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Galois Fields and Galois Rings Made Easy

Galois Fields and Galois Rings Made Easy
  • Author : Maurice Kibler
  • Publisher :Unknown
  • Release Date :2017-09-22
  • Total pages :270
  • ISBN : 9780081023518
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Summary : 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

Computing in Communication Networks

Computing in Communication Networks
  • Author : Frank Fitzek,Fabrizio Granelli,Patrick Seeling
  • Publisher :Unknown
  • Release Date :2020-05-20
  • Total pages :522
  • ISBN : 9780128209042
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Summary : 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

Lectures on Finite Fields and Galois Rings

Lectures on Finite Fields and Galois Rings
  • Author : Zhe-Xian Wan
  • Publisher :Unknown
  • Release Date :2003
  • Total pages :342
  • ISBN : 9812385703
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Summary : 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.

Computer Algebra in Scientific Computing

Computer Algebra in Scientific Computing
  • Author : Andreas Weber
  • Publisher :Unknown
  • Release Date :2019-11-04
  • Total pages :160
  • ISBN : 9783039217304
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Summary : 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.

Dynamics, Statistics and Projective Geometry of Galois Fields

Dynamics, Statistics and Projective Geometry of Galois Fields
  • Author : V. I. Arnold
  • Publisher :Unknown
  • Release Date :2010-12-02
  • Total pages :229
  • ISBN : 9781139493444
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Summary : V. I. Arnold reveals some unexpected connections between such apparently unrelated theories as Galois fields, dynamical systems, ergodic theory, statistics, chaos and the geometry of projective structures on finite sets. The author blends experimental results with examples and geometrical explorations to make these findings accessible to a broad range of mathematicians, from undergraduate students to experienced researchers.

Fields and Galois Theory

Fields and Galois Theory
  • Author : John M. Howie
  • Publisher :Unknown
  • Release Date :2007-10-11
  • Total pages :226
  • ISBN : 1852339861
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Summary : 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

Field and Galois Theory

Field and Galois Theory
  • Author : Patrick Morandi
  • Publisher :Unknown
  • Release Date :2012-12-06
  • Total pages :284
  • ISBN : 9781461240402
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Summary : 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.

Field Extensions and Galois Theory

Field Extensions and Galois Theory
  • Author : Julio R. Bastida
  • Publisher :Unknown
  • Release Date :1984
  • Total pages :294
  • ISBN : 0201135213
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Summary :

Introduction to Abstract Algebra

Introduction to Abstract Algebra
  • Author : Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger
  • Publisher :Unknown
  • Release Date :2014-07-01
  • Total pages :584
  • ISBN : 9781421411774
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Summary : Introduction to Abstract Algebra presents a breakthrough approach to teaching one of math's most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, Benjamin Fine, Anthony M. Gaglione, and Gerhard Rosenberger set a pace that allows beginner-level students to follow the progression from familiar topics such as rings, numbers, and groups to more difficult concepts. Classroom tested and revised until students achieved consistent, positive results, this textbook is designed to keep students focused as they learn complex topics. Fine, Gaglione, and Rosenberger's clear explanations prevent students from getting lost as they move deeper and deeper into areas such as abelian groups, fields, and Galois theory. This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach. Topics covered include: • Rings • Integral domains • The fundamental theorem of arithmetic • Fields • Groups • Lagrange's theorem • Isomorphism theorems for groups • Fundamental theorem of finite abelian groups • The simplicity of An for n5 • Sylow theorems • The Jordan-Hölder theorem • Ring isomorphism theorems • Euclidean domains • Principal ideal domains • The fundamental theorem of algebra • Vector spaces • Algebras • Field extensions: algebraic and transcendental • The fundamental theorem of Galois theory • The insolvability of the quintic

Foundations of Galois Theory

Foundations of Galois Theory
  • Author : M.M. Postnikov
  • Publisher :Unknown
  • Release Date :2014-07-10
  • Total pages :122
  • ISBN : 9781483156477
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Summary : Foundations of Galois Theory is an introduction to group theory, field theory, and the basic concepts of abstract algebra. The text is divided into two parts. Part I presents the elements of Galois Theory, in which chapters are devoted to the presentation of the elements of field theory, facts from the theory of groups, and the applications of Galois Theory. Part II focuses on the development of general Galois Theory and its use in the solution of equations by radicals. Equations that are solvable by radicals; the construction of equations solvable by radicals; and the unsolvability by radicals of the general equation of degree n ? 5 are discussed as well. Mathematicians, physicists, researchers, and students of mathematics will find this book highly useful.

A Course in Galois Theory

A Course in Galois Theory
  • Author : D. J. H. Garling
  • Publisher :Unknown
  • Release Date :1986
  • Total pages :167
  • ISBN : 0521312493
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Summary : This textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to Galois theory.

