Arkadii Slinko: Algebra for Applications

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Cover: 9783030440732 | Algebra for Applications | Arkadii Slinko | Taschenbuch | Paperback

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Sprache: Englisch

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Beschreibung

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 computationallyhard 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.

Über den Autor

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.

Zusammenfassung

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

Inhaltsverzeichnis

1 Integers.- 2 Cryptology.- 3 Groups.- 4 Fields.- 5 Polynomials.- 6 Secret Sharing.- 7 Error-Correcting Codes.- 8 Compression.- Appendix A: GAP.- Appendix B: Miscellanea.- Solutions to Exercises.- Index.

Details

Erscheinungsjahr:	2020
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	384
Reihe:	Springer Undergraduate Mathematics Series
Inhalt:	xiv 368 S. 16 s/w Illustr. 1 farbige Illustr. 368 p. 17 illus. 1 illus. in color.
ISBN-13:	9783030440732
ISBN-10:	3030440737
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Slinko, Arkadii
Auflage:	2nd ed. 2020
Hersteller:	Springer International Publishing Springer Undergraduate Mathematics Series
Maße:	235 x 155 x 21 mm
Von/Mit:	Arkadii Slinko
Erscheinungsdatum:	02.06.2020
Gewicht:	0,581 kg

preigu-id: 118028550