代数学
2009年
世界图书出版公司
(美国)(Moh.T.T.)莫
350
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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．
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 NumbersChapter 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 SnChapter 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 IdealsChapter 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 TheoryChapter 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 TheoremAppendix A1 Set Theoretical Notations A2 Peano's Axioms A3 Homological AlgebraIndex
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阅读此书的感觉就好比“吃鱼”，是在享用带刺的美味。一方面，书中抒发了许多独到而精辟的见解，令人拍案叫绝；另一方面，书中也夹杂着不少疏漏及硬伤，让人大跌眼镜。虽则后来，莫宗坚先生补充了一份勘误表，发布于网路：http://www.math.purdue.edu/~ttm/book.html可惜，杯水车薪。总之，建议列位读者：擦亮慧眼，去伪存真。其实，鄙人之所以钟爱此书，只有一条理由，那就是：作者不仅阐述“代数中之方法”(methodsinalgebra)，更传授“代数之方式”(themannerofalgebra)。放眼望去，如今的许多数学书皆沿袭"Definition-Theorem-Proof"的拳法老套路，索然无味。而莫宗坚先生的这本教材却一扫陋习，直指真谛，把“鲜活的代数学”生动地呈现在读者的眼前。善哉！为此书的气质喝彩！