Combinatorics
lastmod 2014-06-12created 2014-06-121 edits
Combinatorics is a branch of pure mathematics that deals with non-continuous objects. It is usually concerned with finite objects. Combinatorics is related to many areas of mathematics, such as algebra, probability theory, ergodic theory, and geometry. It is also related to fields such as computer science and statistical physics. Combinatorics includes enumerative combinatorics, which counts the objects that satisfy certain conditions; combinatorial design theory and matroid theory, which determine when conditions are satisfied and construct and analyze the objects that satisfy them; extremal combinatorics and combinatorial optimization, which find the "largest", "smallest", or "optimal" objects; and algebraic combinatorics, which finds the algebraic structures that objects have.