Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Crandall, Richard E. (1947-2012)
Titre(s) : Prime numbers [Texte électronique] : a computational perspective / Ricahrd Crandall, Carl Pomerance
Édition : 2nd ed.
Publication : New York, NY : Springer, 2005
Description matérielle : 1 online resource (xv, 597 pages)
Collection : Lecture notes in statistics (Springer-Verlag) ; v. 182
Note(s) : Includes bibliographical references (pages 547-575) and index
Prime numbers beckon to the beginner, as the basic notion of primality is accessible
even to children. Yet, some of the simplest questions about primes have confounded
humankind for millennia. In the new edition of this highly successful book, Richard
Crandall and Carl Pomerance have provided updated material on theoretical, computational,
and algorithmic fronts. New results discussed include the AKS test for recognizing
primes, computational evidence for the Riemann hypothesis, a fast binary algorithm
for the greatest common divisor, nonuniform fast Fourier transforms, and more. The
authors also list new computational records and survey new developments in the theory
of prime numbers, including the magnificent proof that there are arbitrarily long
arithmetic progressions of primes, and the final resolution of the Catalan problem.
Numerous exercises have been added. Richard Crandall currently holds the title of
Apple Distinguished Scientist, having previously been Apple's Chief Cryptographer,
the Chief Scientist at NeXT, Inc., and recipient of the Vollum Chair of Science at
Reed College. Though he publishes in quantum physics, biology, mathematics, and chemistry,
and holds various engineering patents, his primary interest is interdisciplinary scientific
computation. Carl Pomerance is the recipient of the Chauvenet and Conant Prizes for
expository mathematical writing. He is currently a mathematics professor at Dartmouth
College, having previously been at the University of Georgia and Bell Labs. A popular
lecturer, he is well known for his research in computational number theory, his efforts
having produced important algorithms now in use. From the reviews of the first edition:
"Destined to become a definitive textbook conveying the most modern computational
ideas about prime numbers and factoring, this book will stand as an excellent reference
for this kind of computation, and thus be of interest to both educators and researchers."
" ... Prime Numbers is a welcome addition to the literature of number theory--comprehensive,
up-to-date and written with style."--American Scientist "It's rare to say this of
a math book, but open Prime Numbers to a random page and it's hard to put down. Crandall
and Pomerance have written a terrific book."--Bulletin of the AMS
Autre(s) auteur(s) : Pomerance, Carl. Fonction indéterminée
Sujet(s) : Nombres premiers
Indice(s) Dewey :
512.723 (23e éd.) = Nombres premiers ; 512.72 (23e éd.) = Théorie élémentaire des nombres
Identifiants, prix et caractéristiques : ISBN 9780387289793
Identifiant de la notice : ark:/12148/cb446419803
Notice n° :
FRBNF44641980
(notice reprise d'un réservoir extérieur)
Table des matières : Preface ; Primes! ; Number-Theoretical Tools ; Recognizing Primes and Composites.-Primality
Proving ; Exponential Factoring Algorithms ; Subexponential Factoring Algorithms
; Elliptic Curve Arithmetic ; The Ubiquity of Prime Numbers ; Fast Algorithms for
Large-Integer Arithmetic ; Book Pseudocode ; References ; Index.
