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Graduate Texts in Mathematics

A Course in Computational Algebraic Number Theory

Authors: Cohen, Henri

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eBook 54,99 €
price for Spain (gross)
valid through October 16, 2017
  • ISBN 978-3-662-02945-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 67,55 €
price for Spain (gross)
valid through October 16, 2017
  • ISBN 978-3-540-55640-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 67,55 €
price for Spain (gross)
  • ISBN 978-3-642-08142-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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 Mathematical Association of America, January, 2011)


Table of contents (10 chapters)

  • Fundamental Number-Theoretic Algorithms

    Cohen, Henri

    Pages 1-44

    Preview Buy Chapter 30,19 €
  • Algorithms for Linear Algebra and Lattices

    Cohen, Henri

    Pages 45-107

    Preview Buy Chapter 30,19 €
  • Algorithms on Polynomials

    Cohen, Henri

    Pages 108-150

    Preview Buy Chapter 30,19 €
  • Algorithms for Algebraic Number Theory I

    Cohen, Henri

    Pages 151-217

    Preview Buy Chapter 30,19 €
  • Algorithms for Quadratic Fields

    Cohen, Henri

    Pages 218-296

    Preview Buy Chapter 30,19 €

Buy this book

eBook 54,99 €
price for Spain (gross)
valid through October 16, 2017
  • ISBN 978-3-662-02945-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 67,55 €
price for Spain (gross)
valid through October 16, 2017
  • ISBN 978-3-540-55640-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 67,55 €
price for Spain (gross)
  • ISBN 978-3-642-08142-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
A Course in Computational Algebraic Number Theory
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
138
Copyright
1993
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-02945-9
DOI
10.1007/978-3-662-02945-9
Hardcover ISBN
978-3-540-55640-4
Softcover ISBN
978-3-642-08142-2
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XXI, 536
Topics