Auburn University
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Auburn University > COSAM > Academic Departments > Mathematics & Statistics > Graduate Program

Prelims

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"). To remain enrolled in the Ph.D. program, a student must pass at least two prelims before the beginning of his or her third year in the Ph.D. program, and all three prelims before the beginning of the fourth year. Failed prelims may be repeated.

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.

    (a) Real Analysis I/II (MATH-7200/7210)
    Functions of a Complex Variable I/II (MATH-7230/7240)
    (b) Algebra I/II (MATH-7310/7320)
    Matrices I/II (MATH-7370/7380)
    (c) Topology I/II (MATH-7500/7510)
    Axiomatic Set Theory I/II (MATH-7150/7160)
    Discrete Geometry and Convexity I/II (MATH-7110/7120)
    (d) Graph Theory (MATH-6750/7750)
    Combinatorial Designs (MATH-6770/7740)
    (e) 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)
    (f) 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 may upload at no charge at Acrobat Reader.

Algebra

Analysis

Topology