基本信息
作 者：（美）班傑明，（美）傑哈德 著出版社：清華大學出版社
出版時間：2009-11-1
開 本：16開
ISBN：9787302214793
代數基本定理定價：￥34.00
內容簡介
本書對數學中最重要的定理——代數基本定理給出了六種證明，方法涉及到分析、代數與拓撲等數學分支。全書以一個問題為主線，縱橫數學的幾乎所有領域，結構嚴謹、文筆流暢、淺顯易懂，適合高年級大學生、研究生自學和討論，特別適合於用作短學期教材或數學選修類課程教材。目錄
Preface1IntroductionandHistoricalRemarksComplexNumbers
2.1FieldsandtheRealField
2.2TheComplexNumberField
2.3GeometricalRepresentationofComplexNumbers
2.4PolarFormandEuler'sIdentity
2.5DeMoivre'sTheoremforPowersandrootsExercises
3PolynomialsandComplexPolynomials
3.1TheKingofPolynomialsoveraField
3.2DivisibilityandUniquefactorizationofPolynomials
3.3RootsofPolynomialsandFactorization
3.4RealandComplexPolynomials
3.5TheFundamentalTheoremofAlgebra:ProofOne
3.6SomeConsequencesoftheFundamentalTheoremExercises
4ComplexAnalysisandAnalyticFunctions
4.1ComplexFunctionsandAnalyticity
5ComplexIntegrationandCauchy'sTheorem
6FieldsandFieldExtensions
7GaloisTheory
8TopologyandTopologicalSpaces
AlgebraicTopologyandtheFinalProof
AppendixA:AVersionofGauss'sOriginalProof
AppendixB:Cauchy'sTheoremRevisited
AppendixC:ThreeAdditionalComplexAnalyticProofsoftheFundamentalTheoremofAlgebra
AppendixD:TwoMoreTopologicalProofsoftheFundamentalTheoremofAlgebra
BibliographyandReferences
Index
