CME-PHD - Computational and Mathematical Engineering (PHD)
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Program Overview
ICME is a degree-granting (MS/PhD) interdisciplinary institute at the intersection of mathematics, computing, engineering, and applied sciences. ICME was founded in 2004, building upon the Scientific Computing and Computational Mathematics Program (est. 1989).
At ICME, we design state-of-the-art mathematical and computational models, methods, and algorithms for engineering and science applications. The program collaborates closely with engineers and scientists in academia and industry to develop improved computational approaches and advance disciplinary fields. In particular, it leverages Stanford’s strength in engineering applications in the physical, biological, mathematical, and information sciences and has established connections with nearly 20 departments across five schools at Stanford.
The program identifies research areas that would benefit from a multidisciplinary approach in which computational mathematics is critical. This multidisciplinary intellectual environment is a core strength of ICME, with interaction among students and faculty with diverse backgrounds and expertise. Students and faculty are active in many research areas: aerodynamics and space applications, fluid dynamics, protein folding, data science, including machine learning and recommender systems, ocean dynamics, climate modeling, reservoir engineering, computer graphics, financial mathematics, and many more.
The program trains students and scholars from across Stanford in mathematical modeling, scientific computing, and advanced computational algorithms at the undergraduate and graduate levels. Courses typically provide strong theoretical foundations for solving real-world problems and numerical computations to facilitate the application of mathematical techniques and theories. Training offered includes matrix computations, computational probability and combinatorial optimization, optimization, stochastics, numerical solution of partial differential equations, parallel computer algorithms, and new computing paradigms.
See Graduate Degrees for more information on the university’s basic requirements for the PhD degree.
Admissions Information
Applications to the PhD program and all required supporting documents must be received by the posted deadline. See Graduate Admissions for information and application materials. See the institute’s admissions site for additional details.
ICME offers direct admission to the PhD program. Admission does not imply that the student is a candidate for the PhD degree. Advancement to candidacy requires superior academic achievement, satisfactory performance on the qualifying exam, and sponsorship by a faculty member.
Minimum Units in the Program
Minimum University Units
The coursework requirements for the ICME PhD total 54 units. The core, seminar, and programming/algorithm requirements must be taken before declaring candidacy (by spring quarter of year two). ICME PhD students take 8-10 units per quarter during the academic year.
Complete CME 302, CME 306, and CME 307. It is required to complete these classes during the first year. Courses must be taken for a letter grade.
Complete three units of seminars before advancing to candidacy. One unit must come from CME 300, one unit from either CME 500 or CME 510, and the remaining unit can come from any other listed seminar.
The programming/algorithm requirement must be satisfied before advancing to candidacy. CME213, CME323, CS246, and CS315B are recommended. Courses must be taken for a letter grade.
Complete nine units of research rotations in the first year. This requirement is satisfied by securing a research rotation agreement with a faculty member and enrolling in CME391. Students may rotate with one or multiple faculty advisors. Research rotations aim to identify a suitable topic for PhD work and align with a faculty advisor by the summer of year one.
Courses must be taken for a letter grade. CME 303, CME 308, and CME 310 are recommended.
The courses below are suggested options for specialized depth electives. If you are considering a class not included on this list, contact ICME student services before enrollment. Courses must be taken for a letter grade.
Enroll in dissertation research under your PhD advisor. This requirement is satisfied by enrolling in units of CME400.
To fulfill the remaining 18 units of your PhD program, please complete any combination of course and/or any classes listed in the Specialized Depth Electives section.
Maintain a grade point average of 3.5 or higher.
The core classes (CME 302, CME 306, CME 307) are strict requirements. Students can substitute courses not on the above lists for the remaining course requirements with the approval of their advisor and the ICME Director of Graduate Studies. They should submit a written request to the ICME student services office to do so. Detailed instructions are provided on the ICME Intranet.
Pass the ICME qualifying exams at the end of the first year. These written exams are held in June and September. Students can attempt each exam twice. The qualifying exams cover material from CME 302, CME 306, and CME 307.
