Order (mathematics)

Order in mathematics may refer to:

In all mathematics

Order (group theory), the cardinality of a group or period of an element
The order of a polynomial may be its degree (old) or its order as a power series
Order of a square matrix, its dimension
Order (ring theory), an algebraic structure
Ordered group
Ordered field

Order of derivation
Order of a power series, the lowest degree of its terms
Orders of approximation in Big O notation
Leading-order (terms)
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

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
Lexicographical order, an ordering method on sequences analogous to alphabetical order on words
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

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