Galois Fields and Galois Rings Made Easy Book

Galois Fields and Galois Rings Made Easy


  • Author : Maurice Kibler
  • Publisher : Elsevier
  • Release Date : 2017-09-22
  • Genre: Mathematics
  • Pages : 270
  • ISBN 10 : 9780081023518

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Galois Fields and Galois Rings Made Easy 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

Computing in Communication Networks Book

Computing in Communication Networks


  • Author : Frank Fitzek
  • Publisher : Academic Press
  • Release Date : 2020-05-20
  • Genre: Computers
  • Pages : 522
  • ISBN 10 : 9780128209042

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Computing in Communication Networks 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

Computer Algebra in Scientific Computing Book

Computer Algebra in Scientific Computing


  • Author : Andreas Weber
  • Publisher : MDPI
  • Release Date : 2019-11-04
  • Genre: Computers
  • Pages : 160
  • ISBN 10 : 9783039217304

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Computer Algebra in Scientific Computing 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.

Central Simple Algebras and Galois Cohomology Book

Central Simple Algebras and Galois Cohomology


  • Author : Philippe Gille
  • Publisher : Cambridge University Press
  • Release Date : 2017-08-10
  • Genre: Mathematics
  • Pages : 430
  • ISBN 10 : 9781107156371

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Central Simple Algebras and Galois Cohomology Excerpt :

The first comprehensive modern introduction to central simple algebra starting from the basics and reaching advanced results.

Cryptography and Network Security Book

Cryptography and Network Security


  • Author : Prof. Bhushan Trivedi
  • Publisher : BPB Publications
  • Release Date : 2021-09-22
  • Genre: Computers
  • Pages : 712
  • ISBN 10 : 9789389328660

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Cryptography and Network Security Excerpt :

Exploring techniques and tools and best practices used in the real world. KEY FEATURES ● Explore private and public key-based solutions and their applications in the real world. ● Learn about security protocols implemented at various TCP/IP stack layers. ● Insight on types of ciphers, their modes, and implementation issues. DESCRIPTION Cryptography and Network Security teaches you everything about cryptography and how to make its best use for both, network and internet security. To begin with, you will learn to explore security goals, the architecture, its complete mechanisms, and the standard operational model. You will learn some of the most commonly used terminologies in cryptography such as substitution, and transposition. While you learn the key concepts, you will also explore the difference between symmetric and asymmetric ciphers, block and stream ciphers, and monoalphabetic and polyalphabetic ciphers. This book also focuses on digital signatures and digital signing methods, AES encryption processing, public key algorithms, and how to encrypt and generate MACs. You will also learn about the most important real-world protocol called Kerberos and see how public key certificates are deployed to solve public key-related problems. Real-world protocols such as PGP, SMIME, TLS, and IPsec Rand 802.11i are also covered in detail. WHAT YOU WILL LEARN ● Describe and show real-world connections of cryptography and applications of cryptography and secure hash functions. ● How one can deploy User Authentication, Digital Signatures, and AES Encryption process. ● How the real-world protocols operate in practice and their theoretical implications. ● Describe different types of ciphers, exploit their modes for solving problems, and finding their implementation issues in system security. ● Explore transport layer security, IP security, and wireless security. WHO THIS BOOK IS FOR This book is for security professionals, network engineers, IT managers, students, a

Finite Commutative Rings and Their Applications Book

Finite Commutative Rings and Their Applications


  • Author : Gilberto Bini
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Technology & Engineering
  • Pages : 176
  • ISBN 10 : 9781461509578

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Finite Commutative Rings and Their Applications Excerpt :

Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in the fields of communication and coding theory. The book is a concrete and self-contained introduction to finite commutative local rings, focusing in particular on Galois and Quasi-Galois rings. The reader is provided with an active and concrete approach to the study of the purely algebraic structure and properties of finite commutative rings (in particular, Galois rings) as well as to their applications to coding theory. Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject. The section on Quasi-Galois rings presents new and unpublished results as well. The authors then introduce some applications of finite rings, in particular Galois rings, to coding theory, using a solid algebraic and geometric theoretical background.

