The requirements below are for students in pure mathematics, not in statistics. For students in Statistics: Qualifying Exams must be passed in Statistics, Probability, and Applied Statistics.

1. Students must pass 2 qualifying exams from the following list:

Algebra (Math 600, 601)
Analysis (Math 630, 660)
Geometry (Math 730, 740; Exam not availble to students entering in 2018 or later)
Probability (Stat 600, 601)
Statistics (Stat 700, 701)

A student in pure mathematics can use at most one of Probability and Statistics to satisfy the exam requirement.

The Geometry exam will be discontinued after January 2020. Until then, it will only be available to students admitted during 2017 or earlier.

2. Students must take four additional semesters of courses from the following list, with a grade point average of 3.3 or better for the four courses used to satisfy this requirement. Courses with grades less than B cannot be included (for example, B− is not allowed).

Math 600, 601 (Algebra)
Math 630, 660 (Analysis)
Math 730, 740 (Geometry)
Stat 600, 601 (Probability)
Stat 700, 701 (Statistics)
Math 634 (Harmonic Analysis)
Math 642 (Dynamical Systems I)
Math 712, Math 713 (Logic)
Math 734 (Algebraic Topology)
AMSC 666, AMSC 667 (Numerical Analysis)
Math 631 (Real Analysis)
Math 670 (ODE)
Math 673, Math 674 (PDE)

The four semesters are not required to be in the same sequence of courses. For example, Math 730, Math 670, AMSC 666, and AMSC 667 would be acceptable. These four semester-long courses must be distinct from the ones supporting the qualifying exams passed in Part 1.

A student may take and pass a third (and possibly, a fourth) qualifying exam in place of taking the actual courses. For example, passing the written exams
in Algebra, Analysis, and Geometry would count as 2 exams plus 2 semesters.

One qualifying exam must be passed by January of the second year, and all requirements must be finished by January of the third year.

Students who have taken courses from the second list elsewhere may petition the graduate chair to have such courses satisfy up to two semesters of the four-semester requirement (although generally students should instead use these courses as preparation for qualifying exams).

Each course on the lists should have serious assessment methods (graded homework, projects, exams, and/or similar). There should be some significant assessment that is guaranteed to be done solely by the student (that is, an exam, not only homework).