Combinatorics is an area of mathematics primarily concerned with counting,
both as a means and an end in obtaining results, and certain properties of
finite structures. It is closely related to many other areas of mathematics
and has many applications ranging from logic to statistical physics and from
evolutionary biology to computer science.
Combinatorics is well known for the breadth of the problems it tackles.
Combinatorial problems arise in many areas of pure mathematics, notably in
algebra, probability theory, topology, and geometry, as well as in its many
application areas. Many combinatorial questions have historically been
considered in isolation, giving an ad hoc solution to a problem arising in
some mathematical context.