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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 10, 2012. See for up-to-date information including departmental deadlines. See for information and application materials.

The University requirements for the coterminal M.S. are described in the "Coterminal Bachelor's and Master's Degrees" section of this bulletin. For University coterminal degree program rules and University application forms, also 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, 211, 212, 302; CS 106A, 106X, , 205, 229; ENGR 62; STATS 116 or 202.

Requirement 2—Students must demonstrate foundational knowledge in the field by completing the courses in two of the three core parts:

  1. Part I
    • CME 303. Partial Differential Equations of Applied Mathematics
    • CME 306. Numerical Solution of Partial Differential Equations
  2. Part II
    • CME 302. Numerical Linear Algebra
    • CME 304. Numerical Optimization
  3. Part III
    • CME 305. Discrete Mathematics and Algorithms
    • 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 breadth of knowledge in technical area. The elective course list 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. 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 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 213. Parallel Comp- MPI and CUDA
    • CME 215 A,B. Advanced Computational Fluid Dynamics
    • CME263. Introduction to Linear Dynamical Systems
    • CME 324. Advanced Methods in Matrix Computation
    • CME 342. Parallel Methods in Numerical Analysis
    • CME 364A. Convex Optimization 1
  3. Computer Science:
    • CS 164. Computing with Physical Objects: Algorithms for Shape and Motion
    • CS 205. Mathematical Methods for Robotics, Vision, and Graphics
    • 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 256. Numerical Electromagnetics
    • 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 376A. Information Theory
  5. Management Science and Engineering:
    • MS&E 220. Probabilistic Analysis
    • MS&E 221. Stochastic Modeling
    • MS&E 223. Simulation
    • MS&E 238. Network Structures and Analysis
    • 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. Mathematics:
    • MATH 136. Stochastic Processes
    • MATH 171. Fundamental Concepts of Real Analysis
    • 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
  7. Mechanical Engineering:
    • ME 335A,B,C. Finite Element Analysis
    • ME 346B. Introduction to Molecular Simulations
    • 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
  8. Statistics:
    • STATS 208. Introduction to the Bootstrap
    • STATS 217. Introduction to Stochastic Processes
    • STATS 219. Stochastic Processes
    • 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
  9. Other:
    • CEE 281. Finite Element Structural Analysis
    • CEE 362G. Stochastic Inverse Modeling and Data Assimilation Methods
    • ENGR 209A. Analysis and Control of Nonlinear Systems

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 the student's professional development and research interests.

Requirement 5—3-6 units of programming course work demonstrating programming efficiency.

Requirement 6—3 units of an ICME graduate seminar or other approved seminar. Additional seminar units may not be counted towards the 45-unit requirement.

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