Ph.D. Degree Requirements
Academic Advising
Each new student will be assigned a faculty advisor (usually the chair of the graduate committee) for consultation in planning a sound program of study. Advising includes the courses to be taken and the areas in which to take the preliminary exams. Incoming students will be prevented from registering until they obtain approval from their faculty advisor. For Ph.D. students, the chair of the student’s thesis committee will assume the duties of the faculty advisor when the committee is formed.
Adequate Progress
Doctoral students must demonstrate adequate progress toward the degree by:
- Maintaining a grade point average of the Graduate School minimum of 3.0 or better in all course work
The Graduate School will not accept any grade below B- (2.7) toward the Ph.D. degree. - Attaining either a pass or a research pass on at least one preliminary exam by the conclusion of the first year in the graduate program and passing three prelims, including applied analysis and numerical analysis (attaining at least two research passes), before starting the third year
(See the Preliminary Examinations section for details.) - Passing the comprehensive examination by the end of the fourth year
- Registering continuously for at least 5 dissertation credit hours every fall and spring semester, beginning the semester following the passing of the comprehensive exam and extending through the academic term (including summer session) the dissertation is successfully defended
Department Course Requirements
A minimum of 60 credits is required for the degree, including 30 credits in courses numbered 5000 or above and 30 hours of Applied Mathematics dissertation credit. A grade of B- (2.7) or higher must be attained in each course. Generally, APPM 4350/5350, 4360/5360, and 4720/5720 do not count toward this requirement. Ph.D. students must maintain a grade point average of 3.0 or better each semester.
To prepare for the preliminary exams, students are advised to take graduate sequences in applied analysis (5440/5450) and numerical analysis (5600/5610). An additional graduate sequence in an application area also is recommended. Refer to the Basic Courses section of this supplement for a list of acceptable 5000-level sequences. Other sequences require faculty advisor approval.
Doctoral candidates must take at least two semesters of seminar courses (8000, 8100, 8300, or 8600). These courses are to be taken no earlier than the second year of graduate study in the department. First-year graduate students are not permitted to enroll in these seminar courses except by special petition to the graduate committee. Note: Transcripts might include the phrase “repeat—not for credit” when seminar courses are taken more than once. This statement is an artifact of the system and should be ignored. Repeated seminars will be credited toward the M.S. or Ph.D.
Finally, each student must take a yearlong graduate sequence outside of applied mathematics in an area where mathematics has significant application. Faculty advisor approval of this sequence is required.
Dissertation Credit-Hour Requirement
Doctoral students are required to enroll in a minimum of 30 dissertation credit hours to complete the requirements for the Ph.D.
As a rule, no more than 10 dissertation credit hours taken in the semesters prior to the academic term during which the comprehensive exam is passed will count toward the dissertation hours required for the Ph.D. degree.
Ph.D. candidates may enroll in a maximum of 10 dissertation credit hours per semester and must be enrolled in a minimum of 5 dissertation credit hours per semester (summer excluded) starting the semester following the passing of the comprehensive exam and extending through the academic term during which the dissertation is successfully defended.
A Ph.D. student must be enrolled full time for a minimum of 5 dissertation credit hours during the academic term (including summer session) the dissertation defense is passed.
Students electing to be part-time after passing the comprehensive exam may enroll in 3+ dissertation hours but must be full-time the semester they defend. See the University Catalog for details.
Dissertation Defense/Final Exam
After the dissertation has been completed, the student’s committee administers an oral final exam (defense) on the thesis and related topics. This exam is open to the public.
More than one dissenting vote will disqualify the candidate. A student who fails the examination may attempt the exam once more after a period of time as determined by the examining committee.
At least two weeks prior to the exam, the Ph.D. student must submit a completed Doctoral Examination Report form, available on the Graduate School website, to the graduate program assistant for approval by both the graduate chair and the Graduate School. Also, the student must submit his/her abstract and title, which should be forwarded to the graduate program assistant in electronic format.
A doctoral candidate will submit a copy of the dissertation to the committee at least two weeks in advance of the defense date, allowing ample time for the reader to review the doctoral thesis. The reader is a committee member, often a co-advisor, who is assigned the task of reading the thesis.
Foreign Language Requirement
The department requires that, before advancing to candidacy, all students must provide evidence of competency in a foreign language. Approved foreign languages include Chinese, French, German, Japanese, Russian, and Spanish, but others may be approved through petition to the graduate committee.
