A Course in Computational Algebraic Number Theory (Graduate Texts in Mathematics)

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9783540556404: A Course in Computational Algebraic Number Theory (Graduate Texts in Mathematics)
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This book describes 148 algorithms, which are fundamental for number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing, and factoring. The first seven chapters lead the reader to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations. The last three chapters give a survey of factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The book ends with a description of available computer packages and some useful tables. The book also contains a large number of exercises. Written by an authority in the field, and one with great practical and teaching experience, it is sure to become the standard and indispensable reference on the subject.

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A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.

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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)

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Other Popular Editions of the Same Title

9780387556406: A Course in Computational Algebraic Number Theory (Graduate Texts in Mathematics)

Featured Edition

ISBN 10:  0387556400 ISBN 13:  9780387556406
Publisher: Springer-Verlag New York Inc., 1993
Hardcover

9783642081422: A Course in Computational Algebraic Number Theory (Graduate Texts in Mathematics)

Springer, 2013
Softcover

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