PSU Mark

Mathematics Department

Graduate Program

Eberly College of Science Mathematics Department

Qualifying exams


Qualifying examinations are offered twice a year: in May, after the end of the Spring semester and in December, after the end of the Fall semester.  Students must pass each exam within three semesters (excluding summer sessions) of entry into the doctoral program. Thus they have three opportunities to pass each exam.

These examinations are focused on two main subjects: Algebra and Analysis.


The Algebra exam contains three parts:

  • Part A: linear algebra (vector spaces, linear transformations)

  • Part B: abstract algebra (theory of groups, rings)

  • Part C: applied algebra (numerical linear algebra)

  • Part A is mandatory for all students. Parts B and C are alternatives to one another.   Each part of the exam will contain four questions, and correct answers to two of these four will ensure a pass on that part.
    To pass the Algebra exam, you must either pass Part A and Part B, or Part A and Part C.

    Similarly, the Analysis exam contains three parts:

  • Part A: real analysis (Lebesgue measure theory)

  • Part B: complex analysis

  • Part C: applied analysis (functional analysis with applications to linear differential equations)


  • Each part will contain four questions, and correct answers to two of these four will ensure a pass on that part. To pass the Analysis exam, you must either pass Part A and Part B, or Part A and Part C.

    The qualifying exams in Algebra and in Analysis are offered on different days, the same week. On the day of each exam, Part A is given in the morning, while parts B and C are given in the afternoon. It is possible for a student to pass Part A in one attempt, and Part B or C at a different date. For example, one may pass Algebra A in December, then pass Algebra B and Parts A and C of Analysis in May the following year.

    The subjects of the exams are given in the table below, which also shows the number of the graduate-level course that prepares for that part of the exam.


    Algebra A Linear Algebra Math 535 Sample Problems
    Algebra B Abstract Algebra Math 536 Sample Problems
    Algebra C Applied Algebra Math 524 Sample Problems
    Analysis A Real Analysis Math 501 Sample Problems
    Analysis B Complex Analysis Math 502 Sample Problems
    Analysis C Functional Analysis Math 503 Sample Problems

    Clicking on the links in the above table will take you to a detailed syllabus for the exam and to a list of sample problems produced by the Qualifying Exam Board. These sample problems are similar to those that will appear on the new qualifying exams themselves. The following is a list of qualifying exams for the past years.

    Spring 2015 Algebra A
    Algebra B
    Algebra C
    Analysis A
    Analysis B
    Analysis C
    Fall 2014 Algebra A
    Algebra B
    Algebra C
    Analysis A
    Analysis B
    Analysis C
    Spring 2014 Algebra A
    Algebra B
    Algebra C
    Analysis A
    Analysis B
    Analysis C
    Fall 2013 Algebra A
    Algebra B
    Algebra C
    Analysis A
    Analysis B
    Analysis C
    Spring 2013 Algebra A
    Algebra B
    Algebra C
    Analysis A
    Analysis B
    Analysis C
    Fall 2012 Algebra A
    Algebra B
    Algebra C
    Analysis A
    Analysis B
    Analysis C
    Spring 2012 Algebra A
    Algebra B
    Algebra C
    Analysis A
    Analysis B
    Analysis C
    Fall 2011 Algebra A
    Algebra B
    Algebra C
    Analysis A
    Analysis B
    Analysis C
    Spring 2011 Algebra A
    Algebra B
    Algebra C
    Analysis A
    Analysis B
    Analysis C
    Fall 2010 Algebra A
    Algebra BC
    Analysis A
    Analysis BC
    Spring 2010 Algebra A
    Algebra BC
    Analysis A
    Analysis BC
    Fall 2009 Algebra A
    Algebra BC
    Analysis A
    Analysis BC
    Spring 2009 Algebra A
    Algebra BC
    Analysis A
    Analysis BC
    Fall 2008 Algebra A
    Algebra B
    Algebra C
    Analysis A
    Analysis B
    Analysis C