I am learning stats. I just read a definition for a score function and hit some unfamiliar notation. I am familiar with the Leibniz notation for the derivative: $\frac{dy}{dx}$
The score function uses what seem to be deltas, which I have not seen before.
Is this an example of a Laplace operator or is this just Leibniz notation for a derivative written with Greek letters? I know this is a very basic notation question -- but I'm learning on my own from books.
$\partial$ is just a stylised $d$, and is for taking partial derivatives, i.e. it is basically for differentiating multivariate functions by assuming the other variables are constant (so $\frac{\partial f}{\partial x}=\frac{df}{dx}$ if $f$ is a function of $x$ only). $\partial$ is just notation to remind you that you are taking the derivative of a function that depends on more than one variable.)
For example, if $f(x,y)=x^2y^3$, then $\frac{\partial f}{\partial x} = 2xy^3$ and $\frac{\partial f}{\partial y}=3x^2y^2$.
On a side note, the Laplacian operator, if you work in one spatial dimension (often mathematicians work with functions that depend on up to three spatial dimensions plus one time dimension), is simply $\frac{\partial^2}{\partial x^2}$, i.e. the second derivative (in space).