  The complete 5.4 kton MINOS far detector has been taking data since the
beginning of August 2003 at a depth of 2070 meters water-equivalent in the
Soudan mine, Minnesota. This paper presents the first MINOS observations of
muon neutrino and muon anti-neutrino charged-current atmospheric neutrino
interactions based on an exposure of 418 days. The ratio of upward to
downward-going events in the data is compared to the Monte Carlo expectation in
the absence of neutrino oscillations giving:
  R_data(up/down)/R_MC(up/down) = 0.62^{+0.19}_{-0.14} (stat.) +- 0.02 (sys.).
  An extended maximum likelihood analysis of the observed L/E distributions
excludes the null hypothesis of no neutrino oscillations at the 98 % confidence
level. Using the curvature of the observed muons in the 1.3 T MINOS magnetic
field muon neutrino and muon anti-neutrino interactions are separated. The
ratio of muon neutrino to muon anti-neutrino events in the data is compared to
the Monte Carlo expectation assuming neutrinos and anti-neutrinos oscillate in
same manner giving:
  R_data(numubar/numu)/R_MC(numubar/numu) = 0.96^{+0.38}_{-0.27} (stat.) +-
0.15 (sys.), where the errors are the statistical and systematic uncertainties.
Although the statistics are limited, this is the first direct observation of
atmospheric neutrino interactions separately for muon neutrinos and muon
anti-neutrinos.
