Discrete mathematics studies the properties of finite sets carrying various sorts of structures.
One may profitably roughly divide up the topics that comprise discrete mathematics into the broad categories of existential combinatorics, enumerative combinatorics and algorithmics. Existential combinatorics asks whether or not structures with certain given properties exist. Enumerative combinatorics has the aim of counting all structures of a given type that one may impose on a set of a given size. Algorithmics considers, among other things, how best to decide whether or not a given finite structure has a certain property, and how to find a structure which optimizes of given objective. We may also cover additional topics as time permits or elide topics as time forbids.