A) PhD students in Mathematics, i.e., not with concentration in Statistics.

- Advanced Calculus and Linear Algebra based on the two-semester sequence Advanced Calculus MATH6001-6002 and the one semester course Advanced Linear Algebra MATH6003.
- Statistics based on the two two-semester sequences Mathematical Statistics STAT6021-6022 and Applied Statistics STAT6031-6032.

The preliminary examinations can be a combination of "old" exams based on a three quarter sequence in one subject or of "new" exams based on two 7000-level semesters in two subjects.

Competency in a 7000 level course can be proven either by passing a prelim on that subject, or by passing the 7000-level course with a grade of A-, or by passing two quarters of the 600-level sequence on the same subject with a GPA of 3.5.

Having passed 3 preliminary examinations with the old system or two preliminary examinations with the new system satisfies this requirement.

**Examples**

- If student has passed no prelims with the old system, then s/he must pass two prelims with the new systems to satisfy the requirement.
- If a student passed one prelim with the old system, say Real Analysis, then the student must pass another prelim with the new system from the remaining 4, that is, not including the Analysis prelim, and must prove competency in Complex Analysis (the companion course of Real Analysis in semesters.) If the prelim passed were Numerical Analysis (which has no 7000-level course), then the student would have to pass another prelim with the new system from the remaining 4 and would have to prove competency in the material of another complete 7000-level sequence.
- If a student passed two prelim with the old system then the student would not need to pass any more prelims, but there would be the following cases:
- Passed Real Analysis and Complex Analysis (part of the same 7000-level sequence). The student would need to show competency in another complete 7000-level sequence.
- Passed Real Analysis and Topology (part of different 7000-level sequences). The student would have to prove competency for Complex Analysis (companion course of Real Analysis) and Algebra (companion course of Topology).
- Passed Real Analysis and Numerical Analysis. The student would have to prove competency for Complex Analysis (companion course of Real Analysis) and one other complete 7000-level sequence.

B) PhD students with concentration in Statistics.

For students who were initially enrolled in the PhD program with concentration in statistics, there are fewer differences between the old and the new rules. The qualifying exam in statistics remains essentially unchanged. Students who have passed two quarter-based preliminary exams are not required to take any further semester-based exams. Students who have taken one of the quarter-based preliminary exams (Theory of Statistics, Linear Models, or Probability) must take one of the semester-based prelims that does not overlap with the exam they have already passed. Thus, for example, a student that passed the quarter-based Theory of Statistics exam must take the semester-based Linear Models exam.