🕷️ Crawler Inspector

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Direct Parameter Lookup

Raw Queries and Responses

1. Shard Calculation

Query:

Response:

Calculated Shard: 180 (from laksa194)

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/degree-charts/master-computational-science-engineering/\')), getAhrefsUnparsedNoserviceFromURL(\'https://catalog.mit.edu/degree-charts/master-computational-science-engineering/\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/catalog.mit.edu\/degree-charts\/master-computational-science-engineering\/","crawl_time":1774384373,"first_indexed_time":1696404481,"http_code":200,"src_unparsed":"edu,mit!catalog,\/degree-charts\/master-computational-science-engineering\/ s443","src_root_hash":"10722954425220430980","history_drop_reason":null,"meta_title":"Master of Science in Computational Science and Engineering | MIT Course Catalog","meta_descriptions":[],"attrs_boilerpipe_text":"Computational Science and Engineering\nCore Subjects\n36\nSelect three of the following subjects:\n6.7300[J]\nIntroduction to Modeling and Simulation\n15.C57[J]\nOptimization Methods\n16.920[J]\nNumerical Methods for Partial Differential Equations\n18.335[J]\nIntroduction to Numerical Methods\nRestricted Electives\n1\n24\nChoose 24 units of coursework from the list below.\nUnrestricted Elective\n1\n12\nChoose any graduate-level subject.\n2\nThesis\nCSE.THG\nGraduate Thesis\n36\nTotal Units\n108\n1\nSubjects that can be repeated for credit cannot be used to satisfy multiple CSE SM requirements.\n2\nSee list of\nsubjects offered at MIT\n.\nRestricted Electives\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\n4.453\nCreative Machine Learning for Design\n12\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\n12\n6.7940\nDynamic Programming and Reinforcement Learning\n1\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\n2\n9\n10.552\nModern Control Design\n2\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\n3\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\n1\nRestricted elective credit 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 restricted elective. See\n6.C51\nfor more information.\n3\nStudents receive credit for either\n10.551\nor\n10.552\nas a CSE concentration subject, but not both.\n4\nSubject to Sloan bidding process.","attrs_markdown":"- [Skip to Content](https:\/\/catalog.mit.edu\/degree-charts\/master-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\/degree-charts\/master-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\nDegree Charts\n\n- [Home](https:\/\/catalog.mit.edu\/)\\>\n- [Degree Charts](https:\/\/catalog.mit.edu\/degree-charts\/)\\>\n- Computational Science and Engineering (SM)\n\nCatalog Navigation\n\n- [This Is MIT](https:\/\/catalog.mit.edu\/mit\/)\n  \n  Toggle This Is MIT\n  - [Overview](https:\/\/catalog.mit.edu\/mit\/overview\/)\n    \n    Toggle Overview\n    - [Around Campus](https:\/\/catalog.mit.edu\/mit\/overview\/campus\/)\n    - [Academic Program](https:\/\/catalog.mit.edu\/mit\/overview\/academic-program\/)\n    - [Administration](https:\/\/catalog.mit.edu\/mit\/overview\/administration\/)\n    - [Alumni](https:\/\/catalog.mit.edu\/mit\/overview\/alumni\/)\n  - [Campus Life](https:\/\/catalog.mit.edu\/mit\/campus-life\/)\n    \n    Toggle Campus Life\n    - [Activities](https:\/\/catalog.mit.edu\/mit\/campus-life\/activities\/)\n    - [Arts at MIT](https:\/\/catalog.mit.edu\/mit\/campus-life\/arts\/)\n    - [Athletics](https:\/\/catalog.mit.edu\/mit\/campus-life\/athletics\/)\n    - [Campus 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Undergraduate Education\n    - [Academic Programs](https:\/\/catalog.mit.edu\/mit\/undergraduate-education\/academic-programs\/)\n      \n      Toggle Academic Programs\n      - [First Year](https:\/\/catalog.mit.edu\/mit\/undergraduate-education\/academic-programs\/freshman-year\/)\n      - [Major Course of Study](https:\/\/catalog.mit.edu\/mit\/undergraduate-education\/academic-programs\/majors\/)\n      - [Minors](https:\/\/catalog.mit.edu\/mit\/undergraduate-education\/academic-programs\/minors\/)\n    - [General Institute Requirements](https:\/\/catalog.mit.edu\/mit\/undergraduate-education\/general-institute-requirements\/)\n    - [Academic and Research Options](https:\/\/catalog.mit.edu\/mit\/undergraduate-education\/academic-research-options\/)\n      \n      Toggle Academic and Research Options\n      - [Independent Activites Period](https:\/\/catalog.mit.edu\/mit\/undergraduate-education\/academic-research-options\/independent-activities-period\/)\n      - [Undergraduate 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[Career and Professional Options](https:\/\/catalog.mit.edu\/mit\/undergraduate-education\/career\/)\n      \n      Toggle Career and Professional Options\n      - [Career Advising and Professional Development](https:\/\/catalog.mit.edu\/mit\/undergraduate-education\/career\/global-education-career-development\/)\n      - [Teacher Licensure and Education](https:\/\/catalog.mit.edu\/mit\/undergraduate-education\/career\/teacher-licensure-education\/)\n      - [ROTC Programs](https:\/\/catalog.mit.edu\/mit\/undergraduate-education\/career\/rotc\/)\n    - [Admissions](https:\/\/catalog.mit.edu\/mit\/undergraduate-education\/admissions\/)\n    - [Costs](https:\/\/catalog.mit.edu\/mit\/undergraduate-education\/costs\/)\n    - [Financial Aid](https:\/\/catalog.mit.edu\/mit\/undergraduate-education\/financial-aid\/)\n    - [Medical Requirements](https:\/\/catalog.mit.edu\/mit\/undergraduate-education\/medical-requirements\/)\n  - [Graduate Education](https:\/\/catalog.mit.edu\/mit\/graduate-education\/)\n    \n    Toggle Graduate Education\n    - [Graduate Study at MIT](https:\/\/catalog.mit.edu\/mit\/graduate-education\/study\/)\n    - [General Degree Requirements](https:\/\/catalog.mit.edu\/mit\/graduate-education\/general-degree-requirements\/)\n    - [Other