Degree (mathematics)

This article is about the term "degree" as used in mathematics. For alternative meanings, see Degree (disambiguation).

In mathematics, there are several meanings of degree depending on the subject.

Unit of angle

Main article: Degree (angle)

A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, representing ¹⁄₃₆₀ of a turn. When that angle is with respect to a reference meridian, it indicates a location along a great circle of a sphere, such as Earth (see Geographic coordinate system), Mars, or the celestial sphere.

Degree of a monomial

The degree of a monomial is equal to sum of the exponents of each of the variables appearing in the monomial, e.g. the degree of $x^2yz^3$ is $2+1+3=6$.

Degree of a field extension

Main article: field extension

Given a field extension K/F, the field K can be considered as a vector space over the field F. The dimension of this vector space is the degree of the extension and is denoted by [K : F].

Degree of a vertex in a graph

Main article: degree (graph theory)

In graph theory, the degree of a vertex in a graph is the number of edges incident to that vertex — in other words, the number of lines coming out of the point. In a directed graph, the indegree and outdegree count the number of directed edges coming into and out of a vertex respectively.

Topological degree

Main article: degree of a continuous mapping

In topology the term degree is used for various generalizations of the winding number in complex analysis. See topological degree theory.

Degree of freedom

A degree of freedom is a concept in mathematics, statistics, physics and engineering. See degrees of freedom.