What's the integral of x^k? If you're up to speed with your calculus, you can probably rattle the answer off by heart. But can you prove it? Chris Sangwin introduces an ingenious method for deriving the integral from first principles.

Want to impress an audience? Then why not become a lightning calculator by learning Burkard Polster and Marty Ross' method for working out the day on which someone was born from their birthday really fast.

David Spiegelhalter explains that waiting for an infinite number of monkeys to produce the complete works of Shakespeare is not just a probabilistic certainty, it also gives us an insight into how long we can expect to wait for a rare event to happen.