This includes passages from the written Torah, the oral Torah, the mystical Zohar, as well as a list of all 613 mitzvos . The Zohar commends those who stay awake in anticipation of receiving the Torah. The giving of the Torah was, as it were, the wedding of the Jewish People and the Torah, and so it is fitting that we should be engaged in preparing the ornaments of the bride the previous night. In order to rectify this, we stay up. But there is a deeper reason that we don't sleep on the night of Shavuot.
Sleep is the taste of death.
One part in 60 is the threshold of perception. Sleep is the taste of death in this world. King David died on Shavuot. But before he died, he never even tasted the taste of death, because he never fell into a deep sleep. The angel of death came to King David to try and take his life.