Master of Science
The M.S. program in Computational and Mathematical Engineering is very unique. In today's world of virtual research, "mathematical modeling" will be the key word. iCME leverages a deep background in mathematical modeling with exceptional breadth in traditional science and engineering fields. It is also an excellent preparation for future entry into a Ph.D. program at Stanford or elsewhere. Individual programs can be customized to enhance any area of physical sciences or traditional engineering fields.
The M.S. degree in Computational and Mathematical Engineering may be a terminal degree or a stepping stone 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 may transfers to the Ph.D. program after the first academic year and will be considered a second year Ph.D. student.
The master's program consists of 45 units of course work taken at Stanford, which usually takes between 4 and 6 quarters to complete. The core course requirements are identical to those for the Ph.D. program. 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.
Requirements
A candidate is required to complete a program of 45 units of courses numbered 200 or above. 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, 130, 220A; CS 106A, 106X, 108, 205, 229, 237B; ENGR 62; ME 346, 355A, 355B; MS&E 211, 310, 311, 312, 314, 315; STATS 116 or 202.
Requirement 2
Students must demonstrate breadth of knowledge in the field by completing the following six 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.
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 iCME graduate adviser, in the areas of Engineering, Mathematics, and Physical, Biological, and other quantitative sciences.
Requirement 5
3 units of iCME Colloquium (CME 500) or other approved seminar sequence.