群與對稱 [Groups and Symmetry] pdf epub mobi txt 電子書 下載 2025

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阿姆斯壯（M.A.Armstrong） 著

齣版社： 世界圖書齣版公司

ISBN：9787510033094

版次：1

商品編碼：10888929

包裝：平裝

外文名稱：Groups and Symmetry

開本：24開

齣版時間：2011-04-01

用紙：膠版紙

頁數：186

內容簡介

《群與對稱》講述瞭 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.

目錄

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

前言/序言

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“對稱”的含義

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半價的時候買的，很值，送貨速度很快，京東包裝得很好。

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專業代數教材，國外影印班的

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（2）雙輻射對稱：隻有兩個輻射軸，彼此互成直角，形式上可以把它看成是從輻射對稱嚮左右對稱的過渡型（例如櫛水母）；

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一般指圖形和形態被點、綫或平麵區分為相等的部分而言。在生物形態上主要的對稱分為下列各種：（1）輻射對稱：與身體主軸成直角且互為等角的幾個軸（輻射軸）均相等，如果通過輻射軸把含有主軸的身體切開時，則常可把身體分為顯鏡像關係的兩個部分。例如海星可見有五個輻射軸。另外在高等植物的莖和花等，也常具有輻射對稱的結構；

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非常淺顯的入門書。。

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