Entropy and Diversity
eBook - PDF

Entropy and Diversity

The Axiomatic Approach

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Entropy and Diversity

The Axiomatic Approach

About this book

The 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.

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Yes, you can access Entropy and Diversity by Tom Leinster in PDF and/or ePUB format, as well as other popular books in Mathematik & Logik in der Mathematik. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half-title
  3. Title page
  4. Copyright information
  5. Dedication
  6. Contents
  7. Acknowledgements
  8. Note to the Reader
  9. Interdependence of Chapters
  10. Introduction
  11. 1 Fundamental Functional Equations
  12. 2 Shannon Entropy
  13. 3 Relative Entropy
  14. 4 Deformations of Shannon Entropy
  15. 5 Means
  16. 6 Species Similarity and Magnitude
  17. 7 Value
  18. 8 Mutual Information and Metacommunities
  19. 9 Probabilistic Methods
  20. 10 Information Loss
  21. 11 Entropy Modulo a Prime
  22. 12 The Categorical Origins of Entropy
  23. Appendix A Proofs of Background Facts
  24. Appendix B Summary of Conditions
  25. References
  26. Index of Notation
  27. Index