Overview

With the advent of powerful computing tools and numerous advances in math­ ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right. Both external and internal pressures gave a powerful impetus to the development of more powerful al­ gorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL algorithm which has a wide range of appli­ cations, including real world applications to integer programming, primality testing and factoring algorithms, sub-exponential class group and regulator algorithms, etc ... Several books exist which treat parts of this subject. (It is essentially impossible for an author to keep up with the rapid pace of progress in all areas of this subject.) Each book emphasizes a different area, corresponding to the author's tastes and interests. The most famous, but unfortunately the oldest, is Knuth's Art of Computer Programming, especially Chapter 4. The present book has two goals. First, to give a reasonably comprehensive introductory course in computational number theory. In particular, although we study some subjects in great detail, others are only mentioned, but with suitable pointers to the literature. Hence, we hope that this book can serve as a first course on the subject. A natural sequel would be to study more specialized subjects in the existing literature.

Full Product Details

Author:   Henri Cohen
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1st ed. 1993. 4th printing 2000
Volume:   138
Dimensions:   Width: 15.50cm , Height: 3.10cm , Length: 23.50cm
Weight:   2.170kg
ISBN:  

9783540556404

ISBN 10:   3540556400
Pages:   536
Publication Date:   05 August 1993
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Fundamental Number-Theoretic Algorithms.- 2. Algorithms for Linear Algebra and Lattices.- 3. Algorithms on Polynomials.- 4. Algorithms for Algebraic Number Theory I.- 5. Algorithms for Quadratic Fields.- 6. Algorithms for Algebraic Number Theory II.- 7. Introduction to Elliptic Curves.- 8. Factoring in the Dark Ages.- 9. Modern Primality Tests.- 10. Modern Factoring Methods.- Appendix A. Packages for Number Theory.- Appendix B. Some Useful Tables.- B.1. Table of Class Numbers of Complex Quadratic Fields.- B.2. Table of Class Numbers and Units of Real Quadratic Fields.- B.3. Table of Class Numbers and Units of Complex Cubic Fields.- B.4. Table of Class Numbers and Units of Totally Real Cubic Fields.- B.5. Table of Elliptic Curves.

Reviews

H. Cohen A Course in Computational Algebraic Number Theory With numerous advances in mathematics, computer science, and cryptography, algorithmic number theory has become an important subject. Undoubtedly, this book, written by one of the leading authorities in the field, is one of the most beautiful books available on the market. --ACTA SCIENTIARUM MATHEMATICARUM

From the reviews: H. Cohen A Course in Computational Algebraic Number Theory With numerous advances in mathematics, computer science, and cryptography, algorithmic number theory has become an important subject. Undoubtedly, this book, written by one of the leading authorities in the field, is one of the most beautiful books available on the market. -ACTA SCIENTIARUM MATHEMATICARUM This book is intended to provide material for a three-semester sequence, introductory, graduate course in computational algebraic number theory. ... The book is excellent. ... The book has 75 sections, making it suitable for a three-semester sequence. There are numerous exercises at all levels ... . The bibliography is quite comprehensive and therefore has intrinsic value in its own right. ... chapters bring the student to the frontiers of the field, covering elliptic curves, modern primality testing and modern factoring methods. (Russell Jay Hendel, The Mathematical Association of America, January, 2011)

From the reviews:H. CohenA Course in Computational Algebraic Number Theory With numerous advances in mathematics, computer science, and cryptography, algorithmic number theory has become an important subject. Undoubtedly, this book, written by one of the leading authorities in the field, is one of the most beautiful books available on the market. -ACTA SCIENTIARUM MATHEMATICARUM This book is intended to provide material for a three-semester sequence, introductory, graduate course in computational algebraic number theory. ... The book is excellent. ... The book has 75 sections, making it suitable for a three-semester sequence. There are numerous exercises at all levels ... . The bibliography is quite comprehensive and therefore has intrinsic value in its own right. ... chapters bring the student to the frontiers of the field, covering elliptic curves, modern primality testing and modern factoring methods. (Russell Jay Hendel, The Mathematical Association of America, January, 2011)

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