Preliminary examinations are offered at the beginning and end of the Spring semester each year. These are four closed-book written examinations in (i) differential equations, (ii) advanced calculus, (iii) complex variables and (iv) linear algebra. The examinations are given at the advanced-undergraduate/beginning-graduate level. For each of the four 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 four exams. A student may retake from one to four 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 four 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 at least three of the four exams.

For details, please see Policies and Procedures.

### Past Exams

- 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

- 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

- 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

- Complex analysis:

Complex Analysis 2007 Exam

Complex Analysis 2008 Exam

Complex Analysis 2009 Exam

Complex Analysis 2010 Exam

Complex Analysis 2011 Exam

Complex Analysis 2012 Exam

Complex Analysis 2013 Exam

Complex Analysis 2014 Exam

Complex Analysis 2015 Exam

Complex Analysis 2016 Exam

Complex Analysis 2017 Exam