计算数论（第2版）

图书标准信息

• 作者 Song Y.Yan 编
• 出版社 世界图书出版公司
• 出版时间 2004-11
• 版次 2
• ISBN 9787506271905
• 定价 59.00元
• 装帧 精装
• 开本 24开
• 纸张 胶版纸
• 页数 435页

【内容简介】

Sincethepublicationofthefirstedition,Ihavereceivedmanycommunicationsfromreadersallovertheworld.Itismygreatpleasuretothankthefollowingpeoplefortheircomments,correctionsandencouragements:Prof.JimAustin,Prof.FriedrichL.Bauer,Dr.HassanDaghighDr.DenizDeveci,Mr.RichFearn,Prof.MartinHellman,Prof.ZixinHou,Mr.WaseemHus-sain,Dr.GerardR.Maze,Dr.PaulMaguire,Dr.HelmutMeyn,Mr.RobertPargeter,Mr.Mok-KongShen,Dr.PeterShiu,Prof.JonathanP.Sorenson,andDr.DavidL.Stern.SpecialthanksmustbegiventoProf.MartinHellmanofStanfordUniversityforwritingthekindForewordtothiseditionandalsoforhishelpfuladviceandkindguidance,toDr.HansWSssner,Mr.AlfredHofmann,Mrs.IngeborgMayer,Mrs.UlrikeStricker,andMr.FrankHolzwarthofSpringer-Verlagfortheirkindhelpandencouragementsduringthepreparationofthisedition,andtoDr.RodneyColeman,Prof.

【目录】

1.ElementaryNumberTheory
1.1Introduction
1.1.1WhatisNumberTheory?
1.1.2ApplicationsofNumberTheory
1.1.3AlgebraicPreliminaries
1.2TheoryofDivisibility
1.2.1BasicConceptsandPropertiesofDivisibility
1.2.2FundamentalTheoremofArithmetic
1.2.3MersennePrimesandFermatNumbers
1.2.4Euclid'sAlgorithm
1.2.5ContinuedFractions
1.3DiophantineEquations
1.3.1BasicConceptsofDiophantineEquations
1.3.2LinearDiophantineEquations
1.3.3Pell'sEquations
1.4ArithmeticFunctions
1.4.1MultiplicativeFunctions
1.4.2Functions（n），（n）ands（n）
1.4.3Perfect，AmicableandSociableNumbers
1.4.4Functions（n），（n）and（n）
1.5DistributionofPrimeNumbers
1.5.1PrimeDistributionjFunction
1.5.2Approximationsof
1.5.3Approximationaof
1.5.4TheRiemanns-Functions
1.5.5ThenthPrime
1.5.6DistributionofTwinPrimes
1.5.7TheArithmeticProgressionofPrimes
1.6TheoryofCongruences
……
1.7ArthmeticofEllipticCurves
1.8BibliographicNotesandFurtherReading

2Computational/AlgorthmicNumberTheory
2.1introduction
2.2ALgorithmsforPrimalityTesting
2.3AlgorithmsforIntegerFactorization
2.4AlgorithmsforDiscreteLogarithms
2.5QuantumNuber-TheoreticAlgorithms
2.6MiscellaneousAlgorithmsinNumberTheory
2.7BibliographicNotesandFurtherReading

3AppliedNuberTheoryinComputing/Cryptography
3.1WhyAppliedNuberTheory?
3.2ComputerSystemsDesign
3.3CryptographyandInformationSecurity
3.4BibliographicNotesandFurtherReading
Bibliography
Index