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Mathematical Biology: A Very Short Introduction
Very Short Introductions: Brilliant, Sharp, Inspiring
Why are English Premier League football shirt patterns very similar to animal coat markings? And what do invasive species have in common with cancer cells in the body? Mathematical biology develops models which answer these questions, as they are applied to processes from the spread of a gene in a population, to predator-prey dynamics in an ecosystem, to the growth of tumours.
In this Very Short Introduction Philip K. Maini describes the art of modelling, what it is, why we do it, and illustrates how the abstract way of thinking that is the essence of mathematics enables us to transfer knowledge from one area of research to another. Using numerous examples, he explains how the same fundamental ideas have been used in different fields, and shows how mathematics is the language of science. The author also points to cases in science where the traditional scientific modelling approach - verbal reasoning - is incorrect and shows how mathematics can uncover, and correct, such flawed reasoning while, at the same time, enhance our intuition. This book provides a guide to the trajectory of mathematical biology from a niche subject in the 1970s to a well-established, popular subject that is truly inter-disciplinary, and points to exciting future challenges.
ABOUT THE The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Why are English Premier League football shirt patterns very similar to animal coat markings? And what do invasive species have in common with cancer cells in the body? Mathematical biology develops models which answer these questions, as they are applied to processes from the spread of a gene in a population, to predator-prey dynamics in an ecosystem, to the growth of tumours.
In this Very Short Introduction Philip K. Maini describes the art of modelling, what it is, why we do it, and illustrates how the abstract way of thinking that is the essence of mathematics enables us to transfer knowledge from one area of research to another. Using numerous examples, he explains how the same fundamental ideas have been used in different fields, and shows how mathematics is the language of science. The author also points to cases in science where the traditional scientific modelling approach - verbal reasoning - is incorrect and shows how mathematics can uncover, and correct, such flawed reasoning while, at the same time, enhance our intuition. This book provides a guide to the trajectory of mathematical biology from a niche subject in the 1970s to a well-established, popular subject that is truly inter-disciplinary, and points to exciting future challenges.
ABOUT THE The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
160 pages, Paperback
Published December 29, 2025
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February 10, 2026
This short book captures the essence of how mathematical modelling operates in biology—and, by extension, in the health sciences. It begins by introducing the concepts of capacity limits and growth, before moving on to steady states and the notion of nullclines, which allow the behaviour of a system to be analysed. From this foundation emerge the key ideas of excitation and oscillation. Simple differential equations, including partial derivatives, are discussed, though the reader is not expected to solve them; this is particularly relevant in the chapter on diffusion and activator–inhibitor systems. Throughout, the book presents a variety of practical examples, several of which are directly relevant to medical advances. The reader is repeatedly reminded that “all models are wrong, but some are useful.” Mathematical modelling is shown to be indispensable to understanding biological systems, and the book succeeds in demonstrating precisely how it delivers such insights.
Displaying 1 of 1 review