Anyone with a foreign language as a native tongue may be judged by the graduate committee to have met this requirement, while others may satisfy the language requirement by having successfully completed a one-year college course.
Alternatives for establishing competency may be proposed to the graduate committee. In any case, providing evidence of competency is the student’s responsibility.
General Ph.D. Degree Requirements
Studies leading to the Doctor of Philosophy degree must be chosen so as to contribute to a high level of scholarship in a broad field of study. Since applied mathematics is by nature interdisciplinary, these studies will include courses in one or more application areas, in addition to those within the department.
The University Catalog provides the general requirements for the degree of Doctor of Philosophy. In all cases not specifically mentioned in this supplement, the general requirements as stated in the catalog apply. The faculty advisor must approve the program of study.
Graduation Application
A Ph.D. candidate must complete an online application for graduation whether or not he/she plans to attend commencement. To apply for graduation, log on to myCUinfo.colorado.edu. On the Student tab, select the Apply for Graduation link under Academic Resources. Contact the graduate program assistant for additional information on applying online for graduation.
The online application for graduation notifies the department and the Graduate School of a student’s intent to graduate and provides necessary information to the Commencement Office for ordering and shipping the diploma.
A student who does not complete the requirements for graduation for the academic term indicated on the online application must apply online to graduate for the new graduation term.
Grievance Policy
If a student feels that he/she has received unfair treatment academically or as a teaching or research assistant, then the student should first attempt to resolve the problem with the faculty member involved. If this fails, the student should speak with the faculty advisor, who will bring the matter before the graduate committee. In the event that the student is dissatisfied with this resolution, he/she may file a written formal complaint with the dean of the Graduate School.
M.S. Degree for Ph.D. Students
Courses taken at the University to satisfy the requirements for the M.S. degree in Applied Mathematics will be counted toward the minimum requirements for the Ph.D. degree in Applied Mathematics.
A student pursuing a Ph.D. degree need not also obtain the M.S. degree in Applied Mathematics. However, any Ph.D. student also intending to receive the master’s degree must satisfy the requirements for that degree. A doctoral candidate may complete the M.S. non-thesis option by passing one of the preliminary exams. Interested students should contact the graduate program assistant for details.
Preliminary Examinations
Preliminary exams are offered in four areas: applied analysis, numerical analysis, partial differential equations, and probability/statistics. Ph.D. students must take the numerical analysis and applied analysis prelims and either one of the other two preliminary exams. Each is a three-hour written exam.
Syllabi and previous preliminary exams are available on the Applied Mathematics website.
The preparatory courses for these prelims are APPM 5440-5450 for applied analysis, APPM 5600-5610 for numerical analysis, APPM 5470 (not MATH 5470) for partial differential equations, and APPM 5520-5560 for probability/statistics. Please note that APPM 5520 and APPM 5560 may be taken in any order, and that APPM 5570-5580 is not a preparatory course sequence for the probability/statistics prelim.
Ph.D. students are expected to sit for at least one prelim by the conclusion of their first year in the program and should complete the preliminary exam requirement successfully prior to the start of their third year, and prior to passing comps and being admitted to candidacy. Continuation of financial support is contingent upon meeting this requirement. Extenuating circumstances will be considered by petition to the graduate committee.
Preliminary exams are given at the beginning of the fall and spring semesters. Notification of results for a given prelim will be sent to students by e-mail within two weeks of the exam date.
Each preliminary exam has three possible grades: Ph.D. Research Pass, Pass, and Fail. To fulfill the preliminary exam requirement, a doctoral candidate must pass three exams, including applied analysis and numerical analysis. At least two of the passes must be Ph.D. research passes. The third may be a pass. No exam may be taken more than twice.
Students who fail the same prelim twice are subject to dismissal from the program.
Thesis Committee
After choosing a field of specialization, the Ph.D. student will present a list of no fewer than five faculty members to serve on her/his thesis committee, for approval by the graduate chair.
The thesis committee chair will serve as the student’s thesis advisor and will supervise his/her research. The chair must be a member of the department faculty or affiliate faculty and must have a current regular or tenured graduate faculty appointment. If an affiliate is selected to serve as chair, the student must first receive approval from the graduate chair, and a member of the department faculty must serve as co-chair.
The other four thesis committee members must hold current regular or special memberships on the graduate faculty. At least three of the committee members must be on the department faculty; any others may be affiliated faculty members or faculty members outside the department.
