Show how Doctor Faustus is a tragedy of Presumption.

Tragedy of presumption isn't generally a well-defined term in literary studies, but it implies situational irony, and in Faustus's case cosmic irony as well. Situational irony occurs when events turn out differently than one expects and cosmic irony occurs when that situation is elevated to expectation of divine realities. In Marlowe's play, Faustus engages in presumptions about these realities and about his own human nature that lead not only to his death and damnation but also, in a more traditional tragic sense, to the loss of the quality that had made him most admirable.
Faustus is among the most gifted minds of his day, and having seemingly exhausted what conventional studies can offer seeks the intrigue of necromancy. After this decision, he is repeatedly disappointed in the results of his choice but unwilling to repent. Further, the quality of mind that made him heroic in the first scene becomes increasingly debased as he continues in his soul-selling bargain.
The first ironic presumption he makes is to say "I think hell is a fable," while speaking to a devil. He then seeks astrological knowledge that medieval scholasticism had failed to supply but which humanist ones were unfolding. Similarly, his magic accomplishes little more than humanist Europe was supplying: stage plays in which ancient figures come to life and distribution channels for exotic goods (such as grapes out of season). The middle section of the play functions largely through these types of ironies, a quality Marlowe was deft at deploying without turning the play into pure satire or farce. The play moves from ironic comedy to ironic tragedy with a tonal complexity of which Marlowe was a master.
At the end, we see Faustus's final presumption. Hours and even minutes before his death, he retains the promise of salvation through repentance. His tragedy might be seen as one of presumption in that he presumes—in the same overweening pride that initiates his story—that he is too great in his error to be forgivable, that his evil is greater than God's ability to pardon. As a result, he dies talking about the value of repentance and regret without actually repenting.

In relation to the character of Dr. Faustus, presumption can be defined as behavior that is arrogant, disrespectful, and which transgresses established social norms and boundaries. Faustus comfortably ticks all of these boxes. Although a learned, intelligent man with a lot going for him, Faustus is profoundly dissatisfied with his life. He feels frustrated by the limits of human knowledge, which severely impede the attainment of the earthly power he so desperately craves.
Egged on by the Evil Angel, Faustus begins dabbling in black magic, hungry for the enormous power and fame it will give him. Even though Faustus knows that messing around with the forces of darkness is in danger of arousing God's "heavy wrath," he still goes ahead anyway. This is a classic example of Faustus's presumption: he's acting like God and defying Him at the same time. Black magic will indeed give Dr. Faustus more power than he could ever have dreamed of. But it will also endanger his mortal soul, and therein lies the tragedy of his presumption.