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.
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"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
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20 of 20 people found the following review helpful:
5.0 out of 5 stars
Instruction by Question,
This review is from: Groups: A Path to Geometry (Paperback)
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
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Inside This Book
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First Sentence:
Throughout the nineteenth century, group theory was a study of permutations and substitutions. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
use qns, wallpaper group, direct isometrics, opposite isometry, opposite isometries, minimal translation, frieze group, direct isometries, same right coset, fundamental square, frieze pattern, reflection axes, cycle notation, distinct complex numbers, translation group, direct similarities, direct similarity, right cosets, disjoint cycles, nonsingular linear transformations, dihedral group, group homomorphism, finite subgroup, normal subgroup, stereographic projection Key Phrases - Capitalized Phrases (CAPs): (learn more)
Summary Definition, Disquisitiones Arithmeticae, Theorem All, Theorem There New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Throughout the nineteenth century, group theory was a study of permutations and substitutions. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
use qns, wallpaper group, direct isometrics, opposite isometry, opposite isometries, minimal translation, frieze group, direct isometries, same right coset, fundamental square, frieze pattern, reflection axes, cycle notation, distinct complex numbers, translation group, direct similarities, direct similarity, right cosets, disjoint cycles, nonsingular linear transformations, dihedral group, group homomorphism, finite subgroup, normal subgroup, stereographic projection Key Phrases - Capitalized Phrases (CAPs): (learn more)
Summary Definition, Disquisitiones Arithmeticae, Theorem All, Theorem There New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
This book cites 26
books:
See all 26 books this book cites
- Disquisitiones Arithmeticae by Carl F. Gauss on 6 pages
- Lectures on the Icosahedron (Dover Phoenix Editions) by Felix Klein on 6 pages
- Fascination of Groups by Budden in Back Matter
- Geometry and the Imagination (CHEL/87.H) (AMS Chelsea Publishing) by David Hilbert in Back Matter
- Regular Polytopes (Dover Books on Mathematics) by H. S. M. Coxeter in Back Matter
See all 26 books this book cites
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