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

God: the Science, the Evidence - Michel-Yves Bolloré and Olivier Bonnassies ***

This is, to say the least, an oddity, but a fascinating one. A translation of a French bestseller, it aims to put forward an examination of the scientific evidence for the existence of a deity… and various other things, as this is a very oddly structured book (more on that in a moment). In The God Delusion , Richard Dawkins suggested that we should treat the existence of God as a scientific claim, which is exactly what the authors do reasonably well in the main part of the book. They argue that three pieces of scientific evidence in particular are supportive of the existence of a (generic) creator of the universe. These are that the universe had a beginning, the fine tuning of natural constants and the unlikeliness of life. To support their evidence, Bolloré and Bonnassies give a reasonable introduction to thermodynamics and cosmology. They suggest that the expected heat death of the universe implies a beginning (for good thermodynamic reasons), and rightly give the impression tha...

Humble Pi - Matt Parker ****

Matt Parker had me thoroughly enjoying this collection of situations where maths and numbers go wrong in everyday life. I think the book's title is a little weak - 'Humble Pi' doesn't really convey what it's about, but that subtitle 'a comedy of maths errors' is far more informative. With his delightful conversational style, honed in his stand-up maths shows, it feels as if Parker is a friend down the pub, relating the story of some technical disaster driven by maths and computing, or regaling us with a numerical cock-up. These range from the spectacular - wobbling and collapsing bridges, for example - to the small but beautifully formed, such as Excel's rounding errors. Sometimes it's Parker's little asides that are particularly attractive. I loved his rant on why phone numbers aren't numbers at all (would it be meaningful for someone to ask you what half your phone number is?). We discover the trials and tribulations of getting cal...

Quantum 2.0 - Paul Davies ****

Unlike the general theory of relativity or cosmology, quantum physics is an aspect of physics that has had a huge impact on everyday lives, particularly through the deployment of electronics, but also, for example, where superconductivity has led to practical applications. But when Paul Davies is talking about version 2.0, he is specifically describing quantum information, where quantum particles and systems are used in information technology. This obviously includes quantum computers, but Davies also brings in, for example, the potential for quantum AI technology. Quantum computers have been discussed for decades - algorithms had already been written for them as early as the 1990s - but it's only now that they are starting to become usable devices, not at the personal level but in servers. In his usual approachable style, Davies gives us four chapters bringing us up to speed on quantum basics, but then brings in quantum computing. After this we don't get solid quantum informat...

Search This Blog