Lectures on Finite Fields and Galois Rings PDF Download
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Author: Zhe-Xian Wan
Publisher: World Scientific
ISBN: 9789812385703
Category : Mathematics
Languages : en
Pages : 360
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Book Description
This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.
Author: Zhe-Xian Wan
Publisher: World Scientific
ISBN: 9789812385703
Category : Mathematics
Languages : en
Pages : 360
Get Book Here
Book Description
This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.
Author: Zhe-xian Wan
Publisher: World Scientific Publishing Company
ISBN: 9813102268
Category : Mathematics
Languages : en
Pages : 354
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Book Description
This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.
Author: Zhe-xian Wan
Publisher: World Scientific Publishing Company
ISBN: 9813108223
Category : Mathematics
Languages : en
Pages : 387
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Book Description
A large portion of the book can be used as a textbook for graduate and upper level undergraduate students in mathematics, communication engineering, computer science and other fields. The remaining part can be used as references for specialists. Explicit construction and computation of finite fields are emphasized. In particular, the construction of irreducible polynomials and normal basis of finite field is included. A detailed treatment of optimal normal basis and Galoi's rings is included. It is the first time that the galois rings are in book form.
Author: Maurice Kibler
Publisher: Elsevier
ISBN: 0081023510
Category : Mathematics
Languages : en
Pages : 272
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Book Description
This book constitutes an elementary introduction to rings and fields, in particular Galois rings and Galois fields, with regard to their application to the theory of quantum information, a field at the crossroads of quantum physics, discrete mathematics and informatics. The existing literature on rings and fields is primarily mathematical. There are a great number of excellent books on the theory of rings and fields written by and for mathematicians, but these can be difficult for physicists and chemists to access. This book offers an introduction to rings and fields with numerous examples. It contains an application to the construction of mutually unbiased bases of pivotal importance in quantum information. It is intended for graduate and undergraduate students and researchers in physics, mathematical physics and quantum chemistry (especially in the domains of advanced quantum mechanics, quantum optics, quantum information theory, classical and quantum computing, and computer engineering). Although the book is not written for mathematicians, given the large number of examples discussed, it may also be of interest to undergraduate students in mathematics. Contains numerous examples that accompany the text Includes an important chapter on mutually unbiased bases Helps physicists and theoretical chemists understand this area of mathematics
Author: Zhexian Wan
Publisher:
ISBN: 9789812795076
Category :
Languages : en
Pages :
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Book Description
Author: Rudolf Lidl
Publisher: Cambridge University Press
ISBN: 9780521392310
Category : Mathematics
Languages : en
Pages : 784
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Book Description
This book is devoted entirely to the theory of finite fields.
Author: John M. Howie
Publisher: Springer Science & Business Media
ISBN: 1852339861
Category : Mathematics
Languages : en
Pages : 230
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Book Description
A modern and student-friendly introduction to this popular subject: it takes a more "natural" approach and develops the theory at a gentle pace with an emphasis on clear explanations Features plenty of worked examples and exercises, complete with full solutions, to encourage independent study Previous books by Howie in the SUMS series have attracted excellent reviews
Author: Juliusz Brzeziński
Publisher: Springer
ISBN: 331972326X
Category : Mathematics
Languages : en
Pages : 296
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Book Description
This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading. A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study.
Author: Irving Kaplansky
Publisher: University of Chicago Press
ISBN: 0226424510
Category : Mathematics
Languages : en
Pages : 217
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Book Description
This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules. "In all three parts of this book the author lives up to his reputation as a first-rate mathematical stylist. Throughout the work the clarity and precision of the presentation is not only a source of constant pleasure but will enable the neophyte to master the material here presented with dispatch and ease."—A. Rosenberg, Mathematical Reviews
Author: James A. Davis
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110622173
Category : Mathematics
Languages : en
Pages : 243
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Book Description
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
