{"product_id":"entropy-and-diversity-the-axiomatic-approach-paperback-9781108965576","title":"Entropy and Diversity; The Axiomatic Approach (Paperback \/ softback) 9781108965576","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eEntropy and Diversity\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eThe Axiomatic Approach\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eDiscover the mathematical riches of 'what is diversity?' in a book that adds mathematical rigour to a vital ecological debate.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eTom Leinster (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781108965576, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 22 April 2021\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e456 pages\u003cbr\u003e15 x 23 x 2.5 cm, 0.69 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'The book is a welcome addition to the theory of biodiversity in that it covers the topics of entropy and diversity in a mathematically rigorous yet fairly accessible way … Recommended.' M. Bona, Choice Magazine\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe global biodiversity crisis is one of humanity's most urgent problems, but even quantifying biological diversity is a difficult mathematical and conceptual challenge. This book brings new mathematical rigour to the ongoing debate. It was born of research in category theory, is given strength by information theory, and is fed by the ancient field of functional equations. It applies the power of the axiomatic method to a biological problem of pressing concern, but it also presents new theorems that stand up as mathematics in their own right, independently of any application. The question 'what is diversity?' has surprising mathematical depth, and this book covers a wide breadth of mathematics, from functional equations to geometric measure theory, from probability theory to number theory. Despite this range, the mathematical prerequisites are few: the main narrative thread of this book requires no more than an undergraduate course in analysis.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction\u003cbr\u003e 1. Fundamental functional equations\u003cbr\u003e 2. Shannon entropy\u003cbr\u003e 3. Relative entropy\u003cbr\u003e 4. Deformations of Shannon entropy\u003cbr\u003e 5. Means\u003cbr\u003e 6. Species similarity and magnitude\u003cbr\u003e 7. Value\u003cbr\u003e 8. Mutual information and metacommunities\u003cbr\u003e 9. Probabilistic methods\u003cbr\u003e 10. Information loss\u003cbr\u003e 11. Entropy modulo a prime\u003cbr\u003e 12. The categorical origins of entropy\u003cbr\u003e Appendix A. Proofs of background facts\u003cbr\u003e Appendix B. Summary of conditions\u003cbr\u003e References\u003cbr\u003e Index of notation\u003cbr\u003e Subject index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Biodiversity [\u003ca title=\"See our other books on Biodiversity\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Biodiversity%20%5BRNCB%5D%22\"\u003eRNCB\u003c\/a\u003e], Mathematical modelling [\u003ca title=\"See our other books on Mathematical modelling\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20modelling%20%5BPBWH%5D%22\"\u003ePBWH\u003c\/a\u003e], Set theory [\u003ca title=\"See our other books on Set theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Set%20theory%20%5BPBCH%5D%22\"\u003ePBCH\u003c\/a\u003e], Information theory [\u003ca title=\"See our other books on Information theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Information%20theory%20%5BGPF%5D%22\"\u003eGPF\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":46001794580760,"sku":"9781108965576","price":37.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781108965576i.jpg?v=1696728167","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/entropy-and-diversity-the-axiomatic-approach-paperback-9781108965576","provider":"Freshly Printed Books","version":"1.0","type":"link"}