**Student Mathematical Library**

Volume: 25;
2004;
246 pp;
Softcover

MSC: Primary 22; 54;

**Print ISBN: 978-0-8218-3643-9
Product Code: STML/25**

List Price: $49.00

Individual Price: $39.20

**Electronic ISBN: 978-1-4704-2137-3
Product Code: STML/25.E**

List Price: $46.00

Individual Price: $36.80

#### Supplemental Materials

# Transformation Groups for Beginners

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*S. V. Duzhin; B. D. Chebotarevsky*

The notion of symmetry is important in many disciplines,
including physics, art, and music. The modern mathematical way of
treating symmetry is through transformation groups. This book
offers an easy introduction to these ideas for the relative novice,
such as undergraduates in mathematics or even advanced undergraduates
in physics and chemistry.

The first two chapters provide a warm-up to the material with, for
example, a discussion of algebraic operations on the points in the
plane and rigid motions in the Euclidean plane. The notions of a
transformation group and of an abstract group are then
introduced. Group actions, orbits, and invariants are covered in the
next chapter. The final chapter gives an elementary
exposition of the basic ideas of Sophus Lie about symmetries of
differential equations.

Throughout the text, examples are drawn from many different areas of
mathematics. Plenty of figures are included, and many exercises with hints and
solutions will help readers master the material.

#### Readership

Students interested in group theory, especially with applications to geometry.

#### Reviews & Endorsements

The book is well written and it contains a lot of exercises with hints and solutions.

-- EMS Newsletter

This is a book that one can hand to a motivated student and expect them to get something out of it ... I imagine that a beginning college students, given the right encouragement to take things slowly and work out all the details, will truly enjoy this book.

-- MAA Reviews

#### Table of Contents

# Table of Contents

## Transformation Groups for Beginners

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- Preface ix10 free
- Introduction 112 free
- Chapter 1. Algebra of Points 718 free
- Chapter 2. Plane Movements 4152
- Chapter 3. Transformation Groups 7384
- Chapter 4. Arbitrary Groups 97108
- Chapter 5. Orbits and Ornaments 127138
- Chapter 6. Other Types of Transformations 165176
- Chapter 7. Symmetries of Differential Equations 197208
- Answers, Hints and Solutions to Exercises 229240
- Index 245256
- Back Cover Back Cover1258