Mathematics Written Preliminary Exam
Here at The University of Arizona, the preliminary exam has two components: written and oral. The purpose of the exam is to prepare the student for mathematical research; usually, this means that a published research paper will be studied and summarized in both written and oral form.
For this exam, I studied the following paper, in which
André Weil first formulated the famous "Weil conjectures" (which
are now theorems).
André Weil, Numbers of solutions of equations in finite fields, Bull. Am. Math. Soc. (1949).