https://exploredegrees.stanford.edu/schoolofengineering/instituteforcomputationalandmathematicalengineering/#masterstext
Master of Science in Computational and Mathematical Engineering
The University’s basic requirements for the M.S. degree are discussed in the "Graduate Degrees" section of this bulletin. The following are specific departmental requirements.
The master's degree in Computational and Mathematical Engineering is intended as a terminal professional degree and does not lead to the Ph.D. program. While there is a M.S. to Ph.D. option, students interested in the doctoral program are strongly encouraged to apply directly to the Ph.D. program.
Admission
Prospective applicants should consult the Graduate Admissions and the ICME admissions web pages for complete information on admission requirements and deadlines.
Applications to the M.S. program and all supporting documents must be submitted and received online by January 12, 2021, the deadline published on the ICME admissions web page.
See below for information on the M.S. to Ph.D. program petition process.
Prerequisites
Fundamental courses in mathematics and computing may be needed as prerequisites for other courses in the program. Check the prerequisites of each required course. Recommended preparatory courses include advanced undergraduate level courses in linear algebra, probability, differential equations, stochastics, and numerical methods and proficiency in programming.
Financial Assistance
The department awards a limited number of fellowships, course assistantships, and research assistantships to incoming graduate students. Most course assistantships and research assistantships are awarded to students in the doctoral program in ICME. If there is an insufficient number of Ph.D. students to staff all course and research assistantship positions available, these positions may be open to master’s students. However, master’s students are not guaranteed financial assistance.
Coterminal Master's Program
Stanford undergraduates who want to apply for the coterminal master's degree must submit their application no later than eight weeks before the start of the proposed admit quarter. The application must give evidence that the student possesses a potential for strong academic performance at the graduate level. Graduate Record Examination (GRE) General Test scores are required for application review. A student is eligible to apply for admission once the following conditions have been met:
- completion of six non-Summer quarters at Stanford or two non-Summer quarters at Stanford for transfer students
- completion of 120 units toward graduation (UTG) as shown on the undergraduate transcript, including transfer, Advanced Placement exam, and other external test credit
- declaration of an undergraduate major
University Coterminal Requirements
Coterminal master’s degree candidates are expected to complete all master’s degree requirements as described in this bulletin. University requirements for the coterminal master’s degree are described in the “Coterminal Master’s Program” section. University requirements for the master’s degree are described in the "Graduate Degrees" section of this bulletin.
After accepting admission to this coterminal master’s degree program, students may request transfer of courses from the undergraduate to the graduate career to satisfy requirements for the master’s degree. Transfer of courses to the graduate career requires review and approval of both the undergraduate and graduate programs on a case by case basis.
In this master’s program, courses taken two quarters prior to the first graduate quarter, or later, are eligible for consideration for transfer to the graduate career. No courses taken prior to the first quarter of the sophomore year may be used to meet master’s degree requirements.
Course transfers are not possible after the bachelor’s degree has been conferred.
The University requires that the graduate advisor be assigned in the student’s first graduate quarter even though the undergraduate career may still be open. The University also requires that the Master’s Degree Program Proposal be completed by the student and approved by the department by the end of the student’s first graduate quarter.
Requirements for the Master of Science in Computational and Mathematical Engineering
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. Although there is no specific background requirement, significant exposure to mathematics and engineering course work is necessary for successful completion of the program.
There are five tracks in the master's program:
- General CME
- Computational Geosciences
- Data Science
- Imaging Science
- Mathematical and Computational Finance
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 | Introduction to Stochastic Control with Applications | 3 |
| 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.
The Computational Geosciences (CompGeo) track is designed for students interested in the skills and knowledge required to develop efficient and robust numerical solutions to Earth Science problems using high-performance computing. The CompGeo curriculum is based on four fundamental areas: modern programming methods for Science and Engineering, applied mathematics with an emphasis on numerical methods, algorithms and architectures for high-performance computing and computationally oriented Earth Sciences courses. Earth Sciences/computational project courses give practice in applying methodologies and concepts. CompGeo students are required to complete general and focused application electives (Requirements 3 and 4) from the approved list of courses from the Computational Geosciences program. All other requirements remain the same as set forth above.
Note: Students interested in pursuing the ICME M.S. in the Computational Geosciences (CompGeo) track are encouraged to contact the Computational Geosciences program director before applying.
Students are required to take 45 units of course work, and research credits to earn a master's degree in Computational Geosciences track. The course work follows the requirements of the ICME M.S. degree as above with additional restrictions placed on the general and focused electives.
Requirement 1: Foundational (12 units)
Identical to the general CME master’s track requirement; see above.
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 used as an elective) | 3 |
| CME 212 | Advanced Software Development for Scientists and Engineers | 3 |
| GEOPHYS 257 | Introduction to Computational Earth Sciences | 2-4 |
Requirement 3: Breadth Electives in Geosciences (18 units)
18 units of general electives to demonstrate breadth of knowledge in technical area. Courses are currently offered but are not limited to the following specific areas of the School of Earth Sciences:
- Reservoir Simulation
- Geophysical Imaging
- Tectonophysics/Geomechanics
- Climate/Atmosphere/Ocean
- Ecology/Geobiology.
The Earth Science courses, offered in EESS, ERE, GES, and Geophysics, are selected based on the area of the student's interest and their research/thesis work, along with the advice and consent of the student's adviser. Students are encouraged to choose a range of courses in order to guarantee breadth of knowledge in Earth Sciences. A maximum of one non-computationally-oriented course can be counted towards the master’s degree requirements. Following is a list of recommended courses (grouped by area) that can be taken to fulfill the Geosciences course requirement.
| Units | ||
|---|---|---|
| Environmental/Climate/Hydrogeology | ||
| ESS 220 | Physical Hydrogeology | 4 |
| ESS 221 | Contaminant Hydrogeology and Reactive Transport | 3 |
| ESS 246B | Atmosphere, Ocean, and Climate Dynamics: the Ocean Circulation | 3 |
| CEE 262A | Hydrodynamics | 3-4 |
| CEE 262B | Transport and Mixing in Surface Water Flows | 3-4 |
| CEE 262C | Coastal Ocean Modeling | 3 |
| CEE 263A | Air Pollution Modeling | 3-4 |
| CEE 361 | Turbulence Modeling for Environmental Fluid Mechanics | 2-4 |
| Geophysical Imaging | ||
| EE 256 | Numerical Electromagnetics | 3 |
| GEOPHYS 210 | Basic Earth Imaging | 2-3 |
| GEOPHYS 211 | Environmental Soundings Image Estimation | 3 |
| GEOPHYS 280 | 3-D Seismic Imaging | 2-3 |
| GEOPHYS 287 | Earthquake Seismology | 3-5 |
| General Computational/Mathematical Geoscineces | ||
| CEE 362G | Imaging with Incomplete Information | 3-4 |
| CHEM 275 | Advanced Physical Chemistry - Single Molecules and Light | 3 |
| CME 372 | Applied Fourier Analysis and Elements of Modern Signal Processing | 3 |
| CME 321B | Mathematical Methods of Imaging | 3 |
| ESS 211 | Fundamentals of Modeling | 3-5 |
| ENERGY 291 | Optimization of Energy Systems | 3-4 |
| ME 335A | Finite Element Analysis | 3 |
| ME 346B | Introduction to Molecular Simulations | 3 |
| ME 361 | Turbulence | 3 |
| ME 469 | Computational Methods in Fluid Mechanics | 3 |
| Reservoir Simulation/Fluid Flow | ||
| ENERGY 223 | Reservoir Simulation | 3-4 |
| ENERGY 224 | Advanced Reservoir Simulation | 3 |
| Subsurface/Reservoir Characterization | ||
| ENERGY 241 | Seismic Reservoir Characterization | 3-4 |
| GEOPHYS 202 | Reservoir Geomechanics | 3 |
| GEOPHYS 260 | Rock Physics for Reservoir Characterization | 3 |
| Structural/Tectonophysics/Geomechanics | ||
| GEOPHYS 220 | Ice, Water, Fire | 3-5 |
| GEOPHYS 288A | Crustal Deformation | 3-5 |
| GEOPHYS 288B | Crustal Deformation | 3-5 |
| GEOPHYS 290 | Tectonophysics | 3 |
Requirement 4: Practical Component (9 units)
9 units of focused research in computational geosciences. Students are required to either complete a Research Project or an Internship as described below.
| Units | ||
|---|---|---|
| Internship and/or Research Project, enrolling in a course such as: | ||
| EARTH 400 | Directed Research | 3 |
| EARTH 401 | Curricular Practical Training | 1 |
Research Project
Students who plan to apply to the Ph.D. program need to take 9 units of research. Students will work with the CompGeo program director to find an appropriate adviser and research topic and then enroll in EARTH 400 Directed Research (or a similar SES research course). The successful outcome of a Research Project can be:
- an oral presentation at an international meeting requiring an extended abstract
- a publication submission in a peer reviewed journal.
- a written report
Internship
As an alternative to the Research Project, students have the option of an internship which is recommended for those students interested in a terminal degree. The individual student is responsible for securing and organizing the internship and is required to obtain a faculty adviser and submit a written report on the internship project. Credit for the internship will be obtained through EARTHSCI 401: Curricular Practical Training (1 unit) and in this case only 8 units of research are required.
Requirement 5: Seminar (3 units)
Three units of ICME graduate seminars or other approved seminars. Additional seminar units may not be counted towards the 45-unit requirement. One of the required seminars for CompGeo must be a seminar course chosen in concert with the student's academic adviser among the seminars offered by the the School of Earth, Energy and Environmental Sciences.
The Data Science track develops strong mathematical, statistical, computational and programming skills through the foundational and programming requirements. In addition, it provides a fundamental data science education through general and focused electives requirement from courses in data sciences and related areas. DS track covers both computational data science and machine learning but can be tailored to be more focused on one of the two areas by taking more credits in that concentration (requirement 3 or 4). Course choices are limited to predefined courses from the data sciences and related courses group for requirements 1-5.
Requirement 1: Mathematical and Statistical Foundations (15 units)
Students must demonstrate foundational knowledge in the field by completing the following courses. Courses in this area must be taken for letter grades.
| Units | ||
|---|---|---|
| CME 302 | Numerical Linear Algebra | 3 |
| CME 308 | Stochastic Methods in Engineering | 3 |
| STATS 200 | Introduction to Statistical Inference | 3 |
| or STATS 300A | Theory of Statistics I | |
| STATS 203 | Introduction to Regression Models and Analysis of Variance | 3 |
| or STATS 305A | Applied Statistics I | |
| STATS 315A | Modern Applied Statistics: Learning | 3 |
| or CS/STATS 229 | Machine Learning | |
Requirement 2: Experimentation (3 units)
Experimental method and causal considerations are fundamental to data science. The course chosen from this area must be taken for letter grades.
| STATS 263 | Design of Experiments | 3 |
| ECON 271 | Intermediate Econometrics II (3 units only) | 2-5 |
| or MS&E 327 | Topics in Causal Inference | |
*If both courses are taken, the additional 3 units can count towards the “Machine Learning Methods and Applications” requirement below.
Requirement 3: Scientific Computing (6-12 units)
To ensure that students have a strong foundation in programming, 3 units of scientific software development (CME212) and 3 units from scientific computing foundations and methods for letter grades is required. CME offers a placement test that can be used to directly enroll in CME 212. Students who pass this placement test are not required to take CME 211. Students can choose to take up to six additional units from this group of courses.
*Students must take 6 units from Requirement 3 and 6 units from Requirement 4, with an additional 6 units from either Requirement 3 or 4, for a total of 18 units in the two areas. The additional 6 units may be taken for a non-letter grade.
| Units | ||
|---|---|---|
| Software Development; take 3 units | ||
| CME 211 | Software Development for Scientists and Engineers | 3 |
| CME 212 | Advanced Software Development for Scientists and Engineers | 3 |
| Scientific Computing Foundations and Methods; take 3 units | ||
| CME 213 | Introduction to parallel computing using MPI, openMP, and CUDA (Scientific Computing Foundations and Methods; take 3 units) | 3 |
| CME 305 | Discrete Mathematics and Algorithms | 3 |
| CME 307 | Optimization | 3 |
| CME 323 | Distributed Algorithms and Optimization | 3 |
| CME 364A | Convex Optimization I | 3 |
| CS 246 | Mining Massive Data Sets | 3-4 |
Requirement 4: Machine Learning Methods and Applications (6-12 units)
Six units of coursework from this area is required and should be taken for letter grades. Students can also choose to take up to six additional units from this group of courses.
*Students must take 6 units from Requirement 3 and 6 units from Requirement 4, with an additional 6 units from either Requirement 3 or 4, for a total of 18 units in the two areas. The additional 6 units may be taken for a non-letter grade.
Courses in this area must be taken for letter grades.
| STATS 231 | ||
| STATS 315B | Modern Applied Statistics: Data Mining | 3 |
| CS 221 | Artificial Intelligence: Principles and Techniques | 3-4 |
| CS 224N | Natural Language Processing with Deep Learning | 3-4 |
| CS 230 | Deep Learning | 3-4 |
| CS 231N | Convolutional Neural Networks for Visual Recognition | 3-4 |
| CS 234 | Reinforcement Learning | 3 |
| CS 236 | Deep Generative Models | 3 |
Requirement 5: Practical component (3 units)
Students are required to take 3 units of practical component that may include any combination of:
-
Analytics Accelerator(CME 217)
-
Master's Research(CME 291): a research project, supervised by a faculty member and approved by the adviser; should be taken for letter grade only. The research project should be computational in nature. Students should submit a one-page proposal, supported by the faculty member, to ICME student services for approval at least one quarter before.
-
Other courses that have a strong hands-on and practical component, such as STATS 390 Consulting Workshop up to 1unit.
Students must take 6 units of additional electives from graduate-level engineering and science courses (a maximum of 3units of research including practical component or seminar) for a total of 45 units to earn the degree.
The Imaging Science track is designed for students interested in the skills and knowledge required to develop efficient and robust computational tools for imaging science. The curriculum is based on four fundamental areas: mathematical models and analysis for imaging sciences and inverse problems, tools and techniques from modern imaging sciences from medicine, biology, physics/chemistry, and earth science, algorithms in numerical methods and scientific computing and high performance computing skills and architecture oriented towards imaging sciences.
The course work follows the requirements of the general master's degree in the core course requirement. The general and focused elective requirements (requirements 3 and 4 below) are limited to approved courses listed below. Programming requirement (requirement 2) is extended to 6 units and includes course work in advanced scientific programming and high performance computing.
Requirement 1: Foundational (12 units)
Identical to the general ICME master’s program; see above.
Requirement 2: Programming (6 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 and three units of parallel computing for letter grade are required. Programming proficiency at the level of CME 211 is a hard prerequisite for CME 212; CME 211 can be applied towards the elective requirement.
| Units | ||
|---|---|---|
| CME 211 | Software Development for Scientists and Engineers (*can only be used as an elective) | 3 |
| Advanced Scientific Programming; take 3 units | ||
| CME 212 | Advanced Software Development for Scientists and Engineers | 3 |
| CME 214 | Software Design in Modern Fortran for Scientists and Engineers | 3 |
| Parallel /HPCComputing; take 3 units | ||
| CME 213 | Introduction to parallel computing using MPI, openMP, and CUDA | 3 |
| CME 323 | Distributed Algorithms and Optimization | 3 |
| CME 342 | Parallel Methods in Numerical Analysis | 3 |
| GEOPHYS 257 | Introduction to Computational Earth Sciences | 2-4 |
Requirement 3: Imaging Sciences electives (18 units)
Imaging Sciences electives should demonstrate breadth of knowledge in the technical area. The elective course list is defined. 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 | ||
|---|---|---|
| Take 18 units of the following: | ||
| APPPHYS 232 | Advanced Imaging Lab in Biophysics | 4 |
| BIOE 220 | Introduction to Imaging and Image-based Human Anatomy | 3 |
| CEE 362G | Imaging with Incomplete Information | 3-4 |
| CME 279 | Computational Biology: Structure and Organization of Biomolecules and Cells | 3 |
| CME 371 | Computational Biology in Four Dimensions | 3 |
| CS 231N | Convolutional Neural Networks for Visual Recognition | 3-4 |
| CS 237A | Principles of Robot Autonomy I | 3-4 |
| EARTHSYS 242 | Remote Sensing of Land | 4 |
| EE 236A | Modern Optics | 3 |
| EE 262 | Three-Dimensional Imaging | 3 |
| EE 355 | Imaging Radar and Applications | 3 |
| EE 367 | Computational Imaging and Display | 3 |
| EE 368 | Digital Image Processing | 3 |
| EE 369A | Medical Imaging Systems I | 3 |
| EE 369B | Medical Imaging Systems II | 3 |
| EE 369C | Medical Image Reconstruction | 3 |
| GEOPHYS 210 | Basic Earth Imaging | 2-3 |
| GEOPHYS 211 | Environmental Soundings Image Estimation | 3 |
| GEOPHYS 280 | 3-D Seismic Imaging | 2-3 |
| MATH 221B | Mathematical Methods of Imaging | 3 |
| MATH 262 | Applied Fourier Analysis and Elements of Modern Signal Processing | 3 |
| PSYCH 204A | Human Neuroimaging Methods | 3 |
Requirement 4: Specialized electives (6 units)
6 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: 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.
