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book: Discrete Algebraic Methods
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Discrete Algebraic Methods

Arithmetic, Cryptography, Automata and Groups
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Language: English
Published/Copyright: 2016
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About this book

The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and Saxena. The account to elliptic curves again focuses on cryptographic applications and algorithms. With combinatorics on words and automata theory, the reader is introduced to two areas of theoretical computer science where semigroups play a fundamental role.The last chapter is devoted to combinatorial group theory and its connections to automata.

Contents:
Algebraic structures
Cryptography
Number theoretic algorithms
Polynomial time primality test
Elliptic curves
Combinatorics on words
Automata
Discrete infinite groups

  • Contains brief chapter summaries as well as examples, problems and solutions.
  • References for further reading in every chapter.
  • Mathematical derivations are illustrated by a plethora of illustrations.

Author / Editor information

Volker Diekert, Manfred Kufleitner and Ulrich Hertrampf, Stuttgart, Germany; Gerhard Rosenberger, Hamburg, Germany.

Reviews

"This extremely reader-friendly textbook covers a broad range of practical topics in the intersection of abstract algebra and computer science. [...] Each chapter ends with a well-chosen set of approachable problems, valuable to instructors and students alike. [...] Overall, authors Diekert, Kufleitner, Rosenberger, and Hertrampf have given us an excellent book on a fascinating area of mathematical practice. I warmly recommend it to readers interested in these topics."
James A. Swenson in: MAA November 2017 https://www.maa.org/press/maa-reviews/discrete-algebraic-methods

Topics

  • Publicly Available

    Frontmatter

    I
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    Preface

    V
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    Contents

    IX
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    1. Algebraic structures

    1
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    2. Cryptography

    49
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    3. Number theoretic algorithms

    83
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    4. Polynomial time primality test

    121
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    5. Elliptic curves

    131
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    6. Combinatorics on words

    161
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    7. Automata

    173
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    8. Discrete infinite groups

    236
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    Solutions to exercises

    286
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    Bibliography

    325
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    Index

    329
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Publishing information
Pages and Images/Illustrations in book
eBook published on:
May 24, 2016
eBook ISBN:
9783110413335
Paperback published on:
May 24, 2016
Paperback ISBN:
9783110413328
Pages and Images/Illustrations in book
Front matter:
12
Main content:
342
Illustrations:
60
https://doi.org/10.1515/9783110413335
eBook ISBN: 9783110413335
Paperback ISBN: 9783110413328
Keywords for this book
Arithmetik; Automaten; Diskrete algebraische Strukturen; Gruppen; Kryptographie
Audience(s) for this book
Students in Computer Science and Mathematics, Lecturers.
Safety & product resources
Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
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