熵与多样性：公理化方法
Entropy and Diversity: The Axiomatic Approach
AI总结：
本书以公理化方法严谨处理生物多样性的量化问题，融合信息论、概率论、范畴论等多领域数学，并兼顾纯数学动机，且只需本科分析基础即可阅读。
摘要：
本书为当前关于如何量化生物多样性的激烈辩论带来了新的数学严谨性。“什么是多样性？”这一问题具有令人惊讶的数学深度和广度：本书涉及的数学部分从信息论、函数方程和概率论，一直延伸到范畴论、几何测度论和数论。它将公理化方法的力量应用于一个备受关注的生物学问题，但其中的新概念和新定理也受到纯数学视角的启发。本书的主要叙述脉络只要求具备本科阶段的分析课程基础，不要求读者预先熟悉熵或多样性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
