Calculus is a collection of tools, such as differentiation and integration, for solving problems in mathematics which involve "rates of change" and "areas". In the second of two articles aimed specially at students meeting calculus for the first time, Chris Sangwin tells us how to move on from first principles to differentiation as we know and love it!

Following on from his article 'The prime number lottery' in last issue of Plus, Marcus du Sautoy continues his exploration of the greatest unsolved problem of mathematics: The Riemann Hypothesis.

The concept of a speed limit seems a simple one - until you think what can happen when a speed camera clocks a rotating wheel...

A biologist has developed a blood test for detecting a certain minor abnormality in infants. Obviously if you have blood samples from 100 children, you could find out which children are affected by running 100 separate tests. But mathematicians are never satisfied by the obvious answer. Keith Ball uses information theory to explain how to cut down the number of tests significantly, by pooling samples of blood.

In 1997 Garry Kasparov, then World Champion, lost an entire chess match to the IBM supercomputer Deep Blue, and it is only a matter of time before the machines become absolutely unbeatable. But the human brain, as Lewis Dartnell explains, is still able to put up a good fight by exploiting computers' weaknesses.

Human beings are famously prone to error, and proof-readers are, after all, only human. But who picks up the errors a proof-reader misses? John D. Barrow challenges readers to estimate the errors that aren't found from the errors that are.

Combinatorial Game Theory is a powerful tool for analysing mathematical games. Lewis Dartnell explains how the technique can be used to analyse games such as Twentyone and Nim, and even some chess endgames.