Galois Theory

Galois Theory
  • Author : Emil Artin
  • Publisher :Unknown
  • Release Date :2012-05-24
  • Total pages :86
  • ISBN : 9780486158259
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Summary : Clearly presented discussions of fields, vector spaces, homogeneous linear equations, extension fields, polynomials, algebraic elements, as well as sections on solvable groups, permutation groups, solution of equations by radicals, and other concepts. 1966 edition.

Galois Theory and Applications

Galois Theory and Applications
  • Author : Mohamed Ayad
  • Publisher :Unknown
  • Release Date :2018-04-26
  • Total pages :452
  • ISBN : 9789813238329
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Summary :

A Guide to Groups, Rings, and Fields

A Guide to Groups, Rings, and Fields
  • Author : Fernando Q. Gouvêa
  • Publisher :Unknown
  • Release Date :2012-12-31
  • Total pages :309
  • ISBN : 9781614442110
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Summary : Insightful overview of many kinds of algebraic structures that are ubiquitous in mathematics. For researchers at graduate level and beyond.

Proceedings of the Conference on Algebra and Geometry

Proceedings of the Conference on Algebra and Geometry
  • Author : Anonim
  • Publisher :Unknown
  • Release Date :1982
  • Total pages :217
  • ISBN : UOM:39015057368394
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Summary :

Handbook of Algebra

Handbook of Algebra
  • Author : M. Hazewinkel
  • Publisher :Unknown
  • Release Date :2006-05-30
  • Total pages :542
  • ISBN : 0080462499
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Summary : Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed. - Thorough and practical source for information - Provides in-depth coverage of new topics in algebra - Includes references to relevant articles, books and lecture notes

Classical Galois Theory

Classical Galois Theory
  • Author : Lisl Gaal
  • Publisher :Unknown
  • Release Date :1998
  • Total pages :248
  • ISBN : 9780821813751
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Summary : Galois theory is considered one of the most beautiful subjects in mathematics, but it is hard to appreciate this fact fully without seeing specific examples. Numerous examples are therefore included throughout this text, in the hope that they will lead to a deeper understanding and genuine appreciation of the more abstract and advanced literature on Galois theory.

Galois Theory

Galois Theory
  • Author : Steven H. Weintraub
  • Publisher :Unknown
  • Release Date :2007-10-23
  • Total pages :190
  • ISBN : 9780387289175
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Summary : Galois theory is a mature mathematical subject of particular beauty. Any Galois theory book written nowadays bears a great debt to Emil Artin’s classic text "Galois Theory," and this book is no exception. While Artin’s book pioneered an approach to Galois theory that relies heavily on linear algebra, this book’s author takes the linear algebra emphasis even further. This special approach to the subject together with the clarity of its presentation, as well as the choice of topics covered, makes this book a more than worthwhile addition to the existing literature on Galois Theory. It will be appreciated by undergraduate and beginning graduate math majors.

Topics in Galois Theory

Topics in Galois Theory
  • Author : Jean-Pierre Serre
  • Publisher :Unknown
  • Release Date :2016-04-19
  • Total pages :120
  • ISBN : 9781439865255
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Summary : 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

Finite Fields and Applications

Finite Fields and Applications
  • Author : Dieter Jungnickel,H. Niederreiter
  • Publisher :Unknown
  • Release Date :2012-12-06
  • Total pages :490
  • ISBN : 9783642567551
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Summary : The Fifth International Conference on Finite Fields and Applications Fq5 held at the University of Augsburg, Germany, from August 2-6, 1999 continued a series of biennial international conferences on finite fields. The proceedings document the steadily increasing interest in this topic. Finite fields have an inherently fascinating structure and are important tools in discrete mathematics. Their applications range from combinatorial design theory, finite geometries, and algebraic geometry to coding theory, cryptology, and scientific computing. A particularly fruitful aspect is the interplay between theory and applications which has led to many new perspectives in research on finite fields. This interplay has always been a dominant theme in Fq conferences and was very much in evidence at Fq5. The proceedings reflect this, and offer an up-to-date collection of surveys and original research articles by leading experts in the area.

Algebra for Secure and Reliable Communication Modeling

Algebra for Secure and Reliable Communication Modeling
  • Author : Mustapha Lahyane, Edgar Martínez-Moro
  • Publisher :Unknown
  • Release Date :2015-06-23
  • Total pages :240
  • ISBN : 9781470410186
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Summary : This volume contains the proceedings of the CIMPA Research School and Conference on Algebra for Secure and Reliable Communication Modeling, held from October 1-13, 2012, in Morelia, State of Michoacán, Mexico. The papers cover several aspects of the theory of coding theory and are gathered into three categories: general theory of linear codes, algebraic geometry and coding theory, and constacyclic codes over rings. The aim of this volume is to fill the gap between the theoretical part of algebraic geometry and the applications to problem solving and computational modeling in engineering, signal processing and information theory. This book is published in cooperation with Real Sociedad Matemática Española (RSME).