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The Delicate Art of Brute Force - Paul Nahin ***

Ever since computers became useful tools, mathematicians have had mixed opinions about using the technology to solve mathematical problems. Obviously this is particularly topical when we look at what AI can (and can't) do - but there are plenty of opportunities for the brute force of computing to deal with a tricky mathematical road block, and that's what Paul Nahin sets out to cover here.

I'll say straight up front that I think this book would have been better and would have had a wider audience if it had not made excessive assumptions of what a reader knows. In his introductory chapter, Nahin says 'There is nothing in this book that attentive high school students who have taken an AP-calculus or AP-statistics class will find beyond them. This assumption lets me, for example write (as I do in the first chapter) the symbol X without explanation with the expectation that a reader will instantly recognise it as denoting the binomial coefficient...' (I have written X here to represent a pair of parentheses enclosing the letter n above the letter k.)

I had two problems with this. First, I had to look up what this 'AP' business was about: apparently in the US this is a school programme called 'advanced placement' where they get college-level detail - a bit like doing a further mathematics A-level. The other is that when a student I would have had this level of understanding, but frankly, having not used any of this stuff in decades, it isn't obvious at all. There frankly was no need for this intentional obscurity.

This is never going to make it as a popular maths or computing book - but I do want to praise it for what it really is: a textbook lite on approaching relatively simply described mathematical problems using computer programs. Nahin starts with a fairly abstract problem about whether you can make triangle from certain bits of wood, but then goes on to gives us topics like predicting wi-fi coverage (and the related problem of distributing anti-submarine depth charges that was one of the main reasons the discipline of operational research began in the Second World War), which amounts to the maths of intersecting circles or spheres, electrical resistance circuits, gamma-ray path calculations and more. Often what's involved is the incorporation of randomness (as used in Monte Carlo methods and other simulations) - but the main point is that computers can be extremely useful for when conventional mathematical solutions fail.

As a former operational research analyst, working in a department that was very computer intensive, at at a time when many OR people regarded it as somewhat heretical, I very much liked what was going on here. Nahin does try to inject some historical context, but even so this is, for me, still too much of a practical guide rather than popular mathematics/computing to read and enjoy.

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