Entropy and Diversity: The Axiomatic Approach
Entropy and Diversity: The Axiomatic Approach
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DOI：
10.1017/9781108963558
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发表时间：
2020-12
期刊：
影响因子：
--
通讯作者：
T. Leinster
中科院分区：
文献类型：
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作者：
T. Leinster
全球生物多样性危机是人类最紧迫的问题之一，但即使是量化生物多样性也是一个困难的数学和概念挑战。这本书带来了新的数学严谨性正在进行的辩论。它诞生于范畴论的研究，由信息论赋予力量，并由古老的函数方程领域提供支持。它将公理化方法的力量应用于一个迫切关注的生物学问题，但它也提出了新的定理，这些定理独立于任何应用而独立于数学本身。“什么是多样性？”具有令人惊讶的数学深度，这本书涵盖了广泛的数学，从函数方程到几何测度论，从概率论到数论。尽管范围很广，但数学的先决条件很少：本书的主要叙述线索只需要一门本科分析课程。
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.