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

#### Examination Schedule

The 2019-2020 AIM Qualifying Review Exam Schedule is as follows:

- Fall 2019 dates:
- Advanced Calculus & Complex Variables: Saturday, August 31, 9AM-noon.
- Probability & Discrete Mathematics: Saturday, August 31, 2PM-5PM.
- Differential Equations & Linear Algebra: Monday, September 2, 9AM-noon.

- Winter 2020 dates:
- Advanced Calculus & Complex Variables: Monday, January 6, 9AM-noon.
- Probability & Discrete Mathematics: Monday, January 6, 2PM-5PM.
- Differential Equations & Linear Algebra: Tuesday, January 7, 9AM-noon.

** 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.

#### 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 |

#### 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). - 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:

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 |