Transformation Groups for Beginners
About this Title
S. V. Duzhin, Steklov Institute of Mathematics, St. Petersburg, Russia and B. D. Chebotarevsky, , Minsk, Belarus. Translated by S. V. Duzhin, Steklov Institute of Mathematics, St. Petersburg, Russia
Publication: The Student Mathematical Library
Publication Year 2004: Volume 25
ISBNs: 978-0-8218-3643-9 (print); 978-1-4704-2137-3 (online)
MathSciNet review: MR2085971
MSC: Primary 22-01; Secondary 54H15
This book is intended for undergraduate students and all those interested in mathematics. Its goal is to give an easy introduction to the concept of a transformation group using examples from different areas of mathematics.
The warm-up of the first two chapters includes a discussion of algebraic operations on points in the plane, and of Euclidean plane movements. Then the notions of a transformation group and of an abstract group are introduced. Group actions, orbits, and invariants constitute the subject of the next chapter. The book concludes with an elementary exposition of the basic ideas of Sophus Lie about symmetries of differential equations.
The book contains plenty of figures, as well as many exercises with hints and solutions, which help the reader to master the material.
Students interested in group theory, especially with applications to geometry.
Table of Contents
- 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