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Doctor of Philosophy in Mathematics

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Ph.D. Degree Requirements

In addition to general requirements, the department requires the student to meet the following requirements before being admitted to the comprehensive examination.

  1. Pass written qualifying examinations, 1 in algebra, 1 in analysis, and 1 in either numerical analysis or probability and statistics. The qualifying examinations must be completed by the beginning of the student’s fifth semester.
  2. Pass 1 preliminary examination in an area close to the focus of the eventual doctoral dissertation. The preliminary examination must be completed by the beginning of the student’s eighth semester.
  3. Satisfy the research skills requirement by demonstrating a reading ability in 1 of 4 languages—Chinese, French, German, or Russian—and a working knowledge of a programming language such as C++ or FORTRAN.
  4. Pass a set of required courses, differing in different tracks.

Note: Responsible scholarship requirements were approved after this catalog was finalized. Contact your department or program for more information about this requirement for doctoral students.

Pure Mathematics

This track requires MATH 800, MATH 810, MATH 820, MATH 830, and an approved course in geometry (e.g., MATH 840, MATH 910, or MATH 920).

Applied Mathematics

This track requires MATH 727 (or the corresponding qualifying examination); MATH 781 (or the corresponding qualifying examination); MATH 800; MATH 810; MATH 881 and MATH 882 or MATH 865 and MATH 866 or MATH 850 and MATH 851; and one of MATH 840, MATH 850, or MATH 950.

Examination Preparation

Normally the work required to prepare a student for the oral comprehensive examination (and to do research) includes 1 or more semesters of advanced courses, directed readings, and seminars. In the oral comprehensive examination, a student must show proficiency in the chosen area of mathematics. Precise areas of responsibility on this examination are discussed in detail with the advisory committee (the student’s adviser and two other members of the department’s Graduate Faculty).

The student must complete 4 additional courses at the 800 level or above before the final examination. Mathematics courses at the 700 level, or courses outside the department at the 700 level or higher, may be substituted with the approval of the graduate studies committee.

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