Combinatorics, or discrete mathematics, studies mathematical objects whose constituents are discrete, i.e. finite or at least separated, as opposed to continuous objects. It is a vibrant field that has major interactions with algebra, analysis, and probability. In fact, combinatorics has substantive connections with almost every field in mathematics. There are many, many interconnected topics of research within combinatorics, but graphs, hypergraphs, partially ordered sets, probabilistic combinatorics, algebraic combinatorics, enumeration, and combinatorial geometry are some of the major areas.