Degree Requirements for PhD in Applied Mathematics

The following is only a summary of the program requirements. The authoritative source describing program rules and expectations on students is the Graduate Handbook (bottom of page).

The core requirements for a PhD in Applied Mathematics are:

  • 40 semester hours of non-dissertation graduate courses. The following courses will not count toward a graduate degree in applied mathematics: MATH 5000, MATH 5012, MATH 5017, MATH 5198, and MATH 5220. 
  • Students must complete preliminary exams in Applied Analysis and Applied Linear Algebra within three semesters of their entry into the program.  Students who do not complete the preliminary exams in the allotted time may appeal to the graduate studies committee for one additional semester to attempt one or both exams.  
  • Students must complete a comprehensive exam in their major area of study prior to the start of their fourth year of study.  The comprehensive exam is based on a syllabus developed by the student and their advisory committee, and has both an oral and written component.  
  • Within 6 months of completing their comprehensive exam, students must complete a research proposal, which includes a written summary of proposed work and an oral presentation.  
  • By graduate school rules, courses taken more than five years prior to applying for candidacy (including transfer courses) must be validated by the graduate program director to ensure their content is still current. For mathematics courses taken within 10 years of applying for candidacy, the validation request will be automatically approved. For courses taken more than 10 years prior to applying for candidacy, the validation process will require an assessment of the student's knowledge of the subject matter
  • One readings course (MATH 7921-7926) is required as part of the formal coursework. The readings courses are one-hour seminar courses that are announced prior to the start of each semester.

All courses should be chosen in consultation with an advisor. Course replacements and equivalencies should be approved by the Graduate Committee.

Within the coursework requirement, students must satisfy a breadth requirement by completing six graduate math courses from the following categories. No more than three of these courses can come from any one category:

  • computational mathematics
  • discrete mathematics
  • operations research (including probability)
  • statistics
  • general

A list of which courses are included in each of the areas is available on within this website by exploring Graduate Courses listings. The breadth courses must be formal courses excluding MATH 5070, Applied Analysis; MATH 5718, Applied Linear Algebra; MATH 5779, Math Clinic; readings courses; and independent studies. Transfer courses and/or courses earned at another campus of the University of Colorado system may be used to satisfy this requirement, with consent of the student's advisory committee and approval by the graduate committee.

A maximum of 30 credit hours of graduate coursework (including courses applied to a master's degree) may be transferred into the PhD program. Up to six credit hours of this 30 may be awarded for a master's thesis. Only graduate courses completed with a grade of B- or better may be considered for transfer credit. Credit cannot be transferred until the student has established a satisfactory record of at least one term of full-time enrollment at UC Denver with a minimum GPA of 3.0. All transfer courses must be approved by the graduate committee. Courses taken while registered as a nondegree student are considered transfer courses. By graduate school rules, courses taken while enrolled as a graduate student at any campus of the University of Colorado system are considered resident coursework. However, all courses taken outside of the Department of Mathematical and Statistical Sciences must be approved by the graduate committee to be applied toward the PhD. In addition, courses taken at other campuses prior to enrollment in the PhD program will be counted as part of the 30 credit hour limit on transfer courses. Courses taken outside the Department of Mathematical and Statistical Sciences while enrolled in the PhD program should be approved before they are taken in order to be counted toward the PhD degree.

All PhD coursework must be completed with at least a 3.25 grade point average. Grades below a B- are not acceptable for the PhD. A student who receives a grade of C+ or lower, or whose overall GPA as a doctoral student falls below 3.25, will be reviewed by the Graduate Committee and may be put on probation or suspended.