Mathematicians do not study objects, but relations among objectsj they are indifferent to the replacement of objects by others as long as relations do not change. Matter is not important, only form interests them. HENRI POINCARE (1854-1912) Computer scientists working on algorithms for factorization would be well advised to brush up on their number theory. IAN STEWART [219] The theory of numbers, in mathematics, is primarily the theory of the prop erties of integers (i.e., the whole numbers), particularly the positive integers. For example, Euclid proved 2000 years aga in his Elements that there exist infinitely many prime numbers. The subject has long been considered as the purest branch of mathematics, with very few applications to other areas. How ever, recent years have seen considerable increase in interest in several central topics of number theory, precisely because of their importance and applica tions in other areas, particularly in computing and information technology.
Rezensionen / Stimmen
From the reviews of the second edition:
"This book gives a profound and detailed insight at an undergraduate level in abstract and computational number theory as well as in applications in computing and cryptography. . The author has done a lot of work in providing a plenty of examples, in adding many historical comments including sketchy biographies . and in presenting the whole topic in a very accessible style. So the book can be recommended warmly for the laymen as well as for the mathematician without experience in applied number theory." (G. Kowol, Monatshefte für Mathematik, Vol. 140 (4), 2003)
Sprache
Verlagsort
Verlagsgruppe
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Dateigröße
ISBN-13
978-3-662-04053-9 (9783662040539)
DOI
10.1007/978-3-662-04053-9
Schweitzer Klassifikation
Preface.- Notations.- Elementary Number Theory: Introduction. Theory of Divisibility. Diophantine Equations. Arithmetical Functions. Theory of Congruences. Arithmetic of Elliptic Curves. Bibliographic Notes and Further Reading.- Algorithmic Number Theory: Introduction. Algorithms for Primality Testing. Algorithms for Integer Factorization. Algorithms for Discrete Logarithms. Quantum Algorithmic Number Theory. Bibliographic Notes and Further Reading.- Applied Number Theory: Why Applied Number Theory. Computer Systems Design. Cryptology and Information Security.- Bibliographic Notes and Further Reading.- Bibliography.- Index.
