A Course in Computational Algebraic Number Theory by Henri Cohen (English) Paper

Description: A Course in Computational Algebraic Number Theory by Henri Cohen 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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 authors tastes and interests. The most famous, but unfortunately the oldest, is Knuths 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. Notes This book describes 148 algorithms which are essential for serious number-theoretic computations, in particular for computations related to lattices, algebraic number theory, elliptic curves, primality testing and factoring. For each algorithm, a complete theoretical introduction is given so that prerequisites are reduced to a minimum. Many implementation hints and exercises are also provided. Author Biography Cohen, Universite de Bordeaux 1, Talence, France. 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. Review 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 MathematicalAssociation of America, January, 2011) Promotional Corrected second printing Long Description With the advent of powerful computing tools and numerous advances in math Review Quote 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 Promotional "Headline" Corrected second printing Feature Immediate bestselling graduate textbook Description for Sales People This book describes 148 algorithms which are essential for serious number-theoretic computations, in particular for computations related to lattices, algebraic number theory, elliptic curves, primality testing and factoring. For each algorithm, a complete theoretical introduction is given so that prerequisites are reduced to a minimum. Many implementation hints and exercises are also provided. Details ISBN3642081428 Author Henri Cohen Year 2010 ISBN-10 3642081428 ISBN-13 9783642081422 Format Paperback Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany DEWEY 512.74 Edition 1st Short Title COURSE IN COMPUTATIONAL ALGEBR Language English Media Book Series Number 138 Residence US Birth 1945 Illustrations XXI, 536 p. Pages 536 Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Edition Description Softcover reprint of the original 1st ed. 1993 Series Graduate Texts in Mathematics Publication Date 2010-12-08 Alternative 9783540556404 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96231004;

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