Algebra is the discipline of pure mathematics that is concerned with the study of the abstract properties of a set, once this is endowed with one or more operations that respect certain rules (axioms). For instance, rings are sets with two operations which generalize the usual numbers. An area of research at Michigan Tech is commutative algebra, namely the study of those rings where both operations satisfy the commutative property.
Combinatorics is the art of counting. Its main goal is to, given a set, determine how many elements it contains. Relevant areas of research at Michigan Tech are enumerative and algebraic combinatorics. They employ, respectively, bijective and commutative algebraic methods in the study of combinatorial problems.
Another field of interest of some Michigan Tech faculty members is partition theory, a discipline which lies at the crossroads of algebra, combinatorics, and number theory.