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This archived information is dated to the 2008-09 academic year only and may no longer be current.

For currently applicable policies and information, see the current Stanford Bulletin.

Master of Science in Computational and Mathematical Engineering

The M.S. degree in Computational and Mathematical Engineering is intended as a terminal professional degree and does not lead to the Ph.D. program. Students interested in the doctoral program should apply directly to the Ph.D. program. Master's students who have maintained a minimum grade point average (GPA) of 3.5 are eligible to take the Ph.D. qualifying exam; those who pass this examination and secure a research adviser may continue into the Ph.D. program upon acceptance by the institute.

The master's program consists of 45 units of course work taken at Stanford. No thesis is required; however, students may become involved in research projects during the master's program, particularly to explore an interest in continuing to the doctoral program. Although there is no specific background requirement, significant exposure to mathematics and engineering course work is necessary for successful completion of the program.

Applications to the M.S. program and all required supporting documents must be received by January 13, 2009. See for up-to-date information including departmental deadlines. See for information and application materials.

For University coterminal degree program rules and University application forms, see


A candidate is required to complete a program of 45 units of courses numbered 200 or above. Courses below 200 level will require special approval from the program office. At least 36 of these must be graded units, passed with a grade point average (GPA) of 3.0 (B) or better. Master's students interested in continuing to the doctoral program must maintain a 3.5 or better grade point average in the program.

Requirement 1—The following courses may be needed as prerequisites for other courses in the program: MATH 41, 42, 51, 52, 53, 103, 113; CME 100, 102, 104, 108, 200, 204, 302; CS 106A, 106X, 108, 205, 229; ENGR 62; STATS 116 or 202.

Requirement 2—Students must demonstrate breadth of knowledge in the field by completing the following core courses:

CME 302. Numerical Linear Algebra

CME 303. Partial Differential Equations of Applied Mathematics

CME 304. Numerical Optimization

CME 305. Discrete Mathematics and Algorithms

CME 306. Numerical Solution of Partial Differential Equations

CME 308. Stochastic Methods in Engineering

Courses in this area must be taken for letter grades. Deviations from the core curriculum must be justified in writing and approved by the student's iCME adviser and the chair of the iCME curriculum committee. Courses that are waived may not be counted towards the master's degree.

Requirement 3—12 units of general electives to demonstrate foundational breadth of knowledge. The elective course list represents automatically accepted electives within the program but is not limited to the list below and the list is expanded on a continuing basis; the elective part of the iCME program is meant to be broad and inclusive of relevant courses of comparable rigor to iCME courses. Courses outside this list can be accepted as electives subject to approval by the student's iCME adviser.

  1. Aeronautics and Astronautics:

    AA 214A. Numerical Methods in Fluid Mechanics

    AA 214B. Numerical Computation of Compressible Flow

    AA 214C. Numerical Computation of Viscous Flow

    AA 218. Introduction to Symmetry Analysis

  2. Computational and Mathematical Engineering:

    CME 208. Mathematical Programming and Combinatorial Optimization

    CME 212. Introduction to Large Scale Computing in Engineering

    CME 215 A,B. Advanced Computational Fluid Dynamics

    CME 324. Advanced Methods in Matrix Computation

    CME 340. Large-Scale Data Mining

    CME 342. Parallel Methods in Numerical Analysis

    CME 380. Constructing Scientific Simulation Codes

  3. Computer Science:

    CS 205. Mathematical Methods for Robotics, Vision, and Graphics

    CS 164. Computing with Physical Objects: Algorithms for Shape and Motion

    CS 221. Artificial Intelligence: Principles and Techniques

    CS 228. Probabilistic Models in Artificial Intelligence

    CS 229. Machine Learning

    CS 255. Introduction to Cryptography

    CS 261. Optimization and Algorithmic Paradigms

    CS 268. Geometric Algorithms

    CS 315A. Parallel Computer Architecture and Programming

    CS 340. Level Set Methods

    CS 348A. Computer Graphics: Geometric Modeling

    CS 364A. Algorithmic Game Theory

  4. Electrical Engineering:

    EE 222. Applied Quantum Mechanics I

    EE 223. Applied Quantum Mechanics II

    EE 262. Two-Dimensional Imaging

    EE 278. Introduction to Statistical Signal Processing

    EE 292E. Analysis and Control of Markov Chains

    EE 363. Linear Dynamic Systems

    EE 364. Convex Optimization

    EE 376A. Information Theory

  5. Management Science and Engineering:

    MS&E 220. Probabilistic Analysis

    MS&E 221. Stochastic Modeling

    MS&E 223. Simulation

    MS&E 251. Stochastic Decision Models

    MS&E 310. Linear Programming

    MS&E 313. Vector Space Optimization

    MS&E 316. Pricing Algorithms and the Internet

    MS&E 321. Stochastic Systems

    MS&E 322. Stochastic Calculus and Control

    MS&E 323. Stochastic Simulation

  6. Mechanical Engineering:

    ME 335A,B,C. Finite Element Analysis

    ME 408. Spectral Methods in Computational Physics

    ME 412. Engineering Functional Analysis and Finite Elements

    ME 469A,B. Computational Methods in Fluid Mechanics

    ME 484. Computational Methods in Cardiovascular Bioengineering

  7. Statistics:

    STATS 208. Introduction to the Bootstrap

    STATS 227. Statistical Computing

    STATS 237. Time Series Modeling and Forecasting

    STATS 250. Mathematical Finance

    STATS 305. Introduction to Statistical Modeling

    STATS 310A,B,C. Theory of Probability

    STATS 324. Classical Multivariate and Random Matrix Theory

    STATS 345. Computational Molecular Biology

    STATS 362. Monte Carlo Sampling

    STATS 366. Computational Biology

  8. Other:

    CEE 281. Finite Element Structural Analysis

    CEE 362G. Stochastic Inverse Modeling and Data Assimilation Methods

    ENGR 209A. Analysis and Control of Nonlinear Systems

    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

Requirement 4—9 units of focused graduate application electives, approved by the iCME graduate adviser, in the areas of engineering, mathematics, physical, biological, information and other quantitative sciences. These courses should be foundational depth courses relevant to student's professional development and research interests.

Requirement 5—3 units of an iCME graduate seminar or other approved seminar.

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