Mirrors and Reflections: The Geometry of Finite Reflection Groups (Universitext)

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9780387790657: Mirrors and Reflections: The Geometry of Finite Reflection Groups (Universitext)

Starting with basic principles, this book provides a comprehensive classification of the various types of finite reflection groups and describes their underlying geometric properties. Numerous exercises at various levels of difficulty are included.

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From the Back Cover:

Mirrors and Reflections presents an intuitive and elementary introduction to finite reflection groups. Starting with basic principles, this book provides a comprehensive classification of the various types of finite reflection groups and describes their underlying geometric properties.

 

Unique to this text is its emphasis on the intuitive geometric aspects of the theory of reflection groups, making the subject more accessible to the novice. Primarily self-contained, necessary geometric concepts are introduced and explained. Principally designed for coursework, this book is saturated with exercises and examples of varying degrees of difficulty. An appendix offers hints for solving the most difficult problems. Wherever possible, concepts are presented with pictures and diagrams intentionally drawn for easy reproduction.

 

Finite reflection groups is a topic of great interest to many pure and applied mathematicians. Often considered a cornerstone of modern algebra and geometry, an understanding of finite reflection groups is of great value to students of pure or applied mathematics. Requiring only a modest knowledge of linear algebra and group theory, this book is intended for teachers and students of mathematics at the advanced undergraduate and graduate levels.

Review:

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)

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Alexander V. Borovik, Anna Borovik
Editore: Springer-Verlag New York Inc., United States (2010)
ISBN 10: 0387790659 ISBN 13: 9780387790657
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Descrizione libro Springer-Verlag New York Inc., United States, 2010. Paperback. Condizione libro: New. Language: English . Brand New Book. This graduate/advanced undergraduate textbook contains a systematic and elementary treatment 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. Key features include: many important concepts in the proofs are illustrated in simple drawings, which give easy access to the theory; a large number of exercises at various levels of difficulty; some Euclidean geometry is included along with the theory of convex polyhedra; no prerequisites are necessary beyond the basic concepts of linear algebra and group theory; and a good index and bibliography The exposition is directed at advanced undergraduates and first-year graduate students. Codice libro della libreria LIB9780387790657

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Alexandre V. Borovik, Anna Borovik
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Descrizione libro Springer New York 2009-11-10, New York, 2009. paperback. Condizione libro: New. Codice libro della libreria 9780387790657

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Alexandre V. Borovik, Anna Borovik
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Descrizione libro Springer-Verlag New York Inc., United States, 2010. Paperback. Condizione libro: New. Language: English . Brand New Book. This graduate/advanced undergraduate textbook contains a systematic and elementary treatment 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. Key features include: many important concepts in the proofs are illustrated in simple drawings, which give easy access to the theory; a large number of exercises at various levels of difficulty; some Euclidean geometry is included along with the theory of convex polyhedra; no prerequisites are necessary beyond the basic concepts of linear algebra and group theory; and a good index and bibliography The exposition is directed at advanced undergraduates and first-year graduate students. Codice libro della libreria LIB9780387790657

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Descrizione libro Springer-Verlag New York Inc., 2009. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IQ-9780387790657

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Borovik, Alexandre V.
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Descrizione libro Springer, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780387790657_lsuk

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Descrizione libro Springer-Verlag New York Inc., 2009. PAP. Condizione libro: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria LQ-9780387790657

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ALEXANDRE V. BOROVIK
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Descrizione libro Springer, 2009. Paperback. Condizione libro: NEW. 9780387790657 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0274783

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Descrizione libro Springer. Paperback. Condizione libro: New. Paperback. 172 pages. Dimensions: 9.2in. x 6.1in. x 0.6in.This graduateadvanced undergraduate textbook contains a systematic and elementary treatment 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. Key features include: many important concepts in the proofs are illustrated in simple drawings, which give easy access to the theory; a large number of exercises at various levels of difficulty; some Euclidean geometry is included along with the theory of convex polyhedra; no prerequisites are necessary beyond the basic concepts oflinear algebra and group theory; and a good index and bibliography The exposition is directed at advanced undergraduates and first-year graduate students. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Codice libro della libreria 9780387790657

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Descrizione libro Springer, 2009. Condizione libro: New. Codice libro della libreria L9780387790657

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Alexandre V. Borovik, Anna Borovik
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Descrizione libro Springer, 2009. Paperback. Condizione libro: New. 2010. This item is printed on demand. Codice libro della libreria DADAX0387790659

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