The idea is this. To start with, you will choose an envelope at random, say by tossing a coin, and look at its contents, which is a cheque for some number - say n. (By randomising like this, you can be sure I haven't subconsciously induced you to prefer one envelope or the other.) You want to make sure that the bigger the number is, the more likely you are to keep it, in other words, the less likely you are to swap.

There are many sorts of games played in a "bunco booth", where a trickster or sleight-of-hand expert tries to relieve you of your money by getting you to place bets - on which cup the ball is under, for instance, or where the queen of spades is. Lots of these games can be analysed using probability theory, and it soon becomes obvious that the games are tipped heavily in favour of the trickster!

John Haigh takes the above quote as the epigraph for "Taking Chances", and makes his own significant contribution to scientific literacy. He concerns himself with "games of chance" in the broadest sense, from the National Lottery, quiz shows, casino games and card, dice and coin games, through game-theoretic "games" such as military conflicts, to all types of sports.

This is one of the world's outstanding pedagogic texts. It has the rare distinction of being a mathematics book that has sold a million copies. The COMAP project is a coalition of leading mathematicians and educators, directed by Solomon Garfunkel, who over a period of twelve years and five ever-expanding editions have created a beautiful introduction to the practical applications of some of the most important areas of discrete mathematics.

"The pleasure and interest of being a scientist need not be confined to those gifted people who have the ability to pursue the highly specialised studies which are necessary for those who would reach the main frontiers of scientific advance." G. I. Taylor, one of the great physicists of the twentieth century, among the last masters of both theory and experiment.

Computers can do many things, but there are some things they can't do. They certainly can't play tennis or the violin, but those aren't the kinds of thing we're concerned with. There are computational questions, questions of the kind that we would naturally turn to a computer to help us with, that, in fact, they cannot answer (and nor, therefore, can we).

A greek soldier, and a persion soldier walk into a battle...

Jenni Barker plots the path from astrophysics to science journalism.

Why can't human beings walk as fast as they run? And why do we prefer to break into a run rather than walk above a certain speed? Using mathematical modelling, R. McNeill Alexander finds some answers.