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代数(英文版)

代数(英文版)

作者:[美]Michael Artin

分类:文学

ISBN:9787111139133

出版时间:2004-3-1

出版社:机械工业出版社

标签: 数学  代数  algebra  抽象代数  math  Mathematics  教材  近世代数 

章节目录

Preface A Note for the Teacher Chapter I Matrix Operations 1. The Basic Operations 1 2. Row Reduction 9 3. Determinants 18 4. Permutation Matrices 24 5. Cramer's Rule 28 EXERCISES 31 Chapter 2 Groups 1. The Definition of a Group 38 2. Subgroups 44 3. Isomorphisms 48 4. Homomorphisms 51 $. Equivalence Relations and Partitions 53 6. Cosets 57 7. Restriction of a Homomorphism to a Subgroup 59 8. Products of Groups 61 9. Modular Arithmetic 64 10. Quotient Groups 66 EXERCISES 69 Chapter 3 Vector Spaces 1. Real Vector Spaces 78 2. Abstract Fields 82 3. Bases and Dimension 87 4. Computation with Bases 94 5. Infinite-Dimensional Spaces 100 6. Direct Sums 102 EXERCISES 104 Chapter 4 Linear Transformations 1. The Dimension Formula 109 2. The Matrix of a Linear Transformation 111 3. Linear Operators and Eigenvectors 115 4. The Characteristic Polynomial 120 5. Orthogonal Matrices and Rotations 123 6. Diagonalization 130 7. Systems of Differential Equations 133 8. The Matrix Exponential 138 EXERCISES 145 Chapter 5 Symmetry 1. Symmetry of Plane Figures 155 2. The Group of Motions of the Plane 157 3. Finite Groups of Motions 162 4. Discrete Groups of Motions 166 5. Abstract Symmetry: Group Operations 175 6. The Operation on Cosets 178 7. The Counting Formula 180 8. Permutation Representations 182 9. Finite Subgroups of the Rotation Group 184 EXERCISES 188 Chapter 6 More Group Theory 1. The Operations of a Group on Itself 197 2. The Class Equation of the Icosahedral Group 200 3. Operations on Subsets 203 4. The Sylow Theorems 205 5. The Groups of Order 12 209 6. Computation in the Symmetric Group 211 7. The Free Group 217 8. Generators and Relations 219 9. The Todd-Coxeter Algorithm 223 EXERCISES 229 Chapter 7 Bilinear Forms 1. Definition of Bilinear Form 237 2. Symmetric Forms: Orthogonality 243 3. The Geometry Associated to a Positive Form 247 4. HermitianForms 249 5. The Spectral Theorem 253 6. Conics and Quadrics 255 7. The Spectral Theorem for Normal Operators 259 8. Skew-Symmetric Forms 260 9. Summary of Results, in Matrix Notation 261 EXERCISES 262 Chapter 8 Linear Groups 1. The Classical Linear Groups 270 2. The Special Unitary Group SU2 272 3. The Orthogonal Representation of SU2 276 4. The Special Linear Group SL2(R) 281 5. One-Parameter Subgroups 283 6. The Lie Algebra 286 7. Translation in a Group 292 8. Simple Groups 295 EXERCISES 300 Chapter 9 Group Representations 1. Definition of a Group Representation 307 2. G-Invariant Forms and Unitary Representations 310 3. Compact Groups 312 4. G-Invariant Subspaces and Irreducible Representations 5. Characters 316 6. Permutation Representations and the Regular Representation 321 7. The Representations of the Icosahedral Group 323 8. One-Dimensional Representations 325 9. Schur's Lemma, and Proof of the Orthogonality Relations 325 10. Representations of the Group SU2 330 EXERCISES 335 Chapter 10 Rings 345 1. Definition of a Ring 345 2. Formal Construction of Integers and Polynomials 347 3. Homomorphisms and Ideals 353 4. Quotient Rings and Relations in a Ring 359 5. Adjunction of Elements 364 6. Integral Domains and Fraction Fields 368 7. Maximal Ideals 370 8. Algebraic Geometry 373 EXERCISES 379 Chapter 11 Factorization 389 1. Factorization of Integers and Polynomials 389 2. Unique Factorization Domains, Principal Ideal Domains, and Euclidean Domains 392 3. Gauss's Lemma 398 4. Explicit Factorization of Polynomials 402 5. Primes in the Ring of Gauss Integers 406 6. Algebraic Integers 409 7. Factorization in Imaginary Quadratic Fields 414 8. Ideal Factorization 419 9. The Relation Between Prime Ideals of R and Prime Integers 424 10. Ideal Classes in Imaginary Quadratic Fields 425 11. Real Quadratic Fields 433 12. Some Diophantine Equations 437 EXERCISES 440 Chapter 12 Modules 1. The Definition of a Module 450 2. Matrices, Free Modules, and Bases 452 3. The Principle of Permanence of Identities 456 4. Diagonalization of Integer Matrices 457 5. Generators and Relations for Modules 464 6. The Structure Theorem for Abelian Groups 471 7. Application to Linear Operators 476 8. Free Modules over Polynomial Rings 482 EXERCISES 483 Chapter 13 Fields 1. Examples of Fields 492 2. Algebraic and Transcendental Elements 493 3. The Degree of a Field Extension 496 4. Constructions with Ruler and Compass 500 5. Symbolic Adjunction of Roots 506 6. Finite Fields 509 7. Function Fields 515 8. Transcendental Extensions 525 9. Algebraically Closed Fields 527 EXERCISES 530 Chapter 14 Galois Theory 1. The Main Theorem of Galois Theory 537 2. Cubic Equations 543 3. Symmetric Functions 547 4. Primitive Elements 552 5. Proof of the Main Theorem 556 6. QuarticEquations 560 7. Kummer Extensions 565 8. Cyclotomic Extensions 567 9. QuinticEquations 570 EXERCISES 575 Appendix Background Material 1. Set Theory 585 2. Techniques of Proof 589 3. Topology 593 4. The Implicit Function Theorem 597 EXERCISES 599 Notation Suggestions for Further Reading Index

