advanced topics in computational number theory graduate texts in mathematics

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Advanced Topics In Computational Number Theory

Author : Henri Cohen
ISBN : 0387987274
Genre : Mathematics
File Size : 34. 49 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.

Advanced Topics In Computational Number Theory

Author : Henri Cohen
ISBN : 9781441984890
Genre : Mathematics
File Size : 66. 15 MB
Format : PDF
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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 : 3540556400
Genre : Mathematics
File Size : 25. 97 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.

Number Theory

Author : Henri Cohen
ISBN : 0387498931
Genre : Mathematics
File Size : 30. 99 MB
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This book deals with several aspects of what is now called "explicit number theory." The central theme is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The local aspect, global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject.

A Course In Number Theory And Cryptography

Author : Neal Koblitz
ISBN : 0387942939
Genre : Mathematics
File Size : 74. 64 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.

A Classical Introduction To Modern Number Theory

Author : Kenneth Ireland
ISBN : 038797329X
Genre : Mathematics
File Size : 70. 27 MB
Format : PDF, ePub
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Bridging the gap between elementary number theory and the systematic study of advanced topics, A Classical Introduction to Modern Number Theory is a well-developed and accessible text that requires only a familiarity with basic abstract algebra. Historical development is stressed throughout, along with wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. An extensive bibliography and many challenging exercises are also included. This second edition has been corrected and contains two new chapters which provide a complete proof of the Mordell-Weil theorem for elliptic curves over the rational numbers, and an overview of recent progress on the arithmetic of elliptic curves.

Problems In Algebraic Number Theory

Author : M. Ram Murty
ISBN : 9780387269986
Genre : Mathematics
File Size : 89. 30 MB
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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

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