Institutions](https:\/\/catalog.mit.edu\/mit\/graduate-education\/other-institutions\/)\n    - [Admissions](https:\/\/catalog.mit.edu\/mit\/graduate-education\/admissions\/)\n    - [Costs](https:\/\/catalog.mit.edu\/mit\/graduate-education\/costs\/)\n    - [Financial Aid](https:\/\/catalog.mit.edu\/mit\/graduate-education\/financial-aid\/)\n    - [Medical Requirements](https:\/\/catalog.mit.edu\/mit\/graduate-education\/medical-requirements\/)\n  - [Academic Procedures](https:\/\/catalog.mit.edu\/mit\/procedures\/)\n    \n    Toggle Academic Procedures\n    - [Registration](https:\/\/catalog.mit.edu\/mit\/procedures\/registration\/)\n    - [Term Regulations and 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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# Master of Science in Computational Science and Engineering\n[Computational Science and Engineering](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/computational-science-engineering\/)\n\n|   |   |   |\n|---|---|---|\n| Core Subjects | 36 |   |\n| *Select three of the following subjects:* |   |   |\n| [6\\.7300\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=6.7300 \"6.7300[J]\") | Introduction to Modeling and Simulation |   |\n| [15\\.C57\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=15.C57 \"15.C57[J]\") | Optimization Methods |   |\n| [16\\.920\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=16.920 \"16.920[J]\") | Numerical Methods for Partial Differential Equations |   |\n| [18\\.335\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=18.335 \"18.335[J]\") | Introduction to Numerical Methods |   |\n| Restricted Electives 1 | 24 |   |\n| Choose 24 units of coursework from the list below. |   |   |\n| Unrestricted Elective 1 | 12 |   |\n| Choose any graduate-level subject. 2 |   |   |\n| Thesis |   |   |\n| [CSE.THG](https:\/\/catalog.mit.edu\/search\/?P=CSE.THG \"CSE.THG\") | Graduate Thesis | 36 |\n| Total Units | 108 |   |\n\n|   |   |\n|---|---|\n| *1* | *Subjects that can be repeated for credit cannot be used to satisfy multiple CSE SM requirements.* |\n| *2* | *See list of [subjects offered at MIT](https:\/\/catalog.mit.edu\/subjects\/).* |\n### Restricted Electives\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| [4\\.453](https:\/\/catalog.mit.edu\/search\/?P=4.453 \"4.453\") | Creative Machine Learning for Design | 12 |\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 | 12 |\n| [6\\.7940](https:\/\/catalog.mit.edu\/search\/?P=6.7940 \"6.7940\") | Dynamic Programming and Reinforcement Learning 1 | 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 2 | 9 |\n| [10\\.552](https:\/\/catalog.mit.edu\/search\/?P=10.552 \"10.552\") | Modern Control Design 2 | 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 3 | 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\n|   |   |\n|---|---|\n| *1* | *Restricted elective 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 restricted elective. See [6\\.C51](https:\/\/catalog.mit.edu\/search\/?P=6.C51 \"6.C51\") for more information.* |\n| *3* | *Students 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\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\/degree-charts\/master-computational-science-engineering\/#header)\n\nPrint Options\n\n[Send Page to Printer](https:\/\/catalog.mit.edu\/degree-charts\/master-computational-science-engineering\/)\n\n*Print this page.*\n\n[Download PDF of this Page](https:\/\/catalog.mit.edu\/degree-charts\/master-computational-science-engineering\/master-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\/degree-charts\/master-computational-science-engineering\/)","attrs_readable_markdown":"[Computational Science and Engineering](https:\/\/catalog.mit.edu\/interdisciplinary\/graduate-programs\/computational-science-engineering\/)\n\n|   |   |   |\n|---|---|---|\n| Core Subjects | 36 |   |\n| *Select three of the following subjects:* |   |   |\n| [6\\.7300\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=6.7300 \"6.7300[J]\") | Introduction to Modeling and Simulation |   |\n| [15\\.C57\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=15.C57 \"15.C57[J]\") | Optimization Methods |   |\n| [16\\.920\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=16.920 \"16.920[J]\") | Numerical Methods for Partial Differential Equations |   |\n| [18\\.335\\[J\\]](https:\/\/catalog.mit.edu\/search\/?P=18.335 \"18.335[J]\") | Introduction to Numerical Methods |   |\n| Restricted Electives 1 | 24 |   |\n| Choose 24 units of coursework from the list below. |   |   |\n| Unrestricted Elective 1 | 12 |   |\n| Choose any graduate-level subject. 2 |   |   |\n| Thesis |   |   |\n| [CSE.THG](https:\/\/catalog.mit.edu\/search\/?P=CSE.THG \"CSE.THG\") | Graduate Thesis | 36 |\n| Total Units | 108 |   |\n\n|   |   |\n|---|---|\n| *1* | *Subjects that can be repeated for credit cannot be used to satisfy multiple CSE SM requirements.* |\n| *2* | *See list of [subjects offered at MIT](https:\/\/catalog.mit.edu\/subjects\/).* |\n### Restricted Electives\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| [4\\.453](https:\/\/catalog.mit.edu\/search\/?P=4.453 \"4.453\") | Creative Machine Learning for Design | 12 |\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 | 12 |\n| [6\\.7940](https:\/\/catalog.mit.edu\/search\/?P=6.7940 \"6.7940\") | Dynamic Programming and Reinforcement Learning 1 | 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 2 | 9 |\n| [10\\.552](https:\/\/catalog.mit.edu\/search\/?P=10.552 \"10.552\") | Modern Control Design 2 | 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 3 | 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\n|   |   |\n|---|---|\n| *1* | *Restricted elective 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 restricted elective. See [6\\.C51](https:\/\/catalog.mit.edu\/search\/?P=6.C51 \"6.C51\") for more information.* |\n| *3* | *Students 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.* |","meta_canonical":null}