The Mathematical & Computational Finance (MCF) track is an interdisciplinary program that provides education in applied and computational mathematics, statistics, and financial applications for individuals with strong mathematical skills. Upon successful completion of the MCF track in the ICME master's program, students will be prepared to assume positions in the financial industry as data and information scientists, quantitative strategists, risk managers, regulators, financial technologists, or to continue on to advanced graduate work in applied mathematics, statistics, finance, and other disciplines.
The Institute for Computational and Mathematical Engineering, in close cooperation with Mathematics, Management Science and Engineering and Statistics provides many of the basic courses.
Requirement 1: Foundational (9 units)
Students must demonstrate foundational knowledge in the field by completing the following core courses. Courses in this area must be taken for letter grades.
| Units | ||
|---|---|---|
| CME 302 | Numerical Linear Algebra | 3 |
| or CME 303 | Partial Differential Equations of Applied Mathematics | |
| or CME 305 | Discrete Mathematics and Algorithms | |
| CME 307 | Optimization | 3 |
| or CME 364A | Convex Optimization I | |
| CME 308 | Stochastic Methods in Engineering | 3 |
| or MATH 236 | Introduction to Stochastic Differential Equations | |
Requirement 2: Programming (6-9 units)
To ensure that students have a strong foundation in programming, six units of advanced programming for letter grade at the level of CME 212 and three units of parallel computing for letter grade are required. Programming proficiency at the level of CME 211 is a hard prerequisite for CME 212.
| Units | ||
|---|---|---|
| Advanced Scientific Programming; take 3-6 units | ||
| CME 211 | Software Development for Scientists and Engineers | 3 |
| CME 212 | Advanced Software Development for Scientists and Engineers | 3 |
| CME 214 | Software Design in Modern Fortran for Scientists and Engineers | 3 |
| Parallel/HPC Computing; take 3 units | ||
| CME 213 | Introduction to parallel computing using MPI, openMP, and CUDA | 3 |
| CME 323 | Distributed Algorithms and Optimization | 3 |
| CME 342 | Parallel Methods in Numerical Analysis | 3 |
| CS 149 | Parallel Computing | 3-4 |
| CS 315B | Parallel Computing Research Project | 3 |
| CS 316 | Advanced Multi-Core Systems | 3 |
Requirement 3: Finance electives (9 units)
Choose three courses from the following list. Courses outside this list can be accepted as electives subject to approval by the student’s program adviser.
| Units | ||
|---|---|---|
| Financial Mathematics | ||
| MATH 238 | Mathematical Finance | 3 |
| Financial Markets | ||
| FINANCE 320 | Debt Markets | 3 |
| FINANCE 620 | Financial Markets I | 3 |
| FINANCE 622 | Dynamic Asset Pricing Theory | 4 |
| Other | ||
| CS 251 | Cryptocurrencies and blockchain technologies | 3 |
| MS&E 245B | Advanced Investment Science | 3 |
| MS&E 347 | Credit Risk: Modeling and Management | 3 |
| MS&E 348 | Optimization of Uncertainty and Applications in Finance | 3 |
| MS&E 349 | Financial Statistics | 3 |
| STATS 240 | Statistical Methods in Finance | 3 |
| STATS 241 | Data-driven Financial Econometrics | 3 |
| STATS 244 | Quantitative Trading: Algorithms, Data, and Optimization | 2-4 |
Requirement 4: Data Science electives (12 units)
Data Science electives should demonstrate breadth of knowledge in the technical area. Courses outside this list can be accepted as electives subject to approval by the student’s program adviser.
