Doctoral Degree Requirements

The PhD in Mathematics requires completing at least 36 credits of graduate coursework beyond the bachelor’s degree, preliminary written and oral examinations, 24 thesis credits, and a doctoral thesis with final defense. 

PhD students in Mathematics earn an MS degree upon completion of their preliminary written examination requirements and 30 cumulative course credits.

Coursework

Entering students

  • Required to have completed an undergraduate degree prior to matriculation into the program.
  • Some students enter with previous graduate coursework which can include having completed a Master’s degree.

Course requirements for a doctoral degree

  • 36 credits of coursework —  Students normally complete the coursework for the PhD at the University of Minnesota. Students may transfer up to 18 credits of previously completed graduate coursework toward their PhD in consultation with their advisor and the Director of Graduate Studies upon completing preliminary written examinations.
  • MATH 8001: Preparation for College Teaching — All PhD students must complete MATH 8001 in the Fall semester of their first year.

Credits

  • 18 credits of core coursework — Courses in Mathematics that are the foundation for advanced doctoral work in Mathematics. The Core coursework requirement may be met by completing the course with a B or better, passing written exams (up to 6) or a combination of coursework and exams.
    • Credit requirements met by exam will result in additional coursework being needed elsewhere or transfer credit.
  • 18 credits supporting coursework — Mathematics coursework in your research area or that supports this research. Students may take a maximum of 12 credits outside of Mathematics. Coursework used for a formal minor can be counted towards this requirement.
  • 24 thesis credits — Taken upon the completion of the preliminary oral examination. Students are expected to complete their thesis credits no more than two semesters after successfully completing their preliminary oral examination.

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Core courses

Core courses

  • MATH 8202 - General Algebra
  • MATH 8203 - Category Theory and Homological Algebra
  • MATH 8246 - Representation Theory
  • MATH 8301 - Algebraic Topology
  • MATH 8302 - Differential Topology
  • MATH 8365 - Differential Geometry
  • MATH 8402 - Mathematical Modeling and Methods of Applied Mathematics
  • MATH 8441 - Numerical Analysis and Scientific Computing
  • MATH 8442 - Numerical Differential Equations
  • MATH 8601 - Real Analysis with Measure Theory
  • MATH 8602 - Harmonic and Functional Analysis
  • MATH 8651 - Theory of Probability Including Measure Theory
  • MATH 8654 - Probabilistic Modeling and Computation
  • MATH 8701 - Complex Analysis


Beyond coursework

Preliminary written exam

  • Students must demonstrate proficiency in basic areas of mathematics by completing the preliminary written exam requirement.
  • This exam is completed by the end of the second year.

Preliminary oral exam

  • Students complete a preliminary oral examination to demonstrate proficiency in their primary area of study and supporting program or minor program.
  • This exam is completed by the end of the third year.

Final exam/dissertation defense

  • Mathematics PhD students typically complete their degree in the sixth year of their program.
  • The examination is a defense of the thesis that is the culmination of the student’s work in the program.
  • The doctoral final exam must include a public presentation of the candidate’s dissertation to the doctoral final oral examination committee and the invited scholarly community, followed by a closed session for questions by the examiners. 

Further information about these requirements as they apply to students enrolled in our doctoral program can be found on the department intranet. A umn.edu login is required.