{"product_id":"introduction-to-geometric-probability-paperback-9780521596541","title":"Introduction to Geometric Probability (Paperback) 9780521596541","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eIntroduction to Geometric Probability\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThe basic ideas of the subject and the analogues with enumerative combinatorics are described and exploited.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDaniel A. Klain (Author), Gian-Carlo Rota (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521596541, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 11 December 1997\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e196 pages, 5 b\/w illus.  1 table\u003cbr\u003e21.6 x 13.8 x 1.2 cm, 0.23 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e' … a brief and useful introduction …' European Mathematical Society\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction\u003cbr\u003e 1. The Buffon needle problem\u003cbr\u003e 2. Valuation and integral\u003cbr\u003e 3. A discrete lattice\u003cbr\u003e 4. The intrinsic volumes for parallelotopes\u003cbr\u003e 5. The lattice of polyconvex sets\u003cbr\u003e 6. Invariant measures on Grassmannians\u003cbr\u003e 7. The intrinsic volumes for polyconvex sets\u003cbr\u003e 8. A characterization theorem for volume\u003cbr\u003e 9. Hadwiger's characterization theorem\u003cbr\u003e 10. Kinematic formulas for polyconvex sets\u003cbr\u003e 11. Polyconvex sets in the sphere\u003cbr\u003e References\u003cbr\u003e Index of symbols\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Probability \u0026amp; statistics [\u003ca title=\"See our other books on Probability \u0026amp; statistics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Probability%20\u0026amp;%20statistics%20%5BPBT%5D%22\"\u003ePBT\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46004690813208,"sku":"9780521596541","price":52.98,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521596541i_f15c6c81-deff-4e69-bc7a-6853cc0b5651.jpg?v=1691370175","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/introduction-to-geometric-probability-paperback-9780521596541","provider":"Freshly Printed Books","version":"1.0","type":"link"}