Galois Fields And Galois Rings Made Easy

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 : Frank H.P. Fitzek
Publisher : Academic Press
ISBN 13 : 0128209046
Total Pages : 524 pages
Book Rating : 4.42/5 ( download)

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Download or read book Computing in Communication Networks written by Frank H.P. Fitzek and published by Academic Press. This book was released on 2020-05-20 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computing in Communication Networks: From Theory to Practice provides comprehensive details and practical implementation tactics on the novel concepts and enabling technologies at the core of the paradigm shift from store and forward (dumb) to compute and forward (intelligent) in future communication networks and systems. The book explains how to create virtualized large scale testbeds using well-established open source software, such as Mininet and Docker. It shows how and where to place disruptive techniques, such as machine learning, compressed sensing, or network coding in a newly built testbed. In addition, it presents a comprehensive overview of current standardization activities. Specific chapters explore upcoming communication networks that support verticals in transportation, industry, construction, agriculture, health care and energy grids, underlying concepts, such as network slicing and mobile edge cloud, enabling technologies, such as SDN/NFV/ ICN, disruptive innovations, such as network coding, compressed sensing and machine learning, how to build a virtualized network infrastructure testbed on one’s own computer, and more. Provides a uniquely comprehensive overview on the individual building blocks that comprise the concept of computing in future networks Gives practical hands-on activities to bridge theory and implementation Includes software and examples that are not only employed throughout the book, but also hosted on a dedicated website

Author : Patrick Morandi
Publisher : Springer Science & Business Media
ISBN 13 : 1461240409
Total Pages : 294 pages
Book Rating : 4.02/5 ( download)

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Download or read book Field and Galois Theory written by Patrick Morandi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the fall of 1990, I taught Math 581 at New Mexico State University for the first time. This course on field theory is the first semester of the year-long graduate algebra course here at NMSU. In the back of my mind, I thought it would be nice someday to write a book on field theory, one of my favorite mathematical subjects, and I wrote a crude form of lecture notes that semester. Those notes sat undisturbed for three years until late in 1993 when I finally made the decision to turn the notes into a book. The notes were greatly expanded and rewritten, and they were in a form sufficient to be used as the text for Math 581 when I taught it again in the fall of 1994. Part of my desire to write a textbook was due to the nonstandard format of our graduate algebra sequence. The first semester of our sequence is field theory. Our graduate students generally pick up group and ring theory in a senior-level course prior to taking field theory. Since we start with field theory, we would have to jump into the middle of most graduate algebra textbooks. This can make reading the text difficult by not knowing what the author did before the field theory chapters. Therefore, a book devoted to field theory is desirable for us as a text. While there are a number of field theory books around, most of these were less complete than I wanted.

Author : Andreas Weber
Publisher : MDPI
ISBN 13 : 3039217305
Total Pages : 160 pages
Book Rating : 4.04/5 ( download)

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Download or read book Computer Algebra in Scientific Computing written by Andreas Weber and published by MDPI. This book was released on 2019-11-04 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although scientific computing is very often associated with numeric computations, the use of computer algebra methods in scientific computing has obtained considerable attention in the last two decades. Computer algebra methods are especially suitable for parametric analysis of the key properties of systems arising in scientific computing. The expression-based computational answers generally provided by these methods are very appealing as they directly relate properties to parameters and speed up testing and tuning of mathematical models through all their possible behaviors. This book contains 8 original research articles dealing with a broad range of topics, ranging from algorithms, data structures, and implementation techniques for high-performance sparse multivariate polynomial arithmetic over the integers and rational numbers over methods for certifying the isolated zeros of polynomial systems to computer algebra problems in quantum computing.

Author : Jean-Pierre Serre
Publisher : CRC Press
ISBN 13 : 1439865256
Total Pages : 120 pages
Book Rating : 4.55/5 ( download)

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Download or read book Topics in Galois Theory written by Jean-Pierre Serre and published by CRC Press. This book was released on 2016-04-19 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt constructi

Author : Emil Artin
Publisher :
ISBN 13 :
Total Pages : 82 pages
Book Rating : 4.99/5 ( download)

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Download or read book Galois Theory written by Emil Artin and published by . This book was released on 1948 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Fernando Q. Gouvêa
Publisher : American Mathematical Soc.
ISBN 13 : 1614442118
Total Pages : 309 pages
Book Rating : 4.10/5 ( download)

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Download or read book A Guide to Groups, Rings, and Fields written by Fernando Q. Gouvêa and published by American Mathematical Soc.. This book was released on 2012-12-31 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: Insightful overview of many kinds of algebraic structures that are ubiquitous in mathematics. For researchers at graduate level and beyond.

Author : Minjia Shi
Publisher : Academic Press
ISBN 13 : 0128133910
Total Pages : 318 pages
Book Rating : 4.10/5 ( download)

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Download or read book Codes and Rings written by Minjia Shi and published by Academic Press. This book was released on 2017-06-12 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Codes and Rings: Theory and Practice is a systematic review of literature that focuses on codes over rings and rings acting on codes. Since the breakthrough works on quaternary codes in the 1990s, two decades of research have moved the field far beyond its original periphery. This book fills this gap by consolidating results scattered in the literature, addressing classical as well as applied aspects of rings and coding theory. New research covered by the book encompasses skew cyclic codes, decomposition theory of quasi-cyclic codes and related codes and duality over Frobenius rings. Primarily suitable for ring theorists at PhD level engaged in application research and coding theorists interested in algebraic foundations, the work is also valuable to computational scientists and working cryptologists in the area. Consolidates 20+ years of research in one volume, helping researchers save time in the evaluation of disparate literature Discusses duality formulas in the context of Frobenius rings Reviews decomposition of quasi-cyclic codes under ring action Evaluates the ideal and modular structure of skew-cyclic codes Supports applications in data compression, distributed storage, network coding, cryptography and across error-correction

Author : Jean-Pierre Serre
Publisher : Springer Science & Business Media
ISBN 13 : 3642591418
Total Pages : 215 pages
Book Rating : 4.19/5 ( download)

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Download or read book Galois Cohomology written by Jean-Pierre Serre and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an updated English translation of Cohomologie Galoisienne, published more than thirty years ago as one of the very first versions of Lecture Notes in Mathematics. It includes a reproduction of an influential paper by R. Steinberg, together with some new material and an expanded bibliography.

Author : D. J. H. Garling
Publisher : Cambridge University Press
ISBN 13 : 9780521312493
Total Pages : 180 pages
Book Rating : 4.93/5 ( download)

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Download or read book A Course in Galois Theory written by D. J. H. Garling and published by Cambridge University Press. This book was released on 1986 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to Galois theory.