Groups: A Path to Geometry (Paperback)

~ (Author) "Throughout the nineteenth century, group theory was a study of permutations and substitutions..." (more)
Key Phrases: use qns, wallpaper group, direct isometrics, Summary Definition, Disquisitiones Arithmeticae, Theorem All (more...)

Editorial Reviews

Review

"What distinguishes this book from all others? Simply, it is not a textbook in the normal sense. The approach of the book is one of development by discovery. There is almost no text as such-the reader being invited to learn about the groups through a sequence of over 800 problems." Times Higher Education Supplement

Product Description

Following the same successful approach as Dr. Burn's previous book on number theory, this text consists of a carefully constructed sequence of questions that will enable the reader, through participation, to study all the group theory covered by a conventional first university course. An introduction to vector spaces, leading to the study of linear groups, and an introduction to complex numbers, leading to the study of Möbius transformations and stereographic projection, are also included. Quaternions and their relationships to 3-dimensional isometries are covered, and the climax of the book is a study of the crystallographic groups, with a complete analysis of these groups in two dimensions.

Product Details

• Paperback: 256 pages
• Publisher: Cambridge University Press (September 25, 1987)
• Language: English
• ISBN-10: 0521347939
• ISBN-13: 978-0521347938
• Product Dimensions: 8.8 x 6 x 0.7 inches
• Shipping Weight: 13.6 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon.com Sales Rank: #1,058,939 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

17 of 17 people found the following review helpful:

5.0 out of 5 stars Instruction by Question, September 2, 2000

By	"humility" (Chicago, IL) - See all my reviews

R. P. Burn is an amazing writer for mathematical textbooks.

This book follows Burn's typical format; therefore, this text is little more than a collection of (very) brief introductions to terminology and concepts, followed by a long list of questions for each chapter. Finally, each chapter has an answer section.

The questions asked typically very short, and at first are very simple and intuitively obvious. As each chapter progresses, however, the questions begin to build from prior questions already answered and express more and more complex concepts.

Typically, by the time a chapter has been completed, the reader will have completed one or more complicated proofs typically found in other texts on the same subject-- small bite by small bite at a time.

Highly recommended