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ALGEBRA(2009年世界图书出版公司出版的图书) 发布于:

《ALGEBRA(代数学)》主要内容包括: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.

《ALGEBRA(代数学)》由世界图书出版公司出版。

作者:(美国)莫 (Moh.T.T.)

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

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.


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