Overview
- Many important concepts in the proofs are illustrated through simple drawings, which give easy access to the theory
- Includes numerous exercises at various levels of difficulty as well as an appendix with hints for solving many of the more difficult problems
- Provides an introduction to the necessary elements of Euclidean geometry and the theory of convex polyhedra
- Few prerequisites are necessary beyond linear algebra and the basic principles of group theory
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (20 chapters)
-
Front Matter
-
Mirrors, Reflections, Roots
-
Coxeter Complexes
-
Three-Dimensional Reflection Groups
Keywords
About this book
"Mirrors and Reflections" presents a systematic and elementary introduction to the properties of finite groups generated by reflections. The approach is based on fundamental geometric considerations in Coxeter complexes, and emphasizes the intuitive geometric aspects of the theory of reflection groups. The exposition is directed at advanced undergraduates and first-year graduate students, and features a large number of exercises at various levels of difficulty.
Reviews
From the reviews:
“In Mirrors and Reflections by Alexandre Borovik (Univ. of Manchester, UK) and Anna Borovik, readers get the whole stage … . Mastering this book not only gives undergraduates a taste of the mathematics of special objects, but prepares the way to various more important abstract theories. Thoughtfully illustrated, compact, leisurely, and unique in its coverage, this work is the way to learn this critical material. Summing Up: Highly recommended. Academics students, all levels, and professionals.” (D. V. Feldman, Choice, Vol. 48 (1), September, 2010)
“A different approach to the study of reflection groups: an intuitive geometric approach, suitable for undergraduate students. … the book provides the reader with the necessary geometric background. … The book ends with a very interesting appendix on the ‘forgotten art of blackboard drawing’, where the authors give advice on making usable mathematical drawings. … the authors believe that pictures are indispensable tools which facilitate mathematical work. They also give hints and solutions to selected exercises.” (Maria Chlouveraki, Mathematical Reviews, Issue 2011 b)
“This is a nice booklet! … the authors present an almost purely geometric approach to the theory of reflection groups which can be followed even by undergraduates. … The authors attach great value to geometric intuition … which makes the theory easily accessible. A very recommendable booklet!” (G. Kowol, Monatshefte für Mathematik, Vol. 162 (2), February, 2011)
Authors and Affiliations
Bibliographic Information
Book Title: Mirrors and Reflections
Book Subtitle: The Geometry of Finite Reflection Groups
Authors: Alexandre V. Borovik, Anna Borovik
Series Title: Universitext
DOI: https://doi.org/10.1007/978-0-387-79066-4
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2010
Softcover ISBN: 978-0-387-79065-7Published: 10 November 2009
eBook ISBN: 978-0-387-79066-4Published: 07 November 2009
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XII, 172
Number of Illustrations: 74 b/w illustrations
Topics: Geometry, Algebra, Group Theory and Generalizations, Topological Groups, Lie Groups, Linear and Multilinear Algebras, Matrix Theory, Mathematical Methods in Physics