An abstract mathematical representation of a process, device or concept; it uses a number of variables to represent inputs, outputs and internal states, and sets of equations and inequalities to describe their interaction.

(logic) A subfield of logic and mathematics consisting of both the mathematical study of logic and the application of this study to other areas of mathematics, exemplified by questions on the expressive power of formal logics and the deductive power of formal proof systems.

(computer science) A study of formal semantics of computer languages, such as denotational semantics.

(statistics) The study of statistics from a purely mathematical standpoint, using probability theory, measure theory, linear algebra and analysis.

(mathematics) The mathematical study of functions, sequences, series, limits, derivatives and integrals.

(philosophy) A doctrine that mathematical entities such as numbers and triangles exist independently of the human mind.

(mathematics) A set together with a collection of mathematical objects such as other sets, relations or operations which endow it with additional structure.

(mathematics) A theory and technique for the analysis and processing of geometrical structures, based on set theory, lattice theory, topology, and random functions.

(mathematics) A method of proof which, in terms of a predicate P, could be stated as: if P(0) is true and if for any natural number n>0, P(n) implies P(n+1), then P(n) is true for any natural number n.

The use of mathematics to construct formal theories about society.