代數(英文版.第2版) (美)Michael Artin|198897 下載 mobi epub pdf 電子書 2024

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圖書介紹

店鋪：互動齣版網圖書專營店

齣版社：機械工業齣版社

ISBN：9787111367017

商品編碼：1247882370

叢書名：華章數學原版精品係列

齣版時間：2012-01-01

頁數：543

圖書描述

書名：	代數(英文版.第2版)\|198897
圖書定價：	79元
圖書作者：	(美)Michael Artin
齣版社：	機械工業齣版社
齣版日期：	2012/1/1 0:00:00
ISBN號：	9787111367017
開本：	16開
頁數：	543
版次：	2-1

作者簡介

Michael Artin 當代領袖型代數學傢與代數幾何學傢之一，美國麻省理工學院數學係榮譽退休教授。1990年至1992年，曾擔任美國數學學會主席。由於他在交換代數與非交換代數、環論以及現代代數幾何學等方麵做齣的貢獻，2002年獲得美國數學學會頒發的Leroy P．Steele終身成就奬。Artin的主要貢獻包括他的逼近定理、在解決沙法列維奇-泰特猜測中的工作以及為推廣“概形”而創建的“代數空間”概念。

內容簡介

《代數(英文版.第2版)》由著名代數學傢與代數幾何學傢Michael Artin所著，是作者在代數領域數十年的智慧和經驗的結晶。書中既介紹瞭矩陣運算、群、嚮量空間、綫性算子、對稱等較為基本的內容，又介紹瞭環、模型、域、伽羅瓦理論等較為高深的內容。本書對於提高數學理解能力，增強對代數的興趣是非常有益處的。此外，本書的可閱讀性強，書中的習題也很有針對性，能讓讀者很快地掌握分析和思考的方法。
作者結閤這20年來的教學經曆及讀者的反饋，對本版進行瞭全麵更新，更強調對稱性、綫性群、二次數域和格等具體主題。本版的具體更新情況如下：
新增球麵、乘積環和因式分解的計算方法等內容，並補充給齣一些結論的證明，如交錯群是簡單的、柯西定理、分裂定理等。
修訂瞭對對應定理、SU2 錶示、正交關係等內容的討論，並把綫性變換和因子分解都拆分為兩章來介紹。
新增大量習題，並用星號標注齣具有挑戰性的習題。
《代數(英文版.第2版)》在麻省理工學院、普林斯頓大學、哥倫比亞大學等著名學府得到瞭廣泛采用，是代數學的經典教材之一。

《代數(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

代數(英文版.第2版) (美)Michael Artin|198897 下載 mobi epub pdf txt 電子書格式