Good Math, book review: Challenging concepts, well explained by Mary Branscombe

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Mary Branscombe, freelance tech journalist summarizes,  "More accessible than Hofstadter or Martin Gardner's classic mathematical columns, Good Math is a fun, if demanding, introduction to the strange, fascinating fundamental concepts of mathematics that underpin programming."

Good Math: A Geek's Guide to the Beauty of Numbers, Logic, and Computation (Pragmatic Programmers).

Understanding maths, logic and computation is becoming increasingly important in business -- especially if you need to evaluate new technology. Can your wi-fi router or your smartphone really make you money by mining Bitcoin in the background? To find out, you need to know something about cryptography, something about hardware design and something about how to calculate power usage so you can figure out whether that crowd-funded device you're thinking of investing in will cost you more in electricity than it will make you in virtual currency. Even if you just want to avoid being fooled by infographics, it's a good idea to think a bit more rigorously about mathematics.

It's been a long time since computing was taught by the maths teacher at school; these days, you can jump straight into programming without knowing much more than algebra. However, a more comprehensive understanding of mathematics will become increasingly useful. If you want to make sense of the principle of machine learning, you need to understand basic statistics and probability. To understand functional programming, you need to know the basics of lambda calculus. And if you're looking at actor frameworks, like the new programming models in the Azure Service Fabric, an understanding of state and Turing Machines will come in handy.

Mark Chu-Carroll's Good Math: A Geek's Guide to the Beauty of Numbers, Logic, and Computation is a good introduction to the appreciation and understanding of maths -- as long as you're already comfortable with mathematical notation and are prepared to pay attention. Chu-Carroll has an engaging style that's easy to read and he makes mathematical discoveries and principles interesting. However, you'll definitely need an aptitude for maths in order to grasp the details. He starts at the beginning, with numbers -- basics like cardinal numbers tell you how many things there are and ordinal numbers tell you what order they're in -- and explains that axioms are sets of rules that define how numbers behave. But in just a few pages you're into Peano arithmetic and induction, with subsequent chapters covering irrational and transcendental numbers, plus 'funny numbers' like zero, Euler's constant, i (the square root of -1) and the golden ratio.
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Source: ZDNet