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  • © 2016

Encyclopedia of Distances

  • 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)

  1. Front Matter

    Pages i-xxii
  2. Mathematics of Distances

    1. Front Matter

      Pages 1-1
    2. General Definitions

      • Michel Marie Deza, Elena Deza
      Pages 3-62
    3. Topological Spaces

      • Michel Marie Deza, Elena Deza
      Pages 63-70
    4. Generalizations of Metric Spaces

      • Michel Marie Deza, Elena Deza
      Pages 71-85
    5. Metric Transforms

      • Michel Marie Deza, Elena Deza
      Pages 87-96
    6. Metrics on Normed Structures

      • Michel Marie Deza, Elena Deza
      Pages 97-108
  3. Geometry and Distances

    1. Front Matter

      Pages 109-109
    2. Distances in Geometry

      • Michel Marie Deza, Elena Deza
      Pages 111-133
    3. Riemannian and Hermitian Metrics

      • Michel Marie Deza, Elena Deza
      Pages 135-168
    4. Distances on Surfaces and Knots

      • Michel Marie Deza, Elena Deza
      Pages 169-182
    5. Distances on Convex Bodies, Cones, and Simplicial Complexes

      • Michel Marie Deza, Elena Deza
      Pages 183-195
  4. Distances in Classical Mathematics

    1. Front Matter

      Pages 197-197
    2. Distances in Algebra

      • Michel Marie Deza, Elena Deza
      Pages 199-214
    3. Distances on Strings and Permutations

      • Michel Marie Deza, Elena Deza
      Pages 215-228
    4. Distances on Numbers, Polynomials, and Matrices

      • Michel Marie Deza, Elena Deza
      Pages 229-246
    5. Distances in Functional Analysis

      • Michel Marie Deza, Elena Deza
      Pages 247-257
    6. Distances in Probability Theory

      • Michel Marie Deza, Elena Deza
      Pages 259-274
  5. Distances in Applied Mathematics

    1. Front Matter

      Pages 275-275
    2. Distances in Graph Theory

      • Michel Marie Deza, Elena Deza
      Pages 277-311

About this book

This 4-th edition of the leading reference volume on distance metrics is characterized by updated and rewritten sections on some items suggested by experts and readers, as well a general streamlining of content and the addition of essential new topics. Though the structure remains unchanged, the new edition also explores recent advances in the use of distances and metrics for e.g. generalized distances, probability theory, graph theory, coding theory, data analysis.

New topics in the purely mathematical sections include e.g. the Vitanyi multiset-metric, algebraic point-conic distance, triangular ratio metric, Rossi-Hamming metric, Taneja distance, spectral semimetric between graphs, channel metrization, and Maryland bridge distance. The multidisciplinary sections have also been supplemented with new topics, including: dynamic time wrapping distance, memory distance, allometry, atmospheric depth, elliptic orbit distance, VLBI distance measurements, the astronomical system of units, and walkability distance.

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

“The fourth edition of the Encyclopedia of Distances appears barely two years after the third (2014) and contains 76 new entries and 23 additional pages. … This latest release will be useful mainly to specialists and collections supporting graduate mathematics programs. Summing Up: Recommended. Graduate students through professionals.” (L. R. Zellmer, Choice, Vol. 54 (8), April, 2017)

Authors and Affiliations

  • Ecole Normale Supérieure, Paris, France

    Michel Marie Deza

  • Moscow State Pedagogical University, Moscow, Russia

    Elena Deza

Bibliographic Information

Buy it now

Buying options

eBook USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access