Arkadii Slinko: Algebra for Applications

Cover: 9783031826252 | Algebra for Applications | Arkadii Slinko | Taschenbuch | xvii | 2025

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Sprache: Englisch

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Beschreibung

This textbook provides mathematical tools and applies them to study key aspects of data transmission such as encryption and compression. Modern societies are awash with data that needs to be manipulated in many ways: encrypted, compressed, shared between users in a prescribed manner, protected from unauthorized access, and transmitted over unreliable channels. All of these operations are based on algebra and number theory. This textbook covers background topics in arithmetic, polynomials, groups, fields, and elliptic curves required for real-life applications like cryptography, secret sharing, error-correcting, fingerprinting, and compression of information.

The book illustrates the work of these applications using the free GAP computational package. It uses this package to help readers understand computationally hard problems and provide insights into protecting data integrity. This textbook covers a wide range of applications including recent developments, primarily intended for use as a textbook, with numerous worked examples and solved exercises suitable for self-study.

This edition has been thoroughly revised with new topics and exercises, introducing hash functions for properly describing digital signatures, blockchains, and digital currencies in the latest version.

Über den Autor

Arkadii Slinko is currently Professor of Mathematics at the University of Auckland, New Zealand.

Inhaltsverzeichnis

Integers.- Cryptology.- Groups.- Fields.- Polynomials.- Secret Sharing.- Error-Correcting Codes.- Compression.- Appendix A: GAP.- Appendix B: Miscellanea.- Solutions to Exercises.- Index.

Erscheinungsjahr:	2025
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Springer Undergraduate Mathematics Series
Inhalt:	xvii 395 S. 9 s/w Illustr. 2 farbige Illustr. 395 p. 11 illus. 2 illus. in color.
ISBN-13:	9783031826252
ISBN-10:	3031826256
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Slinko, Arkadii
Auflage:	Third Edition 2025
Hersteller:	Springer Springer International Publishing AG Springer Undergraduate Mathematics Series
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 23 mm
Von/Mit:	Arkadii Slinko
Erscheinungsdatum:	21.05.2025
Gewicht:	0,628 kg