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Publisher:

AMS

Publication Date:

2004

Number of Pages:

246

Format:

Paperback

Series:

Student Mathematical Library

Price:

39.00

ISBN:

0-8218-3643-9

Category:

Monograph

[Reviewed by , on ]

David Farmer

01/1/2005

This is a book that one can hand to a motivated student and expect them to get something out of it. It opens with a kind of geometrically defined addition that is familiar enough to be accessible, but requires some basic geometry to appreciate what is really going on. Chapter 1 continues with a geometrically defined multiplication, leading to the complex numbers. The following chapters discuss rigid motions and other transformations of the plane, group theory, and other interesting things. The topics come across as a unified journey through an interesting and coherent landscape, and students will realize that they are glimpsing part of a larger beautiful picture.

I imagine that a beginning college student, given the right encouragement to take things slowly and work out all the details, will truly enjoy this book. Except for the final chapter on differential equations, the only prerequisite is some geometry. The level of sophistication is high and students who are new to reading proofs may need some additional encouragement.

* 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

* 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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