Preliminary examinations are offered at the beginning and end of the Spring semester each year. These are three closed-book written examinations in (i) differential equations, (ii) advanced calculus, and (iii) linear algebra. The examinations are given at the advanced-undergraduate/beginning-graduate level. For each of the three exams, students receive a score of 1, 2 or 3, as determined by the faculty committee in charge of the examination. All students in the program are required to take the preliminary exams in the beginning of the Spring semester in the first year of graduate studies. All students must obtain a score of at least 2 on all three exams. A student may retake from one to three of the exams, but exams must be re-taken at the end of the same Spring semester. If the student does not obtain a score of at least 2 on all three exams after two attempts, he or she will be disqualified from further study in the program. Additionally, doctoral students must earn a score of 3 on all three exams.

For details, please see Policies and Procedures.

### Past Exams

- Advanced Calculus:

Calculus 2007 Exam

Calculus 2008 Exam

Calculus 2009 Exam

Calculus 2010 Exam

Calculus 2011 Exam

Calculus 2012 Exam

Calculus 2013 Exam

Calculus 2014 Exam

Calculus 2015 Exam

Calculus 2016 Exam

Calculus 2017 Exam

Calculus 2018 Exam

Calculus 2019 Exam

Calculus 2020 Exam

Calculus 2021 Exam

Calculus 2022 Exam

Calculus 2023 Exam

- Ordinary Differential Equations:

Ordinary Differential Equations 2007 Exam

Ordinary Differential Equations 2008 Exam

Ordinary Differential Equations 2009 Exam

Ordinary Differential Equations 2010 Exam

Ordinary Differential Equations 2011 Exam

Ordinary Differential Equations 2012 Exam

Ordinary Differential Equations 2013 Exam

Ordinary Differential Equations 2014 Exam

Ordinary Differential Equations 2015 Exam

Ordinary Differential Equations 2016 Exam

Ordinary Differential Equations 2017 Exam

Ordinary Differential Equations 2018 Exam

Ordinary Differential Equations 2019 Exam

Ordinary Differential Equations 2020 Exam

Ordinary Differential Equations 2021 Exam

Ordinary Differential Equations 2022 Exam

Ordinary Differential Equations 2023 Exam

- Linear algebra:

Linear Algebra 2007 Exam

Linear Algebra 2008 Exam

Linear Algebra 2009 Exam

Linear Algebra 2010 Exam

Linear Algebra 2011 Exam

Linear Algebra 2012 Exam

Linear Algebra 2013 Exam

Linear Algebra 2014 Exam

Linear Algebra 2015 Exam

Linear Algebra 2016 Exam

Linear Algebra 2017 Exam

Linear Algebra 2018 Exam

Linear Algebra 2019 Exam

Linear Algebra 2020 Exam

Linear Algebra 2021 Exam

Linear Algebra 2022 Exam

Linear Algebra 2023 Exam