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Elementary Number Theory: Primes, Congruences, and Secrets

A Computational Approach
BuchKartoniert, Paperback
168 Seiten
Englisch
Springererschienen am19.11.20102009
In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles´ resolution of Fermat´s Last Theorem.mehr
Verfügbare Formate
BuchGebunden
EUR44,99
BuchKartoniert, Paperback
EUR58,84
E-BookPDF1 - PDF WatermarkE-Book
EUR58,84

Produkt

KlappentextIn the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles´ resolution of Fermat´s Last Theorem.
ZusammenfassungClassical number theory and elliptic curves are examined in this textbook, which moves on from elementary topics such as primes, continued fractions, and quadratic forms, to elliptic curves and their applications to algorithmic and number theory problems.
Details
ISBN/GTIN978-1-4419-2752-1
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2010
Erscheinungsdatum19.11.2010
Auflage2009
ReiheUndergraduate Texts in Mathematics
Seiten168 Seiten
SpracheEnglisch
Gewicht276 g
IllustrationenX, 168 p. 45 illus.
Artikel-Nr.10293040

Inhalt/Kritik

Inhaltsverzeichnis
Prime Numbers.- The Ring of Integers Modulo n.- Public-key Cryptography.- Quadratic Reciprocity.- Continued Fractions.- Elliptic Curves.mehr
Kritik
From the reviews: "This one treats topics that have become standard in recent years ... and it has exercises with selected solutions. ... it gives the students a tool to do calculations that illustrate even the most abstract concepts, and, simultaneously, introduces them to an open source software that can later be applied profitably for studying research problems. ... introducing the reader to a powerful software system." (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1155, 2009) "The cliche that number theory, ever the purest mathematics, now yields very practical applications barely tells the story. Teach undergraduate number theory today, and students demand to hear about public-key cryptography and related technologies. ... Stein (Univ. of Washington) serves undergraduates well by ... opening the way by intimating their power. ... he frames the sophisticated Birch and Swinnerton-Dyer conjecture as the new canonical challenge for the future. Summing Up: Recommended. All undergraduates students, professionals, and general readers." (D. V. Feldman, Choice, Vol. 47 (2), October, 2009) "This book is an introduction to elementary number theory with a computational flavor. ... Many numerical examples are given throughout the book using the Sage mathematical software. The text is aimed at an undergraduate student with a basic knowledge of groups, rings and fields. Each chapter concludes with several exercises." (Samuel S. Wagstaff Jr., Mathematical Reviews, Issue 2009 i)mehr