An introduction to probabilistic combinatorics
This is the story of understanding 'things' by asking 'what does a typical thing 'look like'. The things can be finite (permutations, elements of a finite group, graphs, or integers between 1 and N). They can also be infinite (random matrix theory asks about the eigenvalues of 'typical unitary matrices'). Features of interest can be drawn from mathematics (for groups, one can ask about conjugacy or characters of double cosets) OR from applications. The subject is filled with interesting, new 'universal laws' and many accessible open problems.