Skip to main content

The Calculus Story - David Acheson ***

According to the back cover 'This little book is more ambitious than it looks.' Apart from a distinct feeling of damning with faint praise, there's an element of truth in this, which proves both a negative and a positive, depending on what you're looking for from a book on calculus.

Let's get the negative out of the way first. To make it a mathematical adventure, as the subtitle suggests, it would need rather more story and rather less calculus. Although David Acheson does get some history of maths in, this is much more 'getting your head around calculus for beginners' than it is 'the calculus story.' So, yes, you will discover, for instance, the battle between Newton and Leibniz - and Bishop Berkeley's magnificently titled 'the Analyst, or a discourse addressed to an infidel mathematician' - but only in a few passing lines.

What we get instead is a step by step introduction to calculus from first principles, which builds on Ancient Greek concepts through to limits and far more. Along the way readers will discover why there is such a relationship between calculus and infinite series and how pi and e come into the mix. We even get a spot of calculus using imaginary numbers.

There's frankly far too much grunt work here for this to really qualify as popular maths. But, equally, this little hardback lacks the dull writing style and worked examples of a textbook. It's far too readable to be one of those. 

I'd say there are broadly two types of people who may find this book interesting. If you've done some calculus but just crunch the numbers according to the rules without thinking about why it works, the book will be extremely enlightening. And if you have a general interest in mathematics but don't really understand how many apparently unrelated components come together, it should go down very nicely. But don't expect that promised adventure. This book a far too practically minded for that.

Hardback:  

Kindle:  

Review by Brian Clegg

Comments

Popular posts from this blog

Beyond Weird - Philip Ball *****

It would be easy to think 'Surely we don't need another book on quantum physics.' There are loads of them. Anyone should be happy with The Quantum Age on applications and the basics, Cracking Quantum Physics for an illustrated introduction or In Search of Schrödinger's Cat for classic history of science coverage. Don't be fooled, though - because in Beyond Weird, Philip Ball has done something rare in my experience until Quantum Sense and Nonsense came along. It makes an attempt not to describe quantum physics, but to explain why it is the way it is.

Historically this has rarely happened. It's true that physicists have come up with various interpretations of quantum physics, but these are designed as technical mechanisms to bridge the gap between theory and the world as we see it, rather than explanations that would make sense to the ordinary reader.

Ball does not ignore the interpretations, though he clearly isn't happy with any of them. He seems to come clo…

The AI Delusion - Gary Smith *****

This is a very important little book ('little' isn't derogatory - it's just quite short and in a small format) - it gets to the heart of the problem with applying artificial intelligence techniques to large amounts of data and thinking that somehow this will result in wisdom.

Gary Smith as an economics professor who teaches statistics, understands numbers and, despite being a self-confessed computer addict, is well aware of the limitations of computer algorithms and big data. What he makes clear here is that we forget at our peril that computers do not understand the data that they process, and as a result are very susceptible to GIGO - garbage in, garbage out. Yet we are increasingly dependent on computer-made decisions coming out of black box algorithms which mine vast quantities of data to find correlations and use these to make predictions. What's wrong with this? We don't know how the algorithms are making their predictions - and the algorithms don't kn…

Five Photons - James Geach ****

It is generally acknowledged that Stephen Hawking's A Brief History of Time is one of the most common books to be bought but not read beyond the first few pages. If you are the kind of popular science reader who found Hawking hard going, you can stop now - Five Photons is not for you. If, on the other hand, you found A Brief History of Time a piece of cake and wished you could get into more depth without resorting to heavy mathematics or a tedious textbook style, Five Photons could be just up your street.

Astrophysicist James Geach starts of fairly gently with a chapter on the nature of light that mostly sets aside quantum physics, leading up to the observation that light is our vehicle for for stripping back the history of the universe to its earliest times (or, at least, the point where the universe became transparent). From here on, the five photons of the title take us on different journeys, from the oldest surviving light of the cosmic microwave background radiation to that fr…