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Ser. textos de posgrado en matemáticas: Curso de número algebraico computacional...-
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N.º de artículo de eBay:255696389404
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Características del artículo
- Estado
- En buen estado
- Notas del vendedor
- Educational Level
- Adult & Further Education
- Level
- Advanced
- Country/Region of Manufacture
- United States
- Original/Facsimile
- Original
- ISBN
- 9783540556404
- Subject Area
- Mathematics, Computers
- Publication Name
- Course in Computational Algebraic Number Theory
- Publisher
- Springer Berlin / Heidelberg
- Item Length
- 9.3 in
- Subject
- Computer Science, Number Theory, Algebra / General
- Publication Year
- 1993
- Series
- Graduate Texts in Mathematics Ser.
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Weight
- 76.5 Oz
- Item Width
- 6.1 in
- Number of Pages
- Xxi, 536 Pages
Acerca de este producto
Product Identifiers
Publisher
Springer Berlin / Heidelberg
ISBN-10
3540556400
ISBN-13
9783540556404
eBay Product ID (ePID)
4446926
Product Key Features
Number of Pages
Xxi, 536 Pages
Language
English
Publication Name
Course in Computational Algebraic Number Theory
Publication Year
1993
Subject
Computer Science, Number Theory, Algebra / General
Type
Textbook
Subject Area
Mathematics, Computers
Series
Graduate Texts in Mathematics Ser.
Format
Hardcover
Dimensions
Item Weight
76.5 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Edition Number
2
Intended Audience
Scholarly & Professional
LCCN
93-003701
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), 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, 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." a?ACTA SCIENTIARUM MATHEMATICARUM, 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), 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 MATHEMATICARUMThis 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), 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)
Dewey Edition
20
Series Volume Number
138
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
512.74028551
Table Of Content
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.
Synopsis
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., 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., "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, 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.
LC Classification Number
QA241-247.5
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