Groups and Symmetry: A Guide to Discovering Mathematics (Mathematical World, Vol. 5)

Mathematics is discovered by looking at examples, noticing patterns, making conjectures, and testing those conjectures. Once discovered, the final results get organized and put in textbooks. The details and the excitement of the discovery are lost.
This book introduces the reader to the excitement of the original discovery. By means of a wide variety of tasks, readers are led to find interesting examples, notice patterns, devise rules to explain the patterns, and discover mathematics for themselves.
The subject studied here is the mathematics behind the idea of symmetry, but the methods and ideas apply to all of mathematics. The only prerequisites are enthusiasm and a knowledge of basic high-school math.
The book is only a guide. It will start you off in the right direction and bring you back if you stray too far. The excitement and the discovery are left to you.

"Nicely produced and concentrates on the informal analysis of geometrical patterns with the emphasis on informality ... could serve as a useful collection of activities to precede a formal course and would provide a range of intuitive experiences to which the more formal treatment could refer." ---- The Mathematical Gazette

"On the basis of this book it is possible to tailor a good course for high school students to really discover mathematics ... for anyone who is working with high school students in an advanced level the book is really recommended." ---- Zentralblatt MATH

"Written in a lively conversational style ... entertaining, and sometimes provoking, and will doubtlessly prove useful to its intended audience." ---- Mathematical Reviews