To entice you into trying a new field of maths, I thought I might try introducing a few through some fascinating problems. They may or may not have solutions, and if you want the answers you will have to find them by researching the topic more!
We will start with two.
A fair maiden is trapped in a high tower surrounded by a five meter wide moat filled with lava. Sadly, I only have two 4.8 meter long planks with no rope, nails, or lava-proof scuba-gear. How do I get across?
The princess has luckily been fed by her dragon captor. Every day she drops off 3 boxes: one has bread, one has jam, and the third has bread and jam. Sadly the dragon can't read english, so the boxes are all labeled wrong so that no label is correct.
The princess opens one box, and without looking in the box, takes out one piece of food. She looks at it, and immediately labels all the boxes correctly.
Which box did she open and how did she know?