A Course in Computational Algebraic Number Theory
A Course in Computational Algebraic Number Theory

Author: Henri Cohen

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 556

ISBN-13: 3662029456

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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.

Advanced Topics in Computational Number Theory
Advanced Topics in Computational Number Theory

Author: Henri Cohen

Publisher: Springer Science & Business Media

Published: 2012-10-29

Total Pages: 591

ISBN-13: 1441984895

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Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects.

Computational Algebraic Number Theory
Computational Algebraic Number Theory

Author: M.E. Pohst

Publisher: Springer Science & Business Media

Published: 1993-09

Total Pages: 108

ISBN-13: 9783764329136

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Computational algebraic number theory has been attracting broad interest in the last few years due to its potential applications in coding theory and cryptography. For this reason, the Deutsche Mathematiker-Vereinigung initiated an introductory graduate seminar on this topic in Dusseldorf. The lectures given there by the author served as the basis for this book which allows fast access to the state of the art in this area. Special emphasis has been placed on practical algorithms - all developed in the last five years - for the computation of integral bases, the unit group and the class group of arbitrary algebraic number fields. The workshops organized by the Gesselschaft fur mathematische Forschung in cooperation with the Deutsche Mathematiker-Vereinigung (German Mathematics Society) are intended to help, in particular, students and younger mathematicians, to obtain an introduction to fields of current research. Through the means of these well-organized seminars, scientists from other fields can also be introduced to new mathematical ideas. The publication of these workshops in the series DMV SEMINAR will make the material available to an even larger audience.

Computational Number Theory
Computational Number Theory

Author: Abhijit Das

Publisher: CRC Press

Published: 2016-04-19

Total Pages: 614

ISBN-13: 1482205823

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Developed from the author's popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and pract

Computational Algebra and Number Theory
Computational Algebra and Number Theory

Author: Wieb Bosma

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 326

ISBN-13: 9401711089

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Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for implementing computational methods, the viewing of old techniques from a concrete algorithmic vantage point, to name but a few. Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed. Audience: Students, experts, and those performing current research in any of the topics mentioned above.

Algorithmic Algebraic Number Theory
Algorithmic Algebraic Number Theory

Author: M. Pohst

Publisher: Cambridge University Press

Published: 1997-09-25

Total Pages: 520

ISBN-13: 9780521596695

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Now in paperback, this classic book is addresssed to all lovers of number theory. On the one hand, it gives a comprehensive introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. On the other hand many parts go beyond an introduction an make the user familliar with recent research in the field. For experimental number theoreticians new methods are developed and new results are obtained which are of great importance for them. Both computer scientists interested in higher arithmetic and those teaching algebraic number theory will find the book of value.

Problems in Algebraic Number Theory
Problems in Algebraic Number Theory

Author: M. Ram Murty

Publisher: Springer Science & Business Media

Published: 2005-09-28

Total Pages: 354

ISBN-13: 0387269983

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The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved

Algebraic Number Theory and Fermat's Last Theorem
Algebraic Number Theory and Fermat's Last Theorem

Author: Ian Stewart

Publisher: CRC Press

Published: 2001-12-12

Total Pages: 334

ISBN-13: 143986408X

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First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it

A Brief Guide to Algebraic Number Theory
A Brief Guide to Algebraic Number Theory

Author: H. P. F. Swinnerton-Dyer

Publisher: Cambridge University Press

Published: 2001-02-22

Total Pages: 164

ISBN-13: 9780521004237

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Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.

Algebraic Number Theory
Algebraic Number Theory

Author: H. Koch

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 274

ISBN-13: 3642580955

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From the reviews: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." Medelingen van het wiskundig genootschap, 1995