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Daniel A. Klain
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Introduction to Geometric Probability (Lezioni Lincee) 1st Edition

by Daniel A. Klain (Author), Gian-Carlo Rota (Author)
5.0 5.0 out of 5 stars 2 ratings
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Here is the first modern introduction to geometric probability, also known as integral geometry, presented at an elementary level, requiring little more than first-year graduate mathematics. Klein and Rota present the theory of intrinsic volumes due to Hadwiger, McMullen, Santaló and others, along with a complete and elementary proof of Hadwiger's characterization theorem of invariant measures in Euclidean n-space. They develop the theory of the Euler characteristic from an integral-geometric point of view. The authors then prove the fundamental theorem of integral geometry, namely, the kinematic formula. Finally, the analogies between invariant measures on polyconvex sets and measures on order ideals of finite partially ordered sets are investigated. The relationship between convex geometry and enumerative combinatorics motivates much of the presentation. Every chapter concludes with a list of unsolved problems.
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  1. ISBN-10
    0521596548
  2. ISBN-13
    978-0521596541
  3. Edition
    1st
  4. Publisher
    Cambridge University Press
  5. Publication date
    December 13, 1997
  6. Language
    English
  7. Dimensions
    5.5 x 0.49 x 8.5 inches
  8. Print length
    196 pages
  9. See all details
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Editorial Reviews

Review

"Elementary methods and exceptionally clear exposition bring a once seemingly advanced subject within the ken of a wide audience of mathematics students. Highly recommended for upper-division undergraduate and graduate students." Choice

"The exposition is marvellous: clear and precise... The powerful theory of valuations, intrinsic volumes and invariant measures built by Hadwiger, Groemer, McMullen and others is an impressive development. The beautiful exposition would make this volume worthwhile even if Klain and Rota hadn't 'something new' to say." Bulletin of the AMS

"The text is very elegant...This book is a very tantalizing one in that there is a definite sense that much of the subject is mature, even the combinatorial analogies." Mathematical Reviews

Book Description

The basic ideas of the subject and the analogues with enumerative combinatorics are described and exploited.

Product details

  • Publisher ‏ : ‎ Cambridge University Press; 1st edition (December 13, 1997)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 196 pages
  • ISBN-10 ‏ : ‎ 0521596548
  • ISBN-13 ‏ : ‎ 978-0521596541
  • Item Weight ‏ : ‎ 8.1 ounces
  • Dimensions ‏ : ‎ 5.5 x 0.49 x 8.5 inches
  • Customer Reviews:
    5.0 5.0 out of 5 stars 2 ratings

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Daniel A. Klain

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