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Transformation Groups for Beginners
S. V. Duzhin, Steklov Institute of Mathematics, St. Petersburg, Russia, and B. D. Chebotarevsky, Minsk, Belarus
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Student Mathematical Library
2004; 246 pp; softcover
Volume: 25
ISBN-10: 0-8218-3643-9
ISBN-13: 978-0-8218-3643-9
List Price: US$43
Institutional Members: US$34.40
All Individuals: US$34.40
Order Code: STML/25
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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 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

"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

  • Introduction
  • Algebra of points
  • Plane movements
  • Transformation groups
  • Arbitrary groups
  • Orbits and ornaments
  • Other types of transformations
  • Symmetries of differential equations
  • Answers, hints and solutions to exercises
  • Index
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