Doctor of Philosophy in Computational and Mathematical Engineering
Applications to the Ph.D. program and all required supporting documents must be received by December 6, 2011. See http://icme.stanford.edu /admissions for full information. Prospective graduate students should see http://gradadmissions.stanford.edu for information and application materials. Applicants should take the Graduate Record Examination by October of the academic year in which the application is submitted.
Admission to the Ph.D. program does not imply that the student is a candidate for the Ph.D. degree. Advancement to candidacy requires superior academic achievement and passing the qualifying examination.
- Complete a minimum of 135 units of residency at Stanford, including:
- 45 units from the master's program
- 27 units of focused electives in an area planned with the student's Ph.D. adviser; 12 of these units should come from ICME specialized electives with significant computational content such as the CME 320-380 series. The focused and specialized elective component of the ICME program is meant to be broad and inclusive of relevant courses of comparable rigor to ICME courses. The elective course list following represents automatically accepted electives within the program. However, electives are not limited to the list below, and the list is expanded on a continuing basis; courses outside the list can be accepted as electives subject to approval by the student's ICME adviser.
- 60 units of thesis research
- 3 units of free electives
- Maintain a grade point average (GPA) of 3.5.
- Pass the qualifying examination administered by ICME.
- Complete an approved program of original research.
- Complete a written dissertation based on research.
- Pass the oral examination that is a defense of the dissertation research.
Specialized Elective ListSee requirement 1b above.
CEE 362G. Stochastic Inverse Modeling and Data Assimilation Methods
CME 364A,B. Convex Optimization I,II
CS 348A. Computer Graphics: Geometric Modeling
EE 363. Linear Dynamical Systems
EE 368. Digital Image Processing
MATH 205A. Real Analysis
MATH 215A. Complex Analysis, Geometry and Topology
MATH 217A. Differential Geometry
MATH 221. Mathematical Methods of Imaging
MATH 227. Partial Differential Equations and Diffusion Processes
MATH 236. Introduction to Stochastic Differential Equations
MATH 237. Stochastic Equations and Random Media
MATH 238. Mathematical Finance
ME 335A,B,C. Finite Element Analysis
ME 346B. Introduction to Molecular Simulations
ME 351A,B. Fluid Mechanics
ME 361. Turbulence
ME 408. Spectral Methods in Computational Physics
ME 412. Engineering Functional Analysis and Finite Elements
ME 469A,B. Computational Methods in Fluid Mechanics
MS&E 319. Approximation Algorithms
MS&E 336. Topics in Game Theory with Engineering Applications
STATS 305. Introduction to Statistical Modeling
STATS 306A,B. Methods for Applied Statistics
STATS 318. Modern Markov Chains
STATS 366. Computational Biology
Note: All courses listed under "Requirement 3" under the "Master of Science in Computational and Mathematical Engineering" section can be used for fulfilling the general elective requirement.
The department awards a limited number of fellowships, course assistantships, and research assistantships to incoming graduate students. Applying for such assistance is part of submitting the application for admission to the program. Students are appointed for half-time assistantships which provide a tuition scholarship at the 8, 9, 10 unit rate during the academic year and a monthly stipend. Half-time appointments generally require 20 hours of work per week. Most course assistantships and research assistantships are awarded to students in the doctoral program in ICME. If the number of Ph.D. students is not sufficient to staff all course and research assistantship positions available, these positions may be open to master's students. However, master's students are not guaranteed financial assistance.