Lectures On Finite Fields And Galois Rings

Author : Zhe-Xian Wan
Publisher : World Scientific
ISBN 13 : 9789812385703
Total Pages : 360 pages
Book Rating : 4.03/5 ( download)

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Download or read book Lectures on Finite Fields and Galois Rings written by Zhe-Xian Wan and published by World Scientific. This book was released on 2003 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Zhexian Wan
Publisher :
ISBN 13 : 9789812795076
Total Pages : pages
Book Rating : 4.73/5 ( download)

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Download or read book Lectures on Finite Fields and Galois Rings written by Zhexian Wan and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Zhe-Xian Wan
Publisher : World Scientific Publishing Company
ISBN 13 : 9813108223
Total Pages : 388 pages
Book Rating : 4.26/5 ( download)

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Download or read book Finite Fields and Galois Rings written by Zhe-Xian Wan and published by World Scientific Publishing Company. This book was released on 2011-09-13 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Errata(s) Errata

Author : Xiang-dong Hou
Publisher : American Mathematical Soc.
ISBN 13 : 1470442892
Total Pages : 240 pages
Book Rating : 4.97/5 ( download)

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Download or read book Lectures on Finite Fields written by Xiang-dong Hou and published by American Mathematical Soc.. This book was released on 2018-06-07 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of finite fields encompasses algebra, combinatorics, and number theory and has furnished widespread applications in other areas of mathematics and computer science. This book is a collection of selected topics in the theory of finite fields and related areas. The topics include basic facts about finite fields, polynomials over finite fields, Gauss sums, algebraic number theory and cyclotomic fields, zeros of polynomials over finite fields, and classical groups over finite fields. The book is mostly self-contained, and the material covered is accessible to readers with the knowledge of graduate algebra; the only exception is a section on function fields. Each chapter is supplied with a set of exercises. The book can be adopted as a text for a second year graduate course or used as a reference by researchers.

Author : Irving Kaplansky
Publisher : University of Chicago Press
ISBN 13 : 0226424510
Total Pages : 217 pages
Book Rating : 4.14/5 ( download)

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Download or read book Fields and Rings written by Irving Kaplansky and published by University of Chicago Press. This book was released on 1972 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Maurice Kibler
Publisher : Elsevier
ISBN 13 : 0081023510
Total Pages : 270 pages
Book Rating : 4.18/5 ( download)

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Download or read book Galois Fields and Galois Rings Made Easy written by Maurice Kibler and published by Elsevier. This book was released on 2017-09-22 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : James A. Davis
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110621738
Total Pages : 214 pages
Book Rating : 4.30/5 ( download)

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Download or read book Finite Fields and their Applications written by James A. Davis and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-10-26 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume covers wide-ranging topics from Theory: structure of finite fields, normal bases, polynomials, function fields, APN functions. Computation: algorithms and complexity, polynomial factorization, decomposition and irreducibility testing, sequences and functions. Applications: algebraic coding theory, cryptography, algebraic geometry over finite fields, finite incidence geometry, designs, combinatorics, quantum information science.

Author : International Conference on Finite Fields and Applications
Publisher : American Mathematical Soc.
ISBN 13 : 0821843095
Total Pages : 278 pages
Book Rating : 4.93/5 ( download)

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Download or read book Finite Fields and Applications written by International Conference on Finite Fields and Applications and published by American Mathematical Soc.. This book was released on 2008 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Eighth International Conference on Finite Fields and Applications, held in Melbourne, Australia, July 9-13, 2007. It contains 5 invited survey papers as well as original research articles covering various theoretical and applied areas related to finite fields.Finite fields, and the computational and algorithmic aspects of finite field problems, continue to grow in importance and interest in the mathematical and computer science communities because of their applications in so many diverse areas. In particular, finite fields now play very important roles in number theory, algebra, and algebraic geometry, as well as in computer science, statistics, and engineering. Areas of application include algebraic coding theory, cryptology, and combinatorialdesign theory.

Author : Minking Eie
Publisher : World Scientific
ISBN 13 : 981427190X
Total Pages : 372 pages
Book Rating : 4.05/5 ( download)

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Download or read book A Course on Abstract Algebra written by Minking Eie and published by World Scientific. This book was released on 2010 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the author's lecture notes at the Department of Mathematics, National Chung Cheng University of Taiwan, it begins with a description of the algebraic structures of the ring and field of rational numbers. Abstract groups are then introduced. Technical results such as Lagrange's Theorem and Sylow's Theorems follow as applications of group theory. Ring theory forms the second part of abstract algebra, with the ring of polynomials and the matrix ring as basic examples. The general theory of ideals as well as maximal ideals in the rings of polynomials over the rational numbers are also discussed. The final part of the book focuses on field theory, field extensions and then Galois theory to illustrate the correspondence between the Galois groups and field extensions. This textbook is more accessible and less ambitious than most existing books covering the same subject. Readers will also find the pedagogical material very useful in enhancing the teaching and learning of abstract algebra.

Author : Bernard R. McDonald
Publisher :
ISBN 13 :
Total Pages : 456 pages
Book Rating : 4.71/5 ( download)

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Download or read book Finite Rings with Identity written by Bernard R. McDonald and published by . This book was released on 1974 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: