Definition:Degree


 * Degree of a polynomial: as used in algebra, abstract algebra etc.: the count of the coefficients (minus one) of a polynomial.


 * Degree of a mononomial: a related concept.


 * Degree of an algebraic number: the lowest possible degree of a polynomial of which the algebraic number is a root.


 * Degree of Field Extension: the dimension of a field extension $E/F$ when $E$ is viewed as a vector space over $F$.


 * Transcendence Degree: the largest cardinality of an algebraically independent subset $A \subseteq L$, where $L/K$ is a extension of a field $K$.


 * Degree of a homogeneous function: $f$ is homogeneous of degree $n$ $f \left({\alpha \mathbf v}\right) = \alpha^n f \left({\mathbf v}\right)$.


 * Degree of a homogeneous real function: $f$ is homogeneous of degree $n$ $f \left({t x, t y}\right) = t^n f \left({x, y}\right)$.


 * Degree of a Homogeneous Element of a gradation of a ring.


 * Degree of a vertex: as used in graph theory: the number of edges coming together at a particular vertex.


 * Degree of Arc (Angular Measure): as used in geometry, etc: $360$ of them make a full circle.


 * Degree (Topology):