The IceCube Neutrino Observatory is a 1 km$^{3}$ detector currently taking
data at the South Pole. One of the main strategies used to look for
astrophysical neutrinos with IceCube is the search for a diffuse flux of
high-energy neutrinos from unresolved sources. A hard energy spectrum of
neutrinos from isotropically distributed astrophysical sources could manifest
itself as a detectable signal that may be differentiated from the atmospheric
neutrino background by spectral measurement. This analysis uses data from the
IceCube detector collected in its half completed configuration which operated
between April 2008 and May 2009 to search for a diffuse flux of astrophysical
muon neutrinos. A total of 12,877 upward going candidate neutrino events have
been selected for this analysis. No evidence for a diffuse flux of
astrophysical muon neutrinos was found in the data set leading to a 90 percent
C.L. upper limit on the normalization of an $E^{-2}$ astrophysical $\nu_{\mu}$
flux of $8.9 \times 10^{-9} \ \mathrm{GeV \ cm^{-2} \ s^{-1} \ sr^{-1}}$. The
analysis is sensitive in the energy range between $35 \ \mathrm{TeV} - 7 \
\mathrm{PeV}$. The 12,877 candidate neutrino events are consistent with
atmospheric muon neutrinos measured from 332 GeV to 84 TeV and no evidence for
a prompt component to the atmospheric neutrino spectrum is found.
