Academics

Doctor of Philosophy

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Applications to the Ph.D. program and all required supporting documents must be received by the deadline. See http://icme.stanford.edu /admissions/ for up-to-date 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 year 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.

Requirements:

  1. Complete a minimum of 135 units of residency at Stanford, including:
    • a) 45 units from the master's program; all six core courses have to be completed.
    • b) 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.
    • c)   60 units of thesis research.
    • d)   3 units of free electives.
  2. Maintain a grade point average (GPA) of 3.5.
  3. Pass the qualifying examination administered by iCME.
  4. Complete an approved program of original research.
  5. Complete a written dissertation based on research.
  6. Pass the oral examination that is a defense of the dissertation research.
  • Elective List—See requirement 1b above.

Units

CEE 362G

Stochastic Inverse Modeling and Data Assimilation Methods

3-4

CME 364A/364B

Convex Optimization I

3

CS 348A

Computer Graphics: Geometric Modeling

3-4

EE 368

Digital Image Processing

3

MATH 205A

Real Analysis

3

MATH 215A

Complex Analysis, Geometry, and Topology

3

MATH 217A

Differential Geometry

3

MATH 221A

Mathematical Methods of Imaging

3

MATH 221B

Mathematical Methods of Imaging

3

MATH 227

Partial Differential Equations and Diffusion Processes

3

MATH 236

Introduction to Stochastic Differential Equations

3

MATH 238

Mathematical Finance

3

ME 335A/335B/335C

Finite Element Analysis

3

ME 346B

Introduction to Molecular Simulations

3

ME 351A/351B

Fluid Mechanics

3

ME 361

Turbulence

3

ME 408

Spectral Methods in Computational Physics

3

ME 412

Engineering Functional Analysis and Finite Elements

3

ME 469

Computational Methods in Fluid Mechanics

3

MS&E 319

Approximation Algorithms

3

MS&E 336

Topics in Game Theory with Engineering Applications

3

STATS 305

Introduction to Statistical Modeling

2-4

STATS 306A/306B

Methods for Applied Statistics

2-4

STATS 318

Modern Markov Chains

3

STATS 366

Modern Statistics for Modern Biology

3

 

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.

Financial Assistance

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.


Ph.D. Minor in Computational and Mathematical Engineering

For a minor in Computational and Mathematical Engineering (CME), a doctoral candidate must complete 20 units of approved graduate level courses. These should include three ICME core courses and three ICME graduate electives at the 300 level or above. All courses must be taken for a letter grade and passed with a grade of ‘B’ or better. Minor programs should be developed in close discussion between the student and the student's primary Ph.D. adviser.

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