Authors:
- Offers a unique overview of the theme "distance" in mathematics and science
- Done in a cross-disciplinary fashion
- Includes supplementary material: sn.pub/extras
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Table of contents (29 chapters)
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Front Matter
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Mathematics of Distances
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Front Matter
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Geometry and Distances
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Front Matter
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Distances in Classical Mathematics
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Front Matter
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Distances in Applied Mathematics
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Front Matter
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About this book
This updated and revised third edition of the leading reference volume on distance metrics includes new items from very active research areas in the use of distances and metrics such as geometry, graph theory, probability theory and analysis. Among the new topics included are, for example, polyhedral metric space, nearness matrix problems, distances between belief assignments, distance-related animal settings, diamond-cutting distances, natural units of length, Heidegger’s de-severance distance, and brain distances.
The publication of this volume coincides with intensifying research efforts into metric spaces and especially distance design for applications. Accurate metrics have become a crucial goal in computational biology, image analysis, speech recognition and information retrieval.
Leaving aside the practical questions that arise during the selection of a ‘good’ distance function, this work focuses on providing the research community with an invaluable comprehensive listing of the main available distances.
As well as providing standalone introductions and definitions, the encyclopedia facilitates swift cross-referencing with easily navigable bold-faced textual links to core entries. In addition to distances themselves, the authors have collated numerous fascinating curiosities in their Who’s Who of metrics, including distance-related notions and paradigms that enable applied mathematicians in other sectors to deploy research tools that non-specialists justly view as arcane. In expanding access to these techniques, and in many cases enriching the context of distances themselves, this peerless volume is certain to stimulate fresh research.
Reviews
From the reviews of the second edition:
“This encyclopedia, dedicated to the theme ‘distances’ in the areas of pure mathematics up to abstract spaces, applied mathematics and applications, includes an impressive rich amount of different topics and knowledge areas. … The encyclopedia is highly recommended for students and researchers and everybody who is interested in increasing his knowledge on this fascinating field of distances.” (Gertraud Ehrig, Zentralblatt MATH, Vol. 1259, 2013)
“This is the second edition of the original text (2006). There are several additions, corrections and some streamlining has been done, but the general idea and structure is maintained. The concept of distance is interpreted in its broadest possible sense. In 29 chapters, the concept of distance is placed in as many different contexts by giving an enumeration of definition and properties. … The paper version is clearly a welcome asset in a mathematics library.” (A. Bultheel, The European Mathematical Society, December, 2012)Authors and Affiliations
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Ecole Normale Supérieure, Paris CX 05, France
Michel Marie Deza
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Moscow State Pedagogical University, Moskva, Russia
Elena Deza
Bibliographic Information
Book Title: Encyclopedia of Distances
Authors: Michel Marie Deza, Elena Deza
DOI: https://doi.org/10.1007/978-3-662-44342-2
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2014
Softcover ISBN: 978-3-662-51868-7Published: 23 August 2016
eBook ISBN: 978-3-662-44342-2Published: 08 October 2014
Edition Number: 3
Number of Pages: XX, 733
Number of Illustrations: 3 b/w illustrations
Topics: Geometry, Differential Geometry, Topology, Computational Mathematics and Numerical Analysis, Visualization, Mathematical and Computational Engineering