End of year weariness setting in? Exercise your brain and try some of our favourite puzzles – they're behind Door 2!

What do Caribbean steel drums, the London 2012 Velodrome and the quest for sustainable energy have in common? They all involve the work of engineers. Engineering provides some of the most exciting applications of maths, which impact on all our lives every day. Open Door 1 and discover the mathematics behind engineering.

Most of us take for granted that we can carry our entire music library in our pocket or whip out Google maps on our phones when we get lost. But few of us realise that it's physics and maths we have to thank for these marvellous inventions.

Tomorrow John D. Barrow, cosmologist, best-selling author and director of Plus, will be starting a lecture series on maths and sport at Gresham College in London. The first lecture is entitled How fast can Usain Bolt run? and there'll be five more lectures until the end of March, looking at Olympic sports from rowing to jumping. All lectures are free.

This Friday, 11/11/11, will see the launch of numberphile, a brand new YouTube channel dedicated entirely to numbers. And it's a very special channel too: rather than relying on users to produce and share their videos, YouTube is for the first time paying people to produce original content.

Have you ever wondered what string theory sounds and looks like? If yes, you can find out this weekend at Queen Mary, University of London. Musicians Anna Piva and Edward George, in collaboration with physicist and Plus author David Berman and mathematical physicist James Sparks are developing Explorations in Eleven Dimensions, a multimedia art project based on a series of sonic, visual, and textual readings of string theory's equations, themes and aesthetic concerns.

Whenever you smell the lovely smell of fresh coffee or drop a tea bag into hot water you're benefiting from diffusion: the fact that particles moving at random under the influence of thermal energy spread themselves around. It's this process that wafts coffee particles towards your nose and allows the tea to spread around the water. Diffusion underlies a huge number of processes and it has been studied intensively for over 150 years. Yet it wasn't until very recently that one of the most important assumptions of the underlying theory was confirmed in an experiment.

It's 21st of October and for puzzle lovers this can only mean one thing: the G4G Celebration of mind. This annual party celebrates the legacy of Martin Gardner, magician, writer and father of recreational maths, with mathemagical events in his honour happening all over the world.