论文标题
熵与多样性：公理方法
Entropy and Diversity: The Axiomatic Approach
论文作者
论文摘要
这本书为如何量化生物学多样性的持续有力的辩论带来了新的数学严谨性。问题“什么是多样性？”具有令人惊讶的数学深度和广度：这本书涉及数学的一部分，从信息理论，功能方程式和概率理论到类别理论，几何衡量理论和数字理论。它将公理方法的力量应用于迫切关注的生物学问题，但是从纯粹的数学角度来看，新概念和定理也是动机的。 主要的叙述线程不需要分析的本科课程。不熟悉熵或多样性。
This book brings new mathematical rigour to the ongoing vigorous debate on how to quantify biological diversity. The question "what is diversity?" has surprising mathematical depth, and breadth too: this book involves parts of mathematics ranging from information theory, functional equations and probability theory to category theory, geometric measure theory and number theory. It applies the power of the axiomatic method to a biological problem of pressing concern, but the new concepts and theorems are also motivated from a purely mathematical perspective. The main narrative thread requires no more than an undergraduate course in analysis. No familiarity with entropy or diversity is assumed.
