Springer Undergraduate Mathematics Series

Algebra for Applications

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

Authors: Slinko, Arkadii

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  • Suitable for an undergraduate applied algebra course
  • Covers a wide range of applications of algebra and number theory to information handling, such as encryption and error-correcting codes
  • Uses the free GAP software to illustrate the main concepts
  • Includes numerous worked examples and exercises
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eBook 13,90 €
28,88 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-44074-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 18,71 €
36,39 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-44073-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

Modern societies are awash with data that needs to be manipulated in many different ways: encrypted, compressed, shared between users in a prescribed manner, protected from unauthorised access, and transmitted over unreliable channels. All of these operations are based on algebra and number theory and can only be properly understood with a good knowledge of these fields. This textbook provides the mathematical tools and applies them to study key aspects of data transmission such as encryption and compression.

Designed for an undergraduate lecture course, this textbook provides all of the background in arithmetic, polynomials, groups, fields, and elliptic curves that is required to understand real-life applications such as cryptography, secret sharing, error-correcting, fingerprinting, and compression of information. It explains in detail how these applications really work. The book uses the free GAP computational package, allowing the reader to develop intuition about computationally hard problems and giving insights into how computational complexity can be used to protect the integrity of data.

The first undergraduate textbook to cover such a wide range of applications, including some recent developments, this second edition has been thoroughly revised with the addition of new topics and exercises. Based on a one semester lecture course given to third year undergraduates, it is primarily intended for use as a textbook, while numerous worked examples and solved exercises also make it suitable for self-study.

About the authors

Arkadii M. Slinko is currently Professor of Mathematics at the University of Auckland, New Zealand. Before taking this position in 1993 he was a Senior Research Fellow of the interdisciplinary Institute of Systems Analysis of Russian Academy of Sciences in Moscow. He has published extensively in a wide range of journals in mathematics, computer science, economics, and politics. His current research focuses on the mathematics of social choice, game theory, and secret sharing.

Table of contents (11 chapters)

Table of contents (11 chapters)
  • Integers

    Pages 1-39

    Slinko, Arkadii

  • Cryptology

    Pages 41-77

    Slinko, Arkadii

  • Groups

    Pages 79-127

    Slinko, Arkadii

  • Fields

    Pages 129-146

    Slinko, Arkadii

  • Polynomials

    Pages 147-170

    Slinko, Arkadii

Buy this book

eBook 13,90 €
28,88 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-44074-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 18,71 €
36,39 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-44073-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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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
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-44074-9
DOI
10.1007/978-3-030-44074-9
Softcover ISBN
978-3-030-44073-2
Series ISSN
1615-2085
Edition Number
2
Number of Pages
XIV, 368
Number of Illustrations
16 b/w illustrations, 1 illustrations in colour
Topics