抽象代數(shù)基礎(chǔ)教程

內(nèi)容概要

　　《抽象代數(shù)基礎(chǔ)教程（英文版·第3版）》系統(tǒng)地介紹了抽象代數(shù)的基礎(chǔ)內(nèi)容，包括群、環(huán)、域、模等，每一部分獨(dú)立成章，本科生、研究生等不同層次的讀者可以挑選閱讀。書中范例豐富，風(fēng)趣易懂；另外，每一小節(jié)后都配有一定數(shù)量、難易不等的習(xí)題，書后還附有解答與提示，便于教學(xué)和自學(xué)。　　與第2版相比，第3版的更新如下：　　闡述更清晰，表達(dá)更順暢?！　≡谇拔逭轮?，最重要的節(jié)，小節(jié)，定義，定理，例子旁邊加有箭頭指示?！　“巳我庥蛏系木€性代數(shù)的更多知識。　　增加了一節(jié)介紹分類平面上的楣（frieze）群?！　≡黾恿?00多道習(xí)題　　本書可供高等院校數(shù)學(xué)系師生及有關(guān)工程技術(shù)人員使用。

作者簡介

　　Joseph J.Rotman美國伊利諾伊大學(xué)厄巴納-尚佩恩分校數(shù)學(xué)系教授。他著有多部數(shù)學(xué)方面的書，其中包括《Adanced Modern Algebra》（高等近世代數(shù)，本書中文版由機(jī)械工業(yè)出版社引進(jìn)出版），（Galois Theory）等。

書籍目錄

Preface to the Third EditionSuggested SyllabiTo the ReaderChapter I Number TheorySection 1.1 InductionSection 1.2 Binomial Theorem and Complex NumbersSection 1.3 Greatest Common DivisorsSection 1.4 The Fundamental Theorem of Arithmetic Section 1.5 CongruencesSection 1.6 Dates and DaysChapter 2 Groups ISection 2.1 Some Set Theory FunctionsEquivalence RelationsSection 2.2 Permutations Section 2.3 GroupsSymmetrySection 2.4 Subgroups and Lagrange's Theorem Section 2.5 HomomorphismsSection 2.6 Quotient GroupsSection 2.7 Group ActionsSection 2.8 Counting with GroupsChapter 3 Commutative Rings ISection 3.1 First Properties Section 3.2 FieldsSection 3.3 PolynomialsSection 3.4 HomomorphismsSection 3.5 From Numbers to Polynomials .Euclidean RingsSection 3.6 Unique FactorizationSection 3.7 IrreducibilitySection 3.8 Quotient Rings and Finite FieldsSection 3.9 A Mathematical OdysseyLatin SquaresMagic SquaresDesign of ExperimentsProjective PlanesChapter 4 Linear AlgebraSection 4.1 Vector SpacesGaussian Elimination Section 4.2 Euclidean Constructions Section 4.3 Linear TransformationsSection 4.4 EigenvaluesSection 4.5 CodesBlock CodesLinear CodesDecodingChapter 5 FieldsSection 5.1 Classical FormulasViete's Cubic FormulaSection 5.2 Insolvability of the General QuinticFormulas and Solvability by Radicals Quadratics CubicsQuarticsTranslation into Group TheorySection 5,3 Epilog Chapter 6 Groups HSection 6.1 Finite Abelian GroupsSection 6.2 The Sylow TheoremsSection 6.3 Ornamental SymmetryChapter 7 Commutative Rings IISection 7.1 Prime Ideals and Maximal IdealsSection 7.2 Unique FactorizationSection 7.3 Noetherian RingsSection 7.4 VarietiesSection 7.5 Generalized Divison Algorithm .Monomial OrdersDivision AlgorithmSection 7.6 Grobner BasesAppendix A InequalitiesAppendix B PseudocodesHints for Selected ExercisesBibliographyIndex

圖書封面

圖書標(biāo)簽Tags

無

評論、評分、閱讀與下載

---

    抽象代數(shù)基礎(chǔ)教程 PDF格式下載

---