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 two, we cover applications of the two fully nonlinear second order PDEs of interest - the Hamitlon-Jacobi-Bellman (HJB) and Monge-Ampere (MA) equations. We then introduce the first class of numerical methods colloquially known as ``wide stencil schemes''. These finite difference and finite element methods use the Barles-Souganidis framework to prove convergence to the viscosity solution which requires the numerical methods to have a strong notion of monotonicity.