Introduction to Coding Theory and Algebraic Geometry Book

Introduction to Coding Theory and Algebraic Geometry


  • Author : J. van Lint
  • Publisher : Birkhäuser
  • Release Date : 2012-12-06
  • Genre: Science
  • Pages : 85
  • ISBN 10 : 9783034892865

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Introduction to Coding Theory and Algebraic Geometry Excerpt :

These notes are based on lectures given in the semmar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Diisseldorf, November 16-21, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the Gilbert-Varshamov bound. The result was considered sensational. Furthermore, it was surprising to see these unrelated areas of mathematics collaborating. The aim of this course is to give an introduction to coding theory and to sketch the ideas of algebraic geometry that led to the new result. Finally, a number of applications of these methods of algebraic geometry to coding theory are given. Since this is a new area, there are presently no references where one can find a more extensive treatment of all the material. However, both for algebraic geometry and for coding theory excellent textbooks are available. The combination ofthe two subjects can only be found in a number ofsurvey papers. A book by C. Moreno with a complete treatment of this area is in preparation. We hope that these notes will stimulate further research and collaboration of algebraic geometers and coding theorists. G. van der Geer, J.H. van Lint Introduction to CodingTheory and Algebraic Geometry PartI -- CodingTheory Jacobus H. vanLint 11 1. Finite fields In this chapter we collect (without proof) the facts from the theory of finite fields that we shall need in this course

Fields and Galois Theory Book

Fields and Galois Theory


  • Author : John M. Howie
  • Publisher : Springer Science & Business Media
  • Release Date : 2007-10-11
  • Genre: Mathematics
  • Pages : 226
  • ISBN 10 : 9781852339869

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Fields and Galois Theory Excerpt :

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

Finite Fields and Applications Book

Finite Fields and Applications


  • Author : Dieter Jungnickel
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Mathematics
  • Pages : 490
  • ISBN 10 : 9783642567551

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Finite Fields and Applications Excerpt :

This volume represents the refereed proceedings of the Fifth International Conference on Finite Fields and Applications (F q5) held at the University of Augsburg (Germany) from August 2-6, 1999, and hosted by the Department of Mathematics. The conference continued a series of biennial international conferences on finite fields, following earlier conferences at the University of Nevada at Las Vegas (USA) in August 1991 and August 1993, the University ofGlasgow (Scotland) in July 1995, and the University ofWaterloo (Canada) in August 1997. The Organizing Committee of F q5 comprised Thomas Beth (

Introduction to Abstract Algebra Book

Introduction to Abstract Algebra


  • Author : Benjamin Fine
  • Publisher : JHU Press
  • Release Date : 2014-07-01
  • Genre: Mathematics
  • Pages : 584
  • ISBN 10 : 9781421411774

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Introduction to Abstract Algebra Excerpt :

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

Algebra for Secure and Reliable Communication Modeling Book

Algebra for Secure and Reliable Communication Modeling


  • Author : Mustapha Lahyane
  • Publisher : American Mathematical Soc.
  • Release Date : 2015-06-23
  • Genre: Geometry, Algebraic
  • Pages : 240
  • ISBN 10 : 9781470410186

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Algebra for Secure and Reliable Communication Modeling Excerpt :

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).

Computations in Algebraic Geometry with Macaulay 2 Book

Computations in Algebraic Geometry with Macaulay 2


  • Author : David Eisenbud
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-03-14
  • Genre: Mathematics
  • Pages : 329
  • ISBN 10 : 9783662048511

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Computations in Algebraic Geometry with Macaulay 2 Excerpt :

This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications. The algorithmic tools presented here are designed to serve readers wishing to bring such tools to bear on their own problems. The first part of the book covers Macaulay 2 using concrete applications; the second emphasizes details of the mathematics.

Field and Galois Theory Book

Field and Galois Theory


  • Author : Patrick Morandi
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Mathematics
  • Pages : 284
  • ISBN 10 : 9781461240402

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Field and Galois Theory 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.

Field Extensions and Galois Theory Book
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Field Extensions and Galois Theory


  • Author : Julio R. Bastida
  • Publisher : Cambridge University Press
  • Release Date : 1984-12-28
  • Genre: Mathematics
  • Pages : 294
  • ISBN 10 : 0521302420

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Field Extensions and Galois Theory Excerpt :

This 1984 book aims to make the general theory of field extensions accessible to any reader with a modest background in groups, rings and vector spaces. Galois theory is regarded amongst the central and most beautiful parts of algebra and its creation marked the culmination of generations of investigation.