Galois Fields And Galois Rings Made Easy

Author : Maurice Kibler
Publisher : Elsevier
Page : 270 pages
File Size : 52,8 Mb
Release : 2017-09-22
Category : Mathematics
ISBN : 9780081023518

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Galois Fields and Galois Rings Made Easy by Maurice Kibler Pdf

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,Fabrizio Granelli,Patrick Seeling
Publisher : Academic Press
Page : 524 pages
File Size : 52,6 Mb
Release : 2020-05-20
Category : Technology & Engineering
ISBN : 9780128209042

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Computing in Communication Networks by Frank H.P. Fitzek,Fabrizio Granelli,Patrick Seeling Pdf

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 : Andreas Weber
Publisher : MDPI
Page : 160 pages
File Size : 51,8 Mb
Release : 2019-11-04
Category : Computers
ISBN : 9783039217304

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Computer Algebra in Scientific Computing by Andreas Weber Pdf

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 : Patrick Morandi
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461240402

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Field and Galois Theory by Patrick Morandi Pdf

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 : Jean-Pierre Serre
Publisher : CRC Press
Page : 120 pages
File Size : 51,5 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781439865255

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Topics in Galois Theory by Jean-Pierre Serre Pdf

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 : Unknown
Page : 82 pages
File Size : 50,5 Mb
Release : 1948
Category : Galois theory
ISBN : OCLC:1110469399

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Galois Theory by Emil Artin Pdf

Author : Jean-Pierre Serre
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 46,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642591419

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Galois Cohomology by Jean-Pierre Serre Pdf

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
Page : 180 pages
File Size : 47,7 Mb
Release : 1986
Category : Mathematics
ISBN : 0521312493

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A Course in Galois Theory by D. J. H. Garling Pdf

This textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to Galois theory.

Author : Minjia Shi,Adel Alahmadi,Patrick Solé
Publisher : Academic Press
Page : 318 pages
File Size : 53,5 Mb
Release : 2017-06-12
Category : Business & Economics
ISBN : 9780128133910

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Codes and Rings by Minjia Shi,Adel Alahmadi,Patrick Solé Pdf

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 : David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 50,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662048511

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Computations in Algebraic Geometry with Macaulay 2 by David Eisenbud,Daniel R. Grayson,Mike Stillman,Bernd Sturmfels Pdf

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.

Author : Mustapha Lahyane, Edgar Martínez-Moro
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 51,8 Mb
Release : 2015-06-23
Category : Geometry, Algebraic
ISBN : 9781470410186

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Algebra for Secure and Reliable Communication Modeling by Mustapha Lahyane, Edgar Martínez-Moro Pdf

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).

Author : Francis Borceux,George Janelidze
Publisher : Cambridge University Press
Page : 360 pages
File Size : 48,6 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521803098

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Galois Theories by Francis Borceux,George Janelidze Pdf

Develops Galois theory in a more general context, emphasizing category theory.

Author : Marius van der Put,Michael F. Singer
Publisher : Springer Science & Business Media
Page : 438 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642557507

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Galois Theory of Linear Differential Equations by Marius van der Put,Michael F. Singer Pdf

From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews

Author : Jörg Bewersdorff
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 51,5 Mb
Release : 2006
Category : Galois theory
ISBN : 9780821838174

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Galois Theory for Beginners by Jörg Bewersdorff Pdf

Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. This book follows the historical development of the theory, emphasizing concrete examples along the way. It is suitable for undergraduates and beginning graduate students.

Author : Jean-Pierre Serre
Publisher : CRC Press
Page : 203 pages
File Size : 42,5 Mb
Release : 1997-11-15
Category : Mathematics
ISBN : 9781439863862

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Abelian l-Adic Representations and Elliptic Curves by Jean-Pierre Serre Pdf

This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one