Transformation Groups for Beginners (Student Mathematical Library, Vol. 25) (STUDENT MATHEMATICAL LIBRARY, V. 25) by S. V. Duzhin (PDF)

Description

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.

User’s Reviews

Editorial Reviews: About the Author S.V. Duzhin, Steklov Institute of Mathematics, St Petersburg.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Very descriptive with many examples, links to everyday experiences, invites to think about group characteristics, very well structured. Ideal for someone who wants to familiarize himself with group theory as a non-mathematician or not-yet-mathematician.

⭐This is a relatively easy-going introduction to transformation groups and various related topics, including the typical things found in group theory books with a pop emphasis (wallpaper groups, etc.), occasionally spiced up by references to Russian folklore and so on. The most useful contribution to this genre is probably the chapter on Lie’s theory of differential equations, which everyone agrees is important but for some reason it is not commonly discussed at this level.

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