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美 Michael Artin 著
店铺: 互动出版网图书专营店 出版社: 机械工业出版社 ISBN:9787111367017 商品编码:1247882370 丛书名: 华章数学原版精品系列 出版时间:2012-01-01 页数:543
代数(英文版.第2版) (美)Michael Artin|198897 电子书 下载 mobi epub pdf txt
代数(英文版.第2版) (美)Michael Artin|198897-so88
代数(英文版.第2版) (美)Michael Artin|198897 pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
美 Michael Artin 著
店铺: 互动出版网图书专营店 出版社: 机械工业出版社 ISBN:9787111367017 商品编码:1247882370 丛书名: 华章数学原版精品系列 出版时间:2012-01-01 页数:543
书名: | 代数(英文版.第2版)|198897 |
图书定价: | 79元 |
图书作者: | (美)Michael Artin |
出版社: | 机械工业出版社 |
出版日期: | 2012/1/1 0:00:00 |
ISBN号: | 9787111367017 |
开本: | 16开 |
页数: | 543 |
版次: | 2-1 |
作者简介 |
Michael Artin 当代领袖型代数学家与代数几何学家之一,美国麻省理工学院数学系荣誉退休教授。1990年至1992年,曾担任美国数学学会主席。由于他在交换代数与非交换代数、环论以及现代代数几何学等方面做出的贡献,2002年获得美国数学学会颁发的Leroy P.Steele终身成就奖。Artin的主要贡献包括他的逼近定理、在解决沙法列维奇-泰特猜测中的工作以及为推广“概形”而创建的“代数空间”概念。 |
内容简介 |
《代数(英文版.第2版)》由著名代数学家与代数几何学家Michael Artin所著,是作者在代数领域数十年的智慧和经验的结晶。书中既介绍了矩阵运算、群、向量空间、线性算子、对称等较为基本的内容,又介绍了环、模型、域、伽罗瓦理论等较为高深的内容。本书对于提高数学理解能力,增强对代数的兴趣是非常有益处的。此外,本书的可阅读性强,书中的习题也很有针对性,能让读者很快地掌握分析和思考的方法。 作者结合这20年来的教学经历及读者的反馈,对本版进行了全面更新,更强调对称性、线性群、二次数域和格等具体主题。本版的具体更新情况如下: 新增球面、乘积环和因式分解的计算方法等内容,并补充给出一些结论的证明,如交错群是简单的、柯西定理、分裂定理等。 修订了对对应定理、SU2 表示、正交关系等内容的讨论,并把线性变换和因子分解都拆分为两章来介绍。 新增大量习题,并用星号标注出具有挑战性的习题。 《代数(英文版.第2版)》在麻省理工学院、普林斯顿大学、哥伦比亚大学等著名学府得到了广泛采用,是代数学的经典教材之一。 |
目录 |
《代数(英文版.第2版)》 Preface 1 Matrices 1.1 The Basic Operations 1.2 Row Reduction 1.3 The Matrix Transpose 1.4 Determinants 1.5 Permutations 1.6 Other Formulas for the Determinant Exercises 2 Groups 2.1 Laws of Composition 2.2 Groups and Subgroups 2.3 Subgroups of the Additive Group of Integers. 2.4 Cyclic Groups 2.5 Homomorphisms 2.6 Isomorphisms 2.7 Equivalence Relations and Partitions 2.8 Cosets 2.9 Modular Arithmetic 2.10 The Correspondence Theorem 2.11 Product Groups 2.12 Quotient Groups Exercises 3 Vector Spaces 3.1 Subspaces of Rn 3.2 Fields 3.3 Vector Spaces 3.4 Bases and Dimension 3.5 Computing with Bases 3.6 Direct Sums 3.7 Infinite-Dimensional Spaces Exercises 4 Linear Operators 4.1 The Dimension Formula 4.2 The Matrix of a Linear Transformation 4.3 Linear Operators 4.4 Eigenvectors 4.5 The Characteristic Polynomial 4.6 Triangular and Diagonal Forms 4.7 Jordan Form Exercises 5 Applications of Linear Operators 5.1 Orthogonal Matrices and Rotations 5.2 Using Continuity 5.3 Systems of Differential Equations 5.4 The Matrix Exponential Exercises 6 Symmetry 6.1 Symmetry of Plane Figures 6.2 Isometries 6.3 Isometries of the Plane 6.4 Finite Groups of Orthogonal Operators on the Plane 6.5 Discrete Groups of Isometries 6.6 Plane Crystallographic Groups 6.7 Abstract Symmetry: Group Operations 6.8 The Operation on Cosets 6.9 The Counting Formula 6.10 Operations on Subsets 6.11 Permutation Representations 6.12 Finite Subgroups of the Rotation Group Exercises 7 More Group Theory 7.1 Cayley's Theorem 7.2 The Class