Error Correcting Codes

A Mathematical Introduction

Author: D J. Baylis

Publisher: CRC Press

ISBN: 9780412786907

Category: Mathematics

Page: 232

View: 7295

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Assuming little previous mathematical knowledge, Error Correcting Codes provides a sound introduction to key areas of the subject. Topics have been chosen for their importance and practical significance, which Baylis demonstrates in a rigorous but gentle mathematical style. Coverage includes optimal codes; linear and non-linear codes; general techniques of decoding errors and erasures; error detection; syndrome decoding, and much more. Error Correcting Codes contains not only straight maths, but also exercises on more investigational problem solving. Chapters on number theory and polynomial algebra are included to support linear codes and cyclic codes, and an extensive reminder of relevant topics in linear algebra is given. Exercises are placed within the main body of the text to encourage active participation by the reader, with comprehensive solutions provided. Error Correcting Codes will appeal to undergraduate students in pure and applied mathematical fields, software engineering, communications engineering, computer science and information technology, and to organizations with substantial research and development in those areas.

The Mathematics of Encryption: An Elementary Introduction

Author: Margaret Cozzens, Steven J. Miller

Publisher: American Mathematical Soc.

ISBN: 0821883216

Category: Mathematics

Page: 332

View: 7914

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How quickly can you compute the remainder when dividing by 120143? Why would you even want to compute this? And what does this have to do with cryptography? Modern cryptography lies at the intersection of mathematics and computer sciences, involving number theory, algebra, computational complexity, fast algorithms, and even quantum mechanics. Many people think of codes in terms of spies, but in the information age, highly mathematical codes are used every day by almost everyone, whether at the bank ATM, at the grocery checkout, or at the keyboard when you access your email or purchase products online. This book provides a historical and mathematical tour of cryptography, from classical ciphers to quantum cryptography. The authors introduce just enough mathematics to explore modern encryption methods, with nothing more than basic algebra and some elementary number theory being necessary. Complete expositions are given of the classical ciphers and the attacks on them, along with a detailed description of the famous Enigma system. The public-key system RSA is described, including a complete mathematical proof that it works. Numerous related topics are covered, such as efficiencies of algorithms, detecting and correcting errors, primality testing and digital signatures. The topics and exposition are carefully chosen to highlight mathematical thinking and problem solving. Each chapter ends with a collection of problems, ranging from straightforward applications to more challenging problems that introduce advanced topics. Unlike many books in the field, this book is aimed at a general liberal arts student, but without losing mathematical completeness.

Coding Theory and Quantum Computing

An International Conference on Coding Theory and Quantum Computing, May 20-24, 2003, University of Virginia

Author: David Evans

Publisher: American Mathematical Soc.

ISBN: 0821836005

Category: Mathematics

Page: 147

View: 1307

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A conference, 'Coding Theory and Quantum Computing', was held in Charlottesville, VA, to provide an opportunity for computer scientists, mathematicians, and physicists to interact about subjects of common interest. This proceedings volume grew out of that meeting. It is divided into two parts: 'Coding Theory' and 'Quantum Computing'. In the first part, Harold Ward gives an introduction to coding theory. Other papers survey recent important work, such as coding theory applications of Grobner bases, methods of computing parameters of codes corresponding to algebraic curves, and problems in the theory of designs. The second part of the book covers a wide variety of directions in quantum information with an emphasis on understanding entanglement. The material presented is suitable for graduate students and researchers interested in coding theory and in quantum computing.

Information Theory and Coding by Example

Author: Mark Kelbert,Yuri Suhov

Publisher: Cambridge University Press

ISBN: 0521769353

Category: Computers

Page: 526

View: 3010

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A valuable teaching aid. Provides relevant background material, many examples and clear solutions to problems taken from real exam papers.

