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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.

*** 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 2021-2022 AIM Qualifying Review Exam Schedule is as follows:

August 2021 - In person

  • ACCV - Wednesday, August 18, 2021 9am - 12 noon Eastern Time
  • DELA - Thursday, August 19, 2021 9am - 12 noon Eastern Time
  • PDM - Friday, August 20, 2021 9am - 12 noon Eastern Time

** 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. 

How to Sign up for AIM QR Exams

  1. Approximately 1 month prior to the exam(s), the math-grad-office will send out a Google Form asking which exams in which you are interested to take.
  2. Approximately 2 weeks prior to the exam(s), you will receive a secret number from the math-grad-office.
  3. On the day of the exam, you will write this number on each page of your exam(s) instead of your name.
  4. Approximately 1 week after the exam, you will receive a letter of results from the math-grad-office.
  5. 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:

Syllabus Winter 2011 Fall 2011
Fall 2012 Winter 2013 Fall 2014
Winter 2014 Winter 2015 Fall 2015
Fall 2016 Winter 2017 Fall 2017
Fall 2018 Winter 2019 Fall 2019
Winter 2020 Fall 2020 Winter 2021
Fall 2021 Fall 2021-Solutions  

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 Boundary-Value Problems (Chapters 1-4).
  • 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: 

Syllabus Fall 2010 Winter 2011
Fall 2011 Winter 2012 Fall 2012
Winter 2013 Fall 2013 Winter 2014*
Fall 2014 Winter 2015 Fall 2015
Fall 2016 Winter 2017 Fall 2017
Fall 2018 Winter 2019 Fall 2019
Winter 2020 Fall 2020 Winter 2021
Fall 2021 Fall 2021-Solutions  

* 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:

Syllabus Fall 2010 Winter 2011
Fall 2011 Winter 2012 Fall 2012
Winter 2013 Fall 2013 Winter 2014
Fall 2014 Winter 2015 Fall 2015
Fall 2016 Fall 2017 Fall 2018
Fall 2019 Winter 2020 Fall 2020
Fall 2021 Fall 2021-Solutions