Thanks for that, Patrick. I had both staticfloat-julianightlies-trusty.list and staticfloat-juliareleases-trusty.list in my /etc/apt/sources.list.d directory.
I deleted the files associated with julianightlies, removed julia, then reinstalled, and now I have v0.3.8. When I would "sudo apt-get install julia" before, I guess apt-get would default to julianightlies over juliareleases.
