Mathematics for Biologists

Abstract

Over the past decade or so I have become increasingly concerned that many students on B.Sc. and HND courses in the biological sciences have great difficulty with numerical calculations relating to aspects of biology, whether it is with both the mathematics and the applications, or just a problem applying the mathematics to a particular situation. While many mathematics textbooks exist, these tend to be either too general and lacking in relevant examples, or too advanced, covering topics which are not required by most biology students. (I am using the term ‘biology’ to cover all the biologically-related disciplines such as ecology, zoology, botany, biochemistry, physiology, and microbiology.) This book is intended to be used primarily by such first year students to develop their skills in this area. Rather than provide a conventional textbook, I have chosen to write this as a self-contained workbook. The aim is for most students to be able to work through the book independently of any mathematics lectures. Alternatively, it could be used as part of a variety of courses, whether skills-based or subject-based. In my own university I have used it in place of lectures as the basis of a numeracy skills module for a variety of biology students. The students also received some tutorial help. The book is arranged in chapters which lead from the basic mathematical ideas of fractions, decimals and percentages, through ratio and proportion, multipliers, exponents and logarithms, to straight line graphs, and finally to graphs that are not straight lines, and their transformation. The associated applications covered are the types of problem most commonly encountered in degree and HND courses in the biological sciences and include concentrations and dilutions, changing units, pH, and linear and non-linear rates of change. Each chapter starts with an explanation of the mathematical concepts covered together with worked examples. The main concepts or definitions to be remembered are highlighted. Worked examples of the applications in biology follow the ‘pure’ mathematics sections. The applied examples obviously require some understanding of the science as well as the mathematics; I have tried to explain the science to the extent necessary to tackle the problems. At the end of each chapter are numerous examples of both pure and applied problems. Answers to the problems are at the end of the book. I am indebted to a number of people who have made helpful suggestions and encouraged the development of the book. Peter Robinson, Philip Roberts and Sally Foster read drafts of the text and made useful suggestions. Many of the students who used a draft version also either provided helpful comments or showed me what they found most difficult. Sally Foster also pointed out ambiguities, suggested alternative ways of presenting some arguments, and identified typographical errors and errors of grammar and punctuation. Peter Robinson helped with any information technology problems I had. vii