🕷️ Crawler Inspector

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Raw Queries and Responses

1. Shard Calculation

Query:

Response:

Calculated Shard: 180 (from laksa006)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa180.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://catalog.mit.edu/interdisciplinary/graduate-programs/computational-science-engineering/\')), getAhrefsUnparsedNoserviceFromURL(\'https://catalog.mit.edu/interdisciplinary/graduate-programs/computational-science-engineering/\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/computational-science-engineering\/","crawl_time":1775483961,"first_indexed_time":1695388896,"http_code":200,"src_unparsed":"edu,mit!catalog,\/interdisciplinary\/graduate-programs\/computational-science-engineering\/ s443","src_root_hash":"10722954425220430980","history_drop_reason":null,"meta_title":"Computational Science and Engineering | MIT Course Catalog","meta_descriptions":[],"attrs_boilerpipe_text":"The\nCenter for Computational Science and Engineering (CCSE)\noffers a master's degree and two doctoral programs in computational science and engineering (CSE)—one leading to a standalone PhD degree in CSE offered entirely by CCSE and the other to an interdisciplinary PhD degree offered jointly with participating departments in the School of Engineering and the School of Science.\nWhile both programs enable students to specialize at the doctoral level in a computation-related field via focused coursework and a thesis, they differ in essential ways. The\nstandalone CSE PhD program\nis intended for students who intend to pursue research in cross-cutting methodological aspects of computational science. The resulting doctoral degree is awarded by the Schwarzman College of Computing. In contrast, the\ninterdisciplinary CSE PhD program\nis intended for students who are interested in computation in the context of a specific engineering or science discipline. For this reason, this degree is offered jointly with participating departments across the Institute; the interdisciplinary degree is awarded in a specially crafted thesis field that recognizes the student’s specialization in computation.\nAt the time of application, students are expected to declare which of the two programs they are interested in. Admissions decisions will take into account these declared interests, along with each applicant’s academic background, preparation, and fit to the program they have selected.\nApplicants interested in an advanced degree in computer science should instead apply for admission to the\nDepartment of Electrical Engineering and Computer Science\n.\nMaster of Science in Computational Science and Engineering\nThe\nMaster of Science in Computational Science and Engineering (CSE SM)\nis an interdisciplinary, research-oriented master's program that provides students with a strong foundation in computational methods for the study, design, and operation of complex engineered and natural systems.\nThe curriculum trains students in the formulation, analysis, implementation, and application of computational approaches in science and engineering. It combines a course of study comprising six graduate subjects with a master's thesis describing original research performed under the supervision of a CSE faculty member. The coursework requirements include:\nA three-subject core aimed at developing breadth as well as depth in numerical analysis, simulation, and optimization\nA two-subject restricted elective program aimed at reinforcing multidisciplinary aspects of computation\nOne unrestricted elective subject\nHands-on experience is encouraged and reinforced through projects in the core, the elective subjects, and the master's thesis.\nDoctor of Philosophy in Computational Science and Engineering\nThe standalone doctoral program in Computational Science and Engineering (\nPhD in CSE)\nenables students to specialize at the doctoral level in fundamental, methodological aspects of computational science via focused coursework and a thesis. The emphasis of thesis research activities is the development and analysis of broadly applicable computational approaches that advance the state of the art.\nStudents are awarded the Doctor of Philosophy in Computational Science and Engineering upon successful completion of the program requirements and defense of a thesis describing significant contributions to the CSE field. Program requirements include a course of study comprising nine graduate subjects and a graduate seminar. Core and concentration subjects cover six “ways of thinking” fundamental to CSE: (i) discretization and numerical methods for partial differential equations; (ii) optimization methods; (iii) statistics and data-driven modeling; (iv) high-performance computing and\/or algorithms; (v) mathematical foundations (e.g., functional analysis, probability); and (vi) modeling (i.e., a subject that treats mathematical modeling in any science or engineering discipline). Subjects taken as part of an MIT SM program can be counted toward the coursework requirement provided they satisfy core, concentration, or elective requirements as set forth\nhere\n; consultation and approval by the program director(s) and\/or administrator regarding the application of such courses toward program credit is always required.\nStudents applying to this program are expected to have a degree in CSE, applied mathematics, or another field that prepares them for an advanced degree in CSE. More information about the application process, requirements, and relevant deadlines can be found on the\nAdmissions section of the CCSE website\n.\nInterdisciplinary Doctoral Program in Computational Science and Engineering\nThe interdisciplinary doctoral program in Computational Science and Engineering (\nPhD in CSE + Engineering or Science\n) offers students the opportunity to specialize at the doctoral level in a computation-related field of their choice via computationally-oriented coursework and a doctoral thesis with a disciplinary focus related to one of eight participating host departments, namely, Aeronautics and Astronautics; Chemical Engineering; Civil and Environmental Engineering; Earth, Atmospheric and Planetary Sciences; Materials Science and Engineering; Mathematics; Mechanical Engineering; or Nuclear Science and Engineering.\nDoctoral thesis fields associated with each department are as follows:\nAeronautics and Astronautics\nAerospace Engineering and Computational Science\nComputational Science and Engineering (available only to students who matriculate in 2023–2024 or earlier)\nChemical Engineering\nChemical Engineering and Computation\nCivil and Environmental Engineering\nCivil Engineering and Computation\nEnvironmental Engineering and Computation\nMaterials Science and Engineering\nComputational Materials Science and Engineering\nMechanical Engineering\nMechanical Engineering and Computation\nNuclear Science and Engineering\nComputational Nuclear Science and Engineering\nNuclear Engineering and Computation\nEarth, Atmospheric and Planetary Sciences\nComputational Earth, Science and Planetary Sciences\nMathematics\nMathematics and Computational Science\nAs with the standalone CSE PhD program, the emphasis of thesis research activities is the development of new computational methods and\/or the innovative application of state-of-the-art computational techniques to important problems in engineering and science. In contrast to the standalone PhD program, however, this research is expected to have a strong disciplinary component of interest to the host department.\nThe interdisciplinary CSE PhD program is administered jointly by CCSE and the host departments. Students must submit an application to the CSE PhD program, indicating the department in which they wish to be hosted. To gain admission, CSE program applicants must receive approval from both the host department graduate admission committee and the CSE graduate admission committee. See the website for more information about the\napplication process, requirements, and relevant deadlines\n.\nOnce admitted, doctoral degree candidates are expected to complete the host department's degree requirements (including qualifying exam) with some deviations relating to coursework, thesis committee composition, and thesis submission that are specific to the CSE program and are discussed in more detail on the\nCSE website\n. The most notable coursework requirement associated with this CSE degree is a course of study comprising five graduate subjects in CSE (below).\nComputational Concentration Subjects\n1.125\nArchitecting and Engineering Software Systems\n12\n1.545[J]\nAtomistic Modeling and Simulation of Materials and Structures\n12\n1.583[J]\nTopology Optimization of Structures\n12\n1.723\nComputational Methods for Flow in Porous Media\n12\n2.098\nIntroduction to Finite Element Methods\n12\n2.156\nArtificial Intelligence and Machine Learning for Engineering Design\n12\n2.168\nLearning Machines\n12\n2.29\nNumerical Fluid Mechanics\n12\n3.320\nAtomistic Computer Modeling of Materials\n12\n4.450[J]\nComputational Structural Design and Optimization\n6.7210[J]\nIntroduction to Mathematical Programming\n12\n6.7220[J]\nNonlinear Optimization\n12\n6.7230[J]\nAlgebraic Techniques and Semidefinite Optimization\n12\n6.7300[J]\nIntroduction to Modeling and Simulation\n12\n6.7810\nAlgorithms for Inference\n12\n6.7830\nBayesian Modeling and Inference\n12\n6.7900\nMachine Learning\n1\n12\n6.7940\nDynamic Programming and Reinforcement Learning\n12\n6.8300\nAdvances in Computer Vision\n12\n6.8410\nShape Analysis\n12\n6.C51\nModeling with Machine Learning: from Algorithms to Applications\n2\n6\n9.520[J]\nStatistical Learning Theory and Applications\n12\n9.660\nComputational Cognitive Science\n12\n10.551\nSystems Engineering\n3\n9\n10.552\nModern Control Design\n3\n9\n10.554[J]\nProcess Data Analytics\n12\n10.557\nMixed-integer and Nonconvex Optimization\n12\n10.637[J]\nComputational Chemistry\n12\n12.515\nData and Models\n12\n12.521\nComputational Geophysical Modeling\n12\n12.620[J]\nClassical Mechanics: A Computational Approach\n12\n12.714\nComputational Data Analysis\n12\n12.805\nData Analysis in Physical Oceanography\n12\n12.850\nComputational Ocean Modeling\n12\n15.070[J]\nDiscrete Probability and Stochastic Processes\n12\n15.077[J]\nStatistical Machine Learning and Data Science\n1\n12\n15.083\nInteger Optimization\n12\n15.764[J]\nThe Theory of Operations Management\n12\n15.C57[J]\nOptimization Methods\n12\n16.110\nFlight Vehicle Aerodynamics\n12\n16.225[J]\nComputational Mechanics of Materials\n12\n16.413[J]\nPrinciples of Autonomy and Decision Making\n12\n16.888[J]\nMultidisciplinary Design Optimization\n12\n16.920[J]\nNumerical Methods for Partial Differential Equations\n12\n16.930\nAdvanced Topics in Numerical Methods for Partial Differential Equations\n12\n16.940\nNumerical Methods for Stochastic Modeling and Inference\n12\n18.335[J]\nIntroduction to Numerical Methods\n12\n18.336[J]\nFast Methods for Partial Differential and Integral Equations\n12\n18.337[J]\nParallel Computing and Scientific Machine Learning\n12\n18.338\nEigenvalues of Random Matrices\n12\n18.369[J]\nMathematical Methods in Nanophotonics\n12\n18.435[J]\nQuantum Computation\n12\n22.15\nEssential Numerical Methods\n6\n22.212\nNuclear Reactor Analysis II\n12\n22.213\nNuclear Reactor Physics III\n12\n22.315\nApplied Computational Fluid Dynamics and Heat Transfer\n12\nCSE.999\nExperiential Learning in Computational Science and Engineering\nIDS.131[J]\nStatistics, Computation and Applications\n12\nNote: Students may not use more than 12 units of credit from a \"meets with undergraduate\" subject to fulfill the CSE curriculum requirements\n1\nCredit can only be given for one of\n6.7900\n,\n15.077[J]\n, or\nIDS.147[J]\n.\n2\nStudents cannot receive credit without simultaneous completion of a 6-unit Common Ground disciplinary module. The two subjects together count as one 12-unit subject. See\n6.C51\nfor more information.\n3\nStudents can receive credit for either\n10.551\nor\n10.552\nas a CSE concentration subject, but not both.\n4\nSubject to Sloan bidding process.\nInquiries\nFor more information, please visit the\nCCSE website\n.","attrs_markdown":"- [Skip to Content](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/computational-science-engineering\/#content)\n- [AZ Index](https:\/\/catalog.mit.edu\/azindex\/)\n- [Bulletin Home](https:\/\/catalog.mit.edu\/)\n- [MIT Home](http:\/\/mit.edu\/)\n\n[A – Z](https:\/\/catalog.mit.edu\/azindex\/)[Calendar](https:\/\/catalog.mit.edu\/academic-calendar\/) [Archive](https:\/\/catalog.mit.edu\/archive\/) [Print](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/computational-science-engineering\/#print-dialog)\n\n[![MIT Bulletin](https:\/\/catalog.mit.edu\/images\/mit-bulletin-logo-25-26.png)](https:\/\/catalog.mit.edu\/)\n\n[![MIT](https:\/\/catalog.mit.edu\/images\/mit-logo.svg)](http:\/\/web.mit.edu\/)\n\nInterdisciplinary Programs\n\n- [Home](https:\/\/catalog.mit.edu\/)\\>\n- [Interdisciplinary Programs](https:\/\/catalog.mit.edu\/interdisciplinary\/)\\>\n- [Graduate Programs](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/)\\>\n- Computational Science and Engineering\n\nCatalog Navigation\n\n- [This Is MIT](https:\/\/catalog.mit.edu\/mit\/)\n  \n  Toggle This Is MIT\n  - 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[MIT Media Lab](https:\/\/catalog.mit.edu\/mit\/research\/mit-media-lab\/)\n    - [MIT Open Learning](https:\/\/catalog.mit.edu\/mit\/research\/office-digital-learning\/)\n    - [MIT Portugal Program](https:\/\/catalog.mit.edu\/mit\/research\/mit-portugal-program\/)\n    - [MIT Professional Education](https:\/\/catalog.mit.edu\/mit\/research\/mit-professional-education\/)\n    - [MIT Sea Grant College Program](https:\/\/catalog.mit.edu\/mit\/research\/sea-grant\/)\n    - [Nuclear Reactor Laboratory](https:\/\/catalog.mit.edu\/mit\/research\/nuclear-reactor-laboratory\/)\n    - [Operations Research Center](https:\/\/catalog.mit.edu\/mit\/research\/operations-research-center\/)\n    - [Picower Institute for Learning and Memory](https:\/\/catalog.mit.edu\/mit\/research\/picower-institute-learning-memory\/)\n    - [Plasma Science and Fusion Center](https:\/\/catalog.mit.edu\/mit\/research\/plasma-science-fusion-center\/)\n    - [Research Laboratory of Electronics](https:\/\/catalog.mit.edu\/mit\/research\/research-laboratory-electronics\/)\n    - [Simons Center for the Social Brain](https:\/\/catalog.mit.edu\/mit\/research\/simons-center-social-brain\/)\n    - [Singapore-MIT Alliance for Research and Technology Centre](https:\/\/catalog.mit.edu\/mit\/research\/singapore-mit-alliance-research-technology\/)\n    - [Sociotechnical Systems Research Center](https:\/\/catalog.mit.edu\/mit\/research\/sociotechnical-systems-research-center\/)\n    - [Whitehead Institute for Biomedical Research](https:\/\/catalog.mit.edu\/mit\/research\/whitehead-institute-biomedical-research\/)\n    - [Women's and Gender Studies Program](https:\/\/catalog.mit.edu\/mit\/research\/womens-gender-studies-program\/)\n- [Schools and College](https:\/\/catalog.mit.edu\/schools\/)\n  \n  Toggle Schools and College\n  - [School of Architecture and Planning](https:\/\/catalog.mit.edu\/schools\/architecture-planning\/)\n    \n    Toggle School of Architecture and Planning\n    - [Architecture](https:\/\/catalog.mit.edu\/schools\/architecture-planning\/architecture\/)\n      \n      Toggle Architecture\n      - [Architecture (SB, Course 4)](https:\/\/catalog.mit.edu\/degree-charts\/architecture-course-4\/)\n      - [Architecture (MArch)](https:\/\/catalog.mit.edu\/degree-charts\/master-architecture\/)\n      - [Art and Design (SB, Course 4-B)](https:\/\/catalog.mit.edu\/degree-charts\/architecture-course-4-b\/)\n      - [Art, Culture, and Technology (SM)](https:\/\/catalog.mit.edu\/degree-charts\/master-art-culture-technology\/)\n      - [Architecture Studies (SM)](https:\/\/catalog.mit.edu\/degree-charts\/master-architecture-studies\/)\n    - [Media Arts and Sciences](https:\/\/catalog.mit.edu\/schools\/architecture-planning\/media-arts-sciences\/)\n    - [Urban Studies and Planning](https:\/\/catalog.mit.edu\/schools\/architecture-planning\/urban-studies-planning\/)\n      \n      Toggle Urban Studies and Planning\n      - [Planning (SB, Course 11)](https:\/\/catalog.mit.edu\/degree-charts\/planning-course-11\/)\n      - [Urban Science and Planning with Computer Science (SB, Course 11-6)](https:\/\/catalog.mit.edu\/degree-charts\/urban-science-planning-computer-science-11-6\/)\n  - [School of Engineering](https:\/\/catalog.mit.edu\/schools\/engineering\/)\n    \n    Toggle School of Engineering\n    - [Aeronautics and Astronautics](https:\/\/catalog.mit.edu\/schools\/engineering\/aeronautics-astronautics\/)\n      \n      Toggle Aeronautics and Astronautics\n      - [Aeronautics and Astronautics Fields (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-aeronautics-astronautics\/)\n      - [Aerospace Engineering (SB, Course 16)](https:\/\/catalog.mit.edu\/degree-charts\/aerospace-engineering-course-16\/)\n      - [Engineering (SB, Course 16-ENG)](https:\/\/catalog.mit.edu\/degree-charts\/engineering-aeronautics-astronautics-course-16-eng\/)\n    - [Biological Engineering](https:\/\/catalog.mit.edu\/schools\/engineering\/biological-engineering\/)\n      \n      Toggle Biological Engineering\n      - [Biological Engineering (SB, Course 20)](https:\/\/catalog.mit.edu\/degree-charts\/biological-engineering-course-20\/)\n      - [Biological Engineering (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-biological-engineering\/)\n    - [Chemical Engineering](https:\/\/catalog.mit.edu\/schools\/engineering\/chemical-engineering\/)\n      \n      Toggle Chemical Engineering\n      - [Chemical Engineering (SB, Course 10)](https:\/\/catalog.mit.edu\/degree-charts\/chemical-engineering-course-10\/)\n      - [Chemical-Biological Engineering (SB, Course 10-B)](https:\/\/catalog.mit.edu\/degree-charts\/chemical-biological-engineering-course-10-b\/)\n      - [Chemical Engineering (SB, Course 10-C)](https:\/\/catalog.mit.edu\/degree-charts\/chemical-engineering-course-10-c\/)\n      - [Engineering (SB, Course 10-ENG)](https:\/\/catalog.mit.edu\/degree-charts\/engineering-chemical-engineering-course-10-eng\/)\n    - [Civil and Environmental Engineering](https:\/\/catalog.mit.edu\/schools\/engineering\/civil-environmental-engineering\/)\n      \n      Toggle Civil and Environmental Engineering\n      - [Engineering (SB, Course 1-ENG)](https:\/\/catalog.mit.edu\/degree-charts\/engineering-civil-environmental-engineering-course-1-eng\/)\n      - [Civil and Environmental Engineering (MEng)](https:\/\/catalog.mit.edu\/degree-charts\/master-civil-environmental-engineering-course-1p\/)\n    - [Data, Systems, and Society](https:\/\/catalog.mit.edu\/schools\/engineering\/data-systems-society\/)\n    - [Electrical Engineering and Computer Science](https:\/\/catalog.mit.edu\/schools\/engineering\/electrical-engineering-computer-science\/)\n      \n      Toggle Electrical Engineering and Computer Science\n      - [Computation and Cognition (SB, Course 6-9)](https:\/\/catalog.mit.edu\/degree-charts\/computation-cognition-6-9\/)\n      - [Computer Science and Engineering (SB, Course 6-3)](https:\/\/catalog.mit.edu\/degree-charts\/computer-science-engineering-course-6-3\/)\n      - [Computer Science and Molecular Biology (SB, Course 