對(duì)稱

內(nèi)容概要

本書以通俗易懂的方式講述幾何與群的本質(zhì)，以及兩者問(wèn)的聯(lián)系(即對(duì)稱)，并且自然地延伸到一些高級(jí)的觀點(diǎn)和材料(如有限和仿射Coxeter群，這是李群李代數(shù)以及Kac—Moody代數(shù)的基礎(chǔ)；球面的分割，這是球面幾何的內(nèi)容；上半平面被群SL2(z)的作用，這是雙曲幾何與自守函數(shù)的基礎(chǔ))。閱讀本書所需的幾何與群的知識(shí)在書中均有通俗易懂的介紹(附有大量幾何直觀圖形)。     本書是一本優(yōu)秀的數(shù)學(xué)教材，適用于數(shù)學(xué)系本科生和其他專業(yè)對(duì)數(shù)學(xué)有興趣的本科生用作數(shù)學(xué)參考書或課外讀物。

作者簡(jiǎn)介

作者：(美國(guó))約翰遜(D.L.Johnson)

書籍目錄

1.  Metric Spaces and their Groups　1.1  Metric Spaces　1.2  Isometries　1.3  Isometries of the Real Line　1.4  Matters Arising　1.5  Symmetry Groups2.  Isometries of the Plane　2.1  Congruent Triangles　2.2  Isometries of Different Types　2.3  The Normal Form Theorem　2.4  Conjugation of Isometries3.  Some Basic Group Theory　3.1  Groups　3.2  Subgroups　3.3  Factor Groups　3.4  Semidirect Products4.  Products of Reflections　4.1  The Product of Two Reflections　4.2  Three Reflections　4.3  Four or More5.  Generators and Relations　5.1  Examples　5.2  Semidirect Products Again　5.3  Change of Presentation　5.4  Triangle Groups　5.5  Abelian Groups6.  Discrete Subgroups of the Euclidean Group　6.1  Leonardo's Theorem　6.2 A Trichotomy　6.3  Friezes and Their Groups　6.4  The Classification7.  Plane Crystallographic Groups: OP Case　7.1  The Crystallographic Restriction　7.2  The Parameter n　7.3  The Choice of b　7.4  Conclusion8.  Plane Crystallographic Groups: OR Case　8.1  A Useful Dichotomy　8.2  The Case n = 1　8.3  The Case n = 2　8.4  The Case n = 4　8.5  The Case n = 3　8.6  The Case n - 69.  Tessellations of the Plane　9.1  Regular Tessellations　9.2  Descendants of (4, 4)　9.3  Bricks　9.4  Split Bricks　9.5  Descendants of (3, 6)10. Tessellations of the Sphere　10.1 Spherical Geometry　10.2 The Spherical Excess　10.3 Tessellations of the Sphere　10.4 The Platonic Solids　10.5 Symmetry Groups11. Triangle Groups　11.1 The Euclidean Case　11.2 The Elliptic Case　11.3 The Hyperbolic Case　11.4  Coxeter Groups12. Regular Polytopes　12.1  The Standard Examples　12.2  The Exceptional Types in Dimension Four　12.3  Three Concepts and a Theorem　12.4  Schlafli's TheoremSolutionsGuide to the LiteratureBibliographyIndex of NotationIndex

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