全新正版 代数(英文版第2版)/华章数学原版精品系列 (美)阿廷 9787111367017 机械工业
本店所售图书，保证正版新书，有个别图片和实书封面不一样，以实书封面为准，最快当天，一般隔天发货。支持7天无理由退换货.开票联系客服
￥ 39.2 5.0折 ￥ 79 全新
库存2件
北京西城
认证卖家担保交易快速发货售后保障
作者(美)阿廷
出版社机械工业
ISBN9787111367017
出版时间2012-01
装帧其他
开本其他
定价79元
货号2169318
上书时间2023-03-03
- 最新上架
商品详情
- 品相描述：全新
- 商品描述
-
作者简介
阿廷（MichaelArtin），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LeroyP.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。
目录
Freface
1 Matrices
1.1 The Basic Operations
1.2 Row Reduction
1.3 The Matrix Tianspose
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 Ccsets
2.9 Modular Arithmetic
2.10 The Correspondence Theorem
2.11 Product Groups
2.12 Quotient GrouFs
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 Fcrms
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 Gloups
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 cf 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 QuinticEquations
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
相关推荐
— 没有更多了 —
以下为对购买帮助不大的评价