Computational Introduction to Number Theory and Algebra

Name: Computational Introduction to Number Theory and Algebra
Price: 211.45 USD
Availability: InStock
ISBN: 9780521851541

ISBN-10: 0521851548

ISBN-13: 9780521851541

Edition: 2005

Authors: Victor Shoup

List price: $62.00

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Description:

Number theory and algebra play an increasingly significant role in computing and communications, as evidenced by the striking applications of these subjects to such fields as cryptography and coding theory. This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The mathematical prerequisites are minimal: nothing beyond material in a typical undergraduate course in calculus is presumed, other than some experience in doing proofs - everything else is developed from scratch. Thus the book can serve several purposes. It can be used as a reference and for self-study by readers who want to learn the…

Book details

List price: $62.00
Copyright year: 2005
Publisher: Cambridge University Press
Publication date: 4/28/2005
Binding: Hardcover
Pages: 534
Size: 7.05" wide x 10.04" long x 1.57" tall
Weight: 2.684
Language: English

Victor Shoup is a Professor in the Department of Computer Science at the Courant Institute of Mathematical Sciences, New York University.



Preface


Preliminaries



Basic properties of the integers



Congruences



Computing with large integers



Euclid's algorithm



The distribution of primes



Finite and discrete probability distributions



Probabilistic algorithms



Abelian groups



Rings



Probabilistic primality testing



Finding generators and discrete logarithms in Zp*



Quadratic residues and quadratic reciprocity



Computational problems related to quadratic residues



Modules and vector spaces



Matrices



Subexponential-time discrete logarithms and factoring



More rings



Polynomial arithmetic and applications



Linearly generated sequences and applications



Finite fields



Algorithms for finite fields



Deterministic primality testing


Appendix: some useful facts


Bibliography


Index of notation


Index