Upon arrival, new students may take the preliminary exams. Students who pass the exams can by-pass the 500-level sequences and take the beginning Ph.D. 600-level courses as outlined in The Second Year.

In addition to the general requirements for a Ph.D. mandated by the Graduate School, a minimum of 36 600-level (or above) mathematics credits must be earned. All four basic sequences 630-631, 632-633, 640-641, and 661-662 are required.

Most students will devote their first year to gaining a solid foundation in basic topics by taking three year-long 500-level courses: algebra (MTH 561/562), topology (MTH 531/532), and analysis (MTH 533/534).

Every student must pass the preliminary exams before the start of their second year, to demonstrate their ability to move on to more advanced material. The exams are given once in June and once in August.

Students normally take at least three 600-level courses during their second year. Two of the three courses will concern material for their qualifying exams. In particular, students should pass two qualifying exams (given once in June and once in August) before the start of their third year. The exams are chosen from:

1. One exam covering material from either MTH 630/631 or MTH 632/633
2. One exam covering material from either MTH 661/662 or MTH 640/641

No exam may be taken more than twice.

A specialty is chosen and coursework will begin concentrating in this area. Any remaining required 600-level courses will be completed this year. Find a dissertation advisor and discuss a topic for your last exam. This exam can cover topics from any year long 600-level course or any two one-semester 600-level courses, subject to approval of faculty in your speciality.

Research and coursework in your area of research.

Research continues and the dissertation is written. For students who wish to continue in academics, applications are sent out in the fall.

Only in exceptional cases will support be extended to a sixth year.