6-7)](https:\/\/catalog.mit.edu\/degree-charts\/computer-science-molecular-biology-course-6-7\/)\n      - [Electrical Engineering with Computing (Course 6-5)](https:\/\/catalog-dev.mit.edu\/degree-charts\/electrical-engineering-computing-course-6-5\/)\n      - [Urban Science and Planning with Computer Science (SB, Course 11-6)](https:\/\/catalog.mit.edu\/degree-charts\/urban-science-planning-computer-science-11-6\/)\n      - [Electrical Engineering and Computer Science (MEng)](https:\/\/catalog.mit.edu\/degree-charts\/master-electrical-engineering-computer-science-course-6-p\/)\n      - [Computer Science and Molecular Biology (MEng)](https:\/\/catalog.mit.edu\/degree-charts\/master-computer-science-molecular-biology-course-6-7p\/)\n    - [Health Sciences and Technology](https:\/\/catalog.mit.edu\/schools\/engineering\/harvard-mit-health-sciences-technology\/)\n    - [Materials Science and Engineering](https:\/\/catalog.mit.edu\/schools\/engineering\/materials-science-engineering\/)\n      \n      Toggle Materials Science and Engineering\n      - [Archaeology and Materials (SB, Course 3-C)](https:\/\/catalog.mit.edu\/degree-charts\/archaeology-materials-course-3-c\/)\n      - [Materials Science and Engineering (SB, Course 3)](https:\/\/catalog.mit.edu\/degree-charts\/materials-science-engineering-course-3\/)\n      - [Materials Science and Engineering (SB, Course 3-A)](https:\/\/catalog.mit.edu\/degree-charts\/materials-science-engineering-course-3-a\/)\n      - [Materials Science and Engineering (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-materials-science-engineering\/)\n    - [Mechanical Engineering](https:\/\/catalog.mit.edu\/schools\/engineering\/mechanical-engineering\/)\n      \n      Toggle Mechanical Engineering\n      - [Mechanical Engineering (SB, Course 2)](https:\/\/catalog.mit.edu\/degree-charts\/mechanical-engineering-course-2\/)\n      - [Mechanical and Ocean Engineering (SB, Course 2-OE)](https:\/\/catalog.mit.edu\/degree-charts\/mechanical-ocean-engineering-course-2-oe\/)\n      - [Engineering (SB, Course 2-A)](https:\/\/catalog.mit.edu\/degree-charts\/mechanical-engineering-course-2-a\/)\n    - [Nuclear Science and Engineering](https:\/\/catalog.mit.edu\/schools\/engineering\/nuclear-science-engineering\/)\n      \n      Toggle Nuclear Science and Engineering\n      - [Nuclear Science and Engineering (SB, Course 22)](https:\/\/catalog.mit.edu\/degree-charts\/nuclear-science-engineering-course-22\/)\n      - [Engineering (SB, Course 22-ENG)](https:\/\/catalog.mit.edu\/degree-charts\/engineering-nuclear-science-engineering-course-22-eng\/)\n  - [School of Humanities, Arts, and Social Sciences](https:\/\/catalog.mit.edu\/schools\/humanities-arts-social-sciences\/)\n    \n    Toggle School of Humanities, Arts, and Social Sciences\n    - [Anthropology](https:\/\/catalog.mit.edu\/schools\/humanities-arts-social-sciences\/anthropology\/)\n      \n      Toggle Anthropology\n      - [Anthropology (SB, Course 21A)](https:\/\/catalog.mit.edu\/degree-charts\/anthropology-course-21a\/)\n    - [Comparative Media Studies\/Writing](https:\/\/catalog.mit.edu\/schools\/humanities-arts-social-sciences\/comparative-media-studies-writing\/)\n      \n      Toggle Comparative Media Studies\/Writing\n      - [Comparative Media Studies (SB, CMS)](https:\/\/catalog.mit.edu\/degree-charts\/comparative-media-studies-cms\/)\n      - [Writing (SB, Course 21W)](https:\/\/catalog.mit.edu\/degree-charts\/writing-course-21w\/)\n    - [Economics](https:\/\/catalog.mit.edu\/schools\/humanities-arts-social-sciences\/economics\/)\n      \n      Toggle Economics\n      - [Data, Economics, and Design of Policy (MASc)](https:\/\/catalog.mit.edu\/degree-charts\/master-applied-science-data-economics-development-policy\/)\n      - [Economics (SB, Course 14-1)](https:\/\/catalog.mit.edu\/degree-charts\/economics-course-14\/)\n      - [Economics (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-economics\/)\n      - [Mathematical Economics (SB, Course 14-2)](https:\/\/catalog.mit.edu\/degree-charts\/mathematical-economics-course-14-2\/)\n    - [Global Languages](https:\/\/catalog.mit.edu\/schools\/humanities-arts-social-sciences\/global-studies-languages\/)\n      \n      Toggle Global Languages\n      - [Global Studies and Languages (SB, Course 21G)](https:\/\/catalog.mit.edu\/degree-charts\/global-studies-languages-course-21g\/)\n    - [History](https:\/\/catalog.mit.edu\/schools\/humanities-arts-social-sciences\/history\/)\n      \n      Toggle History\n      - [History (SB, Course 21H)](https:\/\/catalog.mit.edu\/degree-charts\/history-course-21h\/)\n    - [Humanities](https:\/\/catalog.mit.edu\/schools\/humanities-arts-social-sciences\/humanities\/)\n    - [Linguistics and Philosophy](https:\/\/catalog.mit.edu\/schools\/humanities-arts-social-sciences\/linguistics-philosophy\/)\n      \n      Toggle Linguistics and Philosophy\n      - [Linguistics and Philosophy (SB, Course 24-2)](https:\/\/catalog.mit.edu\/degree-charts\/linguistics-philosophy-course-24-2\/)\n      - [Philosophy (SB, Course 24-1)](https:\/\/catalog.mit.edu\/degree-charts\/philosophy-course-24-1\/)\n      - [Linguistics (SM)](https:\/\/catalog.mit.edu\/degree-charts\/sm-linguistics\/)\n    - [Literature](https:\/\/catalog.mit.edu\/schools\/humanities-arts-social-sciences\/literature\/)\n      \n      Toggle Literature\n      - [Literature (SB, Course 21L)](https:\/\/catalog.mit.edu\/degree-charts\/literature-course-21l\/)\n    - [Music and Theater Arts](https:\/\/catalog.mit.edu\/schools\/humanities-arts-social-sciences\/music-theater-arts\/)\n      \n      Toggle Music and Theater Arts\n      - [Music (SB, Course 21M)](https:\/\/catalog.mit.edu\/degree-charts\/music-course-21m\/)\n      - [Theater Arts (SB, Course 21T)](https:\/\/catalog.mit.edu\/degree-charts\/theater-arts-course-21t\/)\n    - [Political Science](https:\/\/catalog.mit.edu\/schools\/humanities-arts-social-sciences\/political-science\/)\n      \n      Toggle Political Science\n      - [Political Science (SB, Course 17)](https:\/\/catalog.mit.edu\/degree-charts\/political-science-course-17\/)\n    - [Science, Technology, and Society](https:\/\/catalog.mit.edu\/schools\/humanities-arts-social-sciences\/science-technology-society\/)\n      \n      Toggle Science, Technology, and Society\n      - [Science, Technology, and Society\/Second Major (SB, STS)](https:\/\/catalog.mit.edu\/degree-charts\/science-technology-society-sts\/)\n  - [MIT Sloan School of Management](https:\/\/catalog.mit.edu\/schools\/sloan-management\/)\n    \n    Toggle MIT Sloan School of Management\n    - [Management](https:\/\/catalog.mit.edu\/schools\/sloan-management\/management\/)\n      \n      Toggle Management\n      - [Business Analytics (SB, Course 15-2)](https:\/\/catalog.mit.edu\/degree-charts\/business-analytics-course-15-2\/)\n      - [Finance (SB, Course 15-3)](https:\/\/catalog.mit.edu\/degree-charts\/finance-course-15-3\/)\n      - [Management (SB, Course 15-1)](https:\/\/catalog.mit.edu\/degree-charts\/management-course-15-1\/)\n  - [School of Science](https:\/\/catalog.mit.edu\/schools\/science\/)\n    \n    Toggle School of Science\n    - [Biology](https:\/\/catalog.mit.edu\/schools\/science\/biology\/)\n      \n      Toggle Biology\n      - [Biology (SB, Course 7)](https:\/\/catalog.mit.edu\/degree-charts\/biology-course-7\/)\n      - [Chemistry and Biology (SB, Course 5-7)](https:\/\/catalog.mit.edu\/degree-charts\/chemistry-biology-course-5-7\/)\n      - [Computer Science and Molecular Biology (SB, Course 6-7)](https:\/\/catalog.mit.edu\/degree-charts\/computer-science-molecular-biology-course-6-7\/)\n      - [Computer Science and Molecular Biology (MEng)](https:\/\/catalog.mit.edu\/degree-charts\/master-computer-science-molecular-biology-course-6-7p\/)\n    - [Brain and Cognitive Sciences](https:\/\/catalog.mit.edu\/schools\/science\/brain-cognitive-sciences\/)\n      \n      Toggle Brain and Cognitive Sciences\n      - [Brain and Cognitive Sciences (SB, Course 9)](https:\/\/catalog.mit.edu\/degree-charts\/brain-cognitive-sciences-course-9\/)\n      - [Computation and Cognition (SB, Course 6-9)](https:\/\/catalog.mit.edu\/degree-charts\/computation-cognition-6-9\/)\n    - [Chemistry](https:\/\/catalog.mit.edu\/schools\/science\/chemistry\/)\n      \n      Toggle Chemistry\n      - [Chemistry (SB, Course 5)](https:\/\/catalog.mit.edu\/degree-charts\/chemistry-course-5\/)\n      - [Chemistry and Biology (SB, Course 5-7)](https:\/\/catalog.mit.edu\/degree-charts\/chemistry-biology-course-5-7\/)\n    - [Earth, Atmospheric, and Planetary Sciences](https:\/\/catalog.mit.edu\/schools\/science\/earth-atmospheric-planetary-sciences\/)\n      \n      Toggle Earth, Atmospheric, and Planetary Sciences\n      - [Earth, Atmospheric and Planetary Sciences (SB, Course 12)](https:\/\/catalog.mit.edu\/degree-charts\/earth-atmospheric-planetary-sciences-course-12\/)\n    - [Mathematics](https:\/\/catalog.mit.edu\/schools\/science\/mathematics\/)\n      \n      Toggle Mathematics\n      - [Mathematics (SB, Course 18)](https:\/\/catalog.mit.edu\/degree-charts\/mathematics-course-18\/)\n      - [Mathematics (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-mathematics\/)\n      - [Mathematics with Computer Science (SB, Course 18-C)](https:\/\/catalog.mit.edu\/degree-charts\/mathematics-computer-science-course-18-c\/)\n    - [Physics](https:\/\/catalog.mit.edu\/schools\/science\/physics\/)\n      \n      Toggle Physics\n      - [Physics (SB, Course 8)](https:\/\/catalog.mit.edu\/degree-charts\/physics-course-8\/)\n  - [MIT Schwarzman College of Computing](https:\/\/catalog.mit.edu\/schools\/mit-schwarzman-college-computing\/)\n    \n    Toggle MIT Schwarzman College of Computing\n    - [Electrical Engineering and Computer Science](https:\/\/catalog.mit.edu\/schools\/mit-schwarzman-college-computing\/electrical-engineering-computer-science\/)\n    - [Data, Systems, and Society](https:\/\/catalog.mit.edu\/schools\/mit-schwarzman-college-computing\/data-systems-society\/)\n- [Interdisciplinary Programs](https:\/\/catalog.mit.edu\/interdisciplinary\/)\n  \n  Toggle Interdisciplinary Programs\n  - [Undergraduate Programs](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/)\n    \n    Toggle Undergraduate Programs\n    - [Degrees](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/degrees\/)\n      \n      Toggle Degrees\n      - [Chemistry and Biology](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/degrees\/chemistry-biology\/)\n      - [Climate System Science and Engineering](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/degrees\/climate-system-science-engineering\/)\n      - [Computation and Cognition](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/degrees\/computation-cognition\/)\n      - [Computer Science and Molecular Biology](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/degrees\/computer-science-molecular-biology\/)\n      - [Computer Science, Economics, and Data Science](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/degrees\/computer-science-economics-data-science\/)\n      - [Humanities](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/degrees\/humanities\/)\n      - [Humanities and Engineering](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/degrees\/humanities-engineering\/)\n      - [Humanities and Science](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/degrees\/humanities-science\/)\n      - [Urban Science and Planning with Computer Science](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/degrees\/urban-science-planning-computer-science\/)\n    - [Minors](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/)\n      \n      Toggle Minors\n      - [African and African Diaspora Studies](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/minor-african-studies\/)\n      - [American Studies](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/minor-american-studies\/)\n      - [Ancient and Medieval Studies](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/ancient-medieval-studies\/)\n      - [Applied International Studies](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/applied-international-studies\/)\n      - [Asian and Asian Diaspora Studies](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/asian-studies\/)\n      - [Astronomy](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/astronomy\/)\n      - [Biomedical Engineering](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/biomedical-engineering\/)\n      - [Energy Studies](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/energy-studies\/)\n      - [Entrepreneurship and Innovation](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/entrepreneurship-innovation\/)\n      - [Environment and Sustainability](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/environment-sustainability\/)\n      - [Latin American and Latino\/a Studies](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/latin-american-latino-studies\/)\n      - [Middle Eastern Studies](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/middle-eastern-studies\/)\n      - [Polymers and Soft Matter](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/polymers-soft-matter\/)\n      - [Public Policy](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/public-policy\/)\n      - [Russian and Eurasian Studies](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/russian-eurasian-studies\/)\n      - [Statistics and Data Science](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/statistics-data-science\/)\n      - [Women's and Gender Studies](https:\/\/catalog.mit.edu\/interdisciplinary\/undergraduate-programs\/minors\/womens-gender-studies\/)\n  - [Graduate Programs](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/)\n    \n    Toggle Graduate Programs\n    - [Advanced Urbanism](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/advanced-urbanism\/)\n    - [Computation and Cognition](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/computation-cognition\/)\n    - [Computational and Systems Biology](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/computational-systems-biology\/)\n    - [Computational Science and Engineering](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/computational-science-engineering\/)\n    - [Computer Science and Molecular Biology](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/computer-science-molecular-biology\/)\n    - [Computer Science, Economics, and Data Science](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/computer-science-economics-data-science\/)\n    - [Health Sciences and Technology](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/harvard-mit-health-sciences-technology\/)\n    - [Joint Program with Woods Hole Oceanographic Institution](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/joint-program-woods-hole-oceanographic-institution\/)\n    - [Leaders for Global Operations](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/leaders-global-operations\/)\n    - [Microbiology](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/microbiology\/)\n    - [Music Technology and Computation](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/music-technology-computation\/)\n    - [Operations Research](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/operations-research\/)\n    - [Polymers and Soft Matter](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/polymers-soft-matter\/)\n    - [Real Estate Development](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/real-estate-development\/)\n    - [Social and Engineering Systems](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/social-engineering-systems\/)\n    - [Statistics](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/phd-statistics\/)\n    - [Supply Chain Management](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/supply-chain-management\/)\n    - [System Design and Management](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/system-design-management\/)\n    - [Technology and Policy](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/technology-policy\/)\n    - [Transportation](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/transportation\/)\n- [Degree Charts](https:\/\/catalog.mit.edu\/degree-charts\/)\n  \n  Toggle Degree Charts\n  - School of Architecture and Planning\n  - [Architecture (SB, Course 4)](https:\/\/catalog.mit.edu\/degree-charts\/architecture-course-4\/)\n  - [Architecture (MArch)](https:\/\/catalog.mit.edu\/degree-charts\/master-architecture\/)\n  - [Architecture Studies (SM)](https:\/\/catalog.mit.edu\/degree-charts\/master-architecture-studies\/)\n  - [Art and Design (SB, Course 4-B)](https:\/\/catalog.mit.edu\/degree-charts\/architecture-course-4-b\/)\n  - [Art, Culture, and Technology (SM)](https:\/\/catalog.mit.edu\/degree-charts\/master-art-culture-technology\/)\n  - [City Planning (SM)](https:\/\/catalog.mit.edu\/degree-charts\/master-city-planning\/)\n  - [Planning (SB, Course 11)](https:\/\/catalog.mit.edu\/degree-charts\/planning-course-11\/)\n  - School of Engineering\n  - [Aeronautics and Astronautics Fields (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-aeronautics-astronautics\/)\n  - [Aerospace Engineering (SB, Course 16)](https:\/\/catalog.mit.edu\/degree-charts\/aerospace-engineering-course-16\/)\n  - [Archaeology and Materials (SB, Course 3-C)](https:\/\/catalog.mit.edu\/degree-charts\/archaeology-materials-course-3-c\/)\n  - [Artificial Intelligence and Decision Making (SB, Course 6-4)](https:\/\/catalog.mit.edu\/degree-charts\/artifical-intelligence-decision-making-course-6-4\/)\n  - [Biological Engineering (SB, Course 20)](https:\/\/catalog.mit.edu\/degree-charts\/biological-engineering-course-20\/)\n  - [Biological Engineering (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-biological-engineering\/)\n  - [Civil and Environmental Engineering (SM)](https:\/\/catalog.mit.edu\/degree-charts\/master-civil-environmental-engineering\/)\n  - [Civil and Environmental Engineering (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-civil-environmental-engineering\/)\n  - [Chemical-Biological Engineering (SB, Course 10-B)](https:\/\/catalog.mit.edu\/degree-charts\/chemical-biological-engineering-course-10-b\/)\n  - [Chemical Engineering (SB, Course 10)](https:\/\/catalog.mit.edu\/degree-charts\/chemical-engineering-course-10\/)\n  - [Chemical Engineering (SB, Course 10-C)](https:\/\/catalog.mit.edu\/degree-charts\/chemical-engineering-course-10-c\/)\n  - [Computer Science and Engineering (SB, Course 6-3)](https:\/\/catalog.mit.edu\/degree-charts\/computer-science-engineering-course-6-3\/)\n  - [Electrical Engineering and Computer Science (MEng)](https:\/\/catalog.mit.edu\/degree-charts\/master-electrical-engineering-computer-science-course-6-p\/)\n  - [Electrical Engineering with Computing (SB, Course 6-5)](https:\/\/catalog.mit.edu\/degree-charts\/electrical-engineering-computing-course-6-5\/)\n  - [Engineering (SB, Course 1-ENG)](https:\/\/catalog.mit.edu\/degree-charts\/engineering-civil-environmental-engineering-course-1-eng\/)\n  - [Engineering (SB, Course 2-A)](https:\/\/catalog.mit.edu\/degree-charts\/mechanical-engineering-course-2-a\/)\n  - [Engineering (SB, Course 10-ENG)](https:\/\/catalog.mit.edu\/degree-charts\/engineering-chemical-engineering-course-10-eng\/)\n  - [Engineering (SB, Course 16-ENG)](https:\/\/catalog.mit.edu\/degree-charts\/engineering-aeronautics-astronautics-course-16-eng\/)\n  - [Engineering (SB, Course 22-ENG)](https:\/\/catalog.mit.edu\/degree-charts\/engineering-nuclear-science-engineering-course-22-eng\/)\n  - [Materials Science and Engineering (SB, Course 3)](https:\/\/catalog.mit.edu\/degree-charts\/materials-science-engineering-course-3\/)\n  - [Materials Science and Engineering (SB, Course 3-A)](https:\/\/catalog.mit.edu\/degree-charts\/materials-science-engineering-course-3-a\/)\n  - [Materials Science and Engineering (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-materials-science-engineering\/)\n  - [Mechanical and Ocean Engineering (SB, Course 2-OE)](https:\/\/catalog.mit.edu\/degree-charts\/mechanical-ocean-engineering-course-2-oe\/)\n  - [Mechanical Engineering (SB, Course 2)](https:\/\/catalog.mit.edu\/degree-charts\/mechanical-engineering-course-2\/)\n  - [Nuclear Science and Engineering (SB, Course 22)](https:\/\/catalog.mit.edu\/degree-charts\/nuclear-science-engineering-course-22\/)\n  - [Nuclear Science and Engineering (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-nuclear-science-engineering\/)\n  - [Social and Engineering Systems (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-social-engineering-systems\/)\n  - School of Humanities, Arts, and Social Sciences\n  - [Anthropology (SB, Course 21A)](https:\/\/catalog.mit.edu\/degree-charts\/anthropology-course-21a\/)\n  - [Comparative Media Studies (SB, CMS)](https:\/\/catalog.mit.edu\/degree-charts\/comparative-media-studies-cms\/)\n  - [Data, Economics, and Design of Policy (MASc)](https:\/\/catalog.mit.edu\/degree-charts\/master-applied-science-data-economics-development-policy\/)\n  - [Economics (SB, Course 14-1)](https:\/\/catalog.mit.edu\/degree-charts\/economics-course-14\/)\n  - [Economics (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-economics\/)\n  - [Global Studies and Languages (SB, Course 21G)](https:\/\/catalog.mit.edu\/degree-charts\/global-studies-languages-course-21g\/)\n  - [History (SB, Course 21H)](https:\/\/catalog.mit.edu\/degree-charts\/history-course-21h\/)\n  - [Humanities (SB, Course 21)](https:\/\/catalog.mit.edu\/degree-charts\/humanities-course-21\/)\n  - [Humanities and Engineering (SB, Course 21E)](https:\/\/catalog.mit.edu\/degree-charts\/humanities-engineering-course-21e\/)\n  - [Humanities and Science (SB, Course 21S)](https:\/\/catalog.mit.edu\/degree-charts\/humanities-science-course-21s\/)\n  - [Linguistics (SM)](https:\/\/catalog.mit.edu\/degree-charts\/sm-linguistics\/)\n  - [Linguistics and Philosophy (SB, Course 24-2)](https:\/\/catalog.mit.edu\/degree-charts\/linguistics-philosophy-course-24-2\/)\n  - [Literature (SB, Course 21L)](https:\/\/catalog.mit.edu\/degree-charts\/literature-course-21l\/)\n  - [Mathematical Economics (SB, Course 14-2)](https:\/\/catalog.mit.edu\/degree-charts\/mathematical-economics-course-14-2\/)\n  - [Music (SB, Course 21M)](https:\/\/catalog.mit.edu\/degree-charts\/music-course-21m\/)\n  - [Philosophy (SB, Course 24-1)](https:\/\/catalog.mit.edu\/degree-charts\/philosophy-course-24-1\/)\n  - [Political Science (SB, Course 17)](https:\/\/catalog.mit.edu\/degree-charts\/political-science-course-17\/)\n  - [Science, Technology, and Society\/Second Major (SB, STS)](https:\/\/catalog.mit.edu\/degree-charts\/science-technology-society-sts\/)\n  - [Science Writing (SM)](https:\/\/catalog.mit.edu\/degree-charts\/master-science-writing\/)\n  - [Theater Arts (SB, Course 21T)](https:\/\/catalog.mit.edu\/degree-charts\/theater-arts-course-21t\/)\n  - [Writing (SB, Course 21W)](https:\/\/catalog.mit.edu\/degree-charts\/writing-course-21w\/)\n  - Sloan School of Management\n  - [Business Analytics (SB, Course 15-2)](https:\/\/catalog.mit.edu\/degree-charts\/business-analytics-course-15-2\/)\n  - [Finance (SB, Course 15-3)](https:\/\/catalog.mit.edu\/degree-charts\/finance-course-15-3\/)\n  - [Management (SB, Course 15-1)](https:\/\/catalog.mit.edu\/degree-charts\/management-course-15-1\/)\n  - School of Science\n  - [Biology (SB, Course 7)](https:\/\/catalog.mit.edu\/degree-charts\/biology-course-7\/)\n  - [Brain and Cognitive Sciences (SB, Course 9)](https:\/\/catalog.mit.edu\/degree-charts\/brain-cognitive-sciences-course-9\/)\n  - [Brain and Cognitive Sciences (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-brain-cognitive-sciences\/)\n  - [Chemistry (SB, Course 5)](https:\/\/catalog.mit.edu\/degree-charts\/chemistry-course-5\/)\n  - [Chemistry (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-chemistry\/)\n  - [Earth, Atmospheric and Planetary Sciences (SB, Course 12)](https:\/\/catalog.mit.edu\/degree-charts\/earth-atmospheric-planetary-sciences-course-12\/)\n  - [Earth, Atmospheric and Planetary Sciences Fields (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-earth-atmospheric-planetary-sciences\/)\n  - [Mathematics (SB, Course 18)](https:\/\/catalog.mit.edu\/degree-charts\/mathematics-course-18\/)\n  - [Mathematics (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-mathematics\/)\n  - [Mathematics with Computer Science (SB, Course 18-C)](https:\/\/catalog.mit.edu\/degree-charts\/mathematics-computer-science-course-18-c\/)\n  - [Physics (SB, Course 8)](https:\/\/catalog.mit.edu\/degree-charts\/physics-course-8\/)\n  - Interdisciplinary Programs (SB)\n  - [Chemistry and Biology (SB, Course 5-7)](https:\/\/catalog.mit.edu\/degree-charts\/chemistry-biology-course-5-7\/)\n  - [Climate System Science and Engineering (SB, Course 1-12)](https:\/\/catalog.mit.edu\/degree-charts\/climate-system-science-engineering-course-1-12\/)\n  - [Computation and Cognition (SB, Course 6-9)](https:\/\/catalog.mit.edu\/degree-charts\/computation-cognition-6-9\/)\n  - [Computer Science and Molecular Biology (SB, Course 6-7)](https:\/\/catalog.mit.edu\/degree-charts\/computer-science-molecular-biology-course-6-7\/)\n  - [Computer Science, Economics, and Data Science (SB, Course 6-14)](https:\/\/catalog.mit.edu\/degree-charts\/computer-science-economics-data-science-course-6-14\/)\n  - [Urban Science and Planning with Computer Science (SB, Course 11-6)](https:\/\/catalog.mit.edu\/degree-charts\/urban-science-planning-computer-science-11-6\/)\n  - Interdisciplinary Programs (Graduate)\n  - [Biological Oceanography (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-biological-oceanography\/)\n  - [Computation and Cognition (MEng)](https:\/\/catalog.mit.edu\/degree-charts\/master-computation-cognition-course-6-9p\/)\n  - [Computational and Systems Biology (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-computational-systems-biology\/)\n  - [Computational Science and Engineering (SM)](https:\/\/catalog.mit.edu\/degree-charts\/master-computational-science-engineering\/)\n  - [Computational Science and Engineering (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-computational-science-engineering\/)\n  - [Computer Science and Molecular Biology (MEng)](https:\/\/catalog.mit.edu\/degree-charts\/master-computer-science-molecular-biology-course-6-7p\/)\n  - [Computer Science, Economics, and Data Science (MEng)](https:\/\/catalog.mit.edu\/degree-charts\/master-computer-science-economics-data-science-course-6-14-p\/)\n  - [Engineering and Management (SM)](https:\/\/catalog.mit.edu\/degree-charts\/sm-system-design-management\/)\n  - [Leaders for Global Operations (MBA\/SM and SM)](https:\/\/catalog.mit.edu\/degree-charts\/mba-sm-leaders-global-operations\/)\n  - [Microbiology (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-microbiology\/)\n  - [Music Technology and Computation (SM and MASc)](https:\/\/catalog.mit.edu\/degree-charts\/master-music-technology-computation\/)\n  - [Physical Oceanography (PhD\/ScD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-physical-oceanography\/)\n  - [Real Estate Development (SM)](https:\/\/catalog.mit.edu\/degree-charts\/master-real-estate-development\/)\n  - [Statistics (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/interdisciplinary-doctoral-statistics\/)\n  - [Supply Chain Management (MEng and MASc)](https:\/\/catalog.mit.edu\/degree-charts\/master-supply-chain-management\/)\n  - [Technology and Policy (SM)](https:\/\/catalog.mit.edu\/degree-charts\/master-technology-policy\/)\n  - [Transportation (SM)](https:\/\/catalog.mit.edu\/degree-charts\/master-transportation\/)\n  - [Transportation (PhD)](https:\/\/catalog.mit.edu\/degree-charts\/phd-transportation\/)\n- [Subjects](https:\/\/catalog.mit.edu\/subjects\/)\n  \n  Toggle Subjects\n  - [Aeronautics and Astronautics (Course 16)](https:\/\/catalog.mit.edu\/subjects\/16\/)\n  - [Aerospace Studies (AS)](https:\/\/catalog.mit.edu\/subjects\/as\/)\n  - [Anthropology (Course 21A)](https:\/\/catalog.mit.edu\/subjects\/21a\/)\n  - [Architecture (Course 4)](https:\/\/catalog.mit.edu\/subjects\/4\/)\n  - [Biological Engineering (Course 20)](https:\/\/catalog.mit.edu\/subjects\/20\/)\n  - [Biology (Course 7)](https:\/\/catalog.mit.edu\/subjects\/7\/)\n  - [Brain and Cognitive Sciences (Course 9)](https:\/\/catalog.mit.edu\/subjects\/9\/)\n  - [Chemical Engineering (Course 10)](https:\/\/catalog.mit.edu\/subjects\/10\/)\n  - [Chemistry (Course 5)](https:\/\/catalog.mit.edu\/subjects\/5\/)\n  - [Civil and Environmental Engineering (Course 1)](https:\/\/catalog.mit.edu\/subjects\/1\/)\n  - [Comparative Media Studies \/ Writing (CMS)](https:\/\/catalog.mit.edu\/subjects\/cms\/)\n  - [Comparative Media Studies \/ Writing (Course 21W)](https:\/\/catalog.mit.edu\/subjects\/21w\/)\n  - [Computational and Systems Biology (CSB)](https:\/\/catalog.mit.edu\/subjects\/csb\/)\n  - [Computational Science and Engineering (CSE)](https:\/\/catalog.mit.edu\/subjects\/cse\/)\n  - [Concourse (CC)](https:\/\/catalog.mit.edu\/subjects\/cc\/)\n  - [Data, Systems, and Society (IDS)](https:\/\/catalog.mit.edu\/subjects\/ids\/)\n  - [Earth, Atmospheric, and Planetary Sciences (Course 12)](https:\/\/catalog.mit.edu\/subjects\/12\/)\n  - [Economics (Course 14)](https:\/\/catalog.mit.edu\/subjects\/14\/)\n  - [Edgerton Center (EC)](https:\/\/catalog.mit.edu\/subjects\/ec\/)\n  - [Electrical Engineering and Computer Science (Course 6)](https:\/\/catalog.mit.edu\/subjects\/6\/)\n  - [Engineering Management (EM)](https:\/\/catalog.mit.edu\/subjects\/em\/)\n  - [Experimental Study Group (ES)](https:\/\/catalog.mit.edu\/subjects\/es\/)\n  - [Global Languages (Course 21G)](https:\/\/catalog.mit.edu\/subjects\/21g\/)\n  - [Health Sciences and Technology (HST)](https:\/\/catalog.mit.edu\/subjects\/hst\/)\n  - [History (Course 21H)](https:\/\/catalog.mit.edu\/subjects\/21h\/)\n  - [Humanities (Course 21)](https:\/\/catalog.mit.edu\/subjects\/21\/)\n  - [Linguistics and Philosophy (Course 24)](https:\/\/catalog.mit.edu\/subjects\/24\/)\n  - [Literature (Course 21L)](https:\/\/catalog.mit.edu\/subjects\/21l\/)\n  - [Management (Course 15)](https:\/\/catalog.mit.edu\/subjects\/15\/)\n  - [Materials Science and Engineering (Course 3)](https:\/\/catalog.mit.edu\/subjects\/3\/)\n  - [Mathematics (Course 18)](https:\/\/catalog.mit.edu\/subjects\/18\/)\n  - [Mechanical Engineering (Course 2)](https:\/\/catalog.mit.edu\/subjects\/2\/)\n  - [Media Arts and Sciences (MAS)](https:\/\/catalog.mit.edu\/subjects\/mas\/)\n  - [Military Science (MS)](https:\/\/catalog.mit.edu\/subjects\/ms\/)\n  - [Music (Course 21M)](https:\/\/catalog.mit.edu\/subjects\/21m\/)\n  - [Naval Science (NS)](https:\/\/catalog.mit.edu\/subjects\/ns\/)\n  - [Nuclear Science and Engineering (Course 22)](https:\/\/catalog.mit.edu\/subjects\/22\/)\n  - [Physics (Course 8)](https:\/\/catalog.mit.edu\/subjects\/8\/)\n  - [Political Science (Course 17)](https:\/\/catalog.mit.edu\/subjects\/17\/)\n  - [Science, Technology, and Society (STS)](https:\/\/catalog.mit.edu\/subjects\/sts\/)\n  - [Special Programs](https:\/\/catalog.mit.edu\/subjects\/sp\/)\n  - [Supply Chain Management (SCM)](https:\/\/catalog.mit.edu\/subjects\/scm\/)\n  - [Theater Arts (21T)](https:\/\/catalog.mit.edu\/subjects\/21t\/)\n  - [Urban Studies and Planning (Course 11)](https:\/\/catalog.mit.edu\/subjects\/11\/)\n  - [Women's and Gender Studies (WGS)](https:\/\/catalog.mit.edu\/subjects\/wgs\/)\n\n# Computational Science and Engineering\nThe [Center for Computational Science and Engineering (CCSE)](https:\/\/cse.mit.edu\/programs\/) offers a master's degree and two doctoral programs in computational science and engineering (CSE)—one leading to a standalone PhD degree in CSE offered entirely by CCSE and the other to an interdisciplinary PhD degree offered jointly with participating departments in the School of Engineering and the School of Science.\n\nWhile both programs enable students to specialize at the doctoral level in a computation-related field via focused coursework and a thesis, they differ in essential ways. The **standalone CSE PhD program** is intended for students who intend to pursue research in cross-cutting methodological aspects of computational science. The resulting doctoral degree is awarded by the Schwarzman College of Computing. In contrast, the **interdisciplinary CSE PhD program** is intended for students who are interested in computation in the context of a specific engineering or science discipline. For this reason, this degree is offered jointly with participating departments across the Institute; the interdisciplinary degree is awarded in a specially crafted thesis field that recognizes the student’s specialization in computation.\n\nAt the time of application, students are expected to declare which of the two programs they are interested in. Admissions decisions will take into account these declared interests, along with each applicant’s academic background, preparation, and fit to the program they have selected.\n\nApplicants interested in an advanced degree in computer science should instead apply for admission to the [Department of Electrical Engineering and Computer Science](https:\/\/www.eecs.mit.edu\/).\n\n## Master of Science in Computational Science and Engineering\nThe [Master of Science in Computational Science and Engineering (CSE SM)](https:\/\/catalog.mit.edu\/degree-charts\/master-computational-science-engineering\/) is an interdisciplinary, research-oriented master's program that provides students with a strong foundation in computational methods for the study, design, and operation of complex engineered and natural systems.\n\nThe curriculum trains students in the formulation, analysis, implementation, and application of computational approaches in science and engineering. It combines a course of study comprising six graduate subjects with a master's thesis describing original research performed under the supervision of a CSE faculty member. The coursework requirements include:\n\n- A three-subject core aimed at developing breadth as well as depth in numerical analysis, simulation, and optimization\n- A two-subject restricted elective program aimed at reinforcing multidisciplinary aspects of computation\n- One unrestricted elective subject\n\nHands-on experience is encouraged and reinforced through projects in the core, the elective subjects, and the master's thesis.\n\n## Doctor of Philosophy in Computational Science and Engineering\nThe standalone doctoral program in Computational Science and Engineering ([PhD in CSE)](https:\/\/catalog.mit.edu\/degree-charts\/phd-computational-science-engineering\/) enables students to specialize at the doctoral level in fundamental, methodological aspects of computational science via focused coursework and a thesis. The emphasis of thesis research activities is the development and analysis of broadly applicable computational approaches that advance the state of the art.\n\nStudents are awarded the Doctor of Philosophy in Computational Science and Engineering upon successful completion of the program requirements and defense of a thesis describing significant contributions to the CSE field. Program requirements include a course of study comprising nine graduate subjects and a graduate seminar. Core and concentration subjects cover six “ways of thinking” fundamental to CSE: (i) discretization and numerical methods for partial differential equations; (ii) optimization methods; (iii) statistics and data-driven modeling; (iv) high-performance computing and\/or algorithms; (v) mathematical foundations (e.g., functional analysis, probability); and (vi) modeling (i.e., a subject that treats mathematical modeling in any science or engineering discipline). Subjects taken as part of an MIT SM program can be counted toward the coursework requirement provided they satisfy core, concentration, or elective requirements as set forth [here](https:\/\/catalog.mit.edu\/degree-charts\/phd-computational-science-engineering\/); consultation and approval by the program director(s) and\/or administrator regarding the application of such courses toward program credit is always required.\n\nStudents applying to this program are expected to have a degree in CSE, applied mathematics, or another field that prepares them for an advanced degree in CSE. More information about the application process, requirements, and relevant deadlines can be found on the [Admissions section of the CCSE website](https:\/\/cse.mit.edu\/admissions\/).\n\n## Interdisciplinary Doctoral Program in Computational Science and Engineering\nThe interdisciplinary doctoral program in Computational Science and Engineering ([PhD in CSE + Engineering or Science](https:\/\/catalog.mit.edu\/degree-charts\/phd-computational-science-engineering\/#phdincseengineeringorsciencetext)) offers students the opportunity to specialize at the doctoral level in a computation-related field of their choice via computationally-oriented coursework and a doctoral thesis with a disciplinary focus related to one of eight participating host departments, namely, Aeronautics and Astronautics; Chemical Engineering; Civil and Environmental Engineering; Earth, Atmospheric and Planetary Sciences; Materials Science and Engineering; Mathematics; Mechanical Engineering; or Nuclear Science and Engineering.\n\nDoctoral thesis fields associated with each department are as follows:\n\n- **Aeronautics and Astronautics**\n  - Aerospace Engineering and Computational Science\n  - Computational Science and Engineering (available only to students who matriculate in 2023–2024 or earlier)\n- **Chemical Engineering**\n  - Chemical Engineering and Computation\n- **Civil and Environmental Engineering**\n  - Civil Engineering and Computation\n  - Environmental Engineering and Computation\n- **Materials Science and Engineering**\n  - Computational Materials Science and Engineering\n- **Mechanical Engineering**\n  - Mechanical Engineering and Computation\n- **Nuclear Science and Engineering**\n  - Computational Nuclear Science and Engineering\n  - Nuclear Engineering and Computation\n- **Earth, Atmospheric and Planetary Sciences**\n  - Computational Earth, Science and Planetary Sciences\n- **Mathematics**\n  - Mathematics and Computational Science\n\nAs with the standalone CSE PhD program, the emphasis of thesis research activities is the development of new computational methods and\/or the innovative application of state-of-the-art computational techniques to important problems in engineering and science. In contrast to the standalone PhD program, however, this research is expected to have a strong disciplinary component of interest to the host department.