“I was never any good at mathematics.”
I must have heard this sentence from a thousand different people.
I cannot dispute that it may be true: people do have different strengths and weaknesses, different interests and priorities, different opportunities and obstacles. But, all the same, an understanding of mathematics is not something anyone is born with, not even Pythagoras himself. Like all other skills, from portraiture to computer programming, from knitting to playing cricket, mathematics can only be developed through practice, that is to say through actually doing it.
Nor, in this age, is mathematics something anyone can afford to ignore. Few people stop to worry whether they are good at talking or good at shopping. Abilities may indeed vary, but generally talking and shopping are unavoidable parts of life. And so it is with mathematics. Rather than trying to hide from it, how about meeting it head on and becoming good at it?
Sounds intimidating? Don’t panic! The good news is that just a handful of central ideas and techniques can carry you a very long way. So, I am pleased to present this book: a no-nonsense guide to the essentials of the subject, especially written for anyone who “was never any good at mathematics.” Maybe not, but it’s not too late!
Before we get underway, here’s a final word on philosophy. Mathematical education is split between two rival camps. Traditionalists brandish rusty compasses and dusty books of log tables, while modernists drop fashionable buzzwords like “chunking” and talk about the “number line.” This book has no loyalty to either group. I have simply taken the concepts I consider most important, and illustrated them as clearly and straightforwardly as I can.
Many of the ideas are as ancient as the pyramids, though some have a more recent heritage. Sometimes a modern presentation can bring a fresh clarity to a tired subject; in other cases, the old tried and tested methods are the best.
Richard Elwes