The study of systems consisting of arbitrary sets of elements of unspecified type, together with certain operations satisfying prescribed lists of axioms. Abstract algebra has been developed since the mid-1920s and has become a basic idiom of contemporary mathematics. In contrast to the earlier algebra, which was highly computational and was confined to the study of specific systems generally based on real and complex numbers, abstract algebra is conceptual and axiomatic. A combination of the theories of abstract algebra with the computational speed and complexity of computers has led to significant applications in such areas as information theory and algebraic geometry.