  Type Ia supernovae (SNe Ia) can be calibrated to be good standard candles at
cosmological distances. We propose a supernova pencil beam survey that could
yield between dozens to hundreds of SNe Ia in redshift bins of 0.1 up to
$z=1.5$, which would compliment space based SN searches, and enable the proper
consideration of the systematic uncertainties of SNe Ia as standard candles, in
particular, luminosity evolution and gravitational lensing. We simulate SNe Ia
luminosities by adding weak lensing noise (using empirical fitting formulae)
and scatter in SN Ia absolute magnitudes to standard candles placed at random
redshifts. We show that flux-averaging is powerful in reducing the combined
noise due to gravitational lensing and scatter in SN Ia absolute magnitudes.
The SN number count is not sensitive to matter distribution in the universe; it
can be used to test models of cosmology or to measure the SN rate. The SN
pencil beam survey can yield a wealth of data which should enable accurate
determination of the cosmological parameters and the SN rate, and provide
valuable information on the formation and evolution of galaxies.
  The SN pencil beam survey can be accomplished on a dedicated 4 meter
telescope with a square degree field of view. This telescope can be used to
conduct other important observational projects compatible with the SN pencil
beam survey, such as QSOs, Kuiper belt objects, and in particular, weak lensing
measurements of field galaxies, and the search for gamma-ray burst afterglows.
