Order (mathematics)

For order in other disciplines, see Order.

Order in mathematics may refer to:

In algebra

• Order (group theory), the cardinality of a group or period of an element
• Order, or degree of a polynomial
• Order, or dimension of a matrix
• Order (ring theory), an algebraic structure
• Ordered group
• Ordered field

In arithmetic

• Order (number theory), the multiplicative order in modular arithmetic
• Orders of magnitude, a class of scale or magnitude of any amount
• Order of operations

In analysis

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

In combinatorics

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

In statistics

• Mean, median, quantiles are first-order statistics
• Variance, correlation, power spectrum are second-order statistics
• Skewness, bispectrum, kurtosis are examples of higher-order statistics

In fractals

• Complexor, or complex order in fractals
• Orders of construction in the Pythagoras tree
• Order of extension in Lakes of Wada
• Order of Rényi dimensions

In geometry

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

In graphs

• Graph order, the number of nodes in a graph
• Ordered pair, including undirected and directed graphs
• Ordered triple, or mixed graph
  • Glossary of graph theory

Order theory

• Order theory, which studies various binary relations known as orders
• Order (journal), an academic journal on order theory
• 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
• Dense order, a total order where between any unequal pair of elements there is always an intervening element in the order
• Order topology, a topology of total order for totally ordered sets
• Ordinal numbers, which are assigned to sets based on their set-theoretic order
• Glossary of order theory
• List of order theory topics

In other mathematical theories

• Order in Ramsey theory, uniform structures in consequence to critical set cardinality
• Set theory (music) encompasses ordered pitch and pitch classes (Musical set theory)
• Type theory encompasses: zeroth-order, first-order, second-order and higher-order logic