网站首页  软件下载  游戏下载  翻译软件  电子书下载  电影下载  电视剧下载  教程攻略

请输入您要查询的图书:

 

书名 代数学
分类 科学技术-自然科学-数学
作者 (美)莫
出版社 世界图书出版公司
下载
简介
编辑推荐

The present book comes from the first part of the lecture notes I used for a first-year graduate algebra course at the University of Minnesota, Purdue University, and Peking University. The Chinese versions of these notes were published by The Peking University Press 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 knowledge of algebra, either for future advancement in the field of algebra, or for general background information, but also to show that algebra is truly a master key or a 'skeleton key' to many mathematical problems. As one knows, the teeth of an ordinary key prevent it from opening all but one door, whereas the skeleton key keeps only the essential parts, allowing it to unlock many doors.

目录

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

随便看

 

霍普软件下载网电子书栏目提供海量电子书在线免费阅读及下载。

 

Copyright © 2002-2024 101bt.net All Rights Reserved
更新时间:2025/4/8 13:31:49