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Discrete mathematics, also called finite mathematics, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. Most, if not all, of the objects studied in finite mathematics are countable sets , such as integers , finite graphs , and formal languages .
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions).
In discrete calculus, this is a construction that creates from forms higher order forms: adjoining two cochains of degree and to form a composite cochain of degree +. For cubical complexes , the wedge product is defined on every cube seen as a vector space of the same dimension.
In mathematics, a contraction mapping, or contraction or contractor, on a metric space (M, d) is a function f from M to itself, with the property that there is some real number < such that for all x and y in M,
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic [1] – do not vary smoothly in this way, but have distinct, separated values. [2]
de Bruijn's theorem (discrete geometry) Descartes's theorem on total angular defect ; Erdős–Anning theorem (discrete geometry) Erdős–Nagy theorem (discrete geometry) Erdős–Szekeres theorem (discrete geometry) Fáry's theorem (graph theory) Fenchel's duality theorem (convex analysis) Fenchel–Moreau theorem (mathematical analysis)
In mathematics, the discrete exterior calculus (DEC) is the extension of the exterior calculus to discrete spaces including graphs, finite element meshes, and lately also general polygonal meshes [1] (non-flat and non-convex). DEC methods have proved to be very powerful in improving and analyzing finite element methods: for instance, DEC-based ...
The Dedekind eta-function is an automorphic form in the complex plane.. In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup of the topological group.
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