Entropy and Diversity: The Axiomatic Approach

 

This is a book for all mathematicians and for mathematically trained scientists in other fields. It is not just for those interested in entropy or diversity for their own sakes, but anyone who enjoys discovering unexpected connections within mathematics and beyond.

The global biodiversity crisis is one of humanity's most urgent problems. However, even quantifying biological diversity is a difficult conceptual challenge. This book brings new mathematical rigour to the ongoing debate. 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. This book also calls on a wide range of mathematics, touching on subjects including:

  • functional equations
  • information theory
  • geometric measure theory
  • category theory
  • probability theory
  • number theory.
Even so, the mathematical prerequisites are few: the main narrative thread requires no more than an undergraduate course in analysis.

The Great Blue Hole Publication

The book is published by Cambridge University Press. It will be in all good bookshops from April 2021, and you can pre-order it now.

A free version is also available as arXiv:2012.02113.

The cover shows the Great Blue Hole.

Legal text for the arXiv version: This material will be published by Cambridge University Press as Entropy and Diversity: The Axiomatic Approach by Tom Leinster. This version is free to view and download for personal use only. Not for re-distribution, re-sale or use in derivative works. © Tom Leinster 2020.

 
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