The biodiversity crisis is one of our most urgent problems. This book develops the mathematics behind the measurement of diversity, spanning a great breadth of subjects: from geometry to logic, from algebra to probability theory. The mathematical prerequisites are few, accessible to mathematicians and biologists with a mathematical background.
The biodiversity crisis is one of our most urgent problems. This book develops the mathematics behind the measurement of diversity, spanning a great breadth of subjects: from geometry to logic, from algebra to probability theory. The mathematical prerequisites are few, accessible to mathematicians and biologists with a mathematical background.
Tom Leinster is Professor of Category Theory at the University of Edinburgh, a member of the University of Glasgow's Boyd Orr Centre for Population and Ecosystem Health, and co-author of a highly-cited Ecology article on measuring biodiversity. He was awarded the 2019 Chauvenet Prize for mathematical writing.
Inhaltsangabe
Introduction 1. Fundamental functional equations 2. Shannon entropy 3. Relative entropy 4. Deformations of Shannon entropy 5. Means 6. Species similarity and magnitude 7. Value 8. Mutual information and metacommunities 9. Probabilistic methods 10. Information loss 11. Entropy modulo a prime 12. The categorical origins of entropy Appendix A. Proofs of background facts Appendix B. Summary of conditions References Index of notation Subject index.
Introduction 1. Fundamental functional equations 2. Shannon entropy 3. Relative entropy 4. Deformations of Shannon entropy 5. Means 6. Species similarity and magnitude 7. Value 8. Mutual information and metacommunities 9. Probabilistic methods 10. Information loss 11. Entropy modulo a prime 12. The categorical origins of entropy Appendix A. Proofs of background facts Appendix B. Summary of conditions References Index of notation Subject index.
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