Feb 27, 2024  
USC Catalogue 2023-2024 
USC Catalogue 2023-2024

Mathematics (PhD)

Application deadline: December 15

Completion of the program generally requires a maximum effort by the student for a minimum of four years of full-time work.

Screening Procedure

The screening procedure consists of written examinations covering core mathematics content. Student must pass exams for three of the following five core subjects, one of which must be either Algebra or Analysis:

  • Algebra;
  • Real and Complex Analysis;
  • Ordinary and Partial Differential Equations;
  • Geometry and Topology;
  • Probability and Statistics;

Some subjects are tested by a three-hour exam; others by two separate 90-minute exams. The department offers the exams twice a year, at the end of summer and at the beginning of the spring semester. Students may attempt each of the exams at most three times.

Either the Algebra exam requirement or the Analysis exam requirement must be successfully completed by spring of the second year. All exam requirements must be fulfilled by the spring of the third year.

Qualifying Exam and Committee

After completion of the screening procedure, the student must form a qualifying exam committee. The committee must consist of an adviser and four other faculty members, including at least one from another department.

The qualifying exam consists of written and oral components. The written part consists of a research proposal that should be submitted to the qualifying exam committee at least one week before the oral part. The oral part consists of a presentation by the student and examination by the committee.

Course Requirements

The course requirement includes required and elective courses. Students must complete, with no grade lower than B-, a minimum of 60 units of courses carrying graduate credit. Courses outside of the Mathematics Department must be approved by the Graduate Committee.

Required Courses

The following courses must be completed:

Additional Requirements

Transfer of Credit

No transfer of credit will be considered until the screening examination is passed. A maximum of 30 units of graduate work at another institution may be applied toward the course requirements for the PhD. A grade lower than B will not be accepted and at most two grades of B will be accepted.

Foreign Language Requirement

The student must demonstrate a reading comprehension of mathematics in one language (other than English) in which there is a significant body of research mathematics (such as Chinese, French, German, Japanese and Russian) by passing a written examination, administered by the Mathematics Department, in translation of mathematical content.

Dissertation and Defense

Following completion of the screening procedure and approval of a dissertation topic by the chair of the student’s qualifying exam committee, the student proceeds with research towards the dissertation. The student must form a dissertation committee consisting of at least three members, including the thesis advisor and a member outside the mathematics department. The PhD thesis, based on a substantial amount of original research conducted by the student, must be defended and approved by the dissertation committee.