Overview
- Immediate bestselling graduate textbook
Part of the book series: Graduate Texts in Mathematics (GTM, volume 138)
Access this book
Tax calculation will be finalised at checkout
A Course in Computational Algebraic Number Theory
- Textbook
- © 1993
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.
Similar content being viewed by others
Table of contents (10 chapters)
-
Front Matter
-
Back Matter
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
Accessibility Information
PDF accessibility summary
This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at [email protected] if you require assistance or an alternative format.
Bibliographic Information
Book Title: A Course in Computational Algebraic Number Theory
Authors: Henri Cohen
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-662-02945-9
Publisher: Springer Berlin, Heidelberg
-
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag GmbH Germany, part of Springer Nature 1993
Hardcover ISBN: 978-3-540-55640-4Published: 05 August 1993
Softcover ISBN: 978-3-642-08142-2Published: 08 December 2010
eBook ISBN: 978-3-662-02945-9Published: 17 April 2013
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XXI, 536
Topics: Number Theory, Algebra, Theory of Computation, Algorithm Analysis and Problem Complexity, Algorithms, Symbolic and Algebraic Manipulation