The reference: The ABC's of Number Theory (PDF)
On page 17 of the PDF, or 72 of the scan, he solves a Putnam problem.
In the solution he uses a special case of Mason's theorem, for $F$ a polynomial, and gets the inequality:
$\text{deg}(P') = m-1 \geq 2m -r-s$
Can you explain how to derive this from the statement of Mason's theorem above, and specifically some intuition on what is $F^{-1}(\{0,1,\infty\})$, in relation to $F$ and how it counts roots, discarding multiplicity?