The Department of Mathematics requires all Ph.D. students to pass three departmentally administered written examinations ("preliminary examinations" or "prelims"). These exams are normally counted as the written portion of the general doctoral examination. (The student's advisory committee is free to require an additional written exam.) The oral portion of the general doctoral examination is conducted by the student's advisory committee, in accordance with pertinent graduate school regulations.

Preliminary Examinations

All Ph.D. students must pass three departmentally administered written examinations ("preliminary examinations" or "prelims").  A failed prelim in any subject may be repeated, but no more than onceNo more than four failed prelims are allowed in all.  (The clauses in italics are effective Fall 2012 and do not apply to students who entered the doctoral program prior to Fall 2012.)

In order to retain financial support from the department, a student must pass at least two prelims by the end of his or her second year in the graduate program and must pass all three prelims by the end of the third year.  In order to remain enrolled in the graduate program, a student must pass all three prelims by the end of the fourth year.  (A Ph.D. student who entered the graduate program at Auburn as a master's student is allowed an additional year to meet each of the above requirements.)

Prelim Subjects

Each prelim is based on the material covered in a two-semester sequence of graduate-level courses. The course sequences must be chosen from the following groups, with no two chosen from the same group.

  1. Real Analysis I/II (MATH-7200/7210)
    Functions of a Complex Variable I/II (MATH-7230/7240)

  2. Algebra I/II (MATH-7310/7320)
    Matrices I/II (MATH-7370/7380)

  3. Topology I/II (MATH-7500/7510)
    Axiomatic Set Theory I/II (MATH-7150/7160)
    Discrete Geometry and Convexity I/II (MATH-7110/7120)

  4. Graph Theory (MATH-7700/7750)
    Combinatorial Designs (MATH-6770/7740)

  5. Numerical Analysis (any two of MATH-7600/7610/7620)
    Modern Stochastic Processes I/II (MATH-7800/7810)
    Advanced Theory of Ordinary Differential Equations I/II (MATH-7280/7290)
    Partial Differential Equations I/II (MATH-7440/7450)
    Computational and Applied Algebra (any two: MATH-7180/7190/7720/7730)
    Applied Mathematics (MATH-7000/7010)

  6. Statistics (STAT 7600/7610)

With the approval of his or her advisory committee, a student may petition the Graduate Studies Committee to approve any two-semester sequence of graduate-level courses to meet the prelim requirement of a Prelim Group specified by the student's committee.

For each course sequence that can serve as the basis of a preliminary examination, a syllabus with textbook references and sample exams will be kept on file. These files will be available to students preparing for the exams. Students are not required to take the respective course sequence before attempting a prelim.

Prelim Administration

All preliminary examinations are departmentally administered, usually in April/May or August/September of each year (provided there is demand). The Graduate Program Officer (GPO) is responsible for coordination and record keeping. Each prelim will be designed, administered, and graded by a committee of at least three faculty members, knowledgeable in the respective field. Under normal circumstances, this committee will be comprised of faculty members who regularly teach the course sequence that the exam is based upon and will be chaired by the faculty member who last taught the sequence. The committee will be appointed by the GPO, upon recommendation by the faculty involved. A typical exam should take a capable student about three hours to complete (although up to four hours may be allowed). The committee members will grade the exam and review the results; the committee chair will report the consensus grades (high pass, pass, fail) to the GPO. The GPO will record the grades and keep copies of the individual exams in the student's file. A student will be able to review his/her exams. The GPO and the Graduate Studies Committee will periodically review the results of the preliminary examinations in order to assess the effectiveness of the prelim process.

Old Math Prelims

This site contains copies of some of the old written prelims in mathematics administered at Auburn University. For PDF files, you need Acrobat Reader which you can freely download.


  • Algebra prelim 1990 pdf
  • Algebra prelim 1991 pdf
  • Algebra prelim 1992 pdf
  • Algebra prelim 1993 pdf
  • Algebra prelim 1994 pdf
  • Algebra prelim 1995 pdf
  • Algebra prelim 1996 pdf
  • Algebra prelim 1997 pdf
  • Algebra prelim 1998 pdf
  • Algebra prelim 1999 pdf
  • Algebra prelim 2004 pdf
  • Algebra prelim 2005 pdf
  • Algebra prelim 2007 pdf
  • Algebra prelim 2008 pdf
  • Algebra prelim 2009 pdf
  • Algebra prelim 2010 pdf
  • Algebra prelim 2011 pdf
  • Algebra prelim 2012 pdf
  • Algebra prelim August 2013 pdf
  • Algebra prelim December 2013 pdf
  • Algebra prelim Spring 2015 pdf

