Applied Mathematics - a very short introduction

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.

Paperback:

Kindle:

Using these links earns us commission at no cost to you

Review by Brian Clegg

Comments

David Spiegelhalter Five Way interview

Professor Sir David Spiegelhalter FRS OBE is Emeritus Professor of Statistics in the Centre for Mathematical Sciences at the University of Cambridge. He was previously Chair of the Winton Centre for Risk and Evidence Communication and has presented the BBC4 documentaries Tails you Win: the Science of Chance, the award-winning Climate Change by Numbers. His bestselling book, The Art of Statistics , was published in March 2019. He was knighted in 2014 for services to medical statistics, was President of the Royal Statistical Society (2017-2018), and became a Non-Executive Director of the UK Statistics Authority in 2020. His latest book is The Art of Uncertainty . Why probability? because I have been fascinated by the idea of probability, and what it might be, for over 50 years. Why is the ‘P’ word missing from the title? That's a good question. Partly so as not to make it sound like a technical book, but also because I did not want to give the impression that it was yet another book

The Genetic Book of the Dead: Richard Dawkins ****

When someone came up with the title for this book they were probably thinking deep cultural echoes - I suspect I'm not the only Robert Rankin fan in whom it raised a smile instead, thinking of The Suburban Book of the Dead . That aside, this is a glossy and engaging book showing how physical makeup (phenotype), behaviour and more tell us about the past, with the messenger being (inevitably, this being Richard Dawkins) the genes. Worthy of comment straight away are the illustrations - this is one of the best illustrated science books I've ever come across. Generally illustrations are either an afterthought, or the book is heavily illustrated and the text is really just an accompaniment to the pictures. Here the full colour images tie in directly to the text. They are not asides, but are 'read' with the text by placing them strategically so the picture is directly with the text that refers to it. Many are photographs, though some are effective paintings by Jana Lenzová. T

Everything is Predictable - Tom Chivers *****

There's a stereotype of computer users: Mac users are creative and cool, while PC users are businesslike and unimaginative. Less well-known is that the world of statistics has an equivalent division. Bayesians are the Mac users of the stats world, where frequentists are the PC people. This book sets out to show why Bayesians are not just cool, but also mostly right. Tom Chivers does an excellent job of giving us some historical background, then dives into two key aspects of the use of statistics. These are in science, where the standard approach is frequentist and Bayes only creeps into a few specific applications, such as the accuracy of medical tests, and in decision theory where Bayes is dominant. If this all sounds very dry and unexciting, it's quite the reverse. I admit, I love probability and statistics, and I am something of a closet Bayesian*), but Chivers' light and entertaining style means that what could have been the mathematical equivalent of debating angels on

Search This Blog