What is incumbent upon one who vowed to fast on Thursdays and Fridays and three days of every month during university studies, but did not fast some of the days after the vow, and does not know their number now?

It is obligatory for you to make up the days you vowed to fast but did not fulfill. If you do not know their exact number, you must estimate them and err on the side of caution. If you are unsure of the number, then perform the doubtful amount, because one's obligation is not discharged except with certainty. A vow is a serious matter; it is an obligation that a person has imposed upon himself, and therefore it must be fulfilled if it is in obedience to Allah the Almighty. The Prophet, peace and blessings be upon him, said: "Whoever vows to obey Allah, let him obey Him; and whoever vows to disobey Allah, let him not disobey Him." Allah the Almighty praised His believing servants by saying: "They fulfill [their] vows and fear a Day whose evil will be widespread." Fulfilling a vow is obligatory and does not lapse with the passage of time.