Upon arrival, new students may take the preliminary exams. Students who pass the exams can by-pass the 600-level sequences and take the beginning Ph.D. 700-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 36 700-level (or above) mathematics credits must be earned. All four basic sequences 733-734, 735-736, 741-742, and 761-762 are required.

#### The First Year

Most students will devote their first year to gaining a solid foundation in basic topics by taking three year-long 600-level courses: algebra (MTH 661/662), topology (MTH 631/632), and analysis (MTH 633/634).

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.

#### The Second Year

Students normally take at least three 700-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:

- One exam covering material from either MTH 733/734 or MTH 735/736
- One exam covering material from either MTH 761/762 or MTH 741/742

No exam may be taken more than twice.

#### The Third Year

A specialty is chosen and coursework will begin concentrating in this area. Any remaining required 700-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 700-level course or any two one-semester 700-level courses, subject to approval of faculty in your speciality.

#### The Fourth Year

Research and coursework in your area of research.

#### The Fifth Year

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

#### The Sixth Year

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