  The inclusion equations of the type $f \in T ( x)$ where $T: X \to
2^{X^{\ast}}$ is a maximal monotone map, are extensively studied in nonlinear
analysis. In this paper, we present a new construction of the degree of maximal
monotone maps of the form $T: Y \to 2^{X^*}$, where $Y$ is a locally uniformly
convex and separable Banach space continuously embedded in the uniformly convex
Banach space $X$. The advantage of the new construction lies in the remarkable
simplicity it offers for calculation of degree in comparison with the classical
one suggested by F. Browder. We prove a few classical theorems in convex
analysis through the suggested degree.
