  The strangeness contribution to the electric and magnetic properties of the
nucleon has been under investigation experimentally for many years. Lattice
Quantum Chromodynamics (LQCD) gives theoretical predictions of these
measurements by implementing the continuum gauge theory on a discrete,
mathematical Euclidean space-time lattice which provides a cutoff removing the
ultra-violet divergences. In this dissertation we will discuss effective
methods using LQCD that will lead to a better determination of the strangeness
contribution to the nucleon properties. Strangeness calculations are demanding
technically and computationally. Sophisticated techniques are required to carry
them to completion. In this thesis, new theoretical and computational methods
for this calculation such as twisted mass fermions, perturbative subtraction,
and General Minimal Residual (GMRES) techniques which have proven useful in the
determination of these form factors will be investigated. Numerical results of
the scalar form factor using these techniques are presented. These results give
validation to these methods in future calculations of the strange quark
contribution to the electric and magnetic form factors.