A student who fails two plus qualifying exams after two attempts would not be eligible to advance to candidacy. Such students may be allowed to complete a CME MS degree. A student who fails one qualifying exam after two attempts will be required to undertake remedial action under the supervision of the failed exam’s faculty member. The typical corrective action is for the student to complete a literature survey on the exam topic. The survey scope should be agreed upon with the faculty member responsible for the exam. The faculty member is responsible for certifying the completion of this requirement, which must be concluded before the declaration of candidacy.
Present at a research forum organized by the institute during the second year of the PhD. Students will showcase highlights from research rotations undertaken during the first year or present their PhD work’s initial steps. Students will prepare in consultation with their PhD advisor and receive faculty feedback following the research forum.
Align with a permanent research advisor no later than the summer quarter of year one. Advisors assume responsibility for funding upon alignment. Students must submit the signed advisor agreement to ICME student services before the start of their second year.
It is strongly recommended that students submit a dissertation proposal to their advisor in conjunction with advancing to candidacy. The student and advisor will determine the process and format of this proposal. Students should indicate the dissertation proposal submission in section D of the university candidacy form.
Submit the completed candidacy form to the ICME student services team by the end of spring quarter in year two. The student’s dissertation advisor must review and sign the form.
University policy requires all doctoral students to declare candidacy by the end of the sixth quarter in residence, excluding summers. Candidacy expires five years from the date of submission of the candidacy form, rounded to the end of the quarter. In exceptional cases, the department may extend a student’s candidacy but is under no obligation to do so.
PhD candidacy forms are approved automatically if all the pre-candidacy requirements are satisfied. Exceptional circumstances (such as, but not limited to, extended sickness, visa problems, or leave of absence) will be considered by the ICME director, who will be responsible for making necessary adjustments to the process, if applicable and within the bounds of university policies. Students should petition the ICME director and student services in writing to initiate the process and detail their circumstances.
In all other cases where a student has not met the candidacy requirements by the end of year two, the ICME faculty steering committee will review the student’s progress holistically and provide a recommendation. Students are encouraged to submit a short assessment of their progress and provide further evidence that might be useful to the committee.
In consultation with the advisor, the student must form a Reading Committee. A Reading Committee Form must be completed and filed with the ICME student services office before the approval of TGR status. University policy requires the appointment of a principal dissertation advisor currently on the Academic Council. Former Academic Council members, emeritus Academic Council members, or non-Academic Council members can serve as co-advisor. Please consult the Graduate Academic Policy for guidelines on how to form your Reading Committee.
At least six months before the planned PhD Defense, the student and the Reading Committee must set a Green Light Meeting. In this meeting, a final dissertation proposal will be reviewed and discussed. The student will present a draft PhD thesis outline indicating prior work status and plans for additional work.
The presentation should not be a practice thesis defense but a chapter-by-chapter review of the completion status for each part of the expected PhD thesis. A month-by-month schedule for the time remaining until the PhD defense should be presented at this meeting. The purpose of the Green Light Meeting is to ensure all members of the Reading Committee are familiar with the plans for the completed PhD thesis and agree with the proposed content and schedule. Detailed instructions are provided on the ICME Intranet.
Any time after completing an acceptable draft of the dissertation, with the approval of the advisor and Reading Committee, the student may schedule the University Oral Examination (Dissertation Defense). To do so requires the completion of the University Oral Examination form. Once the examiners, the date, and the time for the oral examination have been established, this form must be submitted to the ICME student services office for approval at least two weeks before the proposed examination date. It is the student’s responsibility to schedule the time and day of the exam and ensure that all examiners can attend. The student is also responsible for ensuring that the exam Chair is given the University Oral Examination Form before the exam starts. If the Chair of the exam does not have the form before the start of the exam, the exam is invalid.
The student must be registered during the term the University Oral Examination is taken. The student is encouraged to email an announcement for the public portion of their Dissertation Defense to the ICME student services office two weeks before the defense to advertise it. For information on forming your Oral Exam Committee, see Stanford’s Graduate Academic Policy.
The Oral Exam can be up to three hours. The student should consider this when scheduling the time with the Oral Exam Committee. The Oral Exam Chair should submit the examination results to the ICME student services office immediately following the exam. See further information on the ICME Intranet and the Graduate Academic Policy page.
Consult the university's page on dissertation information for rules governing the dissertation format, fees, forms, and deadlines.