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:

Using these links earns us commission at no cost to you

Review by Brian Clegg

Comments

The Decline and Fall of the Human Empire - Henry Gee ****

In his last book, Henry Gee impressed with his A (Very) Short History of Life on Earth - this time he zooms in on one very specific aspect of life on Earth - humans - and gives us not just a history, but a prediction of the future - our extinction. The book starts with an entertaining prologue, to an extent bemoaning our obsession with dinosaurs, a story that leads, inexorably towards extinction. This is a fate, Gee points out, that will occur for every species, including our own. We then cover three potential stages of the rise and fall of humanity (the book's title is purposely modelled on Gibbon) - Rise, Fall and Escape. Gee's speciality is palaeontology and in the first section he takes us back to explore as much as we can know from the extremely patchy fossil record of the origins of the human family, the genus Homo and the eventual dominance of Homo sapiens , pushing out any remaining members of other closely related species. As we move onto the Fall section, Gee gives ...

Pagans (SF) - James Alistair Henry *****

There's a fascinating sub-genre of science fiction known as alternate history. The idea is that at some point in the past, history diverged from reality, resulting in a different present. Perhaps the most acclaimed of these books is Kingsley Amis's The Alteration , set in a modern England where there had not been a reformation - but James Alistair Henry arguably does even better by giving us a present where Britain is a third world country, still divided between Celts in the west and Saxons in the East. Neither the Normans nor Christianity have any significant impact. In itself this is a clever idea, but what makes it absolutely excellent is mixing in a police procedural murder mystery, where the investigation is being undertaken by a Celtic DI, Drustan, who has to work in London alongside Aedith, a Saxon reeve of equivalent rank, who also happens to be daughter of the Earl of Mercia. While you could argue about a few historical aspects, it's effectively done and has a plot...

Amazing Worlds of Science Fiction and Science Fact: Keith Cooper ****

There's something appealing (for a reader like me) about a book that brings together science fiction and science fact. I had assumed that the 'Amazing Worlds' part of the title suggested a general overview of the interaction between the two, but Keith Cooper is being literal. This is an examination of exoplanets (planets that orbit a different star to the Sun) as pictured in science fiction and in our best current science, bearing in mind this is a field that is still in the early phases of development. It becomes obvious early on that Cooper, who is a science journalist in his day job, knows his stuff on the fiction side as well as the current science. Of course he brings in the well-known TV and movie tropes (we get a huge amount on Star Trek ), not to mention the likes of Dune, but his coverage of written science fiction goes into much wider picture. He also has consulted some well-known contemporary SF writers such as Alastair Reynolds and Paul McAuley, not just scient...

Search This Blog