Mathematics, PhD


PhD Program

Course Delivery

On Campus, Online, Hybrid

Total Credits

60 Credits

About the Applied Science PhD Program

The Department of Mathematics at UCCS provides a comprehensive graduate program leading to a PhD in Mathematics. Our program is an integral component of the university's Applied Science program, which emphasizes the practical application of scientific principles. 

Students must complete at least 30 credit hours of graduate coursework and 30 credit hours of dissertation work. Coursework must include 18 credit hours of core courses; each PhD student must take a two-semester course sequence in any three of the following areas to complete this requirement: Complex Analysis; Applied Differential Equations; Probability; Real Analysis; Ring Theory; and Scientific Computation.

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

Program Focus of Study

Specific areas of study currently available include probability and statistics, differential equations, applied analysis, algebra, and coding theory.

Program Requirements for Admissions

To be considered for admission into the graduate program, applicants are required to meet certain criteria, which include:

  • Holding a baccalaureate degree in mathematics or a related field with significant math coursework from an accredited college or university
  • Having an undergraduate GPA of at least 3.00 both for math courses and overall
  • Submit GRE General Test scores, taken within the last 2 years, with a recommended percentile of 80 or higher on the Quantitative Reasoning section.

While these requirements are necessary, they are not exhaustive, and decisions regarding admission are made on an individual basis by the Graduate Committee. Applicants who do not meet all of the admission requirements may still be considered for provisional admission if they show promise.

International applicants must also demonstrate English language proficiency and provide additional documentation. 

Application Deadline: Fall & Spring: Rolling Admission*

*Applications are due one week prior to the term start date

Program Coursework


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 Graduate Chair, 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 60. This total may include coursework applied toward a Master's degree.
  • A minimum of 30 hours of dissertation work must be completed.
  • A minimum of 30 hours of graduate coursework must be completed, including: Linear Algebra I (MATH 5130), Modern Analysis II (MATH 5320), 3 two-semester sequences of core courses (see below), and 2 additional courses at the 5000/6000 level.
  • Independent study may not exceed 25% of the minimum number of hours required for the degree.



Each Ph.D. student must take a two-semester course sequence in three of the following areas.

  • Complex Analysis (MATH 6610 and 6620)
  • Applied Differential Equations (MATH 5430 and 6440)
  • Probability (MATH 6910 and 6920)
  • Real Analysis (MATH 6330 and 6350)
  • Ring Theory (MATH 6170 and 6180)
  • Scientific Computation (MATH 5670 and 6680)

For program coursework, please visit the Academic Catalog.


  • Students in the Ph.D. program normally take two written preliminary examinations and two 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 two Ph.D. comprehensive examinations each cover material corresponding to one of the three required Ph.D. core sequences. Additional information can be found here.
  • Copies of preliminary and comprehensive exams from prior years can be found on the PhD Exams page.
  • 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.