\begin{definition}[Definition:Degree of Polynomial/Field]
Let $\struct {F, +, \times}$ be a field whose zero is $0_F$.
Let $\struct {K, +, \times}$ be a subfield of $F$.
Let $x \in F$.
Let $\ds f = \sum_{j \mathop = 0}^n \paren {a_j x^j} = a_0 + a_1 x + \cdots + a_n x^n$ be a polynomial over $K$ in $x$ such that $a_n \ne 0$.
Then the '''degree of $f$''' is $n$.
The '''degree of $f$''' can be denoted $\map \deg f$ or $\partial f$.
\end{definition}