advanced topics in computational number theory graduate texts in mathematics

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Advanced Topics In Computational Number Theory

Author : Henri Cohen
ISBN : 9781441984890
Genre : Mathematics
File Size : 53. 91 MB
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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.

A Course In Computational Algebraic Number Theory

Author : Henri Cohen
ISBN : 9783662029459
Genre : Mathematics
File Size : 40. 76 MB
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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.

Algorithmic Number Theory

Author : Duncan Buell
ISBN : 9783540248477
Genre : Mathematics
File Size : 72. 88 MB
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The sixth Algorithmic Number Theory Symposium was held at the University of Vermont, in Burlington, from 13–18 June 2004. The organization was a joint e?ort of number theorists from around the world. There were four invited talks at ANTS VI, by Dan Bernstein of the Univ- sity of Illinois at Chicago, Kiran Kedlaya of MIT, Alice Silverberg of Ohio State University, and Mark Watkins of Pennsylvania State University. Thirty cont- buted talks were presented, and a poster session was held. This volume contains the written versions of the contributed talks and three of the four invited talks. (Not included is the talk by Dan Bernstein.) ANTS in Burlington is the sixth in a series that began with ANTS I in 1994 at Cornell University, Ithaca, New York, USA and continued at Universit ́eB- deaux I, Bordeaux, France (1996), Reed College, Portland, Oregon, USA (1998), the University of Leiden, Leiden, The Netherlands (2000), and the University of Sydney, Sydney, Australia (2002). The proceedings have been published as volumes 877, 1122, 1423, 1838, and 2369 of Springer-Verlag’s Lecture Notes in Computer Science series. The organizers of the 2004 ANTS conference express their special gratitude and thanks to John Cannon and Joe Buhler for invaluable behind-the-scenes advice.

Algorithmic Number Theory

Author : Claus Fieker
ISBN : 9783540454557
Genre : Mathematics
File Size : 47. 97 MB
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An Introduction To Number Theory

Author : G. Everest
ISBN : 9781852339173
Genre : Mathematics
File Size : 32. 35 MB
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Includes up-to-date material on recent developments and topics of significant interest, such as elliptic functions and the new primality test Selects material from both the algebraic and analytic disciplines, presenting several different proofs of a single result to illustrate the differing viewpoints and give good insight

A Course In Number Theory And Cryptography

Author : Neal Koblitz
ISBN : 9781441985927
Genre : Mathematics
File Size : 84. 94 MB
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This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.

Introduction To Modern Number Theory

Author : Yu. I. Manin
ISBN : 3540276920
Genre : Mathematics
File Size : 35. 91 MB
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This edition has been called ‘startlingly up-to-date’, and in this corrected second printing you can be sure that it’s even more contemporaneous. It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory. Illuminated by elementary problems, the central ideas of modern theories are laid bare. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories.

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