 363
Book Description
The book provides an introduction to modern abstract algebra and its applications. It covers all major topics of classical theory of numbers, groups, rings, fields and finite dimensional algebras. The book also provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. In particular, it considers algorithm RSA, secret sharing algorithms, Diffie-Hellman Scheme and ElGamal cryptosystem based on discrete logarithm problem. It also presents Buchberger’s algorithm which is one of the important algorithms for constructing Gröbner basis. Key Features: Covers all major topics of classical theory of modern abstract algebra such as groups, rings and fields and their applications. In addition it provides the introduction to the number theory, theory of finite fields, finite dimensional algebras and their applications. Provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. Presents numerous examples illustrating the theory and applications. It is also filled with a number of exercises of various difficulty. Describes in detail the construction of the Cayley-Dickson construction for finite dimensional algebras, in particular, algebras of quaternions and octonions and gives their applications in the number theory and computer graphics.
Author: Nadiya Gubareni Publisher: CRC Press ISBN: 1000209474 Category : Mathematics Languages : en Pages : 395
Book Description
The book provides an introduction to modern abstract algebra and its applications. It covers all major topics of classical theory of numbers, groups, rings, fields and finite dimensional algebras. The book also provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. In particular, it considers algorithm RSA, secret sharing algorithms, Diffie-Hellman Scheme and ElGamal cryptosystem based on discrete logarithm problem. It also presents Buchberger’s algorithm which is one of the important algorithms for constructing Gröbner basis. Key Features: Covers all major topics of classical theory of modern abstract algebra such as groups, rings and fields and their applications. In addition it provides the introduction to the number theory, theory of finite fields, finite dimensional algebras and their applications. Provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. Presents numerous examples illustrating the theory and applications. It is also filled with a number of exercises of various difficulty. Describes in detail the construction of the Cayley-Dickson construction for finite dimensional algebras, in particular, algebras of quaternions and octonions and gives their applications in the number theory and computer graphics.
Author: J.P. Ward
Author: J.P. Ward
Author: Anthony P. Cotroneo
Author: 
Author: 
Author: Michael E. Taylor
Author: Kevin McCrimmon
Author: John H. Conway
Author: T. A. Lamke
Author: Nadiya Gubareni
Author: Nadiya Gubareni