The graduate committee and the dean of the Graduate School must approve the composition of the thesis committee. Modifications to the committee membership may be made, provided the graduate committee and the dean of the Graduate School approve all changes.
Thesis Proposal/Comprehensive Examination
Prior to admission to candidacy, and no later than the end of the fourth year in the department, each doctoral student must pass the comprehensive examination.
Note: Ph.D. students must satisfy the preliminary exam requirement before attempting the comprehensive exam. (See the Preliminary Examinations section for details.)
The purpose of the comprehensive exam is to ensure that the student has a sufficient grasp of the fundamentals of the chosen thesis area to begin research, the ability to exchange ideas and information with the members of the examining board (thesis committee), and a broad base of knowledge in applied mathematics.
No fewer than two weeks before attempting the comprehensive exam, the Ph.D. student must formally apply for admission to candidacy for the doctoral degree by completing a Candidacy Application for an Advanced Degree, available on the Graduate School website. The application for admission to candidacy for the Ph.D. must be submitted to the graduate program assistant with the student’s signature and the approval signature of his/her faculty advisor.
At the same time, the Ph.D. student must forward a completed Doctoral Examination Report form, available on the Graduate School website, to the graduate program assistant for approval by both the graduate chair and the Graduate School. Upon filing the exam form, the student must forward his/her abstract and title to the graduate program assistant, preferably in electronic format.
Also, at least two weeks before attempting the comprehensive exam, the student must submit a completed Ph.D. degree audit form to his/her faculty advisor for approval. Once signed by the student and the faculty advisor, the form should be submitted to the graduate program assistant.
One week before the comprehensive exam, the Ph.D. student must submit a 5-10 page thesis proposal, complete with motivation for the topic and references to key papers, to each member of the thesis committee. This proposal should be written in consultation with the chair of the thesis committee.
The exam will consist of a presentation by the student on his/her research proposal for a maximum of one hour in length, followed by a questioning period of up to one additional hour. The presentation portion is open to all faculty and students in the program.
The thesis committee will constitute the examining board. A passing grade is given if at least four of the five members (including the chair) of the examining committee vote satisfactory performance.
Thesis Requirement
A thesis must be based on original investigation and reflect a mature understanding and critical judgment of the subject matter, as well as familiarity with tools and methods of research. The thesis subject must be approved by the thesis committee and must be submitted to the committee at least 30 days before the defense. The thesis should contain material that is publishable in a peer-reviewed journal in, or related to, applied mathematics, and its format must comply with the specifications outlined on the Graduate School website, www.colorado.edu/graduateschool.
There is an expectation that students submit for publication in peer-reviewed journals prior to graduation.
The Ph.D. candidate is required to submit both an electronic copy (in PostScript or PDF format) and an unbound copy, printed single-sided on 8.5 x 11 watermarked bond paper of at least 25 percent cotton content and 20-pound weight, of his/her dissertation to the department, by the posted Graduate School deadline for online submission of the dissertation for the semester the Ph.D. degree is to be conferred. The dissertation should be formatted according to Graduate School specifications, available on the Graduate School website, www.colorado.edu/graduateschool.
Time Limit
Doctoral candidates are expected to complete all degree requirements within six years of beginning graduate studies. See the University Catalog for details.
Students may enroll in the Time Off Program through the Registrar’s Office with faculty advisor approval. Through this leave program, graduate students may take three to four semesters off (including summer) without reapplying to return to the University. This program guarantees students a place in the graduate program when they return and allows access to certain benefits while they are away. However, there is no guarantee of financial support upon return.
Otherwise, the graduate committee may remove an inactive student from the degree program.
Transfer Credit
The Graduate School will allow Ph.D. students to transfer up to 21 semester hours of course work from another institution toward the doctoral degree. All transfer requests must have the approval of the graduate committee in Applied Mathematics.
Course work already applied toward a graduate degree received from CU-Boulder or another institution cannot be accepted for transfer toward another graduate degree of the same level at CU-Boulder. For example, work already applied to meet requirements for a master’s degree earned by a student cannot be used toward a second master’s degree from CU. In addition, work completed for a doctoral degree may not be applied toward a subsequent master’s degree.
Credit may not be transferred until the student has completed 6 credits of graduate-level course work as a regular, degree-seeking student on the CU-Boulder campus with a GPA of 3.0 or above.
