After passing the Tier 2 review, you must arrange and pass an oral examination before October of your fourth year. Begin by seeking the direction of a faculty member as a scientific advisor for the exam. The faculty member will assign a reading list consisting of texts and research-level papers; this material will comprise the major topic of the exam. If and when the scientific advisor feels that you are ready for the exam, the advisor will arrange for a three-member faculty committee to administer it.
You submit a proposal for the Tier 3 exam to the director of graduate studies for approval. This consists of topics for the major and minor area of the examination, a syllabus and a reading list for the major and minor topic, and the list of three faculty members serving as the Tier 3 committee.
These exams are projected to last approximately two hours. One of the committee members must be qualified to examine you in the minor area, where you must demonstrate 500-level mastery. In order to pass the exam, you must:
Demonstrate a level of mathematical ability and maturity sufficient for successfully undertaking a Ph.D. dissertation (normally in the major area of the exam), and
Identify a faculty member willing to serve as Ph.D. advisor. This will typically, but not necessarily, be the faculty member who organized the oral exam.