\n\nThe interdisciplinary CSE PhD program is administered jointly by CCSE and the host departments. Students must submit an application to the CSE PhD program, indicating the department in which they wish to be hosted. To gain admission, CSE program applicants must receive approval from both the host department graduate admission committee and the CSE graduate admission committee. See the website for more information about the [application process, requirements, and relevant deadlines](https:\/\/cse.mit.edu\/admissions\/).\n\nOnce admitted, doctoral degree candidates are expected to complete the host department's degree requirements (including qualifying exam) with some deviations relating to coursework, thesis committee composition, and thesis submission that are specific to the CSE program and are discussed in more detail on the [CSE website](https:\/\/cse.mit.edu\/programs\/phd\/). The most notable coursework requirement associated with this CSE degree is a course of study comprising five graduate subjects in CSE (below).\n\n### Computational Concentration Subjects\n|   |   |   |\n|---|---|---|\n| [1\\.125](https:\/\/catalog.mit.edu\/search\/?P=1.125 \"1.125\") | Architecting and Engineering Software Systems | 12 |\n| [1\\.545\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=1.545 \"1.545[J]\") | Atomistic Modeling and Simulation of Materials and Structures | 12 |\n| [1\\.583\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=1.583 \"1.583[J]\") | Topology Optimization of Structures | 12 |\n| [1\\.723](https:\/\/catalog.mit.edu\/search\/?P=1.723 \"1.723\") | Computational Methods for Flow in Porous Media | 12 |\n| [2\\.098](https:\/\/catalog.mit.edu\/search\/?P=2.098 \"2.098\") | Introduction to Finite Element Methods | 12 |\n| [2\\.156](https:\/\/catalog.mit.edu\/search\/?P=2.156 \"2.156\") | Artificial Intelligence and Machine Learning for Engineering Design | 12 |\n| [2\\.168](https:\/\/catalog.mit.edu\/search\/?P=2.168 \"2.168\") | Learning Machines | 12 |\n| [2\\.29](https:\/\/catalog.mit.edu\/search\/?P=2.29 \"2.29\") | Numerical Fluid Mechanics | 12 |\n| [3\\.320](https:\/\/catalog.mit.edu\/search\/?P=3.320 \"3.320\") | Atomistic Computer Modeling of Materials | 12 |\n| [4\\.450\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=4.450 \"4.450[J]\") | Computational Structural Design and Optimization |   |\n| [6\\.7210\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=6.7210 \"6.7210[J]\") | Introduction to Mathematical Programming | 12 |\n| [6\\.7220\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=6.7220 \"6.7220[J]\") | Nonlinear Optimization | 12 |\n| [6\\.7230\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=6.7230 \"6.7230[J]\") | Algebraic Techniques and Semidefinite Optimization | 12 |\n| [6\\.7300\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=6.7300 \"6.7300[J]\") | Introduction to Modeling and Simulation | 12 |\n| [6\\.7810](https:\/\/catalog.mit.edu\/search\/?P=6.7810 \"6.7810\") | Algorithms for Inference | 12 |\n| [6\\.7830](https:\/\/catalog.mit.edu\/search\/?P=6.7830 \"6.7830\") | Bayesian Modeling and Inference | 12 |\n| [6\\.7900](https:\/\/catalog.mit.edu\/search\/?P=6.7900 \"6.7900\") | Machine Learning 1 | 12 |\n| [6\\.7940](https:\/\/catalog.mit.edu\/search\/?P=6.7940 \"6.7940\") | Dynamic Programming and Reinforcement Learning | 12 |\n| [6\\.8300](https:\/\/catalog.mit.edu\/search\/?P=6.8300 \"6.8300\") | Advances in Computer Vision | 12 |\n| [6\\.8410](https:\/\/catalog.mit.edu\/search\/?P=6.8410 \"6.8410\") | Shape Analysis | 12 |\n| [6\\.C51](https:\/\/catalog.mit.edu\/search\/?P=6.C51 \"6.C51\") | Modeling with Machine Learning: from Algorithms to Applications 2 | 6 |\n| [9\\.520\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=9.520 \"9.520[J]\") | Statistical Learning Theory and Applications | 12 |\n| [9\\.660](https:\/\/catalog.mit.edu\/search\/?P=9.660 \"9.660\") | Computational Cognitive Science | 12 |\n| [10\\.551](https:\/\/catalog.mit.edu\/search\/?P=10.551 \"10.551\") | Systems Engineering 3 | 9 |\n| [10\\.552](https:\/\/catalog.mit.edu\/search\/?P=10.552 \"10.552\") | Modern Control Design 3 | 9 |\n| [10\\.554\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=10.554 \"10.554[J]\") | Process Data Analytics | 12 |\n| [10\\.557](https:\/\/catalog.mit.edu\/search\/?P=10.557 \"10.557\") | Mixed-integer and Nonconvex Optimization | 12 |\n| [10\\.637\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=10.637 \"10.637[J]\") | Computational Chemistry | 12 |\n| [12\\.515](https:\/\/catalog.mit.edu\/search\/?P=12.515 \"12.515\") | Data and Models | 12 |\n| [12\\.521](https:\/\/catalog.mit.edu\/search\/?P=12.521 \"12.521\") | Computational Geophysical Modeling | 12 |\n| [12\\.620\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=12.620 \"12.620[J]\") | Classical Mechanics: A Computational Approach | 12 |\n| [12\\.714](https:\/\/catalog.mit.edu\/search\/?P=12.714 \"12.714\") | Computational Data Analysis | 12 |\n| [12\\.805](https:\/\/catalog.mit.edu\/search\/?P=12.805 \"12.805\") | Data Analysis in Physical Oceanography | 12 |\n| [12\\.850](https:\/\/catalog.mit.edu\/search\/?P=12.850 \"12.850\") | Computational Ocean Modeling | 12 |\n| [15\\.070\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=15.070 \"15.070[J]\") | Discrete Probability and Stochastic Processes | 12 |\n| [15\\.077\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=15.077 \"15.077[J]\") | Statistical Machine Learning and Data Science 1 | 12 |\n| [15\\.083](https:\/\/catalog.mit.edu\/search\/?P=15.083 \"15.083\") | Integer Optimization | 12 |\n| [15\\.764\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=15.764 \"15.764[J]\") | The Theory of Operations Management | 12 |\n| [15\\.C57\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=15.C57 \"15.C57[J]\") | Optimization Methods | 12 |\n| [16\\.110](https:\/\/catalog.mit.edu\/search\/?P=16.110 \"16.110\") | Flight Vehicle Aerodynamics | 12 |\n| [16\\.225\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=16.225 \"16.225[J]\") | Computational Mechanics of Materials | 12 |\n| [16\\.413\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=16.413 \"16.413[J]\") | Principles of Autonomy and Decision Making | 12 |\n| [16\\.888\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=16.888 \"16.888[J]\") | Multidisciplinary Design Optimization | 12 |\n| [16\\.920\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=16.920 \"16.920[J]\") | Numerical Methods for Partial Differential Equations | 12 |\n| [16\\.930](https:\/\/catalog.mit.edu\/search\/?P=16.930 \"16.930\") | Advanced Topics in Numerical Methods for Partial Differential Equations | 12 |\n| [16\\.940](https:\/\/catalog.mit.edu\/search\/?P=16.940 \"16.940\") | Numerical Methods for Stochastic Modeling and Inference | 12 |\n| [18\\.335\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=18.335 \"18.335[J]\") | Introduction to Numerical Methods | 12 |\n| [18\\.336\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=18.336 \"18.336[J]\") | Fast Methods for Partial Differential and Integral Equations | 12 |\n| [18\\.337\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=18.337 \"18.337[J]\") | Parallel Computing and Scientific Machine Learning | 12 |\n| [18\\.338](https:\/\/catalog.mit.edu\/search\/?P=18.338 \"18.338\") | Eigenvalues of Random Matrices | 12 |\n| [18\\.369\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=18.369 \"18.369[J]\") | Mathematical Methods in Nanophotonics | 12 |\n| [18\\.435\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=18.435 \"18.435[J]\") | Quantum Computation | 12 |\n| [22\\.15](https:\/\/catalog.mit.edu\/search\/?P=22.15 \"22.15\") | Essential Numerical Methods | 6 |\n| [22\\.212](https:\/\/catalog.mit.edu\/search\/?P=22.212 \"22.212\") | Nuclear Reactor Analysis II | 12 |\n| [22\\.213](https:\/\/catalog.mit.edu\/search\/?P=22.213 \"22.213\") | Nuclear Reactor Physics III | 12 |\n| [22\\.315](https:\/\/catalog.mit.edu\/search\/?P=22.315 \"22.315\") | Applied Computational Fluid Dynamics and Heat Transfer | 12 |\n| [CSE.999](https:\/\/catalog.mit.edu\/search\/?P=CSE.999 \"CSE.999\") | Experiential Learning in Computational Science and Engineering |   |\n| [IDS.131\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=IDS.131 \"IDS.131[J]\") | Statistics, Computation and Applications | 12 |\n\nNote: Students may not use more than 12 units of credit from a \"meets with undergraduate\" subject to fulfill the CSE curriculum requirements\n\n|   |   |\n|---|---|\n| *1* | *Credit can only be given for one of [6\\.7900](https:\/\/catalog.mit.edu\/search\/?P=6.7900 \"6.7900\"), [15\\.077\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=15.077 \"15.077[J]\"), or [IDS.147\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=IDS.147 \"IDS.147[J]\").* |\n| *2* | *Students cannot receive credit without simultaneous completion of a 6-unit Common Ground disciplinary module. The two subjects together count as one 12-unit subject. See [6\\.C51](https:\/\/catalog.mit.edu\/search\/?P=6.C51 \"6.C51\") for more information.* |\n| *3* | *Students can receive credit for either [10\\.551](https:\/\/catalog.mit.edu\/search\/?P=10.551 \"10.551\") or [10\\.552](https:\/\/catalog.mit.edu\/search\/?P=10.552 \"10.552\") as a CSE concentration subject, but not both.* |\n| *4* | *Subject to Sloan bidding process.* |\n## Inquiries\nFor more information, please visit the [CCSE website](https:\/\/cse.mit.edu\/).\n\n[Admissions](http:\/\/mitadmissions.org\/apply)[Financial Aid](http:\/\/sfs.mit.edu\/)[Registrar](http:\/\/web.mit.edu\/registrar\/)[IAP](http:\/\/web.mit.edu\/iap\/)[Summer](https:\/\/catalog.mit.edu\/summer\/)[Professional Education](http:\/\/professional.mit.edu\/)[MITx](https:\/\/www.edx.org\/school\/mitx)[K-12](https:\/\/outreach.mit.edu\/)[Campus Map](http:\/\/whereis.mit.edu\/)  \n[Directories](https:\/\/officesdirectory.mit.edu\/)[About the Bulletin](https:\/\/catalog.mit.edu\/about-bulletin\/)[Nondiscrimination Policy](https:\/\/catalog.mit.edu\/nondiscrimination-policy\/)[Changes](https:\/\/catalog.mit.edu\/changelog\/)[Help](https:\/\/catalog.mit.edu\/help\/)[Accessibility](https:\/\/accessibility.mit.edu\/)\n\n![MIT](https:\/\/catalog.mit.edu\/images\/mit-logo-footer.svg)\n\n![MIT Academic Bulletin](https:\/\/catalog.mit.edu\/images\/mit-bulletin-logo-footer-25-26.png)\n\n77 Massachusetts Avenue  \nCambridge, MA 02139-4307\n\n[Back to top](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/computational-science-engineering\/#header)\n\nPrint Options\n\n[Send Page to Printer](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/computational-science-engineering\/)\n\n*Print this page.*\n\n[Download PDF of this Page](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/computational-science-engineering\/computational-science-engineering.pdf)\n\n*The PDF includes all information on this page and its related tabs. Subject (course) information includes any changes approved for the current academic year.*\n\n[Download PDF of the Entire Catalog and\/or Subject Descriptions](https:\/\/catalog.mit.edu\/archive\/)\n\n[Cancel](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/computational-science-engineering\/)","attrs_readable_markdown":"The [Center for Computational Science and Engineering (CCSE)](https:\/\/cse.mit.edu\/programs\/) offers a master's degree and two doctoral programs in computational science and engineering (CSE)—one leading to a standalone PhD degree in CSE offered entirely by CCSE and the other to an interdisciplinary PhD degree offered jointly with participating departments in the School of Engineering and the School of Science.\n\nWhile both programs enable students to specialize at the doctoral level in a computation-related field via focused coursework and a thesis, they differ in essential ways. The **standalone CSE PhD program** is intended for students who intend to pursue research in cross-cutting methodological aspects of computational science. The resulting doctoral degree is awarded by the Schwarzman College of Computing. In contrast, the **interdisciplinary CSE PhD program** is intended for students who are interested in computation in the context of a specific engineering or science discipline. For this reason, this degree is offered jointly with participating departments across the Institute; the interdisciplinary degree is awarded in a specially crafted thesis field that recognizes the student’s specialization in computation.\n\nAt the time of application, students are expected to declare which of the two programs they are interested in. Admissions decisions will take into account these declared interests, along with each applicant’s academic background, preparation, and fit to the program they have selected.\n\nApplicants interested in an advanced degree in computer science should instead apply for admission to the [Department of Electrical Engineering and Computer Science](https:\/\/www.eecs.mit.edu\/).\n\n## Master of Science in Computational Science and Engineering\nThe [Master of Science in Computational Science and Engineering (CSE SM)](https:\/\/catalog.mit.edu\/degree-charts\/master-computational-science-engineering\/) is an interdisciplinary, research-oriented master's program that provides students with a strong foundation in computational methods for the study, design, and operation of complex engineered and natural systems.\n\nThe curriculum trains students in the formulation, analysis, implementation, and application of computational approaches in science and engineering. It combines a course of study comprising six graduate subjects with a master's thesis describing original research performed under the supervision of a CSE faculty member. The coursework requirements include:\n\n- A three-subject core aimed at developing breadth as well as depth in numerical analysis, simulation, and optimization\n- A two-subject restricted elective program aimed at reinforcing multidisciplinary aspects of computation\n- One unrestricted elective subject\n\nHands-on experience is encouraged and reinforced through projects in the core, the elective subjects, and the master's thesis.\n\n## Doctor of Philosophy in Computational Science and Engineering\nThe standalone doctoral program in Computational Science and Engineering ([PhD in CSE)](https:\/\/catalog.mit.edu\/degree-charts\/phd-computational-science-engineering\/) enables students to specialize at the doctoral level in fundamental, methodological aspects of computational science via focused coursework and a thesis. The emphasis of thesis research activities is the development and analysis of broadly applicable computational approaches that advance the state of the art.\n\nStudents are awarded the Doctor of Philosophy in Computational Science and Engineering upon successful completion of the program requirements and defense of a thesis describing significant contributions to the CSE field. Program requirements include a course of study comprising nine graduate subjects and a graduate seminar. Core and concentration subjects cover six “ways of thinking” fundamental to CSE: (i) discretization and numerical methods for partial differential equations; (ii) optimization methods; (iii) statistics and data-driven modeling; (iv) high-performance computing and\/or algorithms; (v) mathematical foundations (e.g., functional analysis, probability); and (vi) modeling (i.e., a subject that treats mathematical modeling in any science or engineering discipline). Subjects taken as part of an MIT SM program can be counted toward the coursework requirement provided they satisfy core, concentration, or elective requirements as set forth [here](https:\/\/catalog.mit.edu\/degree-charts\/phd-computational-science-engineering\/); consultation and approval by the program director(s) and\/or administrator regarding the application of such courses toward program credit is always required.\n\nStudents applying to this program are expected to have a degree in CSE, applied mathematics, or another field that prepares them for an advanced degree in CSE. More information about the application process, requirements, and relevant deadlines can be found on the [Admissions section of the CCSE website](https:\/\/cse.mit.edu\/admissions\/).\n\n## Interdisciplinary Doctoral Program in Computational Science and Engineering\nThe interdisciplinary doctoral program in Computational Science and Engineering ([PhD in CSE + Engineering or Science](https:\/\/catalog.mit.edu\/degree-charts\/phd-computational-science-engineering\/#phdincseengineeringorsciencetext)) offers students the opportunity to specialize at the doctoral level in a computation-related field of their choice via computationally-oriented coursework and a doctoral thesis with a disciplinary focus related to one of eight participating host departments, namely, Aeronautics and Astronautics; Chemical Engineering; Civil and Environmental Engineering; Earth, Atmospheric and Planetary Sciences; Materials Science and Engineering; Mathematics; Mechanical Engineering; or Nuclear Science and Engineering.\n\nDoctoral thesis fields associated with each department are as follows:\n\n- **Aeronautics and Astronautics**\n  - Aerospace Engineering and Computational Science\n  - Computational Science and Engineering (available only to students who matriculate in 2023–2024 or earlier)\n- **Chemical Engineering**\n  - Chemical Engineering and Computation\n- **Civil and Environmental Engineering**\n  - Civil Engineering and Computation\n  - Environmental Engineering and Computation\n- **Materials Science and Engineering**\n  - Computational Materials Science and Engineering\n- **Mechanical Engineering**\n  - Mechanical Engineering and Computation\n- **Nuclear Science and Engineering**\n  - Computational Nuclear Science and Engineering\n  - Nuclear Engineering and Computation\n- **Earth, Atmospheric and Planetary Sciences**\n  - Computational Earth, Science and Planetary Sciences\n- **Mathematics**\n  - Mathematics and Computational Science\n\nAs with the standalone CSE PhD program, the emphasis of thesis research activities is the development of new computational methods and\/or the innovative application of state-of-the-art computational techniques to important problems in engineering and science. In contrast to the standalone PhD program, however, this research is expected to have a strong disciplinary component of interest to the host department.\n\nThe interdisciplinary CSE PhD program is administered jointly by CCSE and the host departments. Students must submit an application to the CSE PhD program, indicating the department in which they wish to be hosted. To gain admission, CSE program applicants must receive approval from both the host department graduate admission committee and the CSE graduate admission committee. See the website for more information about the [application process, requirements, and relevant deadlines](https:\/\/cse.mit.edu\/admissions\/).\n\nOnce admitted, doctoral degree candidates are expected to complete the host department's degree requirements (including qualifying exam) with some deviations relating to coursework, thesis committee composition, and thesis submission that are specific to the CSE program and are discussed in more detail on the [CSE website](https:\/\/cse.mit.edu\/programs\/phd\/). The most notable coursework requirement associated with this CSE degree is a course of study comprising five graduate subjects in CSE (below).