Softcover ISBN:  9780821836439 
Product Code:  STML/25 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470421373 
Product Code:  STML/25.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9780821836439 
eBook: ISBN:  9781470421373 
Product Code:  STML/25.B 
List Price:  $108.00 $83.50 
Softcover ISBN:  9780821836439 
Product Code:  STML/25 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470421373 
Product Code:  STML/25.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9780821836439 
eBook ISBN:  9781470421373 
Product Code:  STML/25.B 
List Price:  $108.00 $83.50 

Book DetailsStudent Mathematical LibraryVolume: 25; 2004; 246 ppMSC: Primary 22; 54
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 warmup 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.
ReadershipStudents interested in group theory, especially with applications to geometry.

Table of Contents

Chapters

Introduction

Chapter 1. Algebra of points

Chapter 2. Plane movements

Chapter 3. Transformation groups

Chapter 4. Arbitrary groups

Chapter 5. Orbits and ornaments

Chapter 6. Other types of transformations

Chapter 7. Symmetries of differential equations

Answers, hints and solutions to exercises


Additional Material

Reviews

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


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

Chapters

Introduction

Chapter 1. Algebra of points

Chapter 2. Plane movements

Chapter 3. Transformation groups

Chapter 4. Arbitrary groups

Chapter 5. Orbits and ornaments

Chapter 6. Other types of transformations

Chapter 7. Symmetries of differential equations

Answers, hints and solutions to exercises

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