The Ph.D. qualifying examination in Mathematics is a written examination in two parts. The purpose of the PHD qualifying examination is to demonstrate that the student has achieved a degree of mathematical depth and maturity in the core areas of real analysis and abstract linear algebra, has additionally cultivated advanced problem solving skills in graduate level mathematics, and is poised to undertake independent mathematical research. The content and timing of the qualifying exam allows this determination to be made within the first two years of graduate study.

The two parts of the examination are as follows. Part 1 covers roughly the material presented in the core course Mth 511, Real Analysis, while Part 2 covers roughly the material in Mth 543, Abstract Linear Algebra. The qualifying exam is given twice each year, near the beginning of Fall and Spring terms. The two parts of the exam are usually given one or more days apart. A student may take each part of the PhD qualifying examination a maximum of three times, with one additional free attempt before a student's first term in the program. To advance in the PhD program, a student must pass both parts, but they do not need to be passed at the same time. A student must pass both parts of the exam by the end of spring term of the student’s second year of study.

Questions about the qualifying exam can be directed to the Chair of the Qualifying Examination Committee.

Syllabus of Qualifying Exams starting Fall 2018.


To register for the Ph.D. Qualifying Examinations please email Nikki Sullivan at
Real Analysis
Linear Algebra


Past Exams

Fall 2021 Real Analysis  Fall 2021 Linear Algebra

Summer 2021 Real Analysis  Summer 2021 Linear Algebra

Spring 2021 Real Analysis (UPDATED 6/4/21)  Spring 2021 Linear Algebra

Fall 2020 Real Analysis  Fall 2020 Linear Algebra

Fall 2019 Real Analysis  Fall 2019 Linear Algebra

Spring 2019 Real Analysis  Spring 2019 Linear Algebra

Fall 2018 Real Analysis  Fall 2018 Linear Algebra

Qualifying Exam Syllabus 2000-Spring 2018

Spring 2018 Real Analysis  Spring 2018 Complex and Linear Algebra
Fall 2017 Real Analysis  Fall 2017 Complex and Linear Algebra
Spring 2017 Real Analysis  Spring 2017 Complex and Linear Algebra
Fall 2016 Real Analysis  Fall 2016 Complex and Linear Algebra
Spring 2016 Real Analysis  Spring 2016 Complex and Linear Algebra
Fall 2015 Real Analysis  Fall 2015 Complex and Linear Algebra
Spring 2015 Real Analysis  Spring 2015 Complex and Linear Algebra
Fall 2014 Real Analysis  Fall 2014 Complex and Linear Algebra
2013 Real Analysis
  2013 Complex and Linear Algebra
2012 Real Analysis  2012 Complex and Linear Algebra
2011 Real Analysis  2011 Complex and Linear Algebra
Fall 2010 Real Analysis  Fall 2010 Complex and Linear Algebra
Fall 2009 Real Analysis  Fall 2009 Complex and Linear Algebra
Fall 2008 Real Analysis  Fall 2008 Complex and Linear Algebra
Fall 2007  Spring 2007  Fall 2006  Fall 2005  Fall 2004  Fall 2003  Fall 2002  Fall 2001  Fall 2000  Fall 1999  Fall 1998