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CME-PHD - Computational and Mathematical Engineering (PHD)
Overview
Program Overview
Doctor of Philosophy in Computational and Mathematical Engineering
The University’s basic requirements for the Ph.D. degree are outlined in the Graduate Degrees section of this bulletin.
Applications to the Ph.D. program and all required supporting documents must be received by November 30, 2021. See Graduate Admissions for information and application materials. See the institute's admissions site for additional details. Applicants should take the Graduate Record Examination by October of the academic year in which the application is submitted.
ICME offers direct admission to the Ph.D. program. Admission does not imply that the student is a candidate for the Ph.D. degree. Advancement to candidacy requires superior academic achievement, satisfactory performance on the qualifying exam, and sponsorship by a faculty member.
The requirements seek to balance research activities and coursework.
Director of Graduate Studies
Free Form Requisites
Filing for candidacy (before the end of the second year):
Complete 18 units of the ICME core classes (course, course, course, course, course, course) for letter grade and pass the ICME qualifying exam before the beginning of the second year.
Complete three units of the programming class (course); programming proficiency at the level of course is a hard prerequisite. Students can place out of course. These classes should be taken for letter grade.
Maintain a grade point average of 3.5 or higher.
Complete a minimum of six units of research rotations in years one and two (can be with same faculty adviser). course can be taken for three units at a time for credit/no credit.
Complete three units of seminars: one unit must come from course.
Submit the Ph.D. candidacy form: University policy requires that all doctoral students declare candidacy by the end of the sixth quarter in residence, excluding summers. However, after completing the integrated first year coursework, passing qualifying exam, and aligning with a permanent adviser, a student is eligible to file for candidacy prior to the sixth quarter. The candidacy form serves as a "contract" between the department and the student. Candidacy expires five years from the date of submission of the candidacy form, rounded to the end of the quarter. In special cases, the department may extend a student's candidacy, but is under no obligation to do so.
Progress toward the degree:
Complete nine units of specialized depth electives – to be agreed on with the graduate research adviser. These are intended to provide foundational knowledge of the selected research field and exposure to relevant applications. The specialized depth component of the ICME program is meant to be broad and inclusive of relevant courses of comparable rigor to ICME core courses.
Complete three units of advanced programming classes (course, course, course, etc.).
Complete nine units of computational breadth electives – advanced graduate level courses with computational content.
Complete at least 60 units of thesis research (course).
File the dissertation Reading Committee Form and a succinct research proposal (approved by your adviser) by the end of the third year in the program
Organize a “Green Light” meeting with the committee members no less than six months prior to the expected defense. This meeting should be completed in the autumn quarter of the fifth year in the program or six months before scheduling oral exams if program is expected to be completed earlier. In this meeting, a final dissertation proposal will be reviewed and discussed, and the student will present a "draft Ph.D. thesis outline" indicating status of prior work and plans for additional work. The presentation should not be a "practice thesis defense presentation", but rather should be a chapter-by-chapter review of the status of completion of each part of the expected Ph.D. thesis. A month-by-month schedule for the time remaining until the Ph.D. Defense should be presented at this meeting. The purpose of this Green Light meeting is to make sure that the entire reading committee is familiar with the plans for the completed Ph.D. thesis, and is comfortable with the proposed content and the schedule.
Degree Completion:
Complete a minimum of 135 units of residency at Stanford.
The student must pass a University oral examination in the form of a defense of the dissertation. This is typically held after all or a substantial portion of the dissertation research has been completed.
The student is expected to demonstrate the ability to present scholarly material orally in the dissertation defense.
Some Additional details:
ICME Qualifying Exam: exams involving material covered in the core courses are held in June and September. Students need to pass all six exams and each exam can be attempted twice prior to the beginning of the second year in the program.
ICME Research Rotations: research rotations must be arranged by each student on a topic of their interest; the objective is to secure commitment from a faculty member to become the Ph.D. research adviser. ICME will gather information on potential research topics and faculty with open positions by the beginning of the academic year. The course seminars will be organized to introduce research opportunities, faculty members and current ICME Ph.D. students. Furthermore, contact information of prior ICME students and faculty advisers will be made available.
ICME Research Presentations: a one-day research forum will be organized in the fall quarter for the students to present the research outcomes of the rotations to faculty and students. Presentation at the forum is a requirement to file for candidacy.
Mentoring and Monitoring: incoming Ph.D. students are assigned an academic adviser from among the ICME affiliated faculty who can provide help and advice and act as a point of contact for general inquires. The ICME Director and the student services office are also available for consultation. Students enrolled in the Ph.D. program are considered to be in good standing if they have submitted the candidacy form before the end of the second year at Stanford. After that, academic progress towards the degree is routinely overseen by the research adviser. Every year, over the summer, the ICME Director reviews all students' progress with regard to units, course work and research progress. All research advisers are solicited for their evaluation. Each student receives a program progress report based on these sources of information.
Master's in ICME: This program does not automatically satisfy the requirement for the Master's degree in ICME. However, ICME Ph.D. students may choose to obtain a Master's degree in addition to their Ph.D. by fulfilling the Master's course requirements as described in the Bulletin.
Specialized Elective List
See requirement 2 above.
Course List | ||
Units | ||
---|---|---|
Imaging with Incomplete Information | 3-4 | |
Computational Biology: Structure and Organization of Biomolecules and Cells | 3 | |
Convex Optimization II | 3 | |
Computational Biology in Four Dimensions | 3 | |
Computer Graphics: Geometric Modeling & Processing | 3-4 | |
Digital Image Processing | 3 | |
Real Analysis | 3 | |
Algebraic Topology | 3 | |
Introduction to Stochastic Differential Equations | 3 | |
Mathematical Finance | 3 | |
Finite Element Analysis | 3 | |
Introduction to Molecular Simulations | 3 | |
Fluid Mechanics | 3 | |
Turbulence | 3 | |
Spectral Methods in Computational Physics | 3 | |
Computational Methods in Fluid Mechanics | 3 | |
Approximation Algorithms | 3 | |
Applied Statistics I | 3 | |
Applied Statistics II: Generalized Linear Models, Survival Analysis, and Exponential Families | 3 | |
Applied Statistics III | 3 | |
Modern Markov Chains | 3 | |
Modern Statistics for Modern Biology | 3 |
Program Policies
Advising Expectations
ICME PhD students must align with a principal dissertation advisor no later than spring quarter of year two.
The principal dissertation advisor must be an academic council member. It is recommended, but not required, for the dissertation advisor to be an ICME-affiliated faculty member. If a student chooses to align with a faculty member who is not ICME-affiliated, it is required that they select an ICME-affiliated co-advisor.
Learning Outcomes
Program Learning Outcomes
The Ph.D. is conferred upon candidates who have demonstrated substantial scholarship and the ability to conduct independent research. Through course work and guided research, the program prepares students to make original contributions in Computational and Mathematical Engineering and related fields.