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.

Lectures on Finite Fields and Galois Rings

Lectures on Finite Fields and Galois Rings
  • Author : Zhe-Xian Wan
  • Publisher : World Scientific
  • Release : 26 February 2021
GET THIS BOOKLectures on Finite Fields and Galois Rings

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

Fields and Galois Theory

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

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

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

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,

Dynamics, Statistics and Projective Geometry of Galois Fields

Dynamics, Statistics and Projective Geometry of Galois Fields
  • Author : V. I. Arnold
  • Publisher : Cambridge University Press
  • Release : 02 December 2010
GET THIS BOOKDynamics, Statistics and Projective Geometry of Galois Fields

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.

Foundations of Galois Theory

Foundations of Galois Theory
  • Author : M.M. Postnikov
  • Publisher : Elsevier
  • Release : 10 July 2014
GET THIS BOOKFoundations of Galois Theory

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.