Applied Mathematics

  • Applied Mathematics prelim 2007 pdf
  • Applied Mathematics prelim 2012 pdf

Coding Theory

  • Coding Theory prelim 1994 pdf
  • Coding Theory prelim fall 2004 pdf
  • Coding Theory prelim 2005 pdf 
  • Coding Theory prelim 2006 pdf 
  • Coding Theory prelim 2009 pdf   
  • Coding Theory prelim 2013 pdf

Complex Analysis

  • Complex Analysis prelim 2011 pdf

Design Theory

  • Design Theory prelim 2004 pdf
  • Design Theory prelim 2005 pdf
  • Design Theory prelim 2007 pdf
  • Design Theory prelim 2009 pdf
  • Design Theory prelim 2010 pdf
  • Design Theory prelim 2012 with key pdf


  • Convex and Discrete Geometry prelim 2008 pdf
  • Geometry prelim 2012 pdf

Graph Theory

  • Graph Theory prelim 2004 pdf
  • Graph Theory prelim 2005 pdf
  • Graph Theory prelim 2007 pdf
  • Graph Theory prelim 2007 #2 pdf
  • Graph Theory prelim 2008 pdf
  • Graph Theory prelim 2008 #2 pdf
  • Graph Theory prelim 2009 pdf
  • Graph Theory prelim 2010 pdf
  • Graph Theory prelim 2011 pdf
  • Graph Theory prelim 2012 pdf
  • Graph Theory prelim 2013 pdf

Harmonic Analysis

  • Harmonic Analysis prelim 2011 pdf

Linear Algebra / Matrix Theory

  • Linear Algebra prelim 2000 pdf
  • Linear Algebra prelim 2003 pdf
  • Linear Algebra prelim 2005 pdf
  • Linear Algebra prelim 2007 pdf
  • Linear Algebra prelim 2008 pdf
  • Matrix Theory prelim 2009 pdf
  • Matrix Theory prelim 2010 pdf
  • Linear Algebra prelim 2011 pdf
  • Matrix Theory prelim 2012 pdf
  • Matrix Theory prelim 2013 pdf

Ordinary Differential Equations

  • ODE prelim 2010 pdf

Partial Differential Equations

  • PDE prelim 2008 pdf
  • PDE prelim 2010 pdf

Probability / Stochastic Analysis

  • Probability prelim 2008 pdf
  • Modern Stochastic Processes 2009 pdf
  • Modern Stochastic Processes 2010 pdf
  • Probability prelim 2011 pdf

Real Analysis

  • Analysis prelim 1990 pdf
  • Topics for analysis prelim 1992 by Dr. Jack Brown pdf
  • Analysis prelim 1992 pdf
  • Analysis prelim 1993 pdf
  • Topics for analysis prelim 1994 by Dr. Jack Brown pdf
  • Analysis prelim 1994 pdf
  • Analysis prelim 1997 pdf
  • Analysis prelim 2008 pdf
  • Analysis prelim 2010 pdf
  • Analysis prelim 2011 pdf
  • Analysis prelim 2012 pdf
  • Analysis prelim 2013 pdf


  • Statistics prelim 2005 pdf
  • Statistics prelim 2006 pdf
  • Statistics prelim 2007 pdf
  • Statistics prelim with solutions 2008 pdf
  • Statistics prelim 2010 pdf
  • Statistics prelim 2011 pdf
  • Special Statistics prelim 2011 pdf
  • Statistics prelim 2012 pdf
  • Statistics prelim 2013 pdf


  • Topology prelim 1991 pdf
  • Topology prelim 1992 pdf
  • Topology prelim 1993 pdf
  • Topology prelim 1994 pdf
  • Topology prelim 1995 pdf
  • Study help for General Topology 1996-1997 by Dr. Phil Zenor pdf
  • Topology prelim 1996 - 1 pdf
  • Topology prelim 1996 - 2 pdf
  • Topology prelim 1997 pdf
  • Topology prelim 1999 pdf
  • Topology prelim 2000 pdf
  • Topology prelim 2001 pdf
  • Topology prelim 2003 pdf
  • Topology prelim 2005 pdf
  • Topology prelim 2006 pdf
  • Topology prelim 2007 pdf
  • Topology prelim 2009 pdf
  • Topology prelim 2010 pdf
  • Topology prelim 2011 pdf
  • Topology prelim 2012 pdf
  • Topology prelim 2014 pdf

 Suggested literature:
Topology by James Dugundji 
General Topology by John L. Kelley 
Topology: A First Course by James R. Munkres, 1st ed. 
  or Topology by James R. Munkres, 2nd ed.

Last updated: 06/11/2015