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# Preliminary Examinations

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.

## Requirements

All Ph.D. students must pass three departmentally administered written examinations ("preliminary examinations" or "prelims"). A failed prelim in any subject may be repeated*.

- *Students enrolling in the doctoral program in Fall 2012 or later may not repeat a prelim more than once, and no more than four failed prelims are allowed in all.

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.

- Real Analysis I/II (MATH-7200/7210)

Functions of a Complex Variable I/II (MATH-7230/7240) - Algebra I/II (MATH-7310/7320)

Matrices I/II (MATH-7370/7380) - Topology I/II (MATH-7500/7510)

Axiomatic Set Theory I/II (MATH-7150/7160)

Discrete Geometry and Convexity I/II (MATH-7110/7120) - Graph Theory (MATH-7700/7750)

Combinatorial Designs (MATH-6770/7740) - Numerical Analysis (any two of MATH-7600/7610/7620)

Probability I/II (MATH-7800/7810)

Applied Stochastic Processes I/II (MATH-7820/7830)

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) - 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.

## Archived Examinations

Below are links to an archive of previously administered preliminary exams at Auburn University, available in PDF format.

- Algebra
- Applied Mathematics
- Coding Theory
- Complex Analysis
- Design Theory
- Geometry
- Graph Theory
- Harmonic Analysis
- Linear Algebra
- Matrix Theory
- Ordinary Differential Equations
- Partial Differential Equations
- Probability
- Real Analysis
- Statistics
- Stochastic Analysis
- Topology
- 1991
- 1992
- 1993
- 1994
- 1995
- 1996 (Study Guide)
- 1996 (#1)
- 1996 (#2)
- 1997
- 1999
- 2000
- 2001
- 2003
- 2005
- 2006
- 2007
- 2009
- 2010
- 2011
- 2012
- 2014
- 2018
- Suggested literature for Topology exams:
- Topology by James Dugundji
- General Topology by John L. Kelley
- Topology: A First Course by James R. Munkres, 1st ed.
- Topology by James R. Munkres, 2nd ed.

Last Updated: 09/10/2018