 Admissions
 Awards & Fellowships
 Courses
 Programs

 Applied & Interdisciplinary Mathematics Master's Degree
 Marjorie Lee Browne MS to PhD Bridge Program
 Mathematics Master's Degrees
 Quantitative Finance & Risk Management Master's Program
 Dual Degree MS  Current UM Graduate Students Only
 Applied & Interdisciplinary Mathematics Ph.D.
 Mathematics Ph.D.
 Recent Ph.D. Recipients
 Student Handbook  AIM & Math
 Students On the Job Market  AIM & Math
 Student Spotlight  AIM & Math
 Thesis Defense Schedule
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 threehour 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.
*** Due to the necessity of remote teaching and learning caused by the COVID 19 pandemic, University of Michigan AIM PhD students will be given one extra term to meet QR deadlines. This accommodation will be given to PhD students entering their program in Winter 2020, Fall 2019, and Fall 2018.
Adjusted Deadline: 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 four attempts, that is, by the beginning of the fourth semester 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
Schedule
The 20222023 AIM Qualifying Review Exam Schedule is as follows:
January 2023  In person
 DELA  Saturday, January 7, 9am  12pm
 PDM  Saturday, January 7, 2pm  5pm
 ACCV  Sunday, January 8, 9am  12pm
August 2023  In person  week of August 1418
** 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 7347633000. 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 mathgradoffice 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 3digit 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.
How to Sign up for AIM QR Exams
 Approximately 1 month prior to the exam(s), the mathgradoffice will send out a Google Form asking which exams in which you are interested to take.
 Approximately 2 weeks prior to the exam(s), you will receive a secret number from the mathgradoffice.
 On the day of the exam, you will write this number on each page of your exam(s) instead of your name.
 Approximately 1 week after the exam, you will receive a letter of results from the mathgradoffice.
 After receiving the results, students needing counseling with meet with the AIM Director.
The AIM QR Examination in Advanced Calculus & Complex Variables
ACCV Resources
We recommend the following references for students preparing for this examination:
 J. Stewart, Multivariable Calculus.
 K. Ross, Elementary Analysis: The Theory of Calculus.
 J. W. Brown and R. V. Churchill, Complex Variables and Applications.
Some of the recent AIM QR Examinations (and syllabus) in Advanced Calculus & Complex Variables are available for study:
The AIM QR Examination in Differential Equations & Linear Algebra
DELA Resources
We recommend the following references for students preparing for this examination:
 W. E. Boyce and R. C. DiPrima, Elementary Differential Equations.
 R. Haberman, Applied Partial Differential Equations with Fourier Series and BoundaryValue Problems (Chapters 14).
 Thomas Hillen, I. E. Leonard, and Henry van Roessel, Partial Differential Equations : Theory and Completely Solved Problems, Wiley, 2012 (please consult DELA syllabus for relevant topics).
 G. Strang, Linear Algebra and its Applications.
Some of the recent AIM QR Examinations (and syllabus) in Differential Equations & Linear Algebra are available for study:
* No students took the Winter 2014 Exam
The AIM QR Examination in Probability & Discrete Mathematics
PDM Resources
We recommend the following references for students preparing for this examination:
 S. Ross, A First Course in Probability.
 R. A. Brualdi, Introductory Combinatorics.
 J. Kleinberg and É. Tardos, Algorithm Design
Some of the recent AIM QR Examinations (and syllabus) in Probability & Discrete Mathematics are available for study: