After graduating from Saratov State University in 1950, Ulyanov studied at Moscow State University, where he received in 1953 his Russian Candidate of Sciences degree (PhD) under the supervision of Nina Bari.
In 1960 at Moscow State University he received his Russian Doctor of Science degree (habilitation) and became a professor.
In 1970 Ulyanov was an invited speaker in the section Ensembles exceptionelles en analyse with talk Allgemeine Entwicklungen und gemischte Fragen (General developments and special questions) delivered in German at the International Congress of Mathematicians in Nice.
He was the founder of the International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications".
His doctoral students include Sergei Viktorovich Bochkarev, Boris Kashin, and Evgenii Nikishin.