ISBN: 9780521596541

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 mathemati… Mehr…

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. New Textbooks>Trade Paperback>Science>Statistics & Probability>Statistics & Probability, Cambridge University Press Core >1 >T<

2006, ISBN: 0521596548

[EAN: 9780521596541], Neubuch, [PU: Cambridge University Press, United Kingdom], Language: English. Brand new Book. The purpose of this book is to present the three basic ideas of geometr… Mehr…

[EAN: 9780521596541], Neubuch, [PU: Cambridge University Press, United Kingdom], Language: English. Brand new Book. The purpose of this book is to present the three basic ideas of geometrical probability, also known as integral geometry, in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. The first of the three ideas is invariant measures on polyconvex sets. The authors then prove the fundamental lemma of integral geometry, namely the kinematic formula. Finally the analogues between invariant measures and finite partially ordered sets are investigated, yielding insights into Hecke algebras, Schubert varieties and the quantum world, as viewed by mathematicians. Geometers and combinatorialists will find this a most stimulating and fruitful story., Books<

ISBN: 9780521596541

Paperback, [PU: Cambridge University Press], The basic ideas of geometrical probability and the theory of shape are here presented in their natural framework. In this way, the relationshi… Mehr…

Paperback, [PU: Cambridge University Press], The basic ideas of geometrical probability and the theory of shape are here presented in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. Geometers and combinatorialists will find this a most stimulating and fruitful story., Probability & Statistics<

2006, ISBN: 0521596548

Kartoniert / Broschiert MATHEMATICS / Probability & Statistics / General, mit Schutzumschlag 11, [PU:Cambridge University Press]

1997, ISBN: 9780521596541

Buch, Softcover, [PU: Cambridge University Press], Cambridge University Press, 1997