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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

Examination Schedule

The 2017 AIM Qualifying Review Exam Schedule is as follows:

  • Winter 2017 dates: Monday and Tuesday, January 2 and 3.
    • Advanced Calculus & Complex Variables: Monday, January 2, 9AM-noon.
    • Differential Equations & Linear Algebra: Monday, January 2, 2PM-5PM.
    • Probability & Discrete Mathematics: Tuesday, January 3, 9AM-noon.
  • Fall 2017 dates: To be determined.

The AIM QR Examination in Advanced Calculus & Complex Variables

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.

ACCV Resources

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  

The AIM QR Examination in Differential Equations & Linear Algebra

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.

DELA Resources

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    

* No students took the Winter 2014 Exam

The AIM QR Examination in Probability & Discrete Mathematics

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

PDM Resources

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