Groups and Symmetry / Edition 1

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Overview

This is a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal style, the material is divided into short sections, each of which deals with an important result or a new idea. Includes more than 300 exercises and approximately 60 illustrations.

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Editorial Reviews

Booknews
Textbook introduces the vocabulary and some highlights of elementary group theory. Emphasis is placed on concrete examples so that finite rotation groups and the 17 wallpaper groups are treated in detail alongside theoretical results. Over 300 exercises and some 60 illustrations. Annotation c. Book News, Inc., Portland, OR (booknews.com)
From the Publisher
M.A. Armstrong

Groups and Symmetry

"This book is a gentle introductory text on group theory and its application to the measurement of symmetry. It covers most of the material that one might expect to see in an undergraduate course . . . The theory is amplified, exemplified and properly related to what this part of algebra is really for by discussion of a wide variety of geometrical phenomena in which groups measure symmetry. Overall, the author’s plan, to base his treatment on the premise that groups and symmetry go together, is a very good one, and the book deserves to succeed."—MATHEMATICAL REVIEWS

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Product Details

  • ISBN-13: 9780387966755
  • Publisher: Springer New York
  • Publication date: 10/25/1988
  • Series: Undergraduate Texts in Mathematics Series
  • Edition description: 1st ed. 1988. Corr. 2nd printing 1997
  • Edition number: 1
  • Pages: 187
  • Sales rank: 1,373,694
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.50 (d)

Table of Contents

Preface. 1: Symmetries of the Tetrahedron. 2: Axioms. 3: Numbers. 4: Dihedral Groups. 5: Subgroups and Generators. 6: Permutations. 7: Isomorphisms. 8: Plato's Solids and Cayley's Theorem. 9: Matrix Groups. 10: Products. 11: Lagrange's Theorem. 12: Partitions. 13: Cauchy's Theorem. 14: Conjugacy. 15: Quotient Groups. 16: Homomorphisms. 17: Actions, Orbits, and Stabalizers. 18: Counting Orbits. 19: Finite Rotation Groups. 20: The Sylow Theorems. 21: Finitely Generated Abelian Groups. 22: Row and Column Operations. 23: Automorphisms. 24: The Euclidean Group. 25: Lattices and Point Groups. 26: Wallpaper Patterns. 27: Free Groups and Presentations. 28: Trees and the Nielsen-Schreier Theorem. Bibliography. Index.
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Sort by: Showing 1 Customer Reviews
  • Anonymous

    Posted February 4, 2001

    good beginners guide

    dealing with an abstract area on a geometrical basis is very interesting - makes it tangible - the exercises are literally 'hands-on' - don't xpect rigorous stuff

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