# Preliminary Examinations

The Department of Mathematics and Statistics requires all Ph.D. students in mathematics to pass two departmentally administered written examinations ("preliminary examinations" or "prelims") and take two additional year-long prelim sequences. Ph.D. students in mathematics with a statistics concentration must pass prelim exams on theory and inference and method and computation and complete 15 credit hours from a list of selected courses. These prelims are normally counted as the written portion of the general doctoral examination. (A student's advisory committee is free to require an additional written exam.) The oral portion of the general doctoral examination is conducted by a student's advisory committee, in accordance with pertinent graduate school regulations.

## Requirements

All Ph.D. students must pass two departmentally administered written examinations ("preliminary examinations" or "prelims"). A failed prelim in any subject may be repeated. Students may not repeat a prelim more than once, and no more than three failed prelims are allowed in all.

In order to retain financial support from the department, a student must pass the two prelim exams by the end of his or her second year in the graduate program. By the end of the third year in the graduate program, Ph.D. students in mathematics must meet the two additional prelim sequences requirement, and Ph.D. students in mathematics with a statistics concentration must meet the 15 credit hour requirement. In order to remain enrolled in the graduate program, a student must meet all the prelim requirements 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.)

** Ph.D. in Mathematics**

• Pass one preliminary exam in

**Group 1**

o Functions of a Complex Variable I/II (MATH 7230/7240)

o Functional Analysis I/II (MATH 7400/7410)

o Algebra I/II (MATH 7310/7320)

o Matrices I/II (MATH 7370/7380)

o Topology I/II (MATH 7500/7510)

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

o Discrete Geometry and Convexity I/II (MATH 7110/7120)

o Graph Theory (MATH 7700/7750)

o Combinatorial Designs (MATH 6770/7740)

• Pass one preliminary exam in

**Group 2**

o Applied Mathematics (MATH 7000/7010)

o Computational and Applied Algebra (any two: MATH 7180/7190/7720/7730)

o Probability I/II (MATH 7800/7810)

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

o Partial Differential Equations I/II (MATH 7440/7450)

o Advanced Theory of Ordinary Differential Equations I/II (MATH 7280/7290)

o Statistical Inference (STAT 7600/7610)

• Take two additional year-long prelim sequences from the combined list of course sequences

in Group 1 and 2. No need to take the preliminary exams on these two sequences.

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.

** Ph.D. in Mathematics with a concentration in Statistics **

• Pass the preliminary exam on theory and inference (STAT 7600/7610)

• Pass the preliminary exam on method and computation (STAT 7020/7650/7840)

• Take at least 15 credit hours from the courses below:

o MATH 7620 Optimization Theoryo MATH 7800/7810 Probability I/II (one or both)

o MATH/STAT 7820/7830 Applied Stochastic Processes I/II (one or both)

o STAT 7630 Bayesian Statistics

o STAT 7700 Generalized Linear Models

o STAT 7800 Linear Models

o STAT 7860 Applied Time Series Analysis

o STAT 7850 Theory of Statistical Inference

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
- Applied Stochastic Processes
- 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
- 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
- 2024
- 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.