Why is Miranda ignorant of who Prospero was in The Tempest? Which items were necessary for Prospero to practice his magic art?

Prospero has deliberately kept Miranda in a state of ignorance throughout her whole life. He thinks that by doing this he is somehow protecting her. As Miranda has spent her whole life on a remote desert island, there's no one else around to contradict whatever Prospero tells her. Besides, Prospero's still smarting from the humiliation of being banished from Milan. One can quite understand, then, why he wouldn't want to tell Miranda the story of how they came to be on the island.
In order to practice his sorcery, Prospero needs his magic books. They contain all the spells he needs to keep Caliban and Ariel under control and to whip up the violent storm that will bring his enemies to his island domain. It was because Prospero spent so much time poring over his books of magic instead of governing Milan that his brother Antonio and his scheming cohorts conspired to have him banished to a remote desert island.
In due course, Prospero's books come to be an essential means of control over others and over the forces of nature. But by the end of the play, when he's ready to return in triumph to the Duchy of Milan, he has no further use for his magic books and throws them into the sea. Prospero's days as a magician are over.