Order (mathematics)

Order in mathematics may refer to:

Set theory

 * Total order and partial order, a binary relation generalizing the usual ordering of numbers and of words in a dictionary
 * Ordered set
 * Order in Ramsey theory, uniform structures in consequence to critical set cardinality

Algebra

 * Order (group theory), the cardinality of a group or period of an element
 * Order of a polynomial (disambiguation)
 * Order of a square matrix, its dimension
 * Order (ring theory), an algebraic structure
 * Ordered group
 * Ordered field

Analysis

 * Order (differential equation) or order of highest derivative, of a differential equation
 * Leading-order terms
 * NURBS order, a number one greater than the degree of the polynomial representation of a non-uniform rational B-spline
 * Order of convergence, a measurement of convergence
 * Order of derivation
 * Order of an entire function
 * Order of a power series, the lowest degree of its terms
 * Ordered list, a sequence or tuple
 * Orders of approximation in Big O notation
 * Z-order (curve), a space-filling curve

Arithmetic

 * Multiplicative order in modular arithmetic
 * Order of operations
 * Orders of magnitude, a class of scale or magnitude of any amount

Combinatorics

 * Order in the Josephus permutation
 * Ordered selections and partitions of the twelvefold way in combinatorics
 * Ordered set, a bijection, cyclic order, or permutation
 * Unordered subset or combination
 * Weak order of permutations

Fractals

 * Complexor, or complex order in fractals
 * Order of extension in Lakes of Wada
 * Order of fractal dimension (Rényi dimensions)
 * Orders of construction in the Pythagoras tree

Geometry

 * Long-range aperiodic order, in pinwheel tiling, for instance

Graphs

 * Graph order, the number of nodes in a graph
 * First order and second order logic of graphs
 * Topological ordering of directed acyclic graphs
 * Degeneracy ordering of undirected graphs
 * Elimination ordering of chordal graphs
 * Order, the complexity of a structure within a graph: see haven (graph theory) and bramble (graph theory)

Logic
In logic, model theory and type theory:


 * Zeroth-order logic
 * First-order logic
 * Second-order logic
 * Higher-order logic

Order theory

 * Order (journal), an academic journal on order theory
 * Dense order, a total order wherein between any unequal pair of elements there is always an intervening element in the order
 * Glossary of order theory
 * Lexicographical order, an ordering method on sequences analogous to alphabetical order on words
 * List of order topics, list of order theory topics
 * Order theory, study of various binary relations known as orders
 * Order topology, a topology of total order for totally ordered sets
 * Ordinal numbers, numbers assigned to sets based on their set-theoretic order
 * Partial order, often called just "order" in order theory texts, a transitive antisymmetric relation
 * Total order, a partial order that is also total, in that either the relation or its inverse holds between any unequal elements

Statistics

 * Order statistics
 * First-order statistics, e.g., arithmetic mean, median, quantiles
 * Second-order statistics, e.g., correlation, power spectrum, variance
 * Higher-order statistics, e.g., bispectrum, kurtosis, skewness