\n\n### Computational Concentration Subjects\n|   |   |   |\n|---|---|---|\n| [1\\.125](https:\/\/catalog.mit.edu\/search\/?P=1.125 \"1.125\") | Architecting and Engineering Software Systems | 12 |\n| [1\\.545\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=1.545 \"1.545[J]\") | Atomistic Modeling and Simulation of Materials and Structures | 12 |\n| [1\\.583\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=1.583 \"1.583[J]\") | Topology Optimization of Structures | 12 |\n| [1\\.723](https:\/\/catalog.mit.edu\/search\/?P=1.723 \"1.723\") | Computational Methods for Flow in Porous Media | 12 |\n| [2\\.098](https:\/\/catalog.mit.edu\/search\/?P=2.098 \"2.098\") | Introduction to Finite Element Methods | 12 |\n| [2\\.156](https:\/\/catalog.mit.edu\/search\/?P=2.156 \"2.156\") | Artificial Intelligence and Machine Learning for Engineering Design | 12 |\n| [2\\.168](https:\/\/catalog.mit.edu\/search\/?P=2.168 \"2.168\") | Learning Machines | 12 |\n| [2\\.29](https:\/\/catalog.mit.edu\/search\/?P=2.29 \"2.29\") | Numerical Fluid Mechanics | 12 |\n| [3\\.320](https:\/\/catalog.mit.edu\/search\/?P=3.320 \"3.320\") | Atomistic Computer Modeling of Materials | 12 |\n| [4\\.450\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=4.450 \"4.450[J]\") | Computational Structural Design and Optimization |   |\n| [6\\.7210\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=6.7210 \"6.7210[J]\") | Introduction to Mathematical Programming | 12 |\n| [6\\.7220\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=6.7220 \"6.7220[J]\") | Nonlinear Optimization | 12 |\n| [6\\.7230\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=6.7230 \"6.7230[J]\") | Algebraic Techniques and Semidefinite Optimization | 12 |\n| [6\\.7300\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=6.7300 \"6.7300[J]\") | Introduction to Modeling and Simulation | 12 |\n| [6\\.7810](https:\/\/catalog.mit.edu\/search\/?P=6.7810 \"6.7810\") | Algorithms for Inference | 12 |\n| [6\\.7830](https:\/\/catalog.mit.edu\/search\/?P=6.7830 \"6.7830\") | Bayesian Modeling and Inference | 12 |\n| [6\\.7900](https:\/\/catalog.mit.edu\/search\/?P=6.7900 \"6.7900\") | Machine Learning 1 | 12 |\n| [6\\.7940](https:\/\/catalog.mit.edu\/search\/?P=6.7940 \"6.7940\") | Dynamic Programming and Reinforcement Learning | 12 |\n| [6\\.8300](https:\/\/catalog.mit.edu\/search\/?P=6.8300 \"6.8300\") | Advances in Computer Vision | 12 |\n| [6\\.8410](https:\/\/catalog.mit.edu\/search\/?P=6.8410 \"6.8410\") | Shape Analysis | 12 |\n| [6\\.C51](https:\/\/catalog.mit.edu\/search\/?P=6.C51 \"6.C51\") | Modeling with Machine Learning: from Algorithms to Applications 2 | 6 |\n| [9\\.520\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=9.520 \"9.520[J]\") | Statistical Learning Theory and Applications | 12 |\n| [9\\.660](https:\/\/catalog.mit.edu\/search\/?P=9.660 \"9.660\") | Computational Cognitive Science | 12 |\n| [10\\.551](https:\/\/catalog.mit.edu\/search\/?P=10.551 \"10.551\") | Systems Engineering 3 | 9 |\n| [10\\.552](https:\/\/catalog.mit.edu\/search\/?P=10.552 \"10.552\") | Modern Control Design 3 | 9 |\n| [10\\.554\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=10.554 \"10.554[J]\") | Process Data Analytics | 12 |\n| [10\\.557](https:\/\/catalog.mit.edu\/search\/?P=10.557 \"10.557\") | Mixed-integer and Nonconvex Optimization | 12 |\n| [10\\.637\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=10.637 \"10.637[J]\") | Computational Chemistry | 12 |\n| [12\\.515](https:\/\/catalog.mit.edu\/search\/?P=12.515 \"12.515\") | Data and Models | 12 |\n| [12\\.521](https:\/\/catalog.mit.edu\/search\/?P=12.521 \"12.521\") | Computational Geophysical Modeling | 12 |\n| [12\\.620\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=12.620 \"12.620[J]\") | Classical Mechanics: A Computational Approach | 12 |\n| [12\\.714](https:\/\/catalog.mit.edu\/search\/?P=12.714 \"12.714\") | Computational Data Analysis | 12 |\n| [12\\.805](https:\/\/catalog.mit.edu\/search\/?P=12.805 \"12.805\") | Data Analysis in Physical Oceanography | 12 |\n| [12\\.850](https:\/\/catalog.mit.edu\/search\/?P=12.850 \"12.850\") | Computational Ocean Modeling | 12 |\n| [15\\.070\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=15.070 \"15.070[J]\") | Discrete Probability and Stochastic Processes | 12 |\n| [15\\.077\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=15.077 \"15.077[J]\") | Statistical Machine Learning and Data Science 1 | 12 |\n| [15\\.083](https:\/\/catalog.mit.edu\/search\/?P=15.083 \"15.083\") | Integer Optimization | 12 |\n| [15\\.764\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=15.764 \"15.764[J]\") | The Theory of Operations Management | 12 |\n| [15\\.C57\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=15.C57 \"15.C57[J]\") | Optimization Methods | 12 |\n| [16\\.110](https:\/\/catalog.mit.edu\/search\/?P=16.110 \"16.110\") | Flight Vehicle Aerodynamics | 12 |\n| [16\\.225\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=16.225 \"16.225[J]\") | Computational Mechanics of Materials | 12 |\n| [16\\.413\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=16.413 \"16.413[J]\") | Principles of Autonomy and Decision Making | 12 |\n| [16\\.888\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=16.888 \"16.888[J]\") | Multidisciplinary Design Optimization | 12 |\n| [16\\.920\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=16.920 \"16.920[J]\") | Numerical Methods for Partial Differential Equations | 12 |\n| [16\\.930](https:\/\/catalog.mit.edu\/search\/?P=16.930 \"16.930\") | Advanced Topics in Numerical Methods for Partial Differential Equations | 12 |\n| [16\\.940](https:\/\/catalog.mit.edu\/search\/?P=16.940 \"16.940\") | Numerical Methods for Stochastic Modeling and Inference | 12 |\n| [18\\.335\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=18.335 \"18.335[J]\") | Introduction to Numerical Methods | 12 |\n| [18\\.336\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=18.336 \"18.336[J]\") | Fast Methods for Partial Differential and Integral Equations | 12 |\n| [18\\.337\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=18.337 \"18.337[J]\") | Parallel Computing and Scientific Machine Learning | 12 |\n| [18\\.338](https:\/\/catalog.mit.edu\/search\/?P=18.338 \"18.338\") | Eigenvalues of Random Matrices | 12 |\n| [18\\.369\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=18.369 \"18.369[J]\") | Mathematical Methods in Nanophotonics | 12 |\n| [18\\.435\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=18.435 \"18.435[J]\") | Quantum Computation | 12 |\n| [22\\.15](https:\/\/catalog.mit.edu\/search\/?P=22.15 \"22.15\") | Essential Numerical Methods | 6 |\n| [22\\.212](https:\/\/catalog.mit.edu\/search\/?P=22.212 \"22.212\") | Nuclear Reactor Analysis II | 12 |\n| [22\\.213](https:\/\/catalog.mit.edu\/search\/?P=22.213 \"22.213\") | Nuclear Reactor Physics III | 12 |\n| [22\\.315](https:\/\/catalog.mit.edu\/search\/?P=22.315 \"22.315\") | Applied Computational Fluid Dynamics and Heat Transfer | 12 |\n| [CSE.999](https:\/\/catalog.mit.edu\/search\/?P=CSE.999 \"CSE.999\") | Experiential Learning in Computational Science and Engineering |   |\n| [IDS.131\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=IDS.131 \"IDS.131[J]\") | Statistics, Computation and Applications | 12 |\n\nNote: Students may not use more than 12 units of credit from a \"meets with undergraduate\" subject to fulfill the CSE curriculum requirements\n\n|   |   |\n|---|---|\n| *1* | *Credit can only be given for one of [6\\.7900](https:\/\/catalog.mit.edu\/search\/?P=6.7900 \"6.7900\"), [15\\.077\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=15.077 \"15.077[J]\"), or [IDS.147\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=IDS.147 \"IDS.147[J]\").* |\n| *2* | *Students cannot receive credit without simultaneous completion of a 6-unit Common Ground disciplinary module. The two subjects together count as one 12-unit subject. See [6\\.C51](https:\/\/catalog.mit.edu\/search\/?P=6.C51 \"6.C51\") for more information.* |\n| *3* | *Students can receive credit for either [10\\.551](https:\/\/catalog.mit.edu\/search\/?P=10.551 \"10.551\") or [10\\.552](https:\/\/catalog.mit.edu\/search\/?P=10.552 \"10.552\") as a CSE concentration subject, but not both.* |\n| *4* | *Subject to Sloan bidding process.* |\n## Inquiries\nFor more information, please visit the [CCSE website](https:\/\/cse.mit.edu\/).","meta_canonical":null}

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URL	https://catalog.mit.edu/interdisciplinary/graduate-programs/computational-science-engineering/
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Boilerpipe Text	The Center for Computational Science and Engineering (CCSE) offers a master's degree and two doctoral programs in computational science and engineering (CSE)—one leading to a standalone PhD degree in CSE offered entirely by CCSE and the other to an interdisciplinary PhD degree offered jointly with participating departments in the School of Engineering and the School of Science. While both programs enable students to specialize at the doctoral level in a computation-related field via focused coursework and a thesis, they differ in essential ways. The standalone CSE PhD program is intended for students who intend to pursue research in cross-cutting methodological aspects of computational science. The resulting doctoral degree is awarded by the Schwarzman College of Computing. In contrast, the interdisciplinary CSE PhD program is intended for students who are interested in computation in the context of a specific engineering or science discipline. For this reason, this degree is offered jointly with participating departments across the Institute; the interdisciplinary degree is awarded in a specially crafted thesis field that recognizes the student’s specialization in computation. At the time of application, students are expected to declare which of the two programs they are interested in. Admissions decisions will take into account these declared interests, along with each applicant’s academic background, preparation, and fit to the program they have selected. Applicants interested in an advanced degree in computer science should instead apply for admission to the Department of Electrical Engineering and Computer Science . Master of Science in Computational Science and Engineering The Master of Science in Computational Science and Engineering (CSE SM) is an interdisciplinary, research-oriented master's program that provides students with a strong foundation in computational methods for the study, design, and operation of complex engineered and natural systems. The curriculum trains students in the formulation, analysis, implementation, and application of computational approaches in science and engineering. It combines a course of study comprising six graduate subjects with a master's thesis describing original research performed under the supervision of a CSE faculty member. The coursework requirements include: A three-subject core aimed at developing breadth as well as depth in numerical analysis, simulation, and optimization A two-subject restricted elective program aimed at reinforcing multidisciplinary aspects of computation One unrestricted elective subject Hands-on experience is encouraged and reinforced through projects in the core, the elective subjects, and the master's thesis. Doctor of Philosophy in Computational Science and Engineering The standalone doctoral program in Computational Science and Engineering ( PhD in CSE) enables students to specialize at the doctoral level in fundamental, methodological aspects of computational science via focused coursework and a thesis. The emphasis of thesis research activities is the development and analysis of broadly applicable computational approaches that advance the state of the art. Students are awarded the Doctor of Philosophy in Computational Science and Engineering upon successful completion of the program requirements and defense of a thesis describing significant contributions to the CSE field. Program requirements include a course of study comprising nine graduate subjects and a graduate seminar. Core and concentration subjects cover six “ways of thinking” fundamental to CSE: (i) discretization and numerical methods for partial differential equations; (ii) optimization methods; (iii) statistics and data-driven modeling; (iv) high-performance computing and/or algorithms; (v) mathematical foundations (e.g., functional analysis, probability); and (vi) modeling (i.e., a subject that treats mathematical modeling in any science or engineering discipline). Subjects taken as part of an MIT SM program can be counted toward the coursework requirement provided they satisfy core, concentration, or elective requirements as set forth here ; consultation and approval by the program director(s) and/or administrator regarding the application of such courses toward program credit is always required. Students applying to this program are expected to have a degree in CSE, applied mathematics, or another field that prepares them for an advanced degree in CSE. More information about the application process, requirements, and relevant deadlines can be found on the Admissions section of the CCSE website . Interdisciplinary Doctoral Program in Computational Science and Engineering The interdisciplinary doctoral program in Computational Science and Engineering ( PhD in CSE + Engineering or Science ) offers students the opportunity to specialize at the doctoral level in a computation-related field of their choice via computationally-oriented coursework and a doctoral thesis with a disciplinary focus related to one of eight participating host departments, namely, Aeronautics and Astronautics; Chemical Engineering; Civil and Environmental Engineering; Earth, Atmospheric and Planetary Sciences; Materials Science and Engineering; Mathematics; Mechanical Engineering; or Nuclear Science and Engineering. Doctoral thesis fields associated with each department are as follows: Aeronautics and Astronautics Aerospace Engineering and Computational Science Computational Science and Engineering (available only to students who matriculate in 2023–2024 or earlier) Chemical Engineering Chemical Engineering and Computation Civil and Environmental Engineering Civil Engineering and Computation Environmental Engineering and Computation Materials Science and Engineering Computational Materials Science and Engineering Mechanical Engineering Mechanical Engineering and Computation Nuclear Science and Engineering Computational Nuclear Science and Engineering Nuclear Engineering and Computation Earth, Atmospheric and Planetary Sciences Computational Earth, Science and Planetary Sciences Mathematics Mathematics and Computational Science As with the standalone CSE PhD program, the emphasis of thesis research activities is the development of new computational methods and/or the innovative application of state-of-the-art computational techniques to important problems in engineering and science. In contrast to the standalone PhD program, however, this research is expected to have a strong disciplinary component of interest to the host department. The interdisciplinary CSE PhD program is administered jointly by CCSE and the host departments. Students must submit an application to the CSE PhD program, indicating the department in which they wish to be hosted. To gain admission, CSE program applicants must receive approval from both the host department graduate admission committee and the CSE graduate admission committee. See the website for more information about the application process, requirements, and relevant deadlines . Once admitted, doctoral degree candidates are expected to complete the host department's degree requirements (including qualifying exam) with some deviations relating to coursework, thesis committee composition, and thesis submission that are specific to the CSE program and are discussed in more detail on the CSE website . The most notable coursework requirement associated with this CSE degree is a course of study comprising five graduate subjects in CSE (below). Computational Concentration Subjects 1.125 Architecting and Engineering Software Systems 12 1.545[J] Atomistic Modeling and Simulation of Materials and Structures 12 1.583[J] Topology Optimization of Structures 12 1.723 Computational Methods for Flow in Porous Media 12 2.098 Introduction to Finite Element Methods 12 2.156 Artificial Intelligence and Machine Learning for Engineering Design 12 2.168 Learning Machines 12 2.29 Numerical Fluid Mechanics 12 3.320 Atomistic Computer Modeling of Materials 12 4.450[J] Computational Structural Design and Optimization 6.7210[J] Introduction to Mathematical Programming 12 6.7220[J] Nonlinear Optimization 12 6.7230[J] Algebraic Techniques and Semidefinite Optimization 12 6.7300[J] Introduction to Modeling and Simulation 12 6.7810 Algorithms for Inference 12 6.7830 Bayesian Modeling and Inference 12 6.7900 Machine Learning 1 12 6.7940 Dynamic Programming and Reinforcement Learning 12 6.8300 Advances in Computer Vision 12 6.8410 Shape Analysis 12 6.C51 Modeling with Machine Learning: from Algorithms to Applications 2 6 9.520[J] Statistical Learning Theory and Applications 12 9.660 Computational Cognitive Science 12 10.551 Systems Engineering 3 9 10.552 Modern Control Design 3 9 10.554[J] Process Data Analytics 12 10.557 Mixed-integer and Nonconvex Optimization 12 10.637[J] Computational Chemistry 12 12.515 Data and Models 12 12.521 Computational Geophysical Modeling 12 12.620[J] Classical Mechanics: A Computational Approach 12 12.714 Computational Data Analysis 12 12.805 Data Analysis in Physical Oceanography 12 12.850 Computational Ocean Modeling 12 15.070[J] Discrete Probability and Stochastic Processes 12 15.077[J] Statistical Machine Learning and Data Science 1 12 15.083 Integer Optimization 12 15.764[J] The Theory of Operations Management 12 15.C57[J] Optimization Methods 12 16.110 Flight Vehicle Aerodynamics 12 16.225[J] Computational Mechanics of Materials 12 16.413[J] Principles of Autonomy and Decision Making 12 16.888[J] Multidisciplinary Design Optimization 12 16.920[J] Numerical Methods for Partial Differential Equations 12 16.930 Advanced Topics in Numerical Methods for Partial Differential Equations 12 16.940 Numerical Methods for Stochastic Modeling and Inference 12 18.335[J] Introduction to Numerical Methods 12 18.336[J] Fast Methods for Partial Differential and Integral Equations 12 18.337[J] Parallel Computing and Scientific Machine Learning 12 18.338 Eigenvalues of Random Matrices 12 18.369[J] Mathematical Methods in Nanophotonics 12 18.435[J] Quantum Computation 12 22.15 Essential Numerical Methods 6 22.212 Nuclear Reactor Analysis II 12 22.213 Nuclear Reactor Physics III 12 22.315 Applied Computational Fluid Dynamics and Heat Transfer 12 CSE.999 Experiential Learning in Computational Science and Engineering IDS.131[J] Statistics, Computation and Applications 12 Note: Students may not use more than 12 units of credit from a "meets with undergraduate" subject to fulfill the CSE curriculum requirements 1 Credit can only be given for one of 6.7900 , 15.077[J] , or IDS.147[J] . 2 Students cannot receive credit without simultaneous completion of a 6-unit Common Ground disciplinary module. The two subjects together count as one 12-unit subject. See 6.C51 for more information. 3 Students can receive credit for either 10.551 or 10.552 as a CSE concentration subject, but not both. 4 Subject to Sloan bidding process. Inquiries For more information, please visit the CCSE website .
