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AIM Qualifying Review Examinations

Because AIM attracts students with diverse backgrounds, one of the initial requirements is for all students to exhibit a sufficiently strong command of advanced undergraduate level mathematics to be ready to take appropriate graduate level mathematics courses. This is the goal of the written AIM Qualifying Review Examinations. Students may choose to pass any two three-hour exams offered in the following three areas:

  • Advanced Calculus & Complex Variables
  • Differential Equations & Linear Algebra
  • Probability & Discrete Mathematics

Incoming students must sign up to take two exams prior to beginning their coursework. Students not passing the exams on the first attempt will receive counseling regarding options (for example, remedial coursework) for enabling future success. The AIM Qualifying Review Examinations are offered twice each school year, once prior to the start of classes in the Fall semester and again prior to the start of classes in the Winter semester. Successful AIM Ph.D. students will pass two exams within three attempts, that is, by the beginning of the second year of study. Unsuccessful students may continue in the program for one further year to complete an AIM Master's degree.

About the AIM Qualifying Review (QR) Exams


The 2023-2024 AIM Qualifying Review Exam Schedule is as follows:

January 8, 2024 - 9am-12pm, 2pm-5pm

January 9, 2024 - 9am-12pm, 2pm-5pm

** If you think you need an accommodation for a disability, please contact the Services for Students with Disabilities (SSD) Office located at G664 Haven Hall.  The SSD phone number is 734-763-3000.  Once your eligibility for an accommodation has been determined you will be issued a verified individual services accommodation (VISA) form.  Please present this form to the math-grad-office at least two weeks prior to the QR exam.

Exam Protocols & Procedures

There are three QR subjects: Advanced Calculus & Complex Variables, Differential Equations & Linear Algebra, Probability & Discrete Mathematics.  The exams are written by a committee appointed by the chair of the Mathematics Department. The exams are based on the syllabi posted on the AIM website. 

Each exam consists of 5 questions with a 3 hour time limit.  Exams are administered in accordance with any accommodations granted and requested by a student’s Student Services Department Verified Individualized Services and Accommodations (VISA). Students put a 3-digit secret number on the exam as an identifier instead of their name.

The exams are graded by the committee of examiners, who discuss the scores and assign pass/fail grades, based mainly on the results of the exam, but occasionally also on other factors.

The final results are shared with the faculty, communicated to the student by letter, and discussed between the student and the AIM director.  AIM Ph.D. students must pass at least two of the three QR exams by the start of their third term. 

The AIM QR Examination in Advanced Calculus & Complex Variables

The AIM QR Examination in Differential Equations & Linear Algebra

The AIM QR Examination in Probability & Discrete Mathematics