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.

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.

Where's the sweet spot?

Maths is all about patterns and rhythms, so it's no surprise that there's plenty of maths in art. Whether it's the visual or the performing arts, maths can be a tool, an inspiration, or simply something that's naturally contained within the structures and patterns.

Maths for mums and dads by Rob Eastaway and Mike Askew. This book is an absolute triumph. Given the authors' reputations, I would expect nothing less, so it is something of a relief to be able to write that first sentence.

Should you put all your eggs in one basket?

Genomics is one of the fastest moving areas of science and Gavin Harper, a mathematician and statistician, has put himself right at its centre. He works for Oxford Nanopore Technologies, a company which is developing new technology for analysing molecules and sequencing DNA. With 75 employees from 18 different countries and all sorts of scientific backgrounds, Gavin's work environment is nothing like the solitary paper-and-pencil affair traditionally associated with mathematics.

Coming to think of it, is the standard formula for the integral of x^k really the best one? Chris Sangwin makes an interesting case that it is not.

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.