Equation 7.3 p-Groups 7.4 The Class Equation of the Icosahedral Group 7.5 Conjugation in the Symmetric Group 7.6 Normalizers 7.7 The Sylow Theorems 7.8 Groups of Order 12 7.9 The Free Group 7.10 Generators and Relations 7.11 The Todd-Coxeter Algorithm Exercises 8 Bilinear Forms 8.1 Bilinear Forms 8.2 Symmetric Forms 8.3 Hermitian Forms 8.4 Orthogonality 8.5 Euclidean Spaces and Hermitian Spaces 8.6 The Spectral Theorem 8.7 Conics and Quadrics 8.8 Skew-Symmetric Forms 8.9 Summary Exercises 9 Linear Groups 9.1 The Classical Groups 9.2 Interlude: Spheres 9.3 The Special Unitary Group SU2 9.4 The Rotation Group S03 9.5 One-Parameter Groups 9.6 The Lie Algebra 9.7 Translation in a Group 9.8 Normal Subgroups of SL2 Exercises 10 Group Representations 10.1 Definitions 10.2 Irreducible Representations 10.3 Unitary Representations 10.4 Characters 10.5 One-Dimensional Characters 10.6 The Regular Representation 10.7 Schur's Lemma 10.8 Proof of the Orthogonality Relations 10.9 Representations of SU2 Exercises 11 Rings 11.1 Definition of a Ring 11.2 Polynomial Rings 11.3 Homomorphisms and Ideals 11.4 Quotient Rings 11.5 Adjoining Elements 11.6 Product Rings 11.7 Fractions 11.8 Maximal Ideals 11.9 Algebraic Geometry Exercises 12 Factoring 12.1 Factoring Integers 12.2 Unique Factorization Domains 12.3 Gauss's Lemma 12.4 Factoring Integer Polynomials 12.5 Gauss Primes Exercises 13 Quadratic Number Fields 13.1 Algebraic Integers 13.2 Factoring Algebraic Integers 13.3 Ideals in Z 13.4 Ideal Multiplication 13.5 Factoring Ideals 13.6 Prime Ideals and Prime Integers 13.7 Ideal Classes 13.8 Computing the Class Group 13.9 Real Quadratic Fields 13.10 About Lattices Exercises 14 Linear Algebra in a Ring 14.1 Modules 14.2 Free Modules 14.3 Identities 14.4 Diagonalizing Integer Matrices 14.5 Generators and Relations 14.6 Noetherian Rings 14.7 Structure of Abelian Groups 14.8 Application to Linear Operators 14.9 Polynomial Rings in Several Variables Exercises 15 Fields 15.1 Examples of Fields 15.2 Algebraic and Transcendental Elements 15.3 The Degree of a Field Extension 15.4 Finding the Irreducible Polynomial 15.5 Ruler and Compass Constructions 15.6 Adjoining Roots 15.7 Finite Fields 15.8 Primitive Elements 15.9 Function Fields 15.10 The Fundamental Theorem of Algebra Exercises 16 Galois Theory 16.1 Symmetric Functions 16.2 The Discriminant 16.3 Splitting Fields 16.4 Isomorphisms of Field Extensions 16.5 Fixed Fields 16.6 Galois Extensions 16.7 The Main Theorem 16.8 Cubic Equations 16.9 Quartic Equations 16.10 Roots of Unity 16.11 Kummer Extensions 16.12 Quintic Equations Exercises APPENDIX Background Material A.1 About Proofs A.2 The Integers A.3 Zorn's Lemma A.4 The Implicit Function Theorem Exercises Bibliography Notation Index |
代数(英文版.第2版) (美)Michael Artin|198897 电子书 下载 mobi epub pdf txt
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