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## Undergraduate Texts in Mathematics: Groups and Symmetry (Hardback)"As prerequisites I assume a first course in linear algebra (including matrix multiplication and the representation of linear maps between Euclidean spaces by matrices, though not the abstract theory of vector spaces) plus familiarity with the basic properties of the real and complex numbers. It would be a pity to teach group theory without matrix groups available as a rich source of examples, especially since matrices are so heavily used in application." — Mark Anthony Armstrong, Author, in the Preface ## $35.15 |

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## Description

From the back cover: “Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal sytle, the material is divided into short sections, each of which deals with an important result or a new idea. Throughout the book, emphasis is placed on concrete examples, often geometrical in nature, so that finite rotation groups and the 17 wallpaper groups are treated in detail alongside theoretical results such as Lagrange’s theorem, the Sylow theorems, and the classification theorem for finitely generated abelian groups. A novel feature at this level is a proof the Nielsen-Schreier theorem, using group actions on trees. There are more than 300 exercises and approximately 60 illustrations to help develop the student’s intuition.”

**BRIEF CONTENTS**

- 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 – Cauchy’s Theorem
- Chapter 14 – Conjugacy
- 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

## Details

- SKU:
- 1922
- Subject:
- Mathematics
- Author:
- Armstrong, Mark Anthony
- Publisher:
- Springer-Verlag
- Publish Date:
- 1988
- Format:
- Hardback
- Weight (pounds):
- 0.99
- Dimensions (W”xL”xH”):
- 6.3″x9.5″x0.7″
- ISBN-13:
- 9780387966755
- ISBN-10:
- 0387966757
- Grade Level:
- College
- Series:
- Undergraduate Texts in Mathematics (UTM)

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