'The maths handbook'

review by Ilia Rushkin

The maths handbook: Everyday maths made simple

Richard Elwes

Richard Elwes' Maths handbook is a lucid presentation of basic mathematics facts. It is intended for those who "were never any good at mathematics," for grown-ups who wish they remembered more of the maths they studied as children, or those who are intimidated by the subject. It is the latter point the author is most passionate about. This book serves as a proof that mathematics is a very natural way of thinking, and everything in the book is there for a reason.

Elwes follows standard elementary mathematics textbooks rather closely, breaking the book into a large number of chapters. The first one is a note on the language of mathematics — expressing ideas with equations. It touches on the importance of the equality sign, often misinterpreted by the uninitiated as a "Go!" sign as it is on a calculator. The subsequent chapters take the reader through maths fundamentals: arithmetic techniques, prime factors and divisibility, negative numbers, common and decimal fractions, powers, roots and logarithms. The latter of these is a definite success: the book makes the idea of logarithms very natural and explains them in a simple and convincing way.

Next, the author explains the use of letters in algebraic expressions after which he moves onto geometry. It is greatly to the author's credit that he manages to keep these chapters engaging, informative and logically structured: very rarely does the reader have a feeling of being simply faced with a fact. Most of the time, every new fact follows from the previous ones and has a "proof".

Two chapters are devoted to the Pythagorean theorem, complete with a proof, and an introduction of trigonometric functions, together with examples of their use. This is followed by chapters on Cartesian coordinates, both in two and three dimensions, and basic facts about graphs. The three final chapters are dedicated to things at once more complicated and more practical: some notions of probability and statistics. These chapters are of necessity kept on a more basic level than the rest of the book.

I do see some problems with this book. Regrettably, the author follows most elementary textbooks and uses the awkward acronym BEDMAS (Brackets-Exponents-Division-Multiplication-Addition-Subtraction). BEDMAS is a poor device for learning the order of operations. It substitutes understanding with a mnemonic rule and creates a false impression that division must precede multiplication, and addition subtraction. When writing an elementary handbook, one is bound to reuse the material from other books: it is difficult to invent something entirely new in such a narrow area. This gives flawed teaching techniques a chance to creep into yet another book. BEDMAS is just one example but there are others, such as soh-cah-toa. Try guessing what it is if you don't know. The answer is in the chapter on trigonometry.

Undoubtedly the strongest aspect of this book is that it always demonstrates the reason behind a mathematical notion: where it is useful and why the idea is natural. Will this book really help all those who "are no good at maths"? Those who need to be convinced of the usefulness of mathematics will likely remain unimpressed. To be fair, it is hard to imagine a book which would do the trick in that situation. The author's primary task was to show that there is nothing intimidating in mathematics, and this task was fulfilled. All those who would like to know more mathematics but are frightened by it should definitely read this book. It will also be an interesting read for mathematically inclined children.

Book details:
The maths handbook
Richard Elwes
paperback — 224 pages
Quercus (2011)
ISBN: 978-0857385840

About the author

Ilia Rushkin works for a non-profit maths education organisation in Houston, US.