Early Middle Ages

Christianity's success in the first five centuries of its existence was shaped by the Roman experience. Explain how a fringe Jewish sect that was illegal and persecuted became the official religion of the Empire. You should try to mention several important ideas/terms. Maybe not all, but most: Christian writings, missionary work, persecutions, heresy, Constantine, church fathers, the Petrine doctrine, monasticism, Eastern Christianity vs.Western Christianity. 

Arguably, each of the civilizations (Byzantine, Islam, and the Barbarian West) could claim the mantle of the Roman Empire. In your view, briefly state which one has the strongest claim to carry forward the legacies of the classical past? What are the historical circumstances in which Islam emerged [here, you are being asked to spend a few paragraphs analyzing the early history of Islam--The Prophet Muhammad, Arab expansion, Sunni versus Shia, the Umayyad & Abbasid Caliphates]. Finally, what is the significance of the Merovingians, Carolingians, and the Vikings for the formation of Europe. You can end the essay at around the year 1000 AD. 

Answer this question in your own words in 1,200-2,000 words.