Ph.D. Program

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The Department of Mathematics at UCCS offers a curriculum leading to a Ph.D. degree in Mathematics, which is part of the university's Applied Science program. For more information on this graduate program, please contact the department's Graduate Chair. Please refer to the research page for the primary research interests of the department faculty.

The admission criteria include but are NOT limited to the following requirements. Any decision regarding admission is made by the Graduate Committee on an individual basis, after taking into consideration the application materials and supporting documents.

  • Must hold a baccalaureate degree from an accredited college or university. Applicants with degrees other than mathematics (e.g., biological sciences, physics, engineering) should have mathematical preparation comparable to that of a baccalaureate in mathematics.
  • Must have an undergraduate GPA of at least 3.00. ("A" is equivalent to 4.0.)
  • International applicants must demonstrate English language proficiency by one of the approved methods.

Notes

  • Promising students who do not meet all of the admission requirements may be considered for provisional admission.
  • GRE scores are recommended but not required.

See also the admission requirements of the Graduate School.

Please visit the Applications page to apply.

A limited number of scholarships are available each year from the Department of Mathematics to provide financial support to students enrolled in the Ph.D. program. These scholarships are awarded based on the merit as well as the financial need of the applicant.

Students transferring into the program with graduate work or a Master's degree in an appropriate discipline must satisfy the admissions requirements above. Graduate level courses completed outside UCCS prior to admission may be transferable into the program. Normally, transfer credits will not exceed 25% of the total required credit hours. In unusual circumstances, applicants may request a review of their records to determine whether additional credits may be transferred. Decisions regarding transfer of graduate credits are made by the appropriate graduate advisor, and are subject to the regulations of the UCCS Graduate School.

  • Students must satisfy coursework, examination, and dissertation requirements.
  • The total hours of graduate coursework and dissertation work applied to the degree must be 75. This total may include coursework applied toward a Master's degree.
  • Students must complete a minimum of 30 hours of graduate coursework, and a minimum of 30 hours of dissertation work.
  • Independent study may not exceed 25% of the minimum number of hours required for the degree.
  • As part of the graduate coursework, students must complete 3 two-semester sequences from the list of core courses.

Each Ph.D. student in the mathematics track will take one year-long course sequence from three of the following areas.

  • Complex Analysis
  • Applied Differential Equations
  • Probability
  • Real Analysis
  • Ring Theory
  • Scientific Computation
  • Students in the Ph.D. program will normally take 2 written preliminary examinations and 2 written comprehensive examinations.
  • These examinations are closely linked to the content of graduate courses, but they have distinct content descriptions, and may require independent study of material not covered in the courses.
  • The preliminary examinations cover real analysis and linear algebra at the Master's degree level. The Graduate Committee will review the performance on the preliminary examinations to determine if the student may move forward in the Ph.D. program. At the discretion of the Graduate Committee, the required preliminary examinations may be waived for students entering the graduate program with a Master's degree, or with a comparable level of preparation.
  • The 2 Ph.D. comprehensive examinations will each cover material corresponding to one of the 3 required Ph.D. core sequences.
  • Normally, students will have at most two attempts to pass each comprehensive exam, and may attempt exams in no more than three distinct core subject areas. Exceptions must be approved by the graduate committee.
  • There will be an oral dissertation proposal examination administered by the dissertation advisory committee to determine if the dissertation topic is appropriate, and if the student is adequately prepared for work on the dissertation.
  • After the dissertation has been accepted by the dissertation advisor, a final oral dissertation defense examination will be conducted by the dissertation advisory committee.