► Graduate School Rules  apply to this program.

Program Requirements

The Department of Mathematical and Statistical Sciences offers a PhD in applied mathematics. The degree is designed to give candidates a contemporary, comprehensive education in applied mathematics and to provide research opportunities in the special fields of graph theory, combinatorics, optimization, applied probability, computational mathematics, and applied statistics.

There are six phases of the PhD program. A candidate must fulfill course requirements, pass the preliminary examinations, establish a PhD committee, meet the academic residency requirement, pass the comprehensive examination and write and defend a dissertation.

• Students must complete 42 semester hours of non-thesis course work at the graduate level (up to 30 hours of this course work may be transferred in, including courses taken as part of a master’s degree). In addition, 30 hours of dissertation credit must be taken. The following courses are required as part of the formal course work: the math clinic and three readings courses (1 semester hour each). Students must also satisfy a breadth requirement by completing a total of six graduate math courses from among several areas of mathematics, with no more than three of these courses from any one area. A 3.25 GPA must be maintained throughout all course work. [The following MATH courses will NOT count toward a graduate degree:  MATH 5000-5009, 5010, 5012-5015, 5017, 5198, 5250 and 5830.]
• The preliminary examinations are designed to determine that students who intend to pursue the PhD program are qualified to do so. These four-hour written examinations are in the areas of applied analysis and applied linear algebra. Students must pass these exams by the start of their fourth semester.
• Six semesters of full-time scholarly work are required, as specified in the rules of the Graduate School  . All students are strongly advised to spend at least one year doing full-time course work or research with no outside employment.
• The comprehensive examination is taken after completion of the preliminary exams, completion of at least three semesters of residency, and upon completion of all nonthesis coursework. The exam is designed to determine mastery of graduate-level mathematics and the ability to embark on dissertation research. It consists of a six-hour written examination and an oral follow-up examination. Students must pass the comprehensive exam within 4 years of admission. Within six months after passing the comprehensive examination, the candidate must present a dissertation proposal to their dissertation committee.
• Each student must write and defend a dissertation containing original contributions and evidence of significant scholarship. The dissertation defense is public and must be given before an examining committee approved by the Graduate School. 

For more detailed information about the applied mathematics PhD, see www.math.ucdenver.edu/phd.