 The abstract approach, as adopted by such classical texts as Mac Lane and Birkhoff, has a certain purist appeal and is ideally suited to mathematics majors. The concrete approach has the benefit of being able to substitute calculus or less for groups-rings-fields as a prerequisite, suiting it to service courses for scientists and engineers needing only finite-dimensional matrix algebra, which enjoys enormous practical applicability. Linear algebra over other fields, in particular finite fields, is used in coding theory, quantum computing, etc., for which the abstract approach tends to be better suited.