  The equation of state with quantum statistics corrections is used for
particle number fluctuations $\omega$ of isotopically symmetric nuclear matter
with interparticle van der Waals and Skyrme local density interactions. The
fluctuations, $\omega\propto 1/\mathcal{K}$, are analytically derived through
the isothermal incompressibility $\mathcal{K}$ at first order over a small
quantum-statistics parameter. Our approximate analytical results appear to be
in good agreement with the results of accurate numerical calculations. These
results are also close to those obtained by using more accurate Tolman and
Rowlinson expansions of the incompressibility $\mathcal{K}$ near the critical
point. A more general formula for fluctuations $\omega$, improved at the
critical point, was obtained for a finite particle-number average $\langle N
\rangle$ by neglecting, for simplicity, small quantum statistics effects. It is
shown that for a large dimensionless parameter, $\alpha \propto
\mathcal{K}^2\langle N \rangle/\mathcal{K}^{\prime\prime} $, where
$\mathcal{K}^{\prime\prime}$ is the second derivative of the incompressibility
$\mathcal{K}$ as function of the average particle density $n$, far from the
critical point ($\alpha \gg 1$), one finds the traditional asymptote,
$\omega\propto 1/\mathcal{K}$, for the fluctuations $\omega$. For a small
parameter, $\alpha \ll 1$, near the critical point, where $\mathcal{K}=0$ and
$\alpha=0$, one obtains another asymptote of $\omega$. These fluctuations,
having a maximum near the critical point as function of the average density
$n$, for finite values of $\langle N \rangle$ are finite and relatively small,
in contrast to the results of the traditional calculations.
