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Prime Numbers
A Computational Perspective
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Gewicht:
1080 g
Format:
241x160x39 mm
Beschreibung:
Richard Crandall currently holds the title of Apple Distinguished Scientist, having previously been Apples Chief Cryptographer, the Chief Scientist at NeXT, Inc., and recipient of the Vollum Chair of Science at Reed College. His primary interest is interdisciplinary scientific computation, though he has authored numerous theoretical papers in quantum physics, biology, mathematics, and chemistry, as well as various patents across engineering fields.
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. It is also a timely book, since primes and factoring have reached a certain vogue, partly because of cryptography. The final chapter focusses on "applications" of prime numbers, incorporating the mathematics of finance, via quasi-Monte Carlo theory. Historical comments are contained in every chapter.
In the new edition of this highly successful book, Richard Crandall and Carl Pomerance have provided updated material on theoretical, computational, and algorithmic fronts, including the striking new "AKS" test for recognizing prime numbers. Other examples: new computational results on the Riemann hypothesis, a very new and superfast pure-binary algorithm for the greatest common divisor, and new forms of the fast Fourier transform. The authors also list many new computational records and survey new developments in the theory of prime numbers, including the proof that there are arbitrarily long arithmetic progressions of primes and the proof that 8 and 9 are the only consecutive powers. Numerous exercises have also been added.
Fromt the contents:
Primes!
- Number-Theoretical Tools
- Recognizing Primes and Composites
- Primality Proving
- Exponential Factoring Algorithms
- Sub-Exponential Factoring Algorithms
- Elliptic Curve Arithmetic
- The Ubiquity of Prime Numbers
- Fast Algorithms for Large-Integer Arithmetic
Primes!
- Number-Theoretical Tools
- Recognizing Primes and Composites
- Primality Proving
- Exponential Factoring Algorithms
- Sub-Exponential Factoring Algorithms
- Elliptic Curve Arithmetic
- The Ubiquity of Prime Numbers
- Fast Algorithms for Large-Integer Arithmetic
Bridges the gap between theoretical and computational aspects of prime numbers
Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects
Authors are well-known and highly-regarded in the field