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University of Utah    
  Sep 23, 2017
2017-2018 General Catalog

Mathematics, Ph.D.

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Doctoral Requirements for Mathematics, Ph.D.

College of Science

The Ph.D. Program in the Department of Mathematics enjoys an excellent reputation in a diversified set of subjects, such as algebraic geometry, commutative algebra, differential geometry, geometric topology, group and representation theory, and number theory in pure areas, and materials and fluids, mathematical biology, mathematical finance, numerical analysis, partial differential equations, probability, and statistics in applied areas.

The following is a list of departmental requirements, in addition to the requirements of the Graduate School, for candidates seeking a Ph.D. degree in mathematics.

  • at least 42 credit hours numbered 6000 or above
  • three written qualifying examinations
  • an oral qualifying examination
  • two semesters of teaching
  • the final oral examination

More details can be found in the Graduate Bulletin.


The course requirements for the Ph.D. degree consist of at least seven sequences (each sequence contains two consecutive courses on a subject) numbered 6000 or above, or their equivalent, approved by the student’s supervisory committee. They should include at least 14 credit hours of courses numbered 7800-7970 (topics courses, seminars, and thesis research). Exceptions must be approved on an individual basis by the Graduate Committee upon the recommendation by the student’s supervisory committee.

Written Qualifying Examinations

The written qualifying examinations are given twice a year, in January and August, just before the start of the Spring and Fall semesters. A Ph.D. candidate is required to pass three written qualifying examinations chosen from the following set of subjects (corresponding course numbers are included in parenthesis):

  • algebra (6310-6320)
  • applied mathematics (6710-6720)
  • differential equations (6410-6420)
  • numerical analysis (6610-6620)
  • probability (6040)
  • real and complex analysis (6210-6220)
  • statistics (6070)
  • topology and geometry (6510-6520)

Each exam lasts three hours and is written at a first-year graduate level. Entering students are recommended to take the 6000-level course corresponding to a particular exam and use the course materials to prepare for the exams. Students with particularly strong backgrounds can choose to take the exams without taking the courses. Copies of past exams from the last ten years can be obtained by contacting the Graduate Coordinator.

Oral Qualifying Examination

This exam is conducted by the student’s supervisory committee and it can take one of the following two formats: a general exam to measure the student’s overall mathematical maturity and breadth, or a presentation of the proposed dissertation project. The exam also evaluates the student’s skill at chalkboard exposition and verbal exchange.

Teaching Requirement

Each Ph.D. candidate is required to teach a minimum of two courses or equivalent tutorials, or supervise laboratory sessions.

Final Oral Examination

This examination consists of a public thesis defense that summarizes the candidate’s thesis work.

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