  We shall examine various types of equations of state for neutron stars, which
determine the structure of neutron stars. In particular, the relation between
mass and radius of neutron stars is of primary consideration. By combining an
equation of state (EOS) with the Tolmann-Oppenheimer-Volkoff structure
equations, we can determine the theoretical maximum mass of a neutron star for
a given equation of state. One question we seek to answer is whether quark
matter can exist in the core of a neutron star. In light of the discovery of
pulsar PSR J1614-2230, the mass of which is observed to be 1.97 solar masses, a
valid equation of state must achieve a maximum mass that is greater than 2
solar masses. To try to solve this problem, we experiment with different sets
of parameters for the quark matter to try to meet the lower limit 2-solar-mass
criterion. It is found that certain parameters contribute significantly to the
maximum mass of a neutron star.
