Beautiful, Simple, Exact, Crazy - Apoorva Khare and Anna Lachowska ***
This is a rare example of a book that is pretty much a textbook, but works well as entertaining educational maths for a certain section of the audience. To be honest, that's probably quite a small section - but for those it does appeal to, I can heartily recommend to it.
What the authors set out to do is to give those who aren't mathematicians or scientists a feel for how useful mathematics is in the real world. All too often, the maths we are taught at school seems strangely abstract. Okay, they might give you those irritating problems about people filling baths or meeting each other part way on a journey to make the 'numbers come to life' - but these aren't real world applications. And all too often we are just presented with, say, an abstract geometric or algebraic problem to solve and expected to get on with it, with no idea of what the point is in anything vaguely connected with normal life.
The authors assume that the reader has maths to high school algebra level, but then takes off down a whole host of application routes, such as velocities and accelerations, interest and mortgages, the strange behaviour of fractals, the benefits of being able to estimate, ciphers, probability and statistics.
Some of the problems still do seem painfully artificial - a question picked at random is 'Suppose an entire school goes on a picnic - as many boys as girls. The boys all wear jeans; a third of the girls wear skirts, and the rest wear jeans. Given that a randomly picked student is wearing jeans, what is the odds that the student is a girl.' There's no doubt that Bayes' theorem is hugely valuable in real life, but this probably isn't an application many people are going to make of it, so doesn't really fit the book's philosophy of moving away from the artificiality of ordinary textbooks.
Is it going to work? I think the main problem is finding an audience. It's too simplistic for most university science students, and it's too much of textbook to read for fun. (I'm sorry, it just feels like a textbook, and no one remembers those fondly - the eyes tend to skip off the page in protest unless you force them to continue.) So that limits the size of the popular science audience. However, if you have high school maths combined with sufficient drive to find out more about usable mathematics to go along with a textbook approach, you will find that your mathematical toolkit is impressively expanded by this title.