https://exploredegrees.stanford.edu/schoolofengineering/instituteforcomputationalandmathematicalengineering/#masterstext
This track is designed for students interested in studying and developing computational tools in those aspects of applied mathematics central to modeling in the physical and engineering sciences. The curriculum consists of core computational and mathematical engineering courses and programming course work, extensive breadth and depth electives, and seminars. Core courses provide instruction in mathematical and computational tools applicable to a wide range of scientific, industrial and engineering disciplines and augment breadth and depth electives of one’s choosing. The programming requirement ensures proficiency in scientific computing and professional computing skills. Seminars highlight emerging research in engineering and sciences.
Requirements
A candidate is required to complete a program of 45 units of courses numbered 200 or above. Courses below 200 level 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.
Requirement 1: Foundational (12 units)
Students must demonstrate foundational knowledge in the field by completing four of the six core courses. Courses in this area must be taken for letter grades.
| Units | ||
|---|---|---|
| CME 302 | Numerical Linear Algebra | 3 |
| CME 303 | Partial Differential Equations of Applied Mathematics | 3 |
| CME 305 | Discrete Mathematics and Algorithms | 3 |
| CME 306 | Numerical Solution of Partial Differential Equations | 3 |
| CME 307 | Optimization | 3 |
| or CME 364A | Convex Optimization I | |
| CME 308 | Stochastic Methods in Engineering | 3 |
| or CME 298 | Basic Probability and Stochastic Processes with Engineering Applications | |
Requirement 2: Programming (3 units)
To ensure that students have a strong foundation in programming, three units of advanced scientific programming for letter grade at the level of CME 212 is required. Programming proficiency at the level of CME 211 is a hard prerequisite; CME 211 can be applied towards the elective requirement.
| Units | ||
|---|---|---|
| CME 211 | Software Development for Scientists and Engineers (*can only be counted as an elective) | 3 |
| CME 212 | Advanced Software Development for Scientists and Engineers | 3 |
Requirement 3: Breadth Electives (18 units)
18 units of general electives to demonstrate breadth of knowledge in technical areas. 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. It is recommended that the selected courses include offerings from (at least) two engineering departments, in addition to CME course work. Courses outside this list can be accepted as electives subject to approval by the student’s program adviser. Six units of independent research can be used to fulfill this requirement with prior approval.
| Units | ||
|---|---|---|
| Aeronautics and Astronautics | ||
| AA 214C | Numerical Computation of Viscous Flow | 3 |
| AA 218 | Introduction to Symmetry Analysis | 3 |
| Computational and Mathematical Engineering | ||
| CME 215A/215B | Advanced Computational Fluid Dynamics | 3 |
| CME 263 | Introduction to Linear Dynamical Systems | 3 |
| CME 279 | Computational Biology: Structure and Organization of Biomolecules and Cells | 3 |
| CME 342 | Parallel Methods in Numerical Analysis | 3 |
| CME 364A | Convex Optimization I | 3 |
| CME 371 | Computational Biology in Four Dimensions | 3 |
| Computer Science | ||
| CS 221 | Artificial Intelligence: Principles and Techniques | 3-4 |
| CS 228 | Probabilistic Graphical Models: Principles and Techniques | 3-4 |
| CS 229 | Machine Learning | 3-4 |
| CS 255 | Introduction to Cryptography | 3 |
| CS 261 | Optimization and Algorithmic Paradigms | 3 |
| CS 340 | Topics in Computer Systems | 3-4 |
| CS 348A | Computer Graphics: Geometric Modeling & Processing | 3-4 |
| Electrical Engineering | ||
| EE 223 | Applied Quantum Mechanics II | 3 |
| EE 256 | Numerical Electromagnetics | 3 |
| Management Science and Engineering | ||
| MS&E 220 | Probabilistic Analysis | 3-4 |
| MS&E 221 | Stochastic Modeling | 3 |
| MS&E 223 | Simulation | 3 |
| MS&E 226 | Fundamentals of Data Science: Prediction, Inference, Causality | 3 |
| MS&E 251 | ||
| MS&E 310 | Linear Programming | 3 |
| MS&E 316 | Discrete Mathematics and Algorithms | 3 |
| MS&E 321 | Stochastic Systems | 3 |
| MS&E 322 | Stochastic Calculus and Control | 3 |
| Mathematics | ||
| MATH 136 | Stochastic Processes | 3 |
| MATH 171 | Fundamental Concepts of Analysis | 3 |
| MATH 221B | Mathematical Methods of Imaging | 3 |
| MATH 236 | Introduction to Stochastic Differential Equations | 3 |
| MATH 238 | Mathematical Finance | 3 |
| Mechanical Engineering | ||
| ME 335A/335B/335C | Finite Element Analysis | 3 |
| ME 346B | Introduction to Molecular Simulations | 3 |
| ME 408 | Spectral Methods in Computational Physics | 3 |
| ME 469 | Computational Methods in Fluid Mechanics | 3 |
| Statistics | ||
| STATS 208 | Bootstrap, Cross-Validation, and Sample Re-use | 3 |
| STATS 217 | Introduction to Stochastic Processes I | 3 |
| STATS 219 | Stochastic Processes | 3 |
| STATS 250 | Mathematical Finance | 3 |
| STATS 305A | Applied Statistics I | 3 |
| STATS 310A/310B/310C | Theory of Probability I | 3 |
| STATS 362 | Topic: Monte Carlo | 3 |
| Other | ||
| CEE 281 | Mechanics and Finite Elements | 3 |
| CEE 362G | Imaging with Incomplete Information | 3-4 |
| ECON 293 | Machine Learning and Causal Inference | 3 |
| ENGR 209A | Analysis and Control of Nonlinear Systems | 3 |
Requirement 4: Specialized Electives (9 units)
Nine units of focused graduate application electives approved by the program 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: Seminar (3 units)
One seminar unit must come from CME 500; two units are up to the student's choice of ICME graduate seminars or other approved seminars. Additional seminar units may not be counted towards the 45-unit requirement.