| Units | ||
|---|---|---|
| Statistical Modeling | ||
| STATS 200 | Introduction to Statistical Inference | 3 |
| STATS 203 | Introduction to Regression Models and Analysis of Variance | 3 |
| STATS 205 | Introduction to Nonparametric Statistics | 3 |
| STATS 206 | Applied Multivariate Analysis | 3 |
| STATS 207 | Introduction to Time Series Analysis | 3 |
| STATS 270 | A Course in Bayesian Statistics | 3 |
| STATS 285 | Massive Computational Experiments, Painlessly | 2 |
| STATS 290 | Computing for Data Science | 3 |
| STATS 305A | Applied Statistics I | 3 |
| STATS 305B | Applied Statistics II: Generalized Linear Models, Survival Analysis, and Exponential Families | 3 |
| STATS 305C | Applied Statistics III | 3 |
| STATS 361 | Causal Inference | 3 |
| Learning | ||
| CME 241 | Reinforcement Learning for Stochastic Control Problems in Finance | 3 |
| CS 224N | Natural Language Processing with Deep Learning | 3-4 |
| CS 230 | Deep Learning | 3-4 |
| CS 246 | Mining Massive Data Sets | 3-4 |
| EE 277 | Reinforcement Learning: Behaviors and Applications | 3 |
| MS&E 338 | Reinforcement Learning: Frontiers | 3 |
| STATS 315A | Modern Applied Statistics: Learning | 3 |
| STATS 315B | Modern Applied Statistics: Data Mining | 3 |
| Other | ||
| MS&E 349 | Financial Statistics | 3 |
| STATS 240 | Statistical Methods in Finance | 3 |
| STATS 241 | Data-driven Financial Econometrics | 3 |
Requirement 5: Practical component (6 units)
Students are required to take six units of practical and project courses ONLY from the courses listed below.
| Units | ||
|---|---|---|
| CS 349F | Technology for Financial Systems | 1 |
| CME 241 | Reinforcement Learning for Stochastic Control Problems in Finance | 3 |
| CME 291 | Master's Research | 1-6 |
| MS&E 246 | Financial Risk Analytics | 3 |
| MS&E 448 | Big Financial Data and Algorithmic Trading | 3 |
Petition Process for Transfer from M.S. to Ph.D. Degree Program
Students admitted to ICME graduate programs are enrolled specifically either into the terminal M.S. or the Ph.D. program. Admission to the Ph.D. program is required for a student to be eligible to work towards the Ph.D. degree.
A student in the terminal M.S. program may petition to be admitted to the Ph.D. program by filing an M.S. to Ph.D. petition form. Petition must include (1) a one-page statement of purpose explaining why the student wishes to transfer to the Ph.D. program, (2) the most recent unofficial transcript, and (3) two letters of recommendation from members of the Stanford faculty, including one from the student’s potential research adviser and at least one from an ICME faculty member belonging to the Academic Council. The M.S. to Ph.D. petition to transfer must be submitted to the student services office before the end of the spring quarter of the first year in the M.S. program.
Students who wish to submit a petition to add the Ph.D. degree, should plan to complete 18 units of the ICME core classes (CME 302, 303, 305, 306, 307, 308) for letter grade and pass the ICME qualifying exam before the beginning of their second year. If the petition is approved, all the other requirements of the Ph.D. program described in the bulletin apply, i.e. filing for candidacy, securing a PhD advisor, satisfactory degree progress and degree completion.
Transferring to the Ph.D. program is a competitive process and only highly qualified M.S. students may be admitted. Student’s original application to the graduate program as well as the materials provided for the transfer petition are reviewed. Students must adhere to requirements for the terminal M.S. degree, and plan to confer the M.S. degree in the event that the Ph.D. petition to transfer is not approved.
M.S. to Ph.D. option requirements:
- Have a cumulative GPA of 3.5 or higher.
- Earn B+ plus or higher grade on all six core courses in the first year.
- Pass all six topics of the qualifying exam before the beginning of the second year.
- Complete a minimum of six units of research rotations in years one and two. CME 291 can be taken for three units at a time for credit/no credit.
- Identify and align with a doctoral dissertation adviser before the end of winter quarter of second year who will act as research supervisor and provide funding through the completion of the program.
- Submit a petition to the ICME Ph.D. admissions committee before the end of winter quarter of second year; transfer to the Ph.D. program subject to committee approval.