PSU Mark

Mathematics Department

Graduate Program

Eberly College of Science Mathematics Department

Qualifying exams


Qualifying examinations are offered twice a year: once in August, before the beginning of the Fall semester, and once in May, after the end of the Spring semester.  Because of the 18-month rule above, students have three opportunities to pass each exam (including an opportunity to do so immediately on arrival).

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 August upon arrival, 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.

    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