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For more information on mathematical structures see Wikipedia: mathematical structure, equivalent definitions of mathematical structures, and transport of structure. The distinction between geometric "spaces" and algebraic "structures" is sometimes clear, sometimes elusive. Clearly, groups are algebraic, while Euclidean spaces are geometric.
An alternative to using mathematical pseudocode (involving set theory notation or matrix operations) for documentation of algorithms is to use a formal mathematical programming language that is a mix of non-ASCII mathematical notation and program control structures. Then the code can be parsed and interpreted by a machine.
The relation between computation and the underlying mathematical structures from fields such as logic, set theory, model theory, category theory, etc. It has close links with other areas of computer science such as programming language design, type theory, compilers and interpreters, program verification and model checking.
The mathematical model represents the physical model in virtual form, and conditions are applied that set up the experiment of interest. The simulation starts – i.e., the computer calculates the results of those conditions on the mathematical model – and outputs results in a format that is either machine- or human-readable, depending upon ...
If the search space is fixed, the computational complexity for this class of problems is usually estimated by: the time and space required to construct the data structure to be searched in; the time (and sometimes an extra space) to answer queries. For the case when the search space is allowed to vary, see "Dynamic problems".
In computer science, purely functional programming usually designates a programming paradigm—a style of building the structure and elements of computer programs—that treats all computation as the evaluation of mathematical functions. Program state and mutable objects are usually modeled with temporal logic, as explicit variables that ...
In mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.
In computer science, an array is a data structure consisting of a collection of elements (values or variables), of same memory size, each identified by at least one array index or key. An array is stored such that the position of each element can be computed from its index tuple by a mathematical formula.