There is a big range of activities here, from genuine degree-level maths (Quadratic reciprocity, Elliptic curves)

to investigations (Siders, Pearl tilings) to recreational mathematics (Kites and Darts),

to pieces of whimsy (Coincidences).

The idea throughout is to encourage new ways to approach a problem mathematically,

and to broaden the range of tools that an A Level mathematician can call upon if necessary.

The aim is also to share the beauty of mathematics,

which is sometimes buried at A Level by the sheer weight of techniques that need to be learned.

There is a delicate balancing act with investigations.

If you direct the investigation too much, you kill it,

but if you don't direct it at all, some excellent mathematics is unexplored,

while the mathematics that is explored remains at a low level.

Fingers crossed that I have achieved the right balance here.