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[Linguistics and Philosophy (SB, Course 24-2)](https://catalog.mit.edu/degree-charts/linguistics-philosophy-course-24-2/) - [Philosophy (SB, Course 24-1)](https://catalog.mit.edu/degree-charts/philosophy-course-24-1/) - [Linguistics (SM)](https://catalog.mit.edu/degree-charts/sm-linguistics/) - [Literature](https://catalog.mit.edu/schools/humanities-arts-social-sciences/literature/) Toggle Literature - [Literature (SB, Course 21L)](https://catalog.mit.edu/degree-charts/literature-course-21l/) - [Music and Theater Arts](https://catalog.mit.edu/schools/humanities-arts-social-sciences/music-theater-arts/) Toggle Music and Theater Arts - [Music (SB, Course 21M)](https://catalog.mit.edu/degree-charts/music-course-21m/) - [Theater Arts (SB, Course 21T)](https://catalog.mit.edu/degree-charts/theater-arts-course-21t/) - [Political Science](https://catalog.mit.edu/schools/humanities-arts-social-sciences/political-science/) Toggle Political Science - [Political Science (SB, Course 17)](https://catalog.mit.edu/degree-charts/political-science-course-17/) - [Science, Technology, and Society](https://catalog.mit.edu/schools/humanities-arts-social-sciences/science-technology-society/) Toggle Science, Technology, and Society - [Science, Technology, and Society/Second Major (SB, STS)](https://catalog.mit.edu/degree-charts/science-technology-society-sts/) - [MIT Sloan School of Management](https://catalog.mit.edu/schools/sloan-management/) Toggle MIT Sloan School of Management - [Management](https://catalog.mit.edu/schools/sloan-management/management/) Toggle Management - [Business Analytics (SB, Course 15-2)](https://catalog.mit.edu/degree-charts/business-analytics-course-15-2/) - [Finance (SB, Course 15-3)](https://catalog.mit.edu/degree-charts/finance-course-15-3/) - [Management (SB, Course 15-1)](https://catalog.mit.edu/degree-charts/management-course-15-1/) - [School of Science](https://catalog.mit.edu/schools/science/) Toggle School of Science - [Biology](https://catalog.mit.edu/schools/science/biology/) Toggle Biology - [Biology (SB, Course 7)](https://catalog.mit.edu/degree-charts/biology-course-7/) - [Chemistry and Biology (SB, Course 5-7)](https://catalog.mit.edu/degree-charts/chemistry-biology-course-5-7/) - [Computer Science and Molecular Biology (SB, Course 6-7)](https://catalog.mit.edu/degree-charts/computer-science-molecular-biology-course-6-7/) - [Computer Science and Molecular Biology (MEng)](https://catalog.mit.edu/degree-charts/master-computer-science-molecular-biology-course-6-7p/) - [Brain and Cognitive Sciences](https://catalog.mit.edu/schools/science/brain-cognitive-sciences/) Toggle Brain and Cognitive Sciences - [Brain and Cognitive Sciences (SB, Course 9)](https://catalog.mit.edu/degree-charts/brain-cognitive-sciences-course-9/) - [Computation and Cognition (SB, Course 6-9)](https://catalog.mit.edu/degree-charts/computation-cognition-6-9/) - [Chemistry](https://catalog.mit.edu/schools/science/chemistry/) Toggle Chemistry - [Chemistry (SB, Course 5)](https://catalog.mit.edu/degree-charts/chemistry-course-5/) - [Chemistry and Biology (SB, Course 5-7)](https://catalog.mit.edu/degree-charts/chemistry-biology-course-5-7/) - [Earth, Atmospheric, and Planetary Sciences](https://catalog.mit.edu/schools/science/earth-atmospheric-planetary-sciences/) Toggle Earth, Atmospheric, and Planetary Sciences - [Earth, Atmospheric and Planetary Sciences (SB, Course 12)](https://catalog.mit.edu/degree-charts/earth-atmospheric-planetary-sciences-course-12/) - [Mathematics](https://catalog.mit.edu/schools/science/mathematics/) Toggle Mathematics - [Mathematics (SB, Course 18)](https://catalog.mit.edu/degree-charts/mathematics-course-18/) - [Mathematics (PhD)](https://catalog.mit.edu/degree-charts/phd-mathematics/) - [Mathematics with Computer Science (SB, Course 18-C)](https://catalog.mit.edu/degree-charts/mathematics-computer-science-course-18-c/) - [Physics](https://catalog.mit.edu/schools/science/physics/) Toggle Physics - [Physics (SB, Course 8)](https://catalog.mit.edu/degree-charts/physics-course-8/) - [MIT Schwarzman College of Computing](https://catalog.mit.edu/schools/mit-schwarzman-college-computing/) Toggle MIT Schwarzman College of Computing - [Electrical Engineering and Computer Science](https://catalog.mit.edu/schools/mit-schwarzman-college-computing/electrical-engineering-computer-science/) - [Data, Systems, and Society](https://catalog.mit.edu/schools/mit-schwarzman-college-computing/data-systems-society/) - [Interdisciplinary Programs](https://catalog.mit.edu/interdisciplinary/) Toggle Interdisciplinary Programs - [Undergraduate Programs](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/) Toggle Undergraduate Programs - [Degrees](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/degrees/) Toggle Degrees - [Chemistry and Biology](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/degrees/chemistry-biology/) - [Climate System Science and Engineering](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/degrees/climate-system-science-engineering/) - [Computation and Cognition](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/degrees/computation-cognition/) - [Computer Science and Molecular Biology](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/degrees/computer-science-molecular-biology/) - [Computer Science, Economics, and Data Science](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/degrees/computer-science-economics-data-science/) - [Humanities](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/degrees/humanities/) - [Humanities and Engineering](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/degrees/humanities-engineering/) - [Humanities and Science](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/degrees/humanities-science/) - [Urban Science and Planning with Computer Science](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/degrees/urban-science-planning-computer-science/) - [Minors](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/) Toggle Minors - [African and African Diaspora Studies](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/minor-african-studies/) - [American Studies](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/minor-american-studies/) - [Ancient and Medieval Studies](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/ancient-medieval-studies/) - [Applied International Studies](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/applied-international-studies/) - [Asian and Asian Diaspora Studies](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/asian-studies/) - [Astronomy](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/astronomy/) - [Biomedical Engineering](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/biomedical-engineering/) - [Energy Studies](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/energy-studies/) - [Entrepreneurship and Innovation](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/entrepreneurship-innovation/) - [Environment and Sustainability](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/environment-sustainability/) - [Latin American and Latino/a Studies](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/latin-american-latino-studies/) - [Middle Eastern Studies](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/middle-eastern-studies/) - [Polymers and Soft Matter](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/polymers-soft-matter/) - [Public Policy](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/public-policy/) - [Russian and Eurasian Studies](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/russian-eurasian-studies/) - [Statistics and Data Science](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/statistics-data-science/) - [Women's and Gender Studies](https://catalog.mit.edu/interdisciplinary/undergraduate-programs/minors/womens-gender-studies/) - [Graduate Programs](https://catalog.mit.edu/interdisciplinary/graduate-programs/) Toggle Graduate Programs - [Advanced Urbanism](https://catalog.mit.edu/interdisciplinary/graduate-programs/advanced-urbanism/) - [Computation and Cognition](https://catalog.mit.edu/interdisciplinary/graduate-programs/computation-cognition/) - [Computational and Systems Biology](https://catalog.mit.edu/interdisciplinary/graduate-programs/computational-systems-biology/) - [Computational Science and Engineering](https://catalog.mit.edu/interdisciplinary/graduate-programs/computational-science-engineering/) - [Computer Science and Molecular Biology](https://catalog.mit.edu/interdisciplinary/graduate-programs/computer-science-molecular-biology/) - [Computer Science, Economics, and Data Science](https://catalog.mit.edu/interdisciplinary/graduate-programs/computer-science-economics-data-science/) - [Health Sciences and Technology](https://catalog.mit.edu/interdisciplinary/graduate-programs/harvard-mit-health-sciences-technology/) - [Joint Program with Woods Hole Oceanographic Institution](https://catalog.mit.edu/interdisciplinary/graduate-programs/joint-program-woods-hole-oceanographic-institution/) - [Leaders for Global Operations](https://catalog.mit.edu/interdisciplinary/graduate-programs/leaders-global-operations/) - [Microbiology](https://catalog.mit.edu/interdisciplinary/graduate-programs/microbiology/) - [Music Technology and Computation](https://catalog.mit.edu/interdisciplinary/graduate-programs/music-technology-computation/) - [Operations Research](https://catalog.mit.edu/interdisciplinary/graduate-programs/operations-research/) - [Polymers and Soft Matter](https://catalog.mit.edu/interdisciplinary/graduate-programs/polymers-soft-matter/) - [Real Estate Development](https://catalog.mit.edu/interdisciplinary/graduate-programs/real-estate-development/) - [Social and Engineering Systems](https://catalog.mit.edu/interdisciplinary/graduate-programs/social-engineering-systems/) - [Statistics](https://catalog.mit.edu/interdisciplinary/graduate-programs/phd-statistics/) - [Supply Chain Management](https://catalog.mit.edu/interdisciplinary/graduate-programs/supply-chain-management/) - [System Design and Management](https://catalog.mit.edu/interdisciplinary/graduate-programs/system-design-management/) - [Technology and Policy](https://catalog.mit.edu/interdisciplinary/graduate-programs/technology-policy/) - [Transportation](https://catalog.mit.edu/interdisciplinary/graduate-programs/transportation/) - [Degree Charts](https://catalog.mit.edu/degree-charts/) Toggle Degree Charts - School of Architecture and Planning - [Architecture (SB, Course 4)](https://catalog.mit.edu/degree-charts/architecture-course-4/) - [Architecture (MArch)](https://catalog.mit.edu/degree-charts/master-architecture/) - [Architecture Studies (SM)](https://catalog.mit.edu/degree-charts/master-architecture-studies/) - [Art and Design (SB, Course 4-B)](https://catalog.mit.edu/degree-charts/architecture-course-4-b/) - [Art, Culture, and Technology (SM)](https://catalog.mit.edu/degree-charts/master-art-culture-technology/) - [City Planning (SM)](https://catalog.mit.edu/degree-charts/master-city-planning/) - [Planning (SB, Course 11)](https://catalog.mit.edu/degree-charts/planning-course-11/) - School of Engineering - [Aeronautics and Astronautics Fields (PhD)](https://catalog.mit.edu/degree-charts/phd-aeronautics-astronautics/) - [Aerospace Engineering (SB, Course 16)](https://catalog.mit.edu/degree-charts/aerospace-engineering-course-16/) - [Archaeology and Materials (SB, Course 3-C)](https://catalog.mit.edu/degree-charts/archaeology-materials-course-3-c/) - [Artificial Intelligence and Decision Making (SB, Course 6-4)](https://catalog.mit.edu/degree-charts/artifical-intelligence-decision-making-course-6-4/) - [Biological Engineering (SB, Course 20)](https://catalog.mit.edu/degree-charts/biological-engineering-course-20/) - [Biological Engineering (PhD)](https://catalog.mit.edu/degree-charts/phd-biological-engineering/) - [Civil and Environmental Engineering (SM)](https://catalog.mit.edu/degree-charts/master-civil-environmental-engineering/) - [Civil and Environmental Engineering (PhD)](https://catalog.mit.edu/degree-charts/phd-civil-environmental-engineering/) - [Chemical-Biological Engineering (SB, Course 10-B)](https://catalog.mit.edu/degree-charts/chemical-biological-engineering-course-10-b/) - [Chemical Engineering (SB, Course 10)](https://catalog.mit.edu/degree-charts/chemical-engineering-course-10/) - [Chemical Engineering (SB, Course 10-C)](https://catalog.mit.edu/degree-charts/chemical-engineering-course-10-c/) - [Computer Science and Engineering (SB, Course 6-3)](https://catalog.mit.edu/degree-charts/computer-science-engineering-course-6-3/) - [Electrical Engineering and Computer Science (MEng)](https://catalog.mit.edu/degree-charts/master-electrical-engineering-computer-science-course-6-p/) - [Electrical Engineering with Computing (SB, Course 6-5)](https://catalog.mit.edu/degree-charts/electrical-engineering-computing-course-6-5/) - [Engineering (SB, Course 1-ENG)](https://catalog.mit.edu/degree-charts/engineering-civil-environmental-engineering-course-1-eng/) - [Engineering (SB, Course 2-A)](https://catalog.mit.edu/degree-charts/mechanical-engineering-course-2-a/) - [Engineering (SB, Course 10-ENG)](https://catalog.mit.edu/degree-charts/engineering-chemical-engineering-course-10-eng/) - [Engineering (SB, Course 16-ENG)](https://catalog.mit.edu/degree-charts/engineering-aeronautics-astronautics-course-16-eng/) - [Engineering (SB, Course 22-ENG)](https://catalog.mit.edu/degree-charts/engineering-nuclear-science-engineering-course-22-eng/) - [Materials Science and Engineering (SB, Course 3)](https://catalog.mit.edu/degree-charts/materials-science-engineering-course-3/) - [Materials Science and Engineering (SB, Course 3-A)](https://catalog.mit.edu/degree-charts/materials-science-engineering-course-3-a/) - [Materials Science and Engineering (PhD)](https://catalog.mit.edu/degree-charts/phd-materials-science-engineering/) - [Mechanical and Ocean Engineering (SB, Course 2-OE)](https://catalog.mit.edu/degree-charts/mechanical-ocean-engineering-course-2-oe/) - [Mechanical Engineering (SB, Course 2)](https://catalog.mit.edu/degree-charts/mechanical-engineering-course-2/) - [Nuclear Science and Engineering (SB, Course 22)](https://catalog.mit.edu/degree-charts/nuclear-science-engineering-course-22/) - [Nuclear Science and Engineering (PhD)](https://catalog.mit.edu/degree-charts/phd-nuclear-science-engineering/) - [Social and Engineering Systems (PhD)](https://catalog.mit.edu/degree-charts/phd-social-engineering-systems/) - School of Humanities, Arts, and Social Sciences - [Anthropology (SB, Course 21A)](https://catalog.mit.edu/degree-charts/anthropology-course-21a/) - [Comparative Media Studies (SB, CMS)](https://catalog.mit.edu/degree-charts/comparative-media-studies-cms/) - [Data, Economics, and Design of Policy (MASc)](https://catalog.mit.edu/degree-charts/master-applied-science-data-economics-development-policy/) - [Economics (SB, Course 14-1)](https://catalog.mit.edu/degree-charts/economics-course-14/) - [Economics (PhD)](https://catalog.mit.edu/degree-charts/phd-economics/) - [Global Studies and Languages (SB, Course 21G)](https://catalog.mit.edu/degree-charts/global-studies-languages-course-21g/) - [History (SB, Course 21H)](https://catalog.mit.edu/degree-charts/history-course-21h/) - [Humanities (SB, Course 21)](https://catalog.mit.edu/degree-charts/humanities-course-21/) - [Humanities and Engineering (SB, Course 21E)](https://catalog.mit.edu/degree-charts/humanities-engineering-course-21e/) - [Humanities and Science (SB, Course 21S)](https://catalog.mit.edu/degree-charts/humanities-science-course-21s/) - [Linguistics (SM)](https://catalog.mit.edu/degree-charts/sm-linguistics/) - [Linguistics and Philosophy (SB, Course 24-2)](https://catalog.mit.edu/degree-charts/linguistics-philosophy-course-24-2/) - [Literature (SB, Course 21L)](https://catalog.mit.edu/degree-charts/literature-course-21l/) - [Mathematical Economics (SB, Course 14-2)](https://catalog.mit.edu/degree-charts/mathematical-economics-course-14-2/) - [Music (SB, Course 21M)](https://catalog.mit.edu/degree-charts/music-course-21m/) - [Philosophy (SB, Course 24-1)](https://catalog.mit.edu/degree-charts/philosophy-course-24-1/) - [Political Science (SB, Course 17)](https://catalog.mit.edu/degree-charts/political-science-course-17/) - [Science, Technology, and Society/Second Major (SB, STS)](https://catalog.mit.edu/degree-charts/science-technology-society-sts/) - [Science Writing (SM)](https://catalog.mit.edu/degree-charts/master-science-writing/) - [Theater Arts (SB, Course 21T)](https://catalog.mit.edu/degree-charts/theater-arts-course-21t/) - [Writing (SB, Course 21W)](https://catalog.mit.edu/degree-charts/writing-course-21w/) - Sloan School of Management - [Business Analytics (SB, Course 15-2)](https://catalog.mit.edu/degree-charts/business-analytics-course-15-2/) - [Finance (SB, Course 15-3)](https://catalog.mit.edu/degree-charts/finance-course-15-3/) - [Management (SB, Course 15-1)](https://catalog.mit.edu/degree-charts/management-course-15-1/) - School of Science - [Biology (SB, Course 7)](https://catalog.mit.edu/degree-charts/biology-course-7/) - [Brain and Cognitive Sciences (SB, Course 9)](https://catalog.mit.edu/degree-charts/brain-cognitive-sciences-course-9/) - [Brain and Cognitive Sciences (PhD)](https://catalog.mit.edu/degree-charts/phd-brain-cognitive-sciences/) - [Chemistry (SB, Course 5)](https://catalog.mit.edu/degree-charts/chemistry-course-5/) - [Chemistry (PhD)](https://catalog.mit.edu/degree-charts/phd-chemistry/) - [Earth, Atmospheric and Planetary Sciences (SB, Course 12)](https://catalog.mit.edu/degree-charts/earth-atmospheric-planetary-sciences-course-12/) - [Earth, Atmospheric and Planetary Sciences Fields (PhD)](https://catalog.mit.edu/degree-charts/phd-earth-atmospheric-planetary-sciences/) - [Mathematics (SB, Course 18)](https://catalog.mit.edu/degree-charts/mathematics-course-18/) - [Mathematics (PhD)](https://catalog.mit.edu/degree-charts/phd-mathematics/) - [Mathematics with Computer Science (SB, Course 18-C)](https://catalog.mit.edu/degree-charts/mathematics-computer-science-course-18-c/) - [Physics (SB, Course 8)](https://catalog.mit.edu/degree-charts/physics-course-8/) - Interdisciplinary Programs (SB) - [Chemistry and Biology (SB, Course 5-7)](https://catalog.mit.edu/degree-charts/chemistry-biology-course-5-7/) - [Climate System Science and Engineering (SB, Course 1-12)](https://catalog.mit.edu/degree-charts/climate-system-science-engineering-course-1-12/) - [Computation and Cognition (SB, Course 6-9)](https://catalog.mit.edu/degree-charts/computation-cognition-6-9/) - [Computer Science and Molecular Biology (SB, Course 6-7)](https://catalog.mit.edu/degree-charts/computer-science-molecular-biology-course-6-7/) - [Computer Science, Economics, and Data Science (SB, Course 6-14)](https://catalog.mit.edu/degree-charts/computer-science-economics-data-science-course-6-14/) - [Urban Science and Planning with Computer Science (SB, Course 11-6)](https://catalog.mit.edu/degree-charts/urban-science-planning-computer-science-11-6/) - Interdisciplinary Programs (Graduate) - [Biological Oceanography (PhD)](https://catalog.mit.edu/degree-charts/phd-biological-oceanography/) - [Computation and Cognition (MEng)](https://catalog.mit.edu/degree-charts/master-computation-cognition-course-6-9p/) - [Computational