基本介紹
- 書名：ALGEBRA
- 出版社：世界圖書出版公司
- 頁數：350頁
- 開本：16
- 品牌：世界圖書出版公司北京公司
- 作者：莫 (Moh.T.T.)
- 出版日期：2009年1月1日
- 語種：英語
- ISBN：9787506292634
基本介紹,內容簡介,作者簡介,圖書目錄,序言,
基本介紹
內容簡介
《ALGEBRA(代數學)》由世界圖書出版公司出版。
作者簡介
作者：(美國)莫 (Moh.T.T.)
圖書目錄
Chapter Ⅰ Set theory and Number Theory
1 Set Theory
2 Unique Factorization Theorem
3 Congruence
4 Chinese Remainder Theorem
5 Complex Integers
6 Real Numbers and p-aclic Numbers
Chapter Ⅱ Group theory
1 Definitions
2 The Transformation Groups on Sets
3 Subgroups
4 Normal Subgroups and Inner Automorphisms
5 Automorphism Groups
6 p-Groups and Sylow Theorems
7 Jordan-Holder Theorem
8 Symmetric Group Sn
Chapter Ⅲ Polynomials
1 Fields and Rings
2 Polynomial Rings and Quotient Fields
3 Unique Factorization Theorem for Polynomials
4 Symmetric Polynomial, Resultant and Discriminant
5 Ideals
Chapter Ⅳ Linear Algebra
1 Vector Spaces
2 Basis and Dimension
3 Linear Transformation and Matrix
4 Module and Module over P.I.D
5 Jordan Canonical Form
6 Characteristic Polynomial
7 Inner Product and Bilinear form
8 Spectral Theory
Chapter Ⅴ Polynomials in One Variable and Field Theory
1 Algebraically Closed Field
2 Algebraic Extension
3 Algebraic Closure
4 Characteristic and Finite Field
5 Separable Algebraic Extension
6 Galois Theory
7 Solve Equation by Radicals
8 Field Polynomial and Field Discriminant
9 Luroth's Theorem
Appendix
A1 Set Theoretical Notations
A2 Peano's Axioms
A3 Homological Algebra
Index
1 Set Theory
2 Unique Factorization Theorem
3 Congruence
4 Chinese Remainder Theorem
5 Complex Integers
6 Real Numbers and p-aclic Numbers
Chapter Ⅱ Group theory
1 Definitions
2 The Transformation Groups on Sets
3 Subgroups
4 Normal Subgroups and Inner Automorphisms
5 Automorphism Groups
6 p-Groups and Sylow Theorems
7 Jordan-Holder Theorem
8 Symmetric Group Sn
Chapter Ⅲ Polynomials
1 Fields and Rings
2 Polynomial Rings and Quotient Fields
3 Unique Factorization Theorem for Polynomials
4 Symmetric Polynomial, Resultant and Discriminant
5 Ideals
Chapter Ⅳ Linear Algebra
1 Vector Spaces
2 Basis and Dimension
3 Linear Transformation and Matrix
4 Module and Module over P.I.D
5 Jordan Canonical Form
6 Characteristic Polynomial
7 Inner Product and Bilinear form
8 Spectral Theory
Chapter Ⅴ Polynomials in One Variable and Field Theory
1 Algebraically Closed Field
2 Algebraic Extension
3 Algebraic Closure
4 Characteristic and Finite Field
5 Separable Algebraic Extension
6 Galois Theory
7 Solve Equation by Radicals
8 Field Polynomial and Field Discriminant
9 Luroth's Theorem
Appendix
A1 Set Theoretical Notations
A2 Peano's Axioms
A3 Homological Algebra
Index
序言
The present book comes from the first part of the lecture notes I used for a first-yeargraduate algebra course at the University of Minnesota，Purdue University，and PekingUniversity．The Chinese versions of these notes were published by The Peking UniversitvPress in 1986，and by Linking Publishing Co of Taiwan in 1987．
The aim of this book is not only to give the student quick access to the basic knowledgeof algebra，either for future advancement in the field of algebra，or for general backgroundinformation，but also to show that algebra is truly a master key or a'skeleton key'tomany mathematical problems．As one knows，the teeth of an ordinary key prevent it fromopening all but one door，whereas the skeleton key keeps only the essential parts，allowinit to unlock many doors．
Sometimes I like to think that'fashion'is a space．traveler，while'wisdom'is a time-traveler．Frequently，the time-traveler only touches a small circle among the elite．Mostpeople think that Mathematics is dry and difficult．Most mathematicians feel the same waytowards algebra．How unfortunate!When Heisenberg presented his quantum theory,hehad to re-invent matrix theory．Mathematicians，and algebraists especially，should presentthe subject more interestingly to attract the attention of the student and the concernedreader．
I wish to present this book as an attempt to help the student to re-establish the contactsbetween algebra and other branches of mathematics and sciences．I prefer the intuitiveapproaches to algebra，and have included many examples and exercises to illustrate itspower．I hope that the present book fulfills these goals．
To teach a core course for one semester，the materials of§6，Chapter I，§7，Chapter II，§4，Chapter III，§3一§7，Chapter IV，part of§3 and§8．§9，Chapter V may be omitted．
We wish to thank Jem Corcoran for proof-readink．
The aim of this book is not only to give the student quick access to the basic knowledgeof algebra，either for future advancement in the field of algebra，or for general backgroundinformation，but also to show that algebra is truly a master key or a'skeleton key'tomany mathematical problems．As one knows，the teeth of an ordinary key prevent it fromopening all but one door，whereas the skeleton key keeps only the essential parts，allowinit to unlock many doors．
Sometimes I like to think that'fashion'is a space．traveler，while'wisdom'is a time-traveler．Frequently，the time-traveler only touches a small circle among the elite．Mostpeople think that Mathematics is dry and difficult．Most mathematicians feel the same waytowards algebra．How unfortunate!When Heisenberg presented his quantum theory,hehad to re-invent matrix theory．Mathematicians，and algebraists especially，should presentthe subject more interestingly to attract the attention of the student and the concernedreader．
I wish to present this book as an attempt to help the student to re-establish the contactsbetween algebra and other branches of mathematics and sciences．I prefer the intuitiveapproaches to algebra，and have included many examples and exercises to illustrate itspower．I hope that the present book fulfills these goals．
To teach a core course for one semester，the materials of§6，Chapter I，§7，Chapter II，§4，Chapter III，§3一§7，Chapter IV，part of§3 and§8．§9，Chapter V may be omitted．
We wish to thank Jem Corcoran for proof-readink．
