  We introduce a method for producing a galaxy sample unbiased by surface
brightness and stellar mass, by selecting star-forming galaxies via the
positions of core-collapse supernovae (CCSNe). Whilst matching $\sim$2400
supernovae from the SDSS-II Supernova Survey to their host galaxies using IAC
Stripe 82 legacy coadded imaging, we find $\sim$150 previously unidentified low
surface brightness galaxies (LSBGs). Using a sub-sample of $\sim$900 CCSNe, we
infer CCSN-rate and star-formation rate densities as a function of galaxy
stellar mass, and the star-forming galaxy stellar mass function. Resultant
star-forming galaxy number densities are found to increase following a
power-law down to our low mass limit of $\sim10^{6.4}$ M$_{\odot}$ by a single
Schechter function with a faint-end slope of $\alpha = -1.41$. Number densities
are consistent with those found by the EAGLE simulations invoking a
$\Lambda$-CDM cosmology. Overcoming surface brightness and stellar mass biases
is important for assessment of the sub-structure problem. In order to estimate
galaxy stellar masses, a new code for the calculation of galaxy photometric
redshifts, zMedIC, is also presented, and shown to be particularly useful for
small samples of galaxies.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics