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Biological systems are often best explored and explained using the power of maths – from the rate at which enzymes catalyse essential life processes, to the way populations ebb and flow as predators and prey interact. Mathematical tools lie at the heart of understanding biological systems – and mathematical skills are essential for success as a bioscientist.
This text introduces the range of mathematical concepts that bioscience students may encounter – and need to master – during the course of their studies. Starting from fundamental concepts, Core Maths for the Biosciences blends clear explanations and biological examples throughout as it takes the reader towards some of the most sophisticated yet elegant mathematical tools in use by biologists today.
Part 1: Arithmetic, Algebra & Functions
1: Arithmetic and Algebra
2: Units, Precision and Accuracy
3: Data tables, graphs, interpolation
4: Molarity and dilutions
5: Variables, functions and equations
6: Linear functions and curve sketching
7: Quadratic and Polynomial Functions
8: Fitting curves, and reciprocal and inverse functions
9: Periodic functions
10: Exponential and logarithmic functions
Part 2: Calculus and Differential Equations
11: Instantaneous rate of change: the derivative
12: Rules of differentiation
13: Applications of differentiation
14: Techniques of integration
15: The Definite Integral
16: Differential equations I
17: Differential equations II
18: Dynamical systems
Dr. Martin Reed is a lecturer in the Department of Mathematical Sciences at the University of Bath, and was for the last five years its Director of Teaching. He has taught maths in universities since 1973, both in the UK and overseas (Swaziland, Papua New Guinea, Tanzania); the latter experience has developed his ability to explain subtle concepts in simple, clear language. Prior to his position at Bath, Martin was a member of the Biosciences Department at Brunel University, where he taught core skills to all first year students. Martin's research interests are in numerical methods and optimization. He has lately worked in the field of evolutionary computation, where biological principles such as natural selection and swarm intelligence are used as inspiration for computer algorithms which can solve challenging practical problems.
"Exactly the sort of thing that will be helpful in showing those with biological problems how mathematics can be very useful – and that what is really important is maintaining an intuitive understanding between the mathematics – which is essentially no more, but no less, than a way of thinking very precisely – and the actual phenomena they are dealing with [...] Very fine indeed."
– Professor Lord May of Oxford, Department of Zoology, University of Oxford
"Fantastic. Easy to understand, interactive, biologically relevant and dictated in a way that seemed as though you are almost having a conversation with the author."
– James Sleigh, Student, University of Oxford
"Coherent and clear. The best I have seen this kind of material treated."
– Stephen Hubbard, University of Dundee
"This book is by far the best of its kind, a spectacular diamond in the rough."
– Helen Smith, student, University of Salford
"The interactive spreadsheets are a work of genius."
– Stuart Fisk, student, University of Essex