群与对称

所属分类:数学  
出版时间:2011-4   出版时间:世界图书出版公司   作者:阿姆斯壮   页数:186  
Tag标签:数学,代数,群论,UTM,Springer,拓扑学  

内容概要

  numbers measure size, groups measure symmetry. the first
statement comes as no surprise; after all, that is what numbers are
for. the second will be exploited here in an attempt to introduce
the vocabulary and some of the highlights of elementary group
theory.
  a word about content and style seems appropriate. in this volume,
the emphasis is on examples throughout, with a weighting towards
the symmetry groups of solids and patterns. almost all the topics
have been chosen so as to show groups in their most natural role,
acting on (or permuting) the members ora set, whether it be the
diagonals of a cube, the edges of a tree, or even some collection
of subgroups of the given group. the material is divided into
twenty-eight short chapters, each of which introduces a new result
or idea.a glance at the contents will show that most of the
mainstays of a first course arc here. the theorems of lagrange,
cauchy, and sylow all have a chapter to themselves, as do the
classifcation of finitely generated abelian groups, the enumeration
of the finite rotation groups  and the plane crystallographic
groups, and the nielsen-schreier theorem.

作者简介

作者:(英国)阿姆斯壮(M.A.Armstrong)

书籍目录

preface
chapter 1 symmetries of the tetrahedron
chapter 2 axioms
chapter 3 numbers
chapter 4 dihedral groups
chapter 5 subgroups and generators
chapter 6 permutations
chapter 7 isomorphisms
chapter 8 plato's solids and cayley's theorem
chapter 9 matrix groups
chapter 10 products
chapter 11 lagrange's theorem
chapter 12 partitions
chapter 13 cauehy's theorem
chapter 14 coujugacy
chapter 15 quotient groups
chapter 16 homomorphisms
chapter 17 actions, orbits, and stabilizers
chapter 18 counting orbits
chapter 19 finite rotation groups
chapter 20 the sylow theorems
chapter 21 finitely generated abelian groups
chapter 22 row and column operations
chapter 23 automorphisms
chapter 24 the euclidean group
chapter 25 lattices and point groups
chapter 26 wallpaper patterns
chapter 27 free groups and presentations
chapter 28 trees and the nielsen-schreier theorem
bibliography
index

章节摘录

版权页:插图:

编辑推荐

《群与对称(英文版)》是由世界图书出版公司出版的。

图书封面

图书标签Tags

数学,代数,群论,UTM,Springer,拓扑学


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用户评论 (总计23条)

 
 

  •     很基础的书,适合大学新生学代数时读一读
  •     老师推荐的好书,印刷。。。。。我都没力气说它了
  •     通俗易懂 更好的群的几何看法
  •     阴影版的,研究生必读
  •     正在使用中,第一次在当当网上买东西
  •     一本经典的代数几何专著,理论与应用结合的比较紧密。
  •     受益匪浅。是作者独特的表示方法。,印刷质量不能算好
  •     老师推荐的教材,是正版
  •     值得细读。,写的不错
  •     敢情拿陈货当新货呢,将就吧!
  •     经典书籍,书不错
  •     好好读才能学好流体力学啊,这本值得收藏!
  •     对自己帮助很大,同事说很好。
  •     不能过分追求,挺好的
  •     给同事买的,理论知识也多
  •     没想到速度那么快。,书内容是ok的
  •     很基础的书,快递很给力
  •     老师推荐的好书!,内容很基本
  •     有几页是模糊的,老师推荐的好书
  •     适合本科生看,内容全面不错
  •     而且讲解详细。,不过书质量还不错
  •     包装的很结实,但是发货实在太慢了!!!!
  •     内容也不算多,经典
 

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