Elementary Number Theory: Primes, Congruen...

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Beschreibung

This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predeterminedsecret; this invention and the ones that followed it revolutionized the world of digital communication. 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.

Zusammenfassung

This is a textbook about classical elementary number theory and elliptic curves. The first part discusses elementary topics such as primes, factorization, continued fractions, and quadratic forms, in the context of cryptography, computation, and deep open research problems. The second part is about elliptic curves, their applications to algorithmic problems, and their connections with problems in number theory. The intended audience of this book is an undergraduate with some familiarity with basic abstract algebra.

Inhaltsverzeichnis

Prime Numbers.- The Ring of Integers Modulo n.- Public-key Cryptography.- Quadratic Reciprocity.- Continued Fractions.- Elliptic Curves.

Details

Erscheinungsjahr:	2008
Fachbereich:	Grundlagen
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Undergraduate Texts in Mathematics
Inhalt:	x 168 S. 45 s/w Illustr. 168 p. 45 illus.
ISBN-13:	9780387855240
ISBN-10:	0387855246
Sprache:	Englisch
Herstellernummer:	10950616
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Stein, William
Hersteller:	Springer US Springer New York Undergraduate Texts in Mathematics
Maße:	241 x 160 x 16 mm
Von/Mit:	William Stein
Erscheinungsdatum:	03.12.2008
Gewicht:	0,442 kg

Artikel-ID: 101734915

Zusammenfassung

Inhaltsverzeichnis

Prime Numbers.- The Ring of Integers Modulo n.- Public-key Cryptography.- Quadratic Reciprocity.- Continued Fractions.- Elliptic Curves.

Details

Erscheinungsjahr:	2008
Fachbereich:	Grundlagen
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Undergraduate Texts in Mathematics
Inhalt:	x 168 S. 45 s/w Illustr. 168 p. 45 illus.
ISBN-13:	9780387855240
ISBN-10:	0387855246
Sprache:	Englisch
Herstellernummer:	10950616
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Stein, William
Hersteller:	Springer US Springer New York Undergraduate Texts in Mathematics
Maße:	241 x 160 x 16 mm
Von/Mit:	William Stein
Erscheinungsdatum:	03.12.2008
Gewicht:	0,442 kg