and Systems Biology (PhD)](https://catalog.mit.edu/degree-charts/phd-computational-systems-biology/) - [Computational Science and Engineering (SM)](https://catalog.mit.edu/degree-charts/master-computational-science-engineering/) - [Computational Science and Engineering (PhD)](https://catalog.mit.edu/degree-charts/phd-computational-science-engineering/) - [Computer Science and Molecular Biology (MEng)](https://catalog.mit.edu/degree-charts/master-computer-science-molecular-biology-course-6-7p/) - [Computer Science, Economics, and Data Science (MEng)](https://catalog.mit.edu/degree-charts/master-computer-science-economics-data-science-course-6-14-p/) - [Engineering and Management (SM)](https://catalog.mit.edu/degree-charts/sm-system-design-management/) - [Leaders for Global Operations (MBA/SM and SM)](https://catalog.mit.edu/degree-charts/mba-sm-leaders-global-operations/) - [Microbiology (PhD)](https://catalog.mit.edu/degree-charts/phd-microbiology/) - [Music Technology and Computation (SM and MASc)](https://catalog.mit.edu/degree-charts/master-music-technology-computation/) - [Physical Oceanography (PhD/ScD)](https://catalog.mit.edu/degree-charts/phd-physical-oceanography/) - [Real Estate Development (SM)](https://catalog.mit.edu/degree-charts/master-real-estate-development/) - [Statistics (PhD)](https://catalog.mit.edu/degree-charts/interdisciplinary-doctoral-statistics/) - [Supply Chain Management (MEng and MASc)](https://catalog.mit.edu/degree-charts/master-supply-chain-management/) - [Technology and Policy (SM)](https://catalog.mit.edu/degree-charts/master-technology-policy/) - [Transportation (SM)](https://catalog.mit.edu/degree-charts/master-transportation/) - [Transportation (PhD)](https://catalog.mit.edu/degree-charts/phd-transportation/) - [Subjects](https://catalog.mit.edu/subjects/) Toggle Subjects - [Aeronautics and Astronautics (Course 16)](https://catalog.mit.edu/subjects/16/) - [Aerospace Studies (AS)](https://catalog.mit.edu/subjects/as/) - [Anthropology (Course 21A)](https://catalog.mit.edu/subjects/21a/) - [Architecture (Course 4)](https://catalog.mit.edu/subjects/4/) - [Biological Engineering (Course 20)](https://catalog.mit.edu/subjects/20/) - [Biology (Course 7)](https://catalog.mit.edu/subjects/7/) - [Brain and Cognitive Sciences (Course 9)](https://catalog.mit.edu/subjects/9/) - [Chemical Engineering (Course 10)](https://catalog.mit.edu/subjects/10/) - [Chemistry (Course 5)](https://catalog.mit.edu/subjects/5/) - [Civil and Environmental Engineering (Course 1)](https://catalog.mit.edu/subjects/1/) - [Comparative Media Studies / Writing (CMS)](https://catalog.mit.edu/subjects/cms/) - [Comparative Media Studies / Writing (Course 21W)](https://catalog.mit.edu/subjects/21w/) - [Computational and Systems Biology (CSB)](https://catalog.mit.edu/subjects/csb/) - [Computational Science and Engineering (CSE)](https://catalog.mit.edu/subjects/cse/) - [Concourse (CC)](https://catalog.mit.edu/subjects/cc/) - [Data, Systems, and Society (IDS)](https://catalog.mit.edu/subjects/ids/) - [Earth, Atmospheric, and Planetary Sciences (Course 12)](https://catalog.mit.edu/subjects/12/) - [Economics (Course 14)](https://catalog.mit.edu/subjects/14/) - [Edgerton Center (EC)](https://catalog.mit.edu/subjects/ec/) - [Electrical Engineering and Computer Science (Course 6)](https://catalog.mit.edu/subjects/6/) - [Engineering Management (EM)](https://catalog.mit.edu/subjects/em/) - [Experimental Study Group (ES)](https://catalog.mit.edu/subjects/es/) - [Global Languages (Course 21G)](https://catalog.mit.edu/subjects/21g/) - [Health Sciences and Technology (HST)](https://catalog.mit.edu/subjects/hst/) - [History (Course 21H)](https://catalog.mit.edu/subjects/21h/) - [Humanities (Course 21)](https://catalog.mit.edu/subjects/21/) - [Linguistics and Philosophy (Course 24)](https://catalog.mit.edu/subjects/24/) - [Literature (Course 21L)](https://catalog.mit.edu/subjects/21l/) - [Management (Course 15)](https://catalog.mit.edu/subjects/15/) - [Materials Science and Engineering (Course 3)](https://catalog.mit.edu/subjects/3/) - [Mathematics (Course 18)](https://catalog.mit.edu/subjects/18/) - [Mechanical Engineering (Course 2)](https://catalog.mit.edu/subjects/2/) - [Media Arts and Sciences (MAS)](https://catalog.mit.edu/subjects/mas/) - [Military Science (MS)](https://catalog.mit.edu/subjects/ms/) - [Music (Course 21M)](https://catalog.mit.edu/subjects/21m/) - [Naval Science (NS)](https://catalog.mit.edu/subjects/ns/) - [Nuclear Science and Engineering (Course 22)](https://catalog.mit.edu/subjects/22/) - [Physics (Course 8)](https://catalog.mit.edu/subjects/8/) - [Political Science (Course 17)](https://catalog.mit.edu/subjects/17/) - [Science, Technology, and Society (STS)](https://catalog.mit.edu/subjects/sts/) - [Special Programs](https://catalog.mit.edu/subjects/sp/) - [Supply Chain Management (SCM)](https://catalog.mit.edu/subjects/scm/) - [Theater Arts (21T)](https://catalog.mit.edu/subjects/21t/) - [Urban Studies and Planning (Course 11)](https://catalog.mit.edu/subjects/11/) - [Women's and Gender Studies (WGS)](https://catalog.mit.edu/subjects/wgs/) # Computational Science and Engineering The [Center for Computational Science and Engineering (CCSE)](https://cse.mit.edu/programs/) offers a master's degree and two doctoral programs in computational science and engineering (CSE)—one leading to a standalone PhD degree in CSE offered entirely by CCSE and the other to an interdisciplinary PhD degree offered jointly with participating departments in the School of Engineering and the School of Science. While both programs enable students to specialize at the doctoral level in a computation-related field via focused coursework and a thesis, they differ in essential ways. The standalone CSE PhD program is intended for students who intend to pursue research in cross-cutting methodological aspects of computational science. The resulting doctoral degree is awarded by the Schwarzman College of Computing. In contrast, the interdisciplinary CSE PhD program is intended for students who are interested in computation in the context of a specific engineering or science discipline. For this reason, this degree is offered jointly with participating departments across the Institute; the interdisciplinary degree is awarded in a specially crafted thesis field that recognizes the student’s specialization in computation. At the time of application, students are expected to declare which of the two programs they are interested in. Admissions decisions will take into account these declared interests, along with each applicant’s academic background, preparation, and fit to the program they have selected. Applicants interested in an advanced degree in computer science should instead apply for admission to the [Department of Electrical Engineering and Computer Science](https://www.eecs.mit.edu/). ## Master of Science in Computational Science and Engineering The [Master of Science in Computational Science and Engineering (CSE SM)](https://catalog.mit.edu/degree-charts/master-computational-science-engineering/) is an interdisciplinary, research-oriented master's program that provides students with a strong foundation in computational methods for the study, design, and operation of complex engineered and natural systems. The curriculum trains students in the formulation, analysis, implementation, and application of computational approaches in science and engineering. It combines a course of study comprising six graduate subjects with a master's thesis describing original research performed under the supervision of a CSE faculty member. The coursework requirements include: - A three-subject core aimed at developing breadth as well as depth in numerical analysis, simulation, and optimization - A two-subject restricted elective program aimed at reinforcing multidisciplinary aspects of computation - One unrestricted elective subject Hands-on experience is encouraged and reinforced through projects in the core, the elective subjects, and the master's thesis. ## Doctor of Philosophy in Computational Science and Engineering The standalone doctoral program in Computational Science and Engineering ([PhD in CSE)](https://catalog.mit.edu/degree-charts/phd-computational-science-engineering/) enables students to specialize at the doctoral level in fundamental, methodological aspects of computational science via focused coursework and a thesis. The emphasis of thesis research activities is the development and analysis of broadly applicable computational approaches that advance the state of the art. Students are awarded the Doctor of Philosophy in Computational Science and Engineering upon successful completion of the program requirements and defense of a thesis describing significant contributions to the CSE field. Program requirements include a course of study comprising nine graduate subjects and a graduate seminar. Core and concentration subjects cover six “ways of thinking” fundamental to CSE: (i) discretization and numerical methods for partial differential equations; (ii) optimization methods; (iii) statistics and data-driven modeling; (iv) high-performance computing and/or algorithms; (v) mathematical foundations (e.g., functional analysis, probability); and (vi) modeling (i.e., a subject that treats mathematical modeling in any science or engineering discipline). Subjects taken as part of an MIT SM program can be counted toward the coursework requirement provided they satisfy core, concentration, or elective requirements as set forth [here](https://catalog.mit.edu/degree-charts/phd-computational-science-engineering/); consultation and approval by the program director(s) and/or administrator regarding the application of such courses toward program credit is always required. Students applying to this program are expected to have a degree in CSE, applied mathematics, or another field that prepares them for an advanced degree in CSE. More information about the application process, requirements, and relevant deadlines can be found on the [Admissions section of the CCSE website](https://cse.mit.edu/admissions/). ## Interdisciplinary Doctoral Program in Computational Science and Engineering The interdisciplinary doctoral program in Computational Science and Engineering ([PhD in CSE + Engineering or Science](https://catalog.mit.edu/degree-charts/phd-computational-science-engineering/#phdincseengineeringorsciencetext)) offers students the opportunity to specialize at the doctoral level in a computation-related field of their choice via computationally-oriented coursework and a doctoral thesis with a disciplinary focus related to one of eight participating host departments, namely, Aeronautics and Astronautics; Chemical Engineering; Civil and Environmental Engineering; Earth, Atmospheric and Planetary Sciences; Materials Science and Engineering; Mathematics; Mechanical Engineering; or Nuclear Science and Engineering. Doctoral thesis fields associated with each department are as follows: - Aeronautics and Astronautics - Aerospace Engineering and Computational Science - Computational Science and Engineering (available only to students who matriculate in 2023–2024 or earlier) - Chemical Engineering - Chemical Engineering and Computation - Civil and Environmental Engineering - Civil Engineering and Computation - Environmental Engineering and Computation - Materials Science and Engineering - Computational Materials Science and Engineering - Mechanical Engineering - Mechanical Engineering and Computation - Nuclear Science and Engineering - Computational Nuclear Science and Engineering - Nuclear Engineering and Computation - Earth, Atmospheric and Planetary Sciences - Computational Earth, Science and Planetary Sciences - Mathematics - Mathematics and Computational Science As with the standalone CSE PhD program, the emphasis of thesis research activities is the development of new computational methods and/or the innovative application of state-of-the-art computational techniques to important problems in engineering and science. In contrast to the standalone PhD program, however, this research is expected to have a strong disciplinary component of interest to the host department. The interdisciplinary CSE PhD program is administered jointly by CCSE and the host departments. Students must submit an application to the CSE PhD program, indicating the department in which they wish to be hosted. To gain admission, CSE program applicants must receive approval from both the host department graduate admission committee and the CSE graduate admission committee. See the website for more information about the [application process, requirements, and relevant deadlines](https://cse.mit.edu/admissions/). Once admitted, doctoral degree candidates are expected to complete the host department's degree requirements (including qualifying exam) with some deviations relating to coursework, thesis committee composition, and thesis submission that are specific to the CSE program and are discussed in more detail on the [CSE website](https://cse.mit.edu/programs/phd/). The most notable coursework requirement associated with this CSE degree is a course of study comprising five graduate subjects in CSE (below). ### Computational Concentration Subjects \| \| \| \| \|---\|---\|---\| \| [1\.125](https://catalog.mit.edu/search/?P=1.125 "1.125") \| Architecting and Engineering Software Systems \| 12 \| \| [1\.545\[J\]](https://catalog.mit.edu/search/?P=1.545 "1.545[J]") \| Atomistic Modeling and Simulation of Materials and Structures \| 12 \| \| [1\.583\[J\]](https://catalog.mit.edu/search/?P=1.583 "1.583[J]") \| Topology Optimization of Structures \| 12 \| \| [1\.723](https://catalog.mit.edu/search/?P=1.723 "1.723") \| Computational Methods for Flow in Porous Media \| 12 \| \| [2\.098](https://catalog.mit.edu/search/?P=2.098 "2.098") \| Introduction to Finite Element Methods \| 12 \| \| [2\.156](https://catalog.mit.edu/search/?P=2.156 "2.156") \| Artificial Intelligence and Machine Learning for Engineering Design \| 12 \| \| [2\.168](https://catalog.mit.edu/search/?P=2.168 "2.168") \| Learning Machines \| 12 \| \| [2\.29](https://catalog.mit.edu/search/?P=2.29 "2.29") \| Numerical Fluid Mechanics \| 12 \| \| [3\.320](https://catalog.mit.edu/search/?P=3.320 "3.320") \| Atomistic Computer Modeling of Materials \| 12 \| \| [4\.450\[J\]](https://catalog.mit.edu/search/?P=4.450 "4.450[J]") \| Computational Structural Design and Optimization \| \| \| [6\.7210\[J\]](https://catalog.mit.edu/search/?P=6.7210 "6.7210[J]") \| Introduction to Mathematical Programming \| 12 \| \| [6\.7220\[J\]](https://catalog.mit.edu/search/?P=6.7220 "6.7220[J]") \| Nonlinear Optimization \| 12 \| \| [6\.7230\[J\]](https://catalog.mit.edu/search/?P=6.7230 "6.7230[J]") \| Algebraic Techniques and Semidefinite Optimization \| 12 \| \| [6\.7300\[J\]](https://catalog.mit.edu/search/?P=6.7300 "6.7300[J]") \| Introduction to Modeling and Simulation \| 12 \| \| [6\.7810](https://catalog.mit.edu/search/?P=6.7810 "6.7810") \| Algorithms for Inference \| 12 \| \| [6\.7830](https://catalog.mit.edu/search/?P=6.7830 "6.7830") \| Bayesian Modeling and Inference \| 12 \| \| [6\.7900](https://catalog.mit.edu/search/?P=6.7900 "6.7900") \| Machine Learning 1 \| 12 \| \| [6\.7940](https://catalog.mit.edu/search/?P=6.7940 "6.7940") \| Dynamic Programming and Reinforcement Learning \| 12 \| \| [6\.8300](https://catalog.mit.edu/search/?P=6.8300 "6.8300") \| Advances in Computer Vision \| 12 \| \| [6\.8410](https://catalog.mit.edu/search/?P=6.8410 "6.8410") \| Shape Analysis \| 12 \| \| [6\.C51](https://catalog.mit.edu/search/?P=6.C51 "6.C51") \| Modeling with Machine Learning: from Algorithms to Applications 2 \| 6 \| \| [9\.520\[J\]](https://catalog.mit.edu/search/?P=9.520 "9.520[J]") \| Statistical Learning Theory and Applications \| 12 \| \| [9\.660](https://catalog.mit.edu/search/?P=9.660 "9.660") \| Computational Cognitive Science \| 12 \| \| [10\.551](https://catalog.mit.edu/search/?P=10.551 "10.551") \| Systems Engineering 3 \| 9 \| \| [10\.552](https://catalog.mit.edu/search/?P=10.552 "10.552") \| Modern Control Design 3 \| 9 \| \| [10\.554\[J\]](https://catalog.mit.edu/search/?P=10.554 "10.554[J]") \| Process Data Analytics \| 12 \| \| [10\.557](https://catalog.mit.edu/search/?P=10.557 "10.557") \| Mixed-integer and Nonconvex Optimization \| 12 \| \| [10\.637\[J\]](https://catalog.mit.edu/search/?P=10.637 "10.637[J]") \| Computational Chemistry \| 12 \| \| [12\.515](https://catalog.mit.edu/search/?P=12.515 "12.515") \| Data and Models \| 12 \| \| [12\.521](https://catalog.mit.edu/search/?P=12.521 "12.521") \| Computational Geophysical Modeling \| 12 \| \| [12\.620\[J\]](https://catalog.mit.edu/search/?P=12.620 "12.620[J]") \| Classical Mechanics: A Computational Approach \| 12 \| \| [12\.714](https://catalog.mit.edu/search/?P=12.714 "12.714") \| Computational Data Analysis \| 12 \| \| [12\.805](https://catalog.mit.edu/search/?P=12.805 "12.805") \| Data Analysis in Physical Oceanography \| 12 \| \| [12\.850](https://catalog.mit.edu/search/?P=12.850 "12.850") \| Computational Ocean Modeling \| 12 \| \| [15\.070\[J\]](https://catalog.mit.edu/search/?P=15.070 "15.070[J]") \| Discrete Probability and Stochastic Processes \| 12 \| \| [15\.077\[J\]](https://catalog.mit.edu/search/?P=15.077 "15.077[J]") \| Statistical Machine Learning and Data Science 1 \| 12 \| \| [15\.083](https://catalog.mit.edu/search/?P=15.083 "15.083") \| Integer Optimization \| 12 \| \| [15\.764\[J\]](https://catalog.mit.edu/search/?P=15.764 "15.764[J]") \| The Theory of Operations Management \| 12 \| \| [15\.C57\[J\]](https://catalog.mit.edu/search/?P=15.C57 "15.C57[J]") \| Optimization Methods \| 12 \| \| [16\.110](https://catalog.mit.edu/search/?P=16.110 "16.110") \| Flight Vehicle Aerodynamics \| 12 \| \| [16\.225\[J\]](https://catalog.mit.edu/search/?P=16.225 "16.225[J]") \| Computational Mechanics of Materials \| 12 \| \| [16\.413\[J\]](https://catalog.mit.edu/search/?P=16.413 "16.413[J]") \| Principles of Autonomy and Decision Making \| 12 \| \| [16\.888\[J\]](https://catalog.mit.edu/search/?P=16.888 "16.888[J]") \| Multidisciplinary Design Optimization \| 12 \| \| [16\.920\[J\]](https://catalog.mit.edu/search/?P=16.920 "16.920[J]") \| Numerical Methods for Partial Differential Equations \| 12 \| \| [16\.930](https://catalog.mit.edu/search/?P=16.930 "16.930") \| Advanced Topics in Numerical Methods for Partial Differential Equations \| 12 \| \| [16\.940](https://catalog.mit.edu/search/?P=16.940 "16.940") \| Numerical Methods for Stochastic Modeling and Inference \| 12 \| \| [18\.335\[J\]](https://catalog.mit.edu/search/?P=18.335 "18.335[J]") \| Introduction to Numerical Methods \| 12 \| \| [18\.336\[J\]](https://catalog.mit.edu/search/?P=18.336 "18.336[J]") \| Fast Methods for Partial Differential and Integral Equations \| 12 \| \| [18\.337\[J\]](https://catalog.mit.edu/search/?P=18.337 "18.337[J]") \| Parallel Computing and Scientific Machine Learning \| 12 \| \| [18\.338](https://catalog.mit.edu/search/?P=18.338 "18.338") \| Eigenvalues of Random Matrices \| 12 \| \| [18\.369\[J\]](https://catalog.mit.edu/search/?P=18.369 "18.369[J]") \| Mathematical Methods in Nanophotonics \| 12 \| \| [18\.435\[J\]](https://catalog.mit.edu/search/?P=18.435 "18.435[J]") \| Quantum Computation \| 12 \| \| [22\.15](https://catalog.mit.edu/search/?P=22.15 "22.15") \| Essential Numerical