Systems of nuclear matter are studied in the condition of near infinite degrees of freedom. First we explore Bardeen-Cooper-Schrieffer pairing in two-dimensional space, where we derive the gap equation for finite interaction range. While BCS theory primarily applies to cold atomic gases, it can be generalized to the 2D nuclear "pasta" phase present in neutron stars. This leads to the next part of this work, in which two nuclear systems, pure neutron matter and symmetric nuclear matter, are modelled by the Skyrme Interaction and analyzed via solving the Hartree-Fock set of equations. The densities of these systems were examined, first in the pure neutron system, then in non-Coloumbic symmetric matter, and then finally in symmetric matter with charge repulsion between the protons.