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Springer Undergraduate Mathematics Series

Algebra for Applications

Cryptography, Secret Sharing, Error-Correcting, Fingerprinting, Compression

Authors: Slinko, Arkadii

  • Shows the incredible power of algebra and number theory in the real world
  • Uses GAP, a system for computational discrete algebra, to illustrate the main ideas
  • Suitable for beginners with a very little background knowledge of the topic
  • Unique to cover such a wide range of applications
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Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-21951-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-21950-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This book examines the relationship between mathematics and data in the modern world. Indeed, modern societies are awash with data which must be manipulated in many different ways: encrypted, compressed, shared between users in a prescribed manner, protected from an unauthorised access and transmitted over unreliable channels. All of these operations can be understood only by a person with knowledge of basics in algebra and number theory.

This book provides the necessary background in arithmetic, polynomials, groups, fields and elliptic curves that is sufficient to understand such real-life applications as cryptography, secret sharing, error-correcting, fingerprinting and compression of information. It is the first to cover many recent developments in these topics. Based on a lecture course given to third-year undergraduates, it is self-contained with numerous worked examples and exercises provided to test understanding. It can additionally be used for self-study.

About the authors

ARKADII SLINKO is currently Professor of Mathematics at the University of Auckland. He has published extensively in a wide range of journals. His current research is in applied discrete mathematics with particular focus on the mathematics of social choice, mathematical politics, decision theory, game theory and secret sharing.

Reviews

“Brief, but thoughtful, exercise sets are presented throughout the text with worked answers to all exercises provided in an appendix. Overall, this book, part of the ‘Springer Undergraduate Mathematics’ series, is an excellent introduction to modern applications of algebra and number theory for advanced students. Summing Up: Highly recommended. Upper-division undergraduates and graduate students.” (D. S. Larson, Choice, Vol. 53 (10), June, 2016)

“The different topics are well motivated and many examples are interweaves through the text as well as small programs in the computer packages GAP. Appendix A describes this package and gives instructions on how to use it. Also a list of exercises are proposed at the end of each subsection and solutions are provided at the end of the book. Biographical and bibliographical references are given as footnotes and at the end of some chapters.” (Juan Tena Ayuso, zbMATH 1345.94002, 2016)


Table of contents (11 chapters)

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-21951-6
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-21950-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Algebra for Applications
Book Subtitle
Cryptography, Secret Sharing, Error-Correcting, Fingerprinting, Compression
Authors
Series Title
Springer Undergraduate Mathematics Series
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-21951-6
DOI
10.1007/978-3-319-21951-6
Softcover ISBN
978-3-319-21950-9
Series ISSN
1615-2085
Edition Number
1
Number of Pages
XIV, 328
Number of Illustrations and Tables
4 b/w illustrations, 1 illustrations in colour
Topics