Finite mathematics

The branch of mathematics concerned with the study of properties of structures of finite (finitistic) character, that arise both within mathematics and in applications. Among these structures one has, e.g., finite groups, finite graphs, and also certain mathematical models of information processing, finite automata, Turing machines, etc. (cf. Finite group; Graph; Automaton, finite; Turing machine). Sometimes the subject of finite mathematics is assumed to extend to arbitrary discrete structures, and this leads to discrete mathematics, identifying the latter with finite mathematics. Certain algebraic systems (cf. Algebraic system), infinite graphs, definite forms of computing schemes, cellular automata, etc., can be regarded as belonging to this area. The term discrete analysis sometimes serves as a synonym for the concepts of "finite mathematics" and "discrete mathematics" .