  We present a detailed analysis of the star formation history (SFH) of three
fields in M33 located ~ 4 - 6 visual scale lengths from its nucleus. These
fields were imaged with the Advanced Camera for Surveys on the Hubble Space
Telescope and reach ~ 2.5 magnitudes below the red clump of core helium burning
stars. The observed color-magnitude diagrams are modeled as linear combinations
of individual synthetic populations with different ages and metallicities. To
gain a better understanding of the systematic errors we have conducted the
analysis with two different sets of stellar evolutionary tracks which we
designate as Padova (Girardi et al. 2000) and Teramo (Pietrinferni et al.
2004). The precise details of the results depend on which tracks are used but
we can make several conclusions that are fairly robust despite the differences.
Both sets of tracks predict the mean age to increase and the mean metallicity
to decrease with radius. Allowing age and metallicity to be free parameters and
assuming star formation began ~ 14 Gyr ago, we find that the mean age of all
stars and stellar remnants increases from ~ 6 Gyr to ~ 8 Gyr and the mean
global metallicity decreases from ~ -0.7 to ~ -0.9. The fraction of stars
formed by 4.5 Gyr ago increases from ~ 65% to ~ 80%. The mean star formation
rate 80 - 800 Myr ago decreases from ~ 30% of the lifetime average to just ~
5%. The random errors on these estimates are ~ 10%, 1.0 Gyr, and 0.1 dex. By
comparing the results of the two sets of stellar tracks for the real data and
for test populations with known SFH we have estimated the systematic errors to
be 15%, 1.0 Gyr, and 0.2 dex. These do not include uncertainties in the
bolometric corrections or variations in alpha-element abundance which deserve
future study.
