probability theory
Take a quick trip to the foundations of probability theory.
Randomness is surprisingly hard to define. Fortunately the mathematical language we use to describe it is beautifully well defined.
The second guiding principle in probability theory is more subtle – universality.
Symmetry is one of the two guiding principles in understanding probabilities – if different outcomes are equivalent they should have the same probability.
The practice of overbooking has made uncomfortable headlines lately. But how do airlines decide how many tickets to sell for a flight? Here's the maths.