In this series of talks, we cover the current finite difference, finite element, and 
discontinuous Galerkin methods used to approximate the solutions of second-order elliptic 
fully nonlinear PDEs.  In part three, we cover a few ``narrow-stencil'' numerical schemes: 
ones that lack monotonicity of the discrete operator but none the less converge.  We focus 
on on particular scheme, called the Vanishing Moment Method (VMM), which seeks to 
approximate the viscosity solution of the PDE by a sequence of weak solutions to a fourth 
order perturbed problem.  The fourth order problem then can be discretized using either 
finite difference, finite element, or discontinuous Galerkin techniques.  The current 
theory and numerical results for the VMM are presented.