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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).

Written portion of my exam

Expository introduction to the Weil conjectures:


Detailed description of Weil's counting technique: