Order (mathematics)

Contents
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
 Zorder (curve), a spacefilling curve
 NURBS order, a number one greater than the degree of the polynomial representation of a nonuniform rational Bspline
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 firstorder statistics
 Variance, correlation, power spectrum are secondorder statistics
 Skewness, bispectrum, kurtosis are examples of higherorder 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
 Longrange 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
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 settheoretic 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: zerothorder, firstorder, secondorder and higherorder logic
Categories: Mathematical terminology
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