  We measure the evolution of the stellar mass function (SMF) from z=0-1 using
multi-wavelength imaging and spectroscopic redshifts from the PRism
MUlti-object Survey (PRIMUS) and the Sloan Digital Sky Survey (SDSS). From
PRIMUS we construct an i<23 flux-limited sample of ~40,000 galaxies at
z=0.2-1.0 over five fields totaling ~5.5 deg^2, and from the SDSS we select
~170,000 galaxies at z=0.01-0.2 that we analyze consistently with respect to
PRIMUS to minimize systematic errors in our evolutionary measurements. We find
that the SMF of all galaxies evolves relatively little since z=1, although we
do find evidence for mass assembly downsizing; we measure a ~30% increase in
the number density of ~10^10 Msun galaxies since z~0.6, and a <10% change in
the number density of all >10^11 Msun galaxies since z~1. Dividing the sample
into star-forming and quiescent using an evolving cut in specific
star-formation rate, we find that the number density of ~10^10 Msun
star-forming galaxies stays relatively constant since z~0.6, whereas the
space-density of >10^11 Msun star-forming galaxies decreases by ~50% between
z~1 and z~0. Meanwhile, the number density of ~10^10 Msun quiescent galaxies
increases steeply towards low redshift, by a factor of ~2-3 since z~0.6, while
the number of massive quiescent galaxies remains approximately constant since
z~1. These results suggest that the rate at which star-forming galaxies are
quenched increases with decreasing stellar mass, but that the bulk of the
stellar mass buildup within the quiescent population occurs around ~10^10.8
Msun. In addition, we conclude that mergers do not appear to be a dominant
channel for the stellar mass buildup of galaxies at z<1, even among massive
(>10^11 Msun) quiescent galaxies.
