A Computational Introduction to Number Theory and Algebra / Edition 2

by Victor Shoup

Overview

This introductory book emphasizes algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The presentation alternates between theory and applications in order to motivate and illustrate the mathematics. The mathematical coverage includes the basics of number theory, abstract algebra and discrete probability theory. This edition now includes over 150 new exercises, ranging from the routine to the challenging, that flesh out the material presented in the body of the text, and which further develop the theory and present new applications. The material has also been reorganized to improve clarity of exposition and presentation. Ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.

Product Details

ISBN-13:	9780521516440
Publisher:	Cambridge University Press
Publication date:	12/04/2008
Edition description:	New Edition
Pages:	600
Product dimensions:	6.80(w) x 9.70(h) x 1.40(d)

About the Author

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

Table of Contents

Preface; Preliminaries; 1. Basic properties of the integers; 2. Congruences; 3. Computing with large integers; 4. Euclid's algorithm; 5. The distribution of primes; 6. Abelian groups; 7. Rings; 8. Finite and discrete probability distributions; 9. Probabilistic algorithms; 10. Probabilistic primality testing; 11. Finding generators and discrete logarithms in Z*p; 12. Quadratic reciprocity and computing modular square roots; 13. Modules and vector spaces; 14. Matrices; 15. Subexponential-time discrete logarithms and factoring; 16. More rings; 17. Polynomial arithmetic and applications; 18. Linearly generated sequences and applications; 19. Finite fields; 20. Algorithms for finite fields; 21. Deterministic primality testing; Appendix: some useful facts; Bibliography; Index of notation; Index.

What People are Saying About This

From the Publisher

"The subject matter is presented in a very thorough way. Detailed and clear proofs are given for (almost) all results. The material is very well organized: definitions, results, and their interrelations fit together perfectly. The book is especially attractive to students with a background or interest in computer science. On the other hand, students who already have a background in abstract algebra can benefit greatly from this book by skipping some parts where algebraic theory is introduced. The suitability of the book for self-study is greatly enhanced by a wealth of exercises and examples that are provided. Last but not least, the book is very well-written, and it is a pleasure to read.
Gregor Kemper, Mathematics of Computation

"It’s a pleasure to find a book that is so masterful and so well written that it has all the hallmarks of a classic. This is such a book.This is a truly magnificent text, deserving of a place on the shelves of any mathematician or computer scientist working in these areas."
Alasdair McAndrew, Computing Reviews

Editorial Reviews

"The subject matter is presented in a very thorough way. Detailed and clear proofs are given for (almost) all results. The material is very well organized: definitions, results, and their interrelations fit together perfectly. The book is especially attractive to students with a background or interest in computer science. On the other hand, students who already have a background in abstract algebra can benefit greatly from this book by skipping some parts where algebraic theory is introduced. The suitability of the book for self-study is greatly enhanced by a wealth of exercises and examples that are provided. Last but not least, the book is very well-written, and it is a pleasure to read.
Gregor Kemper, Mathematics of Computation

"It’s a pleasure to find a book that is so masterful and so well written that it has all the hallmarks of a classic. This is such a book.This is a truly magnificent text, deserving of a place on the shelves of any mathematician or computer scientist working in these areas."
Alasdair McAndrew, Computing Reviews

From the Publisher