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The Mathematics Lover's Companion - Edward Scheinerman ****

The worrying thing about this title is that I'm not sure I am a maths lover. I find some parts of mathematics interesting - infinity and probability, for example - but a lot of it is just a means to an end for me. The good news is that, even if you are like me, there's a lot to like here, though you may find yourself skipping through some parts.

 Edward Scheinerman takes us through 23 mathematical areas, so should you find a particular one doesn't work for you, it's easy enough to move onto another that does. Sometimes it wasn't the obvious ones that intrigued - where I found the section on infinity, for example, a little underwhelming, I really enjoyed the section on factorials. The book opens with prime numbers, which while not the most exciting of its contents, gives the reader a solid introduction to the level of mathematical thought they will be dealing with. It's enough to get the brain working - this isn't a pure fun read and you have to think - but not so challenging that you feel obliged to give up.

 Along the way, Scheinerman is enthusiastic and encouraging with a light, informative style. Each page has side bars (meaning there's a lot of white space), which contain occasional comments and asides. I found these rather irritating for two reasons. In part because it really breaks up the reading process - if it's worth saying, say it in the main text - and partly because (in good Fermat fashion) there's not a lot of room so, for example, when we are told the origin of the RSA algorithm in the side bar, there's space to say it's named after Rivest, Shamir and Adelman but not to say that Cocks came up with it before them.

 Occasionally, as often seems the case with mathematicians, the author seemed to be in a slightly different world. He says that the angle trisection problem is more famous that squaring the circle - which seems very unlikely - and though he notes that pi day is usually considered to be 14 March (when written as 3/14) he doesn't point out it makes much more sense in the non-US world for it to be the 22 July (22/7).

 A typical section for me was the one the constant e (like pi, a number that crops up in nature and is valuable in a number of mathematical applications). There were parts of the section that I found really interesting: I'd never really seen the point of e before, the compound interest example was an eye-opener and there's the beautiful eiÏ€= -1. The two other examples, though, I did have to skip as they were a little dull. 

 My favourite part was at the end - the sections on uncertainty, including non-transitive dice (where you can have a series of dice, each of which can beat one of the others) and equivalent poker hands, Bayesian statistics, how to have a fair election and a fascinating game (Newcomb's paradox) - where it seems that you should choose what's not best for you to come out best - were all great. It would have been even better if the election section had used terms like 'first past the post' and 'single transferable vote' to make a clearer parallel with real election systems - and the Newcomb's paradox section should have made more of the difficulty of predicting an individual's choice - but these are small concerns.

 So will anyone love all of it? Probably not. If you truly do love maths, you'll know a lot of this already. If you aren't sure about your relationship with the field, the book won't all work for you - but that bits that do should be enough to show that mathematics can make an entertaining and stimulating companion.

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Review by Brian Clegg

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