Information Security, Coding Theory and Related Combinatorics

Information Coding and Combinatorics

Author: Dean Crnkovic,Vladimir Tonchev

Publisher: IOS Press

ISBN: 1607506629

Category: Political Science

Page: 451

View: 3769

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Information Coding and Combinatorics. This book contains papers based on the fourteen lectures presented at the NATO Advanced Study Institute Information Security and Related Combinatorics, held in Opatija, Croatia, May 31 June 11, 2010. The conference was widely attended by students and

Signal Processing

A Mathematical Approach, Second Edition

Author: Charles L. Byrne

Publisher: CRC Press

ISBN: 1482241854

Category: Computers

Page: 439

View: 4048

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Signal Processing: A Mathematical Approach is designed to show how many of the mathematical tools the reader knows can be used to understand and employ signal processing techniques in an applied environment. Assuming an advanced undergraduate- or graduate-level understanding of mathematics—including familiarity with Fourier series, matrices, probability, and statistics—this Second Edition: Contains new chapters on convolution and the vector DFT, plane-wave propagation, and the BLUE and Kalman filters Expands the material on Fourier analysis to three new chapters to provide additional background information Presents real-world examples of applications that demonstrate how mathematics is used in remote sensing Featuring problems for use in the classroom or practice, Signal Processing: A Mathematical Approach, Second Edition covers topics such as Fourier series and transforms in one and several variables; applications to acoustic and electro-magnetic propagation models, transmission and emission tomography, and image reconstruction; sampling and the limited data problem; matrix methods, singular value decomposition, and data compression; optimization techniques in signal and image reconstruction from projections; autocorrelations and power spectra; high-resolution methods; detection and optimal filtering; and eigenvector-based methods for array processing and statistical filtering, time-frequency analysis, and wavelets.

Books in Print

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 6168

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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Kryptologie

Methoden und Maximen

Author: Friedrich L. Bauer

Publisher: Springer-Verlag

ISBN: 3642788696

Category: Computers

Page: 357

View: 7578

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Die Kryptologie, eine jahrtausendealte "Geheimwissenschaft", gewinnt für den Informatiker zusehends praktische Bedeutung in Verbindung mit Datenbanken und Telekommunikation. Neben ihre Nutzung in rechnergestützten öffentlichen Nachrichtensystemen ("öffentliche Schlüssel") treten interne Anwendungen, die sich auch auf Zugriffsberechtigungen und den Quellenschutz von Software erstrecken. Der erste Teil des Buches handelt in elf Kapiteln von den Geheimschriften und ihrem Gebrauch - von der Kryptographie. Im zweiten Teil wird in elf weiteren Kapiteln das Vorgehen zum unbefugten Entziffern einer Geheimschrift - die Kryptanalyse - besprochen, wobei sich insbesondere Hinweise für die Verfahrensbeurteilung ergeben. Das Buch setzt nur elementare mathematische Kenntnisse voraus. Mit einer Fülle spannender, lustiger und bisweilen anzüglicher Geschichten aus der historischen Kryptologie gewürzt, ist es selbst für den Laien reizvoll zu lesen.

Elementary Bayesian Biostatistics

Author: Lemuel A. Moyé

Publisher: CRC Press

ISBN: 1584887257

Category: Mathematics

Page: 400

View: 8446

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Bayesian analyses have made important inroads in modern clinical research due, in part, to the incorporation of the traditional tools of noninformative priors as well as the modern innovations of adaptive randomization and predictive power. Presenting an introductory perspective to modern Bayesian procedures, Elementary Bayesian Biostatistics explores Bayesian principles and illustrates their application to healthcare research. Building on the basics of classic biostatistics and algebra, this easy-to-read book provides a clear overview of the subject. It focuses on the history and mathematical foundation of Bayesian procedures, before discussing their implementation in healthcare research from first principles. The author also elaborates on the current controversies between Bayesian and frequentist biostatisticians. The book concludes with recommendations for Bayesians to improve their standing in the clinical trials community. Calculus derivations are relegated to the appendices so as not to overly complicate the main text. As Bayesian methods gain more acceptance in healthcare, it is necessary for clinical scientists to understand Bayesian principles. Applying Bayesian analyses to modern healthcare research issues, this lucid introduction helps readers make the correct choices in the development of clinical research programs.

