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.
| Computational and Mathematical Engineering | |||||
|---|---|---|---|---|---|
| Number | Title | Instructor | Quarter | Units | Notes |
| CME 100 | Vector Calculus for Engineers | Eric Darve | Autumn | 5 | GER:DB-Math |
| CME 102 | Ordinary Differential Equations for Engineers | Eric Darve | Winter | 5 | GER:DB-Math |
| CME 104 | Linear Algebra and Partial Differential Equations for Engineers | Vadim Khayms | Spring | 5 | GER:DB-Math |
| CME 106 | Introduction to Probability and Statistics for Engineers | Vadim Khayms | Winter | 3 - 4 | GER:DB-Math |
| CME 108 | Introduction to Scientific Computing | James Lambers | Winter | 3 - 4 | GER:DB-EngrAppSci |
| CME 200 | Linear Algebra with Application to Engineering Computations | Parviz Moin | Autumn | 3 | |
Requirement 2
Students must demonstrate breadth of knowledge in the field by completing the following six core courses:
| Computational and Mathematical Engineering | |||||
|---|---|---|---|---|---|
| Number | Title | Instructor | Quarter | Units | Notes |
| CME 302 | Numerical Linear Algebra | Gene Golub | Autumn | 3 | |
| CME 303 | Partial Differential Equations of Applied Mathematics | James Nolen | Autumn | 3 | |
| CME 304 | Numerical Optimization | Walter Murray | Winter | 3 | |
| CME 305 | Discrete Mathematics and Algorithms | Amin Saberi | Winter | 3 | |
| CME 306 | Numerical Solution of Partial Differential Equations | Ron Fedkiw | Spring | 3 | |
| CME 308 | Stochastic Methods in Engineering | Peter Glynn | Spring | 3 | |
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 electives in the eight application areas listed below must be completed. The elective course list represents automatically accepted electives within the program 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 of the student's iCME adviser and the chair of the iCME curriculum committee.
| Aeronautics and Astronautics | |||||
|---|---|---|---|---|---|
| Number | Title | Instructor | Quarter | Units | Notes |
| AA 214A | Numerical Methods in Fluid Mechanics | Tom Pulliam | Autumn | 3 | |
| AA 214B | Numerical Computation of Compressible Flow | Robert MacCormack | Winter | 3 | |
| AA 214C | Numerical Computation of Viscous Flow | Robert MacCormack | Spring | 3 | |
| AA 215B | Advanced Computational Fluid Dynamics | Anthony Jameson | Spring | 3 | |
| AA 218 | Introduction to Symmetry Analysis | Brian Cantwell | Spring | 3 | |
| Civil and Environmental Engineering | |||||
| Number | Title | Instructor | Quarter | Units | Notes |
| CEE 281 | Finite Element Structural Analysis | Staff | Spring | 3 - 4 | |
| Computational and Mathematical Engineering | |||||
| Number | Title | Instructor | Quarter | Units | Notes |
| CME 204 | Partial Differential Equations in Engineering | Eric Shaqfeh | Winter | 3 | |
| CME 208 | Mathematical Programming and Combinatorial Optimization | Amin Saberi | Winter | 3 | |
| CME 210 | Multiscale Methods in Engineering | Eric Darve | 3 | ||
| CME 212 | Introduction to Large-Scale Computing in Engineering | James Lambers | Winter | 3 | |
| CME 215A | Advanced Computational Fluid Dynamics | Anthony Jameson | Winter | 3 | |
| CME 300 | Departmental Seminar Series | Walter Murray | Winter | 1 | Will meet in Durand 450 on 1/11/2008 and in Terman 453 for the rest of the quarter from 4:00-5:00pm. |
| CME 324 | Advanced Methods in Matrix Computation: Iterative Methods | Gene Golub | 3 | Not given this year | |
| CME 325 | Numerical Approximations of Partial Differential Equations in Theory and Practice | Staff | Winter | 1 - 2 | Abbreviated meeting pattern: from January 31 to March 8 only. Please be aware that even though the course is starting late, the normal add/drop deadlines will apply. |
| CME 326 | Numerical Methods for Initial Boundary Value Problems | Staff | Winter | 3 | Not given this year |
| CME 330 | Applied Mathematics in the Chemical and Biological Sciences | Eric Shaqfeh | Autumn | 3 | |
| CME 332 | Computational Methods for Scientific Reasoning and Discovery | Pat Langley | 3 | Not given this year | |
| CME 334 | Advanced Methods in Numerical Optimization | Walter Murray | Autumn | 3 | |
| CME 336 | Linear and Conic Optimization with Applications | Yinyu Ye | Autumn | 3 | Not given this year |
| CME 337 | Information Networks | Amin Saberi | Autumn | 3 | Not given this year |
