CME-MS - Computational and Mathematical Engineering (MS)
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Program Overview
ICME is a degree-granting (MS/PhD) interdisciplinary institute at the intersection of mathematics, computing, engineering, and applied sciences. ICME was founded in 2004, building upon the Scientific Computing and Computational Mathematics Program (est. 1989).
At ICME, we design state-of-the-art mathematical and computational models, methods, and algorithms for engineering and science applications. The program collaborates closely with engineers and scientists in academia and industry to develop improved computational approaches and advance disciplinary fields. In particular, it leverages Stanford’s strength in engineering applications in the physical, biological, mathematical, and information sciences and has established connections with nearly 20 departments across five schools at Stanford.
The program identifies research areas that would benefit from a multidisciplinary approach in which computational mathematics is critical. This multidisciplinary intellectual environment is a core strength of ICME, with interaction among students and faculty with diverse backgrounds and expertise. Students and faculty are active in many research areas: aerodynamics and space applications, fluid dynamics, protein folding, data science, including machine learning and recommender systems, ocean dynamics, climate modeling, reservoir engineering, computer graphics, financial mathematics, and many more.
The program trains students and scholars from across Stanford in mathematical modeling, scientific computing, and advanced computational algorithms at the undergraduate and graduate levels. Courses typically provide strong theoretical foundations for solving real-world problems and numerical computations to facilitate the application of mathematical techniques and theories. Training offered includes matrix computations, computational probability and combinatorial optimization, optimization, stochastics, numerical solution of partial differential equations, parallel computer algorithms, and new computing paradigms.
ICME offers service courses for undergraduates and graduate students to fulfill departmental requirements, core courses for master’s and doctoral students in Computational and Mathematical Engineering, and specialized electives in various application areas.
The ICME master’s program offers a general Computational and Mathematical Engineering track as well as three specialized tracks: Data Science, Imaging Science, and Mathematical and Computational Finance.
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 and research assistantships are awarded to students in the doctoral program in ICME. If there are insufficient PhD students to staff all course and research assistantships, these positions may be open to master’s students. However, master’s students are not guaranteed financial assistance.
Admissions Information
Prospective applicants should consult the Graduate Admissions and the ICME admissions webpages for complete information on admission requirements and deadlines.
Applications to the MS program and all supporting documents must be submitted and received online by the posted deadline published on the ICME admissions webpage.
The master's degree in Computational and Mathematical Engineering is intended as a terminal professional degree and does not lead to the PhD program. There is no internal transition process from the MS to the PhD program. Students interested in the doctoral program should apply directly to the PhD program.
Coterm Admissions Information
Coterminal Master’s Program
Stanford undergraduates who want to apply for the coterminal master’s degree are subject to the same application deadline as external applicants. The application must clearly demonstrate that the student has a potential for strong academic performance at the graduate level. 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
More information here: https://icme.stanford.edu/academics-admission/icme-master-science#coterm
Minimum Units in the Program
Minimum University Units
The master’s program consists of 45 units of coursework taken at Stanford. No thesis is required; however, students may participate in research projects during the master’s program. Although there is no specific background requirement, significant exposure to mathematics and engineering coursework is necessary to complete the program successfully.
There are four tracks in the master’s program:
General CME
Data Science
Imaging Science
Mathematical and Computational Finance
Requirements
Unless specified in the Bulletin, a candidate must complete a program of 45 units of courses numbered 200 or above. Courses below the 200 level require special approval from the program office. At least 36 of these must be graded units, and all letter-graded units must be passed with a C- or better and have a grade point average (GPA) of 3.0 (B) or better. A course cannot be used to satisfy more than one requirement for the MS degree unless it can be repeated for credit.
Coterminal Master’s Program
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 Degrees 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. Transferring courses to the graduate career requires review and approval of both the undergraduate and graduate programs on a case-by-case basis.
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.
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, programming coursework, 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 the 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.
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.
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To ensure that students have a strong foundation in programming, six units of computing and programming taken for a letter grade are required.
For the CME track, it is strongly recommended to take CME213.
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Fifteen 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, which is expanded regularly. The elective part of the ICME program is meant to be broad and inclusive of relevant courses of comparable rigor to ICME courses. The selected courses are recommended to include offerings from (at least) two engineering departments and CME coursework. Courses outside this list can be accepted as electives subject to approval by the student’s program advisor. Six units of independent research (course) can be used to fulfill this requirement with prior approval.
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Nine units of focused graduate application electives, approved by the program advisor, in 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.
Students must complete a total of 3 Seminar units.
1 seminar unit must come from course
2 units are up to the student’s choice of ICME graduate seminars or other approved seminars.
course is strongly recommended.
Additional seminar units may not be counted toward the 45-unit requirement.
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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 requirements 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 2 or 4). Course choices are limited to predefined courses from the data sciences and related courses group for requirements 1-5.
Students must demonstrate foundational knowledge in the field by completing the following courses. Courses in this area must be taken for letter grades.
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course is strongly recommended.
To ensure that students have a strong foundation in programming, three units of basic programming and computing algorithms and three units of advanced programming and computing algorithms.
Students must take nine units from Requirement 2 for a letter grade and nine units from Requirement 4 for a letter grade, with an additional six units from either Requirement 2 or 4, for a total of 24 units in the two areas. The other six units may be taken for a non-letter grade.
For the DS track, it is strongly recommended to take CME213, course, CS246.
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Experimental method and causal considerations are fundamental to data science. The course chosen from this area must be taken for letter grades.
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*The additional three units can count toward the “Machine Learning Methods and Applications” requirement below if two courses are taken.
Nine units of coursework from this area are required for a letter grade.
Students must take nine units from Requirement 2 for a letter grade and nine units from Requirement 4 for a letter grade, with an additional six units from either Requirement 2 or 4, for a total of 24 units in the two areas. The other six units may be taken for a non-letter grade.
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Students must take nine units from Requirement 2 for a letter grade and nine units from Requirement 4 for a letter grade, with an additional six units from either Requirement 2 or 4, for a total of 24 units in the two areas. The other six units may be taken for a non-letter grade.
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 toward imaging sciences.
The coursework 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. The programming requirement (requirement 2) is extended to six units and includes advanced scientific programming and high-performance computing coursework.
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.
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OR 2066522 - 2102132
OR 2170262 - 1057882
To ensure that students have a strong foundation in programming, three units of basic programming and computing algorithms and three units of advanced programming and computing algorithms for letter grades are required.
For the IS track, it is strongly recommended to take CME213, CME323, or GEOPHYS257.
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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 advisor. Six units of independent research can be used to fulfill this requirement with prior approval.
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Six units of focused graduate application electives, approved by the ICME graduate advisor, in 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.
Students must complete a total of 3 Seminar units.
1 seminar unit must come from course
2 units are up to the student’s choice of ICME graduate seminars or other approved seminars.
course is strongly recommended.
Additional seminar units may not be counted toward the 45-unit requirement.
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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, and financial technologists or to continue 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 basic courses.
Students must demonstrate foundational knowledge in the field by completing the following core courses. Courses in this area must be taken for letter grades. Additional courses taken from this list beyond 9 units may be applied to Requirements 3 and 4.
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To ensure that students have a strong foundation in programming, three units of basic programming and computing algorithms for a letter grade and three units of advanced programming and computing algorithms for a letter grade are required. Students can take an additional course from this list for a letter grade or credit to fulfill Requirement 4.
For the MCF track, it is strongly recommended to take CME213, CME323, CS149, CS315B, or CS316.
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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.
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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 advisor.
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Students are required to take six units of practical and project courses ONLY from the courses listed below.
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* course is strongly recommended.
The ICME Master of Science with Distinction in Research program is designed for students interested in pursuing in-depth research or preparing for a PhD. This selective program allows students to engage in an extended, original research project for a minimum of three quarters, culminating in a written thesis. The work is conducted under the guidance of a faculty advisor and is associated with the CME 291 research course.
To be eligible, students must be enrolled in the ICME M.S. program, be in good academic standing with a cumulative GPA of 3.6 or higher, and secure a faculty advisor. The advisor must be a member of Stanford’s Academic Council or an ICME Affiliated Faculty member who agrees to supervise the thesis.
Students are encouraged to consult with the ICME Faculty Director and ICME Student Services officers for guidance on identifying a suitable research project and faculty supervisor.
To apply for the program, students must submit the following materials:
A brief research proposal (3–5 pages) describing the planned project and relevant background.
A letter of endorsement from the proposed faculty advisor.
A current unofficial transcript.
Admission to the program is selective. Applications will be reviewed by an ICME faculty committee. Meeting the eligibility criteria does not guarantee acceptance.
Students may submit their application by May 1 or August 31 of each year. Successful applicants will be notified by late September.
Students admitted to the Master of Science with Distinction in Research are expected to:
Enroll in and complete a minimum of 9 research units (course) under their thesis advisor’s supervision.
Produce a thesis or substantial research report to be reviewed and approved by their advisor and ICME faculty director as second faculty reader. Submit the final, approved thesis to ICME Student Services by the university's degree conferral deadline.
Present their thesis work at the ICME symposium either as a poster or oral presentation. Posters must be reviewed and approved by their advisor before presenting.
Maintain a cumulative GPA of 3.6 or higher in courses counted towards the ICME major during their time in the program. The GPA will be reviewed at the end of each quarter.
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