Mathematics, Ph.D.

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Requirements for the Doctor of Philosophy

Requirements for the doctoral degree are primarily qualitative rather than quantitative. All students’ programs require the approval of the guidance committee.

The number of graduate credits usually associated with the PhD in mathematics is 60 credits (course = 3 credits). The courses are to be selected from a well-balanced program in one major and two minor fields. The minor fields are encouraged to be chosen outside the Department of Mathematics, selected from such fields as applied mechanics, financial engineering, control theory, computer science, traffic engineering and electrical engineering. 39 credits of course work and at least 21 credits of thesis are required.

Required (core) courses, 12 credits, 3 credits each:

MA 7033 Linear Algebra I 3 Credits
MA 7043 Linear Algebra II 3 Credits
MA 6213 Elements of Real Analysis I 3 Credits
MA 6223 Elements of Real Analysis II 3 Credits

Note:

A grade of A is necessary in these required courses for PhD credit (they may be repeated).

Only courses with grades of B or better can be used to satisfy the PhD requirements.

Students are required to pass a Part 0 written examination covering fundamental topics; a Part 1 written examination covering real and complex analysis and linear and abstract algebra and a Part 2 oral examination on topics chosen by the student and thesis adviser.

After passing the Part 2 examination, the student writes a dissertation under the supervision of a faculty adviser.

The final requirement for the PhD degree is a public oral exam on the student’s dissertation.

Students must demonstrate the ability to read mathematical text written in French, German, or Russian.