| CME 338 | Large-Scale Numerical Optimization | Michael Saunders | Spring | 3 | |
| CME 340 | Computational Methods in Data Mining | Sep Kamvar | Winter | 1 - 3 | |
| CME 342 | Parallel Methods in Numerical Analysis | Staff | Spring | 3 | |
| CME 346A | Introduction to Molecular Simulations | Eric Darve | Spring | 3 | |
| CME 352 | Molecular Algorithms | Ashish Goel | Winter | 3 | |
| CME 380 | Constructing Scientific Simulation Codes | Patrick Miller | Spring | 3 | This class is web based; it will use podcasts and Skype videocasts to deliver the material. See http://wilkinson.stanford.edu/cme380 |
| CME 444 | Computational Consulting | Margot Gerritsen | Spring | 7 | |
| CME 500 | Numerical Analysis and Computational and Mathematical Engineering Seminar | Amin Saberi | Spring | 1 | |
| CME 510 | Linear Algebra and Optimization Seminar | Michael Saunders | Spring | 1 | |
| Computer Science | |||||
| Number | Title | Instructor | Quarter | Units | Notes |
| CS 205 | Mathematical Methods for Robotics, Vision, and Graphics | Ron Fedkiw | Autumn | 3 | |
| CS 221 | Artificial Intelligence: Principles and Techniques | Andrew Ng | Autumn | 3 - 4 | |
| CS 228 | Probabilistic Models in Artificial Intelligence | Daphne Koller | Winter | 3 | |
| CS 229 | Machine Learning | Andrew Ng | Autumn | 3 | |
| CS 255 | Introduction to Cryptography | Dan Boneh | Winter | 3 | |
| CS 261 | Optimization and Algorithmic Paradigms | Serge Plotkin | Winter | 3 | |
| CS 315A | Parallel Computer Architecture and Programming | Kunle Olukotun | Winter | 3 | |
| CS 348A | Computer Graphics: Geometric Modeling | Leo Guibas | Autumn | 3 | |
| CS 365 | Randomized Algorithms | Rajeev Motwani | Autumn | 3 | |
| Electrical Engineering | |||||
| Number | Title | Instructor | Quarter | Units | Notes |
| EE 222 | Applied Quantum Mechanics I | Staff | Autumn | 3 | |
| EE 223 | Applied Quantum Mechanics II | David Miller | Winter | 3 | |
| EE 262 | Two-Dimensional Imaging | Staff | 3 | Not given this year | |
| EE 278 | Introduction to Statistical Signal Processing | Abbas El Gamal | Spring | 3 | |
| EE 292E | Analysis and Control of Markov Chains | Staff | 3 | Not given this year | |
| EE 363 | Linear Dynamic Systems | Staff | 3 | Not given this year | |
| EE 364 | Convex Optimization | Stephen Boyd | 3 | Not given this year | |
| EE 376A | Information Theory | Tsachy Weissman | Winter | 3 | |
| Engineer | |||||
| Number | Title | Instructor | Quarter | Units | Notes |
| ENGR 209A | Analysis and Control of Nonlinear Systems | Stephen Rock | Winter | 3 | |
| Management Science and Engineering | |||||
| Number | Title | Instructor | Quarter | Units | Notes |
| MS&E 220 | Probabilistic Analysis | Sam Chiu | Autumn | 3 - 4 | |
| MS&E 221 | Stochastic Modeling | Ramesh Johari | Winter | 3 | |
| MS&E 223 | Simulation | Peter Haas | Spring | 3 | |
| MS&E 251 | Stochastic Decision Models | Staff | Winter | 3 | |
| MS&E 310 | Linear Programming | Yinyu Ye | Autumn | 3 | |
| MS&E 313 | Vector Space Optimization | David Luenberger | Autumn | 3 | |
| MS&E 316 | Stochastic Systems | Peter Glynn | Spring | 3 | |
| MS&E 323 | Stochastic Simulation | Peter Glynn | 3 | Not given this year | |
| Mathematics | |||||
| Number | Title | Instructor | Quarter | Units | Notes |
| MATH 220B | Partial Differential Equations of Applied Mathematics | Tai-Ping Liu | Winter | 3 | |
| Mechanical Engineering | |||||
| Number | Title | Instructor | Quarter | Units | Notes |
| ME 335A | Finite Element Analysis | Peter Pinsky | Winter | 3 | |
| ME 335B | Finite Element Analysis | Peter Pinsky | Spring | 3 | |
| ME 335C | Finite Element Analysis | Peter Pinsky | 3 | Not given this year | |
| ME 469A | Computational Methods in Fluid Mechanics | Staff | Winter | 3 | |
| ME 469B | Computational Methods in Fluid Mechanics | Staff | Spring | 3 | |
| ME 484 | Computational Methods in Cardiovascular Bioengineering | Charles Taylor | Spring | 3 | |
| Statistics | |||||
| Number | Title | Instructor | Quarter | Units | Notes |
| STATS 227 | Statistical Computing | Staff | 3 | Not given this year | |
| STATS 237 | Time Series Modeling and Forecasting | Staff | Summer | 3 | |
| STATS 250 | Mathematical Finance | George Papanicolaou | Winter | 3 | |
| STATS 345 | Computational Molecular Biology | Wing Wong | Autumn | 2 - 3 | |
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.



