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A Course in Computational Algebraic Number Theory

  • Textbook
  • © 1993

Overview

Authors:
  1. Henri Cohen

    1. U.F.R. de Mathématiques et Informatique, Université Bordeaux I, Talence Cedex, France

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  • Immediate bestselling graduate textbook

Part of the book series: Graduate Texts in Mathematics (GTM, volume 138)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XXI
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  2. Fundamental Number-Theoretic Algorithms

    • Henri Cohen
    Pages 1-44

  3. Algorithms for Linear Algebra and Lattices

    • Henri Cohen
    Pages 45-107

  4. Algorithms on Polynomials

    • Henri Cohen
    Pages 108-150

  5. Algorithms for Algebraic Number Theory I

    • Henri Cohen
    Pages 151-217

  6. Algorithms for Quadratic Fields

    • Henri Cohen
    Pages 218-296

  7. Algorithms for Algebraic Number Theory II

    • Henri Cohen
    Pages 297-359

  8. Introduction to Elliptic Curves

    • Henri Cohen
    Pages 360-411

  9. Factoring in the Dark Ages

    • Henri Cohen
    Pages 412-436

  10. Modern Primality Tests

    • Henri Cohen
    Pages 437-468

  11. Modern Factoring Methods

    • Henri Cohen
    Pages 469-497

  12. Back Matter

    Pages 498-536
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Keywords

About this book

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.

Reviews

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 MathematicalAssociation of America, January, 2011)

Authors and Affiliations

  • U.F.R. de Mathématiques et Informatique, Université Bordeaux I, Talence Cedex, France

    Henri Cohen

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