Advancement to Candidacy
Course Requirements
Foundational Courses
Students in the AM Ph.D. program must demonstrate mastery in the foundations of scientific computing and applied mathematics, either by submitting evidence of undergraduate transcripts to the AM graduate director for approval or by taking all of the following foundational courses upon entry to the Ph.D. program, or a combination of the two, by the end of their first year:
All of the following five foundational courses
| AM 100 | Mathematical Methods for Engineers | 5 |
| AM 112 | Introduction to Partial Differential Equations | 5 |
| AM 114 | Introduction to Dynamical Systems | 5 |
| AM 129 | Foundations of Scientific Computing for Scientists and Engineers | 5 |
| AM 147 | Computational Methods and Applications | 5 |
These foundational courses can be taken for letter grades or the Satisfactory/Unsatisfactory (S/U) option.
Core Courses
All AM Ph.D. students must complete the following core courses. All five non-seminar core courses (i.e., AM 212, AM 213A, AM 213B, AM 224 and AM 160) must be taken for letter grades. Students must also take at least six credits from a combination of three courses in the AM 280 seminar series (i.e., AM 280A, AM 280B, and AM 280C). The combination must include at least one quarter of AM 280B.
| AM 160 | Introduction to Scientific Machine Learning | 5 |
| AM 212 | Advanced Methods of Applied Mathematics | 5 |
| AM 213A | Numerical Linear Algebra | 5 |
| AM 213B | Numerical Methods for the Solution of Differential Equations | 5 |
| AM 224 | Applied Dynamical Systems | 5 |
| AM 280A | Seminar in Mathematical and Computational Biology | 2 |
| AM 280B | Seminar in Applied Mathematical Modeling | 2 |
| AM 280C | Seminar in Geophysical and Astrophysical Fluid Dynamics | 2 |
Elective Courses
In addition to these 31 credits, Ph.D. students must complete five additional 5-credit elective courses for a total requirement of 56 credits. As part of the five additional courses, students are required to take (at least) one elective course during their first year (called first-year elective) to help them engage in research as early as possible. First-year electives are designed to prepare students for their ultimate research emphasis within applied mathematics. These electives can be selected from any non-core regular 5-credit AM graduate courses (between course numbers 201 and 279).
Ph.D. students will be allowed to substitute up to two elective courses with corresponding numbers of credits of independent study (i.e., 5 or 10), during which they conduct research with their advisor toward their advancement to candidacy.
All elective courses, including the AM courses and non-AM courses, must be approved by the graduate director. Elective courses can be taken for the Satisfactory/Unsatisfactory grading option or the letter grade option.
Transfer of Credit
Up to three UC Santa Cruz courses (15 credits) fulfilling the degree requirements of the Ph.D. degree may be taken during students' undergraduate study at UC Santa Cruz. Note that this 15-credit limit does not apply to the requirements of the five foundational courses (AM 100, AM 112, AM 114, AM 129, and AM 147), which may all be taken prior to the start of the Ph.D. program without penalty. Ph.D. students who have previously earned an M.S. degree in a related field at another institution may substitute courses from their previous university with the approval of the student’s official advisor and the graduate committee.
Petitions should be submitted along with the transcript from the other institution or from their UC Santa Cruz undergraduate study. For courses taken at other institutions, copies of the syllabi, exams, and other coursework should accompany the petition. Such petitions are not considered until the completion of at least one quarter at UC Santa Cruz. At most, a total of three courses may be transferred.
Students who complete at UC Santa Cruz the M.S. degree in AM or the M.S. degree in Scientific Computing and Applied Mathematics (SciCAM) and continue on to the Ph.D. program in AM at UC Santa Cruz can transfer all applicable courses taken during the M.S. to the Ph.D. program, provided that such students meet the minimum residency requirement for Ph.D. programs, as specified by the UC Santa Cruz Graduate Division.
