Overview
- first and unique book dedicated to cellular automata and groups
- 90% of the material presented appears for a first time
- entirely self-contained with more than 300 exercises
- appeals to a large audience including specialists as well as newcomers in the field
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (18 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Reviews
From the reviews:
“The book under review is currently the only text of comparable size and level which devotes its attention to the general case of cellular automata on arbitrary groups … . The book is a great read and a great resource. … The basic material is supported by a trove of exercises (over 300) and notes at the end of each chapter, and the book ends with a selection of 17 open problems.” (Zoran Šunić, Bulletin of the American Mathematical Society, Vol. 51 (2), April, 2014)
“An excellent introduction to the subject of cellular automata on groups, complete with copious exercises. … I like this book very much. The authors have set out to write a self-contained account, and I think they have succeeded. … This is done using conventional notation and without idiosyncrasy, which to mind is important for any reader wanting to supplement their reading using other sources. All this is done whilst presenting some very recent material – a real achievement.” (Charles Eaton, The Mathematical Gazette, Vol. 97 (539), July, 2013)
“The book explores deep connections between two seemingly unrelated mathematical notions, both of which were introduced by J. von Neumann in the first half of the 20th century … . The book is well written and develops very carefully the state of the art of the material sketched above … . It is essentially self-contained … and each chapter contains informative historical notes and a long list of instructive exercises.” (K. Auinger, Monatshefte für Mathematik, Vol. 164 (3), November, 2011)
“This book should be considered as self-contained, in the sense that all the concepts used are developed at length, together with a large choice of exercises. … should make an important contribution to a field in rapid development, and which is at the intersection of algebra, analysis and computer science. It is carefully written, and is especially recommended to graduate students andresearchers, who will find out in what way so many apparently distant concepts can fit together to make this fascinating theory.” (Antonio Machì, Bulletin of the London Mathematical Society, July, 2011)
“This wonderful book is about important links between four areas of mathematics: geometric group theory, theory of cellular automata, dynamical systems and amenability. … the notions are clearly defined and illustrated by several examples and figures, and the proofs of all results are very carefully detailed and presented in an elegant form. For all these reasons I strongly recommend this brilliant book to both experts and students from all the areas of mathematics mentioned in this review, as well as many others.” (Rostislav I. Grigorchuk, Mathematical Reviews, Issue 2011 j)
“The book discusses these and related topics from the theory of cellular automata on groups and explores its deep connections with recent developments in geometric group theory, symbolic dynamics and theoretical computer science. … The book has 8 chapters, 10 appendices and more than 300 exercises. It is oriented towards a broad audience, and shall be useful for experts as a detailed comprehensive account of the recent progress in the field.” (Boris S. Kruglikov, Zentralblatt MATH, Vol. 1218, 2011)
Authors and Affiliations
Bibliographic Information
Book Title: Cellular Automata and Groups
Authors: Tullio Ceccherini-Silberstein, Michel Coornaert
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-642-14034-1
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2010
Hardcover ISBN: 978-3-642-14033-4Published: 03 September 2010
Softcover ISBN: 978-3-642-26475-7Published: 05 November 2012
eBook ISBN: 978-3-642-14034-1Published: 24 August 2010
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XX, 440
Number of Illustrations: 52 b/w illustrations
Topics: Logics and Meanings of Programs, Dynamical Systems and Ergodic Theory, Algebra