عنوان

Algebra for Applications

9783319219509

IR

10406

انگلیسی

IR

Algebra for Applications

[Book]

:Cryptograghy, Secret Sharing, Error-Correctin, Fingerprinting, Compression

/ Arkadii Slinko

NEW YORK

: Springer

, 2015.

xiv, 328 pages

: illustrations

; 24 cm.

(Springer undergraduate mathematics series)

Language: انگلیسی

Includes bibliographical references

Print

ncludes bibliographical references.

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

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.Review: "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).

Computer science - Mathematics.

Algebra - Data processing.

Slinko, Arkadii

ایران

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