内容简介

本书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、线性变换、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。 本书在麻省理工学院、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。

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热门评论

  • 娄娄小雅的评论
    昨天开学第一天 我的感觉却像是回到大一 赤裸裸的线性代数英文版…有木有…… 英国
  • 咔灰啊的评论
    刚刚下载了豆丁文档:《线性代数及其应用》(第三版)(电子工业出版社)(英文版)第七章答案网页链接
  • 千百度72的评论
    微积分和线性代数都是英文版的,就算听不懂,其实真的无所谓,学校重视英语,一些专业所有课都是英语考试。我这又算得了什么呢。
  • ____ZChAnG____的评论
    发书了,大一的和大二部分的[笑cry]还缺了三本:线性代数(英文版),线性代数习题指导,概率论[微笑]
  • just-look哼的评论
    无力吐槽...纯英文版线性代数和微积分...还有没发的工程材料和工程基础... 北京·北京交通大学东...
  • daisymys的评论
    前面的男生在看英文版线性代数,再前面的女生在看古文,旁边的男生在看生物化学,后面的女生在看托福…我就是想要这样的生活,但我睡了一个上午[小骨最萌了][小骨最萌了][小骨最萌了]
  • 夏天从京都回到欧村的评论
    [眼泪][眼泪]学生要我辅导他们数学[眼泪][眼泪]哥以前学的微积分代数啥的是英文版。。。。你这日文版。。。[泪][泪]
  • 北师圈圈app不想换名字的评论
    国商看过来,出近代史 马克思 财务会计中文和英文版 公司理财精要 管理会计中文版和英文版 金融市场与机构 商务统计学 管理信息系统 财务报表分析 商务沟通 组织行为学 国际经济学 线性代数 微积分 管理学 瑜伽垫 插销 要的私信
  • 蜜丝丶晚安的评论
    求根公式是什么,斜率是什么,区域又是啥啊...还是英文版,看到代数我真的是要死了。[泪][泪][泪]
  • 麦兜好笨的评论
    英文版的线性代数+工程力学
  • 2wennnn的评论
    想到不用学大学物理线性代数数学分析程序设计基础纯英文版工程图学普通化学我就[呵呵][呵呵][呵呵][呵呵][呵呵]爽炸!!!!!
  • 北京烤雅的评论
    看英文版的Finite element analysis 之前还得先看中文版的有限元分析,看中文版的有限元分析之前还得重温一下大一的线性代数[顶]