Requirements
All new students in the PhD program shall complete 30 credit hours of courses in the Department of Mathematics numbered 600-699. These are subject to a distribution requirement which requires the student to demonstrate facility in three of the following five areas: algebra, analysis, applied mathematics, foundations, and topology. All courses counting towards this requirement must be passed with a grade of B- or better, and at most six credits may be in courses numbered MATH 649 or MATH 699 . With the written approval of the graduate chair, credit towards this requirement may be given for equivalent courses taken in another mathematics department, or for courses taken at UH Mānoa while in the master’s program, or for additional courses numbered MATH 649 or MATH 699 , or for graduate-level courses taken in another department.
To be admitted to PhD candidacy, the student must pass two written qualifying exams and a comprehensive exam. Qualifying exams are offered in the following areas: algebra; analysis; topology; and applied mathematics. The comprehensive exam is a written or oral examination in a field chosen by the student with the approval of the graduate chair.
The most important requirement for a PhD degree is the successful defense of a doctoral dissertation involving original mathematical research.
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