Methods \| 6 \| \| [22\.212](https://catalog.mit.edu/search/?P=22.212 "22.212") \| Nuclear Reactor Analysis II \| 12 \| \| [22\.213](https://catalog.mit.edu/search/?P=22.213 "22.213") \| Nuclear Reactor Physics III \| 12 \| \| [22\.315](https://catalog.mit.edu/search/?P=22.315 "22.315") \| Applied Computational Fluid Dynamics and Heat Transfer \| 12 \| \| [CSE.999](https://catalog.mit.edu/search/?P=CSE.999 "CSE.999") \| Experiential Learning in Computational Science and Engineering \| \| \| [IDS.131\[J\]](https://catalog.mit.edu/search/?P=IDS.131 "IDS.131[J]") \| Statistics, Computation and Applications \| 12 \| Note: Students may not use more than 12 units of credit from a "meets with undergraduate" subject to fulfill the CSE curriculum requirements \| \| \| \|---\|---\| \| 1 \| Credit can only be given for one of [6\.7900](https://catalog.mit.edu/search/?P=6.7900 "6.7900"), [15\.077\[J\]](https://catalog.mit.edu/search/?P=15.077 "15.077[J]"), or [IDS.147\[J\]](https://catalog.mit.edu/search/?P=IDS.147 "IDS.147[J]"). \| \| 2 \| Students cannot receive credit without simultaneous completion of a 6-unit Common Ground disciplinary module. The two subjects together count as one 12-unit subject. See [6\.C51](https://catalog.mit.edu/search/?P=6.C51 "6.C51") for more information. \| \| 3 \| Students can receive credit for either [10\.551](https://catalog.mit.edu/search/?P=10.551 "10.551") or [10\.552](https://catalog.mit.edu/search/?P=10.552 "10.552") as a CSE concentration subject, but not both. \| \| 4 \| Subject to Sloan bidding process. \| ## Inquiries For more information, please visit the [CCSE website](https://cse.mit.edu/). [Admissions](http://mitadmissions.org/apply)[Financial Aid](http://sfs.mit.edu/)[Registrar](http://web.mit.edu/registrar/)[IAP](http://web.mit.edu/iap/)[Summer](https://catalog.mit.edu/summer/)[Professional Education](http://professional.mit.edu/)[MITx](https://www.edx.org/school/mitx)[K-12](https://outreach.mit.edu/)[Campus Map](http://whereis.mit.edu/) [Directories](https://officesdirectory.mit.edu/)[About the Bulletin](https://catalog.mit.edu/about-bulletin/)[Nondiscrimination Policy](https://catalog.mit.edu/nondiscrimination-policy/)[Changes](https://catalog.mit.edu/changelog/)[Help](https://catalog.mit.edu/help/)[Accessibility](https://accessibility.mit.edu/) ![MIT](https://catalog.mit.edu/images/mit-logo-footer.svg) ![MIT Academic Bulletin](https://catalog.mit.edu/images/mit-bulletin-logo-footer-25-26.png) 77 Massachusetts Avenue Cambridge, MA 02139-4307 [Back to top](https://catalog.mit.edu/interdisciplinary/graduate-programs/computational-science-engineering/#header) Print Options [Send Page to Printer](https://catalog.mit.edu/interdisciplinary/graduate-programs/computational-science-engineering/) Print this page. [Download PDF of this Page](https://catalog.mit.edu/interdisciplinary/graduate-programs/computational-science-engineering/computational-science-engineering.pdf) The PDF includes all information on this page and its related tabs. Subject (course) information includes any changes approved for the current academic year. [Download PDF of the Entire Catalog and/or Subject Descriptions](https://catalog.mit.edu/archive/) [Cancel](https://catalog.mit.edu/interdisciplinary/graduate-programs/computational-science-engineering/)
Readable Markdown	The [Center for Computational Science and Engineering (CCSE)](https://cse.mit.edu/programs/) offers a master's degree and two doctoral programs in computational science and engineering (CSE)—one leading to a standalone PhD degree in CSE offered entirely by CCSE and the other to an interdisciplinary PhD degree offered jointly with participating departments in the School of Engineering and the School of Science. While both programs enable students to specialize at the doctoral level in a computation-related field via focused coursework and a thesis, they differ in essential ways. The standalone CSE PhD program is intended for students who intend to pursue research in cross-cutting methodological aspects of computational science. The resulting doctoral degree is awarded by the Schwarzman College of Computing. In contrast, the interdisciplinary CSE PhD program is intended for students who are interested in computation in the context of a specific engineering or science discipline. For this reason, this degree is offered jointly with participating departments across the Institute; the interdisciplinary degree is awarded in a specially crafted thesis field that recognizes the student’s specialization in computation. At the time of application, students are expected to declare which of the two programs they are interested in. Admissions decisions will take into account these declared interests, along with each applicant’s academic background, preparation, and fit to the program they have selected. Applicants interested in an advanced degree in computer science should instead apply for admission to the [Department of Electrical Engineering and Computer Science](https://www.eecs.mit.edu/). ## Master of Science in Computational Science and Engineering The [Master of Science in Computational Science and Engineering (CSE SM)](https://catalog.mit.edu/degree-charts/master-computational-science-engineering/) is an interdisciplinary, research-oriented master's program that provides students with a strong foundation in computational methods for the study, design, and operation of complex engineered and natural systems. The curriculum trains students in the formulation, analysis, implementation, and application of computational approaches in science and engineering. It combines a course of study comprising six graduate subjects with a master's thesis describing original research performed under the supervision of a CSE faculty member. The coursework requirements include: - A three-subject core aimed at developing breadth as well as depth in numerical analysis, simulation, and optimization - A two-subject restricted elective program aimed at reinforcing multidisciplinary aspects of computation - One unrestricted elective subject Hands-on experience is encouraged and reinforced through projects in the core, the elective subjects, and the master's thesis. ## Doctor of Philosophy in Computational Science and Engineering The standalone doctoral program in Computational Science and Engineering ([PhD in CSE)](https://catalog.mit.edu/degree-charts/phd-computational-science-engineering/) enables students to specialize at the doctoral level in fundamental, methodological aspects of computational science via focused coursework and a thesis. The emphasis of thesis research activities is the development and analysis of broadly applicable computational approaches that advance the state of the art. Students are awarded the Doctor of Philosophy in Computational Science and Engineering upon successful completion of the program requirements and defense of a thesis describing significant contributions to the CSE field. Program requirements include a course of study comprising nine graduate subjects and a graduate seminar. Core and concentration subjects cover six “ways of thinking” fundamental to CSE: (i) discretization and numerical methods for partial differential equations; (ii) optimization methods; (iii) statistics and data-driven modeling; (iv) high-performance computing and/or algorithms; (v) mathematical foundations (e.g., functional analysis, probability); and (vi) modeling (i.e., a subject that treats mathematical modeling in any science or engineering discipline). Subjects taken as part of an MIT SM program can be counted toward the coursework requirement provided they satisfy core, concentration, or elective requirements as set forth [here](https://catalog.mit.edu/degree-charts/phd-computational-science-engineering/); consultation and approval by the program director(s) and/or administrator regarding the application of such courses toward program credit is always required. Students applying to this program are expected to have a degree in CSE, applied mathematics, or another field that prepares them for an advanced degree in CSE. More information about the application process, requirements, and relevant deadlines can be found on the [Admissions section of the CCSE website](https://cse.mit.edu/admissions/). ## Interdisciplinary Doctoral Program in Computational Science and Engineering The interdisciplinary doctoral program in Computational Science and Engineering ([PhD in CSE + Engineering or Science](https://catalog.mit.edu/degree-charts/phd-computational-science-engineering/#phdincseengineeringorsciencetext)) offers students the opportunity to specialize at the doctoral level in a computation-related field of their choice via computationally-oriented coursework and a doctoral thesis with a disciplinary focus related to one of eight participating host departments, namely, Aeronautics and Astronautics; Chemical Engineering; Civil and Environmental Engineering; Earth, Atmospheric and Planetary Sciences; Materials Science and Engineering; Mathematics; Mechanical Engineering; or Nuclear Science and Engineering. Doctoral thesis fields associated with each department are as follows: - Aeronautics and Astronautics - Aerospace Engineering and Computational Science - Computational Science and Engineering (available only to students who matriculate in 2023–2024 or earlier) - Chemical Engineering - Chemical Engineering and Computation - Civil and Environmental Engineering - Civil Engineering and Computation - Environmental Engineering and Computation - Materials Science and Engineering - Computational Materials Science and Engineering - Mechanical Engineering - Mechanical Engineering and Computation - Nuclear Science and Engineering - Computational Nuclear Science and Engineering - Nuclear Engineering and Computation - Earth, Atmospheric and Planetary Sciences - Computational Earth, Science and Planetary Sciences - Mathematics - Mathematics and Computational Science As with the standalone CSE PhD program, the emphasis of thesis research activities is the development of new computational methods and/or the innovative application of state-of-the-art computational techniques to important problems in engineering and science. In contrast to the standalone PhD program, however, this research is expected to have a strong disciplinary component of interest to the host department. The interdisciplinary CSE PhD program is administered jointly by CCSE and the host departments. Students must submit an application to the CSE PhD program, indicating the department in which they wish to be hosted. To gain admission, CSE program applicants must receive approval from both the host department graduate admission committee and the CSE graduate admission committee. See the website for more information about the [application process, requirements, and relevant deadlines](https://cse.mit.edu/admissions/). Once admitted, doctoral degree candidates are expected to complete the host department's degree requirements (including qualifying exam) with some deviations relating to coursework, thesis committee composition, and thesis submission that are specific to the CSE program and are discussed in more detail on the [CSE website](https://cse.mit.edu/programs/phd/). The most notable coursework requirement associated with this CSE degree is a course of study comprising five graduate subjects in CSE (below). ### Computational Concentration Subjects \| \| \| \| \|---\|---\|---\| \| [1\.125](https://catalog.mit.edu/search/?P=1.125 "1.125") \| Architecting and Engineering Software Systems \| 12 \| \| [1\.545\[J\]](https://catalog.mit.edu/search/?P=1.545 "1.545[J]") \| Atomistic Modeling and Simulation of Materials and Structures \| 12 \| \| [1\.583\[J\]](https://catalog.mit.edu/search/?P=1.583 "1.583[J]") \| Topology Optimization of Structures \| 12 \| \| [1\.723](https://catalog.mit.edu/search/?P=1.723 "1.723") \| Computational Methods for Flow in Porous Media \| 12 \| \| [2\.098](https://catalog.mit.edu/search/?P=2.098 "2.098") \| Introduction to Finite Element Methods \| 12 \| \| [2\.156](https://catalog.mit.edu/search/?P=2.156 "2.156") \| Artificial Intelligence and Machine Learning for Engineering Design \| 12 \| \| [2\.168](https://catalog.mit.edu/search/?P=2.168 "2.168") \| Learning Machines \| 12 \| \| [2\.29](https://catalog.mit.edu/search/?P=2.29 "2.29") \| Numerical Fluid Mechanics \| 12 \| \| [3\.320](https://catalog.mit.edu/search/?P=3.320 "3.320") \| Atomistic Computer Modeling of Materials \| 12 \| \| [4\.450\[J\]](https://catalog.mit.edu/search/?P=4.450 "4.450[J]") \| Computational Structural Design and Optimization \| \| \| [6\.7210\[J\]](https://catalog.mit.edu/search/?P=6.7210 "6.7210[J]") \| Introduction to Mathematical Programming \| 12 \| \| [6\.7220\[J\]](https://catalog.mit.edu/search/?P=6.7220 "6.7220[J]") \| Nonlinear Optimization \| 12 \| \| [6\.7230\[J\]](https://catalog.mit.edu/search/?P=6.7230 "6.7230[J]") \| Algebraic Techniques and Semidefinite Optimization \| 12 \| \| [6\.7300\[J\]](https://catalog.mit.edu/search/?P=6.7300 "6.7300[J]") \| Introduction to Modeling and Simulation \| 12 \| \| [6\.7810](https://catalog.mit.edu/search/?P=6.7810 "6.7810") \| Algorithms for Inference \| 12 \| \| [6\.7830](https://catalog.mit.edu/search/?P=6.7830 "6.7830") \| Bayesian Modeling and Inference \| 12 \| \| [6\.7900](https://catalog.mit.edu/search/?P=6.7900 "6.7900") \| Machine Learning 1 \| 12 \| \| [6\.7940](https://catalog.mit.edu/search/?P=6.7940 "6.7940") \| Dynamic Programming and Reinforcement Learning \| 12 \| \| [6\.8300](https://catalog.mit.edu/search/?P=6.8300 "6.8300") \| Advances in Computer Vision \| 12 \| \| [6\.8410](https://catalog.mit.edu/search/?P=6.8410 "6.8410") \| Shape Analysis \| 12 \| \| [6\.C51](https://catalog.mit.edu/search/?P=6.C51 "6.C51") \| Modeling with Machine Learning: from Algorithms to Applications 2 \| 6 \| \| [9\.520\[J\]](https://catalog.mit.edu/search/?P=9.520 "9.520[J]") \| Statistical Learning Theory and Applications \| 12 \| \| [9\.660](https://catalog.mit.edu/search/?P=9.660 "9.660") \| Computational Cognitive Science \| 12 \| \| [10\.551](https://catalog.mit.edu/search/?P=10.551 "10.551") \| Systems Engineering 3 \| 9 \| \| [10\.552](https://catalog.mit.edu/search/?P=10.552 "10.552") \| Modern Control Design 3 \| 9 \| \| [10\.554\[J\]](https://catalog.mit.edu/search/?P=10.554 "10.554[J]") \| Process Data Analytics \| 12 \| \| [10\.557](https://catalog.mit.edu/search/?P=10.557 "10.557") \| Mixed-integer and Nonconvex Optimization \| 12 \| \| [10\.637\[J\]](https://catalog.mit.edu/search/?P=10.637 "10.637[J]") \| Computational Chemistry \| 12 \| \| [12\.515](https://catalog.mit.edu/search/?P=12.515 "12.515") \| Data and Models \| 12 \| \| [12\.521](https://catalog.mit.edu/search/?P=12.521 "12.521") \| Computational Geophysical Modeling \| 12 \| \| [12\.620\[J\]](https://catalog.mit.edu/search/?P=12.620 "12.620[J]") \| Classical Mechanics: A Computational Approach \| 12 \| \| [12\.714](https://catalog.mit.edu/search/?P=12.714 "12.714") \| Computational Data Analysis \| 12 \| \| [12\.805](https://catalog.mit.edu/search/?P=12.805 "12.805") \| Data Analysis in Physical Oceanography \| 12 \| \| [12\.850](https://catalog.mit.edu/search/?P=12.850 "12.850") \| Computational Ocean Modeling \| 12 \| \| [15\.070\[J\]](https://catalog.mit.edu/search/?P=15.070 "15.070[J]") \| Discrete Probability and Stochastic Processes \| 12 \| \| [15\.077\[J\]](https://catalog.mit.edu/search/?P=15.077 "15.077[J]") \| Statistical Machine Learning and Data Science 1 \| 12 \| \| [15\.083](https://catalog.mit.edu/search/?P=15.083 "15.083") \| Integer Optimization \| 12 \| \| [15\.764\[J\]](https://catalog.mit.edu/search/?P=15.764 "15.764[J]") \| The Theory of Operations Management \| 12 \| \| [15\.C57\[J\]](https://catalog.mit.edu/search/?P=15.C57 "15.C57[J]") \| Optimization Methods \| 12 \| \| [16\.110](https://catalog.mit.edu/search/?P=16.110 "16.110") \| Flight Vehicle Aerodynamics \| 12 \| \| [16\.225\[J\]](https://catalog.mit.edu/search/?P=16.225 "16.225[J]") \| Computational Mechanics of Materials \| 12 \| \| [16\.413\[J\]](https://catalog.mit.edu/search/?P=16.413 "16.413[J]") \| Principles of Autonomy and Decision Making \| 12 \| \| [16\.888\[J\]](https://catalog.mit.edu/search/?P=16.888 "16.888[J]") \| Multidisciplinary Design Optimization \| 12 \| \| [16\.920\[J\]](https://catalog.mit.edu/search/?P=16.920 "16.920[J]") \| Numerical Methods for Partial Differential Equations \| 12 \| \| [16\.930](https://catalog.mit.edu/search/?P=16.930 "16.930") \| Advanced Topics in Numerical Methods for Partial Differential Equations \| 12 \| \| [16\.940](https://catalog.mit.edu/search/?P=16.940 "16.940") \| Numerical Methods for Stochastic Modeling and Inference \| 12 \| \| [18\.335\[J\]](https://catalog.mit.edu/search/?P=18.335 "18.335[J]") \| Introduction to Numerical Methods \| 12 \| \| [18\.336\[J\]](https://catalog.mit.edu/search/?P=18.336 "18.336[J]") \| Fast Methods for Partial Differential and Integral Equations \| 12 \| \| [18\.337\[J\]](https://catalog.mit.edu/search/?P=18.337 "18.337[J]") \| Parallel Computing and Scientific Machine Learning \| 12 \| \| [18\.338](https://catalog.mit.edu/search/?P=18.338 "18.338") \| Eigenvalues of Random Matrices \| 12 \| \| [18\.369\[J\]](https://catalog.mit.edu/search/?P=18.369 "18.369[J]") \| Mathematical Methods in Nanophotonics \| 12 \| \| [18\.435\[J\]](https://catalog.mit.edu/search/?P=18.435 "18.435[J]") \| Quantum Computation \| 12 \| \| [22\.15](https://catalog.mit.edu/search/?P=22.15 "22.15") \| Essential Numerical Methods \| 6 \| \| [22\.212](https://catalog.mit.edu/search/?P=22.212 "22.212") \| Nuclear Reactor Analysis II \| 12 \| \| [22\.213](https://catalog.mit.edu/search/?P=22.213 "22.213") \| Nuclear Reactor Physics III \| 12 \| \| [22\.315](https://catalog.mit.edu/search/?P=22.315 "22.315") \| Applied Computational Fluid Dynamics and Heat Transfer \| 12 \| \| [CSE.999](https://catalog.mit.edu/search/?P=CSE.999 "CSE.999") \| Experiential Learning in Computational Science and Engineering \| \| \| [IDS.131\[J\]](https://catalog.mit.edu/search/?P=IDS.131 "IDS.131[J]") \| Statistics, Computation and Applications \| 12 \| Note: Students may not use more than 12 units of credit from a "meets with undergraduate" subject to fulfill the CSE curriculum requirements \| \| \| \|---\|---\| \| 1 \| Credit can only be given for one of [6\.7900](https://catalog.mit.edu/search/?P=6.7900 "6.7900"), [15\.077\[J\]](https://catalog.mit.edu/search/?P=15.077 "15.077[J]"), or [IDS.147\[J\]](https://catalog.mit.edu/search/?P=IDS.147 "IDS.147[J]"). \| \| 2 \| Students cannot receive credit without simultaneous completion of a 6-unit Common Ground disciplinary module. The two subjects together count as one 12-unit subject. See [6\.C51](https://catalog.mit.edu/search/?P=6.C51 "6.C51") for more information. \| \| 3 \| Students can receive credit for either [10\.551](https://catalog.mit.edu/search/?P=10.551 "10.551") or [10\.552](https://catalog.mit.edu/search/?P=10.552 "10.552") as a CSE concentration subject, but not both. \| \| 4 \| Subject to Sloan bidding process. \| ## Inquiries For more information, please visit the [CCSE website](https://cse.mit.edu/).
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Root Hash	10722954425220430980
Unparsed URL	edu,mit!catalog,/interdisciplinary/graduate-programs/computational-science-engineering/ s443