Teaching Requirement
Ph.D. students will be required to serve as teaching assistants for at least two quarters during their graduate study. Certain exceptions may be permitted for those with extensive prior teaching experience, for those who are not allowed to be employed due to visa regulations, or for other reasons approved by the graduate director.
Ph.D. students whose native language is not English must take the Test of English as a Foreign Language (TOEFL) exam or the International English Language Testing System (IELTS) exam and score a minimum of 26 on the spoken portion of the Internet-based TOEFL or an overall 8 on the IELTS before being considered for a position of teaching assistant. The English-language requirement for teaching assistants is may be waived for students who have received an M.S. degree from an English-speaking institution and with the experience as a teaching assistant at that university. International students may also participate in the Graduate Preparation Program (GPP) (the registration deadline is mid-July annually) prior to starting the graduate program. Successful completion of the GPP satisfies the English-language requirement for teaching assistants. See more details on the English language waiver for teaching assistantship.
Pre-Qualifying Requirements
Under normal progress, Ph.D. students are expected to find a Ph.D. advisor and complete their core course requirements by the end of their second year. Soon after identifying an advisor, they are expected to prepare for a pre-candidacy exam under the guidance of their advisor(s) to demonstrate their suitability and commitment to research. Students are expected to pass the pre-candidacy exam after completing all core courses and no later than by the end of the summer quarter of their second year, or they will be put on academic probation. The pre-candidacy exam has two parts (written and oral), in which students are expected to review the literature and present a research proposal relevant to the subject area of their intended Ph.D. The written report must not exceed 10 pages and must be submitted to their committee at least one week prior to the planned oral exam date. The oral examination must cover, in no more than 30 minutes, both literature review and planned work. This will be followed by a question-and-answer session between the student and the committee during which the committee members can ask questions on core courses, literature review and proposed research. The committee will assess the student's suitability for future research in the Ph.D. program based on both written and oral performance on the exam.
The committee, which must be formed at least one month prior to the planned pre-candidacy exam date, is approved by the graduate director, and must include:
(i) The student's primary Ph.D. advisor (a ladder-rank faculty member in or outside of AM)
(ii) Another ladder-rank AM faculty member, and
(iii) Another ladder-rank UCSC faculty member who is recognized as an expert in the student's research interest area with credentials equivalent to a ladder-rank UCSC faculty member as judged by the graduate director.
Students who do not pass the exam in their first attempt will be allowed to retake it once, and must do so at the very latest before the end of the fall quarter of their third year. If they fail the second examination they will not be allowed to continue in the Ph.D. program but will have the option to continue into the M.S. program and exit with the M.S. as the terminal degree.
Qualifying Examination
Under normal progress Ph.D. students are expected to advance to candidacy anytime between the quarter they pass the pre-candidacy exam and the spring quarter of their third year. A student who has not advanced to candidacy by the start of the fourth year will be subject to academic probation.
Ph.D. students must form a Qualifying Exam (QE) committee in preparation of the exam. This committee must consist of at least four members as follows (for continuity, the members of this committee are ideally the same as those of the pre-candidacy exam committee, augmented with an external member):
- QE Chair: This person must be a tenured AM faculty and cannot be the student's Ph.D. advisor(s).
- Member 1: Ladder-rank AM faculty member
- Member 2: Ladder-rank UCSC faculty member (any department).
- External Member: This person must be tenured UCSC faculty from outside AM or tenured faculty in the same discipline at another institution or a recognized non-faculty expert in the student's research area with credentials equivalent to a ladder-rank UCSC faculty member as judged by the graduate director and the dean of Graduate Studies. The External Member cannot be the student's faculty advisor(s).
