Overview

Distance metrics and distances have become an essential tool in many areas of pure and applied Mathematics, and this encyclopedia is the first one to treat the subject in full. The book appears just as research intensifies into metric spaces and especially, distance design for applications. These distances are particularly crucial, for example, in computational biology, image analysis, speech recognition, and information retrieval. Here, an assessment of the practical questions arising during selection of a 'good' distance function has been left aside in favor of a comprehensive listing of the main available distances, a useful tool for the distance design community. This reader-friendly reference offers both independent introductions and definitions, while at the same time making cross-referencing easy through hyperlink-like boldfaced references to original definitions. This high-quality publication is a mix of reference resource and coffee-table book.

Full Product Details

Author:   Michel Marie Deza ,  Elena Deza
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Dimensions:   Width: 15.50cm , Height: 2.80cm , Length: 23.50cm
Weight:   0.957kg
ISBN:  

9783642002335

ISBN 10:   3642002331
Pages:   604
Publication Date:   February 2009
Audience:   Professional and scholarly ,  Professional & Vocational
Replaced By:   9783642309571
Format:   Mixed media product
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

Part I. Mathematics of Distances.- 1 General Definitions.- 2 Topological Spaces.- 3 Generalization of Metric Spaces.- 4 Metric Transforms.- 5 Metrics on Normed Structures.- Part II. Geometry and Distances.- 6 Distances in Geometry.- 7 Riemannian and Hermitian Metrics.- 8 Distances on Surfaces and Knots.- 9 Distances on Convex Bodies, Cones and Simplicial Complexes.- Part III. Distances in Classical Mathematics.- 10 Distances in Algebra.- 11 Distances on Strings and Permutations.- 12 Distances on Numbers, Polynominals and Matrices.- 13 Distances in Functional Analysis.- 14 Distances in Probability Theory.- Part IV. Distances in Applied Mathematics.- 15 Distances in Graph theory.- 16 Distances in Coding Theory.- 17 Distances and Similarities in Data Analysis.- 18 Distances in Mathematical Engineering.- Part V. Computer-Related Distances.- 19 Distances on Real and Digital Planes.- 20 Voronoi Diagram Distances.- 21 Image and Audio Distances.- 22 Distances in Internet and Similar Networks.- Part VI. Distances in Natural Sciences.- 23 Distances in Biology.- 24 Distances in Physics and Chemistry.- 25 Distances in Geography, Geophysics and Astronomy.- 26 Distances in Cosmology and Theory of Relativity.- Part VII. Real-World Distances.- 27 Length Measures and Scales.- 28 Distances in Applied Social Sciences.- 29 Other Distances.

Reviews

From the reviews: Michel Marie Deza and Elena Deza's Encyclopedia of Distances is exactly what it says, it is -- an encyclopedia of topics that relate to measuring distance. ! the book is packaged with a digital copy on CD-ROM. The disk contains the entire text ! with all references hyperlinked to the appropriate section of the main text or the bibliography. ! It is a truly original compilation of material, one that almost anyone with some mathematical experience might enjoy browsing. (Bill Wood, The Mathematical Association of America, September, 2009) Encyclopedia of Distances is a revision of the earlier Dictionary of Distances (2006). ! Toward the end of the encyclopedia several chapters address the definition of distances in other areas of the sciences including astronomy, biology, geography, relativity, and even some of the social sciences. Non-mathematicians will find these chapters more approachable ! . This volume is suitable ! for institutions with graduate programs in mathematics. Summing Up: Recommended. Graduate students through professionals/practitioners. (J. O. Christensen, Choice, Vol. 47 (5), January, 2010) It does, though, contain an interesting collection of articles; mainly related to distances used in maths ! . Its main audience is researchers who are interested in an aspect of distance and its measurement. ! Each definition clearly identifies where it is building on other definitions in the book so the reader can refer to those entries as well. Overall, this is a specialist reference book ! . For those who are already knowledgeable in this subject then it would be an interesting review ! . (Clari Gosling, Reference Reviews, Vol. 24 (6), 2010)

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions