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Computational Introduction to Number Theory and Algebra

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 mathematical foundations of modern cryptography. It is also ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.
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Book details

List price: $62.00
Copyright year: 2005
Publisher: Cambridge University Press
Publication date: 4/28/2005
Binding: Hardcover
Pages: 534
Size: 7.00" wide x 10.00" long x 1.00" 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