Now I know that in Islam Mohamed is supposed to be the last prophet, and I believe Judaism believes that there have been no prophets since the fall of the Temple but the Christian position on this is something I am less clear on. An English professor of mine maintained that there was a council which ruled against modern prophets around 371 or something but my searches on this have so far proven in vain. Can anyone help?
It depends on exactly what question you are asking.
If I read it correctly, the theory you're discussing is that after the Council of Nicea, the Bible was brought to full completion. The Word had been given, the Acts of the Spirit that had led the early-church saints and leadership gave way to the Gospel. The Gospel, the Word of the Living God, would guide individuals along the path of God rather than one individual blessed by the Spirit to lead the tribes.
That is the theory. The problem is how do you define a Prophet? Or a Saint? The Catholic Church has canonized more than a few people who are holy beyond belief; they have also made saints of several individuals who might not even be allowed in Heaven, but who served the Roman Church very well. And then you have faux saints like Santa Muerte and Jesus Malverde of weird sub-religions of Catholicism that aren't acknowledged by Rome, but are fervently worshipped in the towns and villages of the narco-cartels.
The modern definition of a prophet, however, has become someone who can discern events that have not yet happened in time. Nostrodamus, Edgar Cayce, Joseph Smith, Jean Dixon, etc. would fit into varying subcategories of this discussion. And discussing this will open an entirely different can of worms and is capable of bringing about some rather violent responses.
That is the definition of the terms. I hope it helps.