# 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:

16K

105K

### Detailed description of Weil's counting technique:

45K

167K