# Order (mathematics)

From HandWiki

**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:

## 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

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