数论基础

图书标准信息

• 作者 [美]史迪威（Stillwell.J.） 著
• 出版社 世界图书出版公司
• 出版时间 2010-05
• 版次 1
• ISBN 9787510004674
• 定价 35.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 254页
• 正文语种 英语

【内容简介】

ThisbookisintendedtocomplementmyElementsofAlgebra，anditissimilarlymotivatedbytheproblemofsolvingpolynomialequations.However，itisindependentofthealgebrabook，andprobablyeasier.InElementsofAlgebrawesoughtsolutionbyradicals，andthisledtotheconceptsoffieldsandgroupsandtheirfusioninthecelebratedtheoryofGalois.Inthepresentbookweseekintegersolutions，andthisleadstotheconceptsofringsandidealswhichmergeintheequallycelebratedtheoryofidealsduetoKummerandDedekind.
Thebookisbasedontwoshortcourses（about20lectureseach）givenatMonashUniversityinrecentyears;oneonelementarynumbertheoryandoneonringtheorywithapplicationstoalgebraicnumbertheory.Thustheamountofmaterialissuitableforaone-semestercourse，withsomevariationpossiblethroughomissionoftheoptionalstarredsections.Aslower~pacedcoursecouldstopattheendofChapter9，atwhichpointmostofthestandardresultshavebeencovered，fromEuclid'stheoremthatthereareinfinitelvmanyprimestoquadraticreciprocity.

【目录】

Preface
1Naturalnumbersandintegers
1.1Naturalnumbers
1.2Induction
1.3Integers
1.4Divisionwithremainder
1.5Binarynotation
1.6Diophantineequations
1.7TheDiophantuschordmethod
1.8Gaussianintegers
1.9Doscission

2TheEuclideanalgorithm
2.1Thegcdbysubtraction
2.2Thegcdbydivisionwithremainder
2.3Linearrepresentationofthegod
2.4Primesandfactorization
2.5Consequencesofuniqueprimefactorization
2.6LinearDiophantineequations
2.7ThevectorEudideanalgorithm
2.8Themapofrelativelyprimepairs
2.9Doscission

3Congruencearithmetic
3.1Congruencemodn
3.2Congruenceclassesandtheirarithmetic
3.3Inversesmodp
3.4Fermat'slittletheorem
3.5CongruencetheoremsofWilsonandLagrange
3.6Inversesmodk
3.7QuadraticDiophantineequations
3.8Primitiveroots
3.9Existenceofprimitiveroots
3.10Discussion

4TheRSAcryptosystem
4.1Trapdoorfunctions
4.2IngredientsofRSA
4.3Exponentiationmodn
4.4RSAencryptionanddecryption
4.5Digitalsignatures
4.60thercomputationalissues
4.7Discussion

5ThePellequation
6TheGaussianintegers
7Quadraticintegers_
8Thefoursquaretheorem
9Quadraticreciprocity
10Rings
11Ideals
12Primeideals
Bibliography
Index