degree

1. (education) A stage of proficiency or qualification in a course of study, now especially an award bestowed by a university/college, as a certification of academic achievement. (In the United States, can include secondary schools.)Examples: "She has two bachelor's degrees and is studying towards a master's degree."

2. (geometry) A unit of measurement of angle equal to ¹⁄₃₆₀ of a circle's circumference.Examples: "A right angle is a ninety-degree angle."; "Most humans have a field of vision of almost 180 degrees."Synonyms: °, arcdegree

3. (physics) A unit of measurement of temperature on any of several scales, such as Celsius or Fahrenheit.Examples: "212 degrees Fahrenheit is equal to 100 degrees Celsius."; "Water boils at 100 degrees Celsius."Synonyms: °

4. (algebra) The sum of the exponents of a term; the order of a polynomial.Examples: "A quadratic polynomial is a polynomial of degree 2."

5. (algebra, field theory) The dimensionality of a field extension.Examples: "The set of complex numbers constitutes a field extension of degree 2 over the real numbers."; "The Galois field #92;operatorname#123;GF#125;(125)#61;#92;operatorname#123;GF#125;(5³) has degree 3 over its subfield #92;operatorname#123;GF#125;(5)."

6. (graph theory) The number of edges that a vertex takes part in; a valency.