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Applied Mathematics - a very short introduction - Alain Goriely ***

This little book in Oxford University Press's vast, ever-expanding 'A Very Short Introduction' series starts off with a very positive note. After a quote from Groucho Marx, Alain Goriely takes us on a jovial tour of what 'applied mathematics' means. I was slightly surprised it needed such an introduction. It seems fairly obvious that it's mathematics that is, erm, applied, rather than maths for maths' sake. However, in the process Goriely gives us some of the basics involved. 

 One thing I would have liked to have seen, but didn't get, was more of an exploration of the boundary between applied maths and theoretical physics. (Cambridge even has a 'Department of Applied Mathematics and Theoretical Physics'.) I appreciate that some applied mathematics is used in other disciplines, but it does seem that the bulk of it is in physics, and the distinction between what an applied mathematician and a theoretical physicist does seems fairly fuzzy, to say the least.

 After the introduction, Goriely starts with simple applications, such as working out the cooking time for a turkey, through more and more complex uses, gradually adding in more powerful mathematics. Although you don't need to know how to use the heavier duty tools, you will meet differential equations and even partial differential equations along the way. The trouble with familiar applications, of course, is that it's easy to get lost in the reality of it, which left me worrying for Goriely's health. He reckons a 5 kg turkey cooks in 2.5 hours, where Delia Smith (who surely knows better) would give it at least 4 hours. I'm with Delia on this.

 There's some really good material here on the use of dimensions and scaling, but already the way the information is presented is becoming quite difficult to absorb. Not surprisingly there are equations - but they are used far too liberally, while technical terms are introduced often without explanation, or with explanations that don't really work. We move on to mathematical modelling and solving equations. Once again, simply following the argument is difficult without already having a reasonable grasp of at least A-level maths.

 There are all sorts of good things covered in the book, from knot theory (and its relevance to DNA) to JPEG compression. It's just a shame that, either because the book is so short, or because the author expects too much of the reader, the information in it is not presented in a way that is particularly accessible.

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Review by Brian Clegg
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