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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.

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Review by Brian Clegg

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