Introduction to Geometric Probability (Lezioni Lincee) - Softcover

Klain, Daniel A.; Rota, Gian-Carlo

Softcover

ISBN 10: 0521596548 ISBN 13: 9780521596541

Publisher: Cambridge University Press, 1997

Synopsis

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.

About this title

Book Description

Elementary geometry in n-dimensional Euclidean space is a subject that, under the stimulus of computational geometry, is regaining its former position. This is the first textbook that addresses some fundamental problems of Euclidean geometry that have been solved over the last half-century. The authors, who have made significant contributions to the subject, have taken pains to keep the exposition elementary, making the relationship between it and combinatorics transparent. It should be required reading of anyone in mathematics or computer science who deals with the visual display of information.

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

Edition details

• Publisher: Cambridge University Press
• Publication date: 1997
• ISBN 10: 0521596548
• ISBN 13: 9780521596541
• Binding: Paperback
• Language: English
• Edition number: 1
• Number of pages: 196