I would like to provide some additional grammatical background:
un' and una are used with female nouns.
Writing una universita' is correct, but not common. It's used when una and universita' are not on the same line (which is not your case); so whenever there are two vowels, the one from the definite article is dropped in Italian.
uno and un are used with male nouns. un is NOT the same as uno without "o". In fact, un corresponds to "il" and "l' ' and uno corresponds to "lo":
il maestro , un maestro (masculine)
l'uncinetto, un uncinetto
lo stivale, uno stivale