  The physical analysis of condensed matter systems can be difficult due to
strong coupling, but the mathematical context of the AdS/CFT correspondence
enables non-perturbative descriptions in terms of dual weakly coupled systems.
This brief review explores the holographic condensed matter applications of
AdS/CFT, particularly through the lens of a high-$T_c$ superconductor outside a
Schwarzchild black hole in Anti-de Sitter space. A simple two-dimensional
electron condensate Lagrangian is examined first, as employed by G. T.
Horowitz, later used to calculate a frequency-dependent conductivity and a free
energy analysis; the asymptotics of both in this procedure, as examined by P.
S\"aterskog, are also reviewed. An extended Lagrangian with a higher order
Maxwell term is assessed thereafter, with a conductivity peak obtained at low
frequencies described well by the Drude model in certain limits. The behavior
of Drude model parameters in these limits is also investigated.