The candidacy exam also has two parts (written and oral), in which students are expected to review the literature, present a substantially completed research project that is appropriate for submission to an international journal or conference, and present a plan to complete further research projects in pursuit of their Ph.D. The written report, that should not exceed 60 pages, must be submitted to their committee at least two weeks prior to the planned oral exam date. The oral examination must cover, in no more than 45 minutes, both literature review, and existing and planned research. This will be followed by a question-and-answer session between the student and the committee during which the committee members can ask questions on the literature review, and current and proposed research. The committee will assess the student's suitability for advancement to candidacy based on both written and oral performance on the exam.
Students can only advance to candidacy after they have completed all course requirements (including removal of all incomplete grades), passed both pre-candidacy and candidacy examinations, nominated their dissertation reading committee, and paid the advancement to candidacy fee.
Dissertation
Upon successful completion of the qualifying examination, a dissertation reading committee must be formed consisting of the dissertation supervisor and at least two additional readers appointed by the graduate director upon recommendation of the dissertation supervisor. Students should consult their advisor(s) about the membership of their committee.
The committee must include the following:
- Committee Chair: This person should be an AM faculty member (usually the student’s Ph.D. advisor).
- Member 1: Ladder-rank AM faculty member who is not the student's primary Ph.D. advisor.
- Member 2: Ladder-rank UCSC faculty (may be the student’s Ph.D. advisor) or a recognized expert in the student's research area with credentials equivalent to a ladder-rank UCSC faculty member as judged by the graduate director and the dean of Graduate Studies.
At least two members of the committee must be AM faculty. If a student has two co-advisors, they should both be listed as co-chairs. Additional members may be added to the committee. The committee is subject to the approval of the Graduate Division.
Post-Qualifying Requirements
After the advancement, Ph.D. students shall consult with their dissertation committee at least once every year to present and discuss progress made and receive comments and suggestions from their committee members.
Relationship of AM Master's Program and AM Doctoral Program
The M.S. and Ph.D. programs are freestanding and independent, so that students can be admitted to either program. Students completing the M.S. program may request to transfer into the Ph.D. program (provided they pass the pre-qualifying examination). Students in the Ph.D. program can receive a non-terminal M.S. degree upon completion of the M.S. requirements, including the capstone research project. Each Ph.D. student will be required to have knowledge of applied mathematics equivalent to that required for the M.S. degree. In addition, Ph.D. candidates will be required to complete coursework beyond the M.S. level.
Dissertation
Dissertation
A dissertation is required for the Ph.D. degree. The dissertation will consist of a minimum of three chapters composed of material suitable for submission and publication in major professional journals in applied mathematics (or related subject areas of application), in addition to an introductory chapter that thoroughly reviews the literature, and a conclusion chapter that provides a broad perspective of the results in the context of the existing literature, and describes future work.
Dissertation Defense
The completed dissertation will be submitted to the reading committee at least one month before the dissertation defense. The defense consists of a public presentation (open session) of the research followed by a private examination (closed session) by the reading committee. Successful completion of the dissertation defense is the final requirement for the Ph.D. degree.
Review of Academic Progress
Each year, the faculty reviews the progress of every student in the graduate programs. Students who do not make adequate progress toward completion of degree requirements are subject to dismissal from the program (see the UC Santa Cruz Graduate Handbook and the AM Graduate Handbook for the policy on satisfactory academic progress). Also, please refer to the Graduate Division's specific guidelines on annual student reviews. In addition, students will work with their academic advisors (e.g., first-year advisor or official Ph.D. advisor) and their dissertation reading committee to fill out an AM advising form at least once a year to discuss the overall academic progress, research relationship, and students’ welfare.
Applying for Graduation
All candidates for a degree must submit an application for the Ph.D. degree to the Baskin Engineering Graduate Advising Office by the date stated in the Academic and Administrative Calendar for the quarter you wish to receive the degree. The deadline for degree applications is typically in the second week of the quarter.
A student is required to be registered or on Filing Fee Status, whichever is applicable, during the quarter in which the degree is conferred. Students should consult the department staff advisor to determine which option fits their situation. For more information about applying for graduation, visit the Baskin Engineering Graduate Studies website.