  For a smooth map $g\colon X \to U(N)$, where $X$ is a three-dimensional,
oriented, and closed manifold, the winding number or the map's degree is
defined by $W_3 = \frac{1}{24\pi^2} \int_{X}
\mathrm{Tr}\left[(g^{-1}dg)^3\right]$. We introduce a method to compute $W_3$
using a discrete approximation of $X$ so that the result is manifestly
quantized.
