Galois Fields and Galois Rings Made Easy

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

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  • Author : Maurice Kibler
  • Publisher : Elsevier
  • Pages : 270 pages
  • ISBN : 0081023510
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKGalois Fields and Galois Rings Made Easy

Galois Fields and Galois Rings Made Easy

Galois Fields and Galois Rings Made Easy
  • Author : Maurice Kibler
  • Publisher : Elsevier
  • Release : 22 September 2017
GET THIS BOOKGalois Fields and Galois Rings Made Easy

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

Computing in Communication Networks

Computing in Communication Networks
  • Author : Frank Fitzek,Fabrizio Granelli,Patrick Seeling
  • Publisher : Academic Press
  • Release : 20 May 2020
GET THIS BOOKComputing in Communication Networks

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,

Computer Algebra in Scientific Computing

Computer Algebra in Scientific Computing
  • Author : Andreas Weber
  • Publisher : MDPI
  • Release : 04 November 2019
GET THIS BOOKComputer Algebra in Scientific Computing

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.

Field and Galois Theory

Field and Galois Theory
  • Author : Patrick Morandi
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKField and Galois Theory

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

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Fields and Galois Theory
  • Author : John M. Howie
  • Publisher : Springer Science & Business Media
  • Release : 11 October 2007
GET THIS BOOKFields and Galois Theory

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

Fields and Rings

Fields and Rings
  • Author : Irving Kaplansky
  • Publisher : University of Chicago Press
  • Release : 17 October 1972
GET THIS BOOKFields and Rings

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

A Guide to Groups, Rings, and Fields

A Guide to Groups, Rings, and Fields
  • Author : Fernando Q. Gouvêa
  • Publisher : MAA
  • Release : 17 October 2021
GET THIS BOOKA Guide to Groups, Rings, and Fields

This Guide offers a concise overview of the theory of groups, rings, and fields at the graduate level, emphasizing those aspects that are useful in other parts of mathematics. It focuses on the main ideas and how they hang together. It will be useful to both students and professionals. In addition to the standard material on groups, rings, modules, fields, and Galois theory, the book includes discussions of other important topics that are often omitted in the standard graduate course,

Finite Fields and Applications

Finite Fields and Applications
  • Author : Dieter Jungnickel,H. Niederreiter
  • Publisher : Springer Science & Business Media
  • Release : 06 December 2012
GET THIS BOOKFinite Fields and Applications

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

Galois Theory

Galois Theory
  • Author : Emil Artin
  • Publisher : Courier Corporation
  • Release : 24 May 2012
GET THIS BOOKGalois Theory

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.

Algebra for Secure and Reliable Communication Modeling

Algebra for Secure and Reliable Communication Modeling
  • Author : Mustapha Lahyane, Edgar Martínez-Moro
  • Publisher : American Mathematical Soc.
  • Release : 23 June 2015
GET THIS BOOKAlgebra for Secure and Reliable Communication Modeling

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

Introduction to Abstract Algebra

Introduction to Abstract Algebra
  • Author : Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger
  • Publisher : JHU Press
  • Release : 01 July 2014
GET THIS BOOKIntroduction to Abstract Algebra

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;

Galois Theory

Galois Theory
  • Author : Ian Nicholas Stewart
  • Publisher : CRC Press
  • Release : 06 March 2015
GET THIS BOOKGalois Theory

Since 1973, Galois Theory has been educating undergraduate students on Galois groups and classical Galois theory. In Galois Theory, Fourth Edition, mathematician and popular science author Ian Stewart updates this well-established textbook for today's algebra students. New to the Fourth EditionThe replacement of the topological proof of the fundame