Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Table of contents (11 chapters)
Keywords
- BCH Codes
- Cryptography
- Cryptology
- Elgamal Cryptosystem
- Elliptic Curves
- Error-Correcting Codes
- Euler Totient Function
- Factorisation
- Fingerprinting Codes
- Finite Field
- Fitingof’s Compression Code
- Integers
- Lagrange Interpolation
- Linear Codes
- Linear Secret Sharing Scheme
- Miller-Rabin Pseudoprimality Test
- Permutation Groups
- Polynomial
- Prefix Codes
- Primality Testing
About this book
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.
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)
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Algebra for Applications
Book Subtitle: Cryptography, Secret Sharing, Error-Correcting, Fingerprinting, Compression
Authors: Arkadii Slinko
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-3-319-21951-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
eBook ISBN: 978-3-319-21951-6Published: 19 August 2015
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: XIV, 328
Number of Illustrations: 4 b/w illustrations, 1 illustrations in colour
Topics: Algebra, Information and Communication, Circuits, Discrete Mathematics