Semantic Web

Grundlagen

Author: Pascal Hitzler,Markus Krötzsch,Sebastian Rudolph,York Sure

Publisher: Springer-Verlag

ISBN: 3540339949

Category: Computers

Page: 277

View: 4982

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Das Buch Semantic Web – Grundlagen vermittelt als erstes deutschsprachiges Lehrbuch die Grundlagen des Semantic Web in verständlicher Weise. Es ermöglicht einen einfachen und zügigen Einstieg in Methoden und Technologien des Semantic Web und kann z.B. als solide Grundlage für die Vorbereitung und Durchführung von Vorlesungen genutzt werden. Die Autoren trennen dabei sauber zwischen einer intuitiven Hinführung zur Verwendung semantischer Technologien in der Praxis einerseits, und der Erklärung formaler und theoretischer Hintergründe andererseits. Nur für letzteres werden Grundkenntnisse in Logik vorausgesetzt, die sich bei Bedarf jedoch durch zusätzliche Lektüre und mit Hilfe eines entsprechenden Kapitels im Anhang aneignen lassen. Das Lehrbuch richtet sich primär an Studenten mit Grundkenntnissen in Informatik sowie an interessierte Praktiker welche sich im Bereich Semantic Web fortbilden möchten. Aus den Rezensionen: "... RDF, RDF-S und OWL. Diese Sprachen ... werden von den Autoren dargestellt. Bei der Darstellung ... fallen sie selten zu schwierigen Fachslang, sondern liefern eine gut nachvollziehbare Schilderung mit einfachen Beispielen, auch Übungsaufgaben runden die Kapitel ab. ... Semantic Web ist ein einfach geschriebenes und anschauliches Buch, das In die Grundkonzepte der Semantic-Web-Techniken einführt. Wer sich schnell in RDF, RDF-S und Co. einarbeiten muss und etwas Vorbildung in Logik und Algebra mitbringt, der trifft mit diesem Lehrbuch sicherlich eine gute Wahl ..." (http://www.literaturnetz.com/content/view/8742/44/)

Kompendium Systembiologie

Mathematische Modellierung und Modellanalyse

Author: Andreas Kremling

Publisher: Springer-Verlag

ISBN: 3834886076

Category: Science

Page: 300

View: 8047

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Das Buch beschreibt die Grundlagen der mathematischen Modellierung zellulärer Systeme. Nach einer Klassifikation von Modellen wird schwerpunktmäßig auf deterministische Modelle eingegangen und für alle relevanten zellulären Prozesse entsprechende Gleichungen angegeben. Anschließend werden eine Reihe von Verfahren zur Modellanalyse vorgestellt. Etwas kürzer werden Verfahren zum Reverse Engineering und zur Analyse von Netzwerkgraphen abgehandelt. Am Ende werden noch Verfahren der Parameteridentifikation besprochen.

Einführung in die computerorientierte Mathematik mit Sage

Author: Thorsten Theobald,Sadik Iliman

Publisher: Springer-Verlag

ISBN: 3658104538

Category: Computers

Page: 195

View: 4994

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Das an Studienanfänger der Mathematik gerichtete Lehrbuch bietet eine breit angelegte Einführung in verschiedene Facetten der computerorientierten Mathematik. Es ermöglicht eine frühzeitige und wertvolle Auseinandersetzung mit computerorientierten Methoden, Denkweisen und Arbeitstechniken innerhalb der Mathematik. Hierzu werden grundlegende mathematische Teilgebiete behandelt, die eine enge Beziehung zu computerorientierten Aspekten haben: Graphen, mathematische Algorithmen, Rekursionsgleichungen, computerorientierte lineare Algebra, Zahlen, Polynome und ihre Nullstellen. Anhand des mathematischen Kernstrangs werden Einblicke in die Modellierung, Analyse und algorithmische Aufbereitung fundamentaler mathematischer Sachverhalte gegeben. Eine Besonderheit des Buches ist die Verwendung des sich immer stärker in Forschung und Lehre verbreitenden, frei verfügbaren Software-Systems Sage. Das Buch eignet sich besonders gut zur Komplementierung der klassischen Grundvorlesungen in Analysis und linearer Algebra.