All Mathematics PhD students must pass the following two qualifying exams.

• Advanced Calculus based on the two-semester sequence Advanced Calculus MATH6001-6002.
• Abstract Linear Algebra based on the one semester course Advanced Linear Algebra MATH6003.
  

All incoming PhD students are required to take the qualifying exams before the beginning of their first semester. Students who do not pass the exams are placed in the appropriate 6000 - level courses. In order to remain in the PhD program, the student must pass the qualifying exams by the beginning of the Fall Semester following their admission into the program.

All PhD students must also pass four of the following seven preliminary exams. Exams are offered on a rotating schedule and can be attempted at most twice. Exams taken by incoming students in August do not count against this two-attempt rule. All four preliminary exams must be passed within one and a half years of completing the qualifying exam.

• Real Analysis
• Complex Analysis
• Algebra
• Topology
• Ordinary Differential Equations
• Partial Differential Equations
• Probability

Note: From 2013-2018 there were five Prelim exams covering two subjects each:

• Algebra and Topology
• Analysis
• Differential Equations
• Linear Models
• Probability and Statistics