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URL	https://catalog.mit.edu/degree-charts/master-computational-science-engineering/
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Meta Title	Master of Science in Computational Science and Engineering \| MIT Course Catalog
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Boilerpipe Text	Computational Science and Engineering Core Subjects 36 Select three of the following subjects: 6.7300[J] Introduction to Modeling and Simulation 15.C57[J] Optimization Methods 16.920[J] Numerical Methods for Partial Differential Equations 18.335[J] Introduction to Numerical Methods Restricted Electives 1 24 Choose 24 units of coursework from the list below. Unrestricted Elective 1 12 Choose any graduate-level subject. 2 Thesis CSE.THG Graduate Thesis 36 Total Units 108 1 Subjects that can be repeated for credit cannot be used to satisfy multiple CSE SM requirements. 2 See list of subjects offered at MIT . Restricted Electives 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 4.453 Creative Machine Learning for Design 12 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 12 6.7940 Dynamic Programming and Reinforcement Learning 1 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 2 9 10.552 Modern Control Design 2 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 3 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 1 Restricted elective 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 restricted elective. See 6.C51 for more information. 3 Students receive credit for either 10.551 or 10.552 as a CSE concentration subject, but not both. 4 Subject to Sloan bidding process.
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Observatory](https://catalog.mit.edu/mit/research/haystack-observatory/) - [Initiative on the Digital Economy](https://catalog.mit.edu/mit/research/initiative-digital-economy/) - [Institute for Medical Engineering and Science](https://catalog.mit.edu/mit/research/institute-medical-engineering-science/) - [Institute for Soldier Nanotechnologies](https://catalog.mit.edu/mit/research/institute-soldier-nanotechnologies/) - [Institute for Work and Employment Research](https://catalog.mit.edu/mit/research/institute-work-employment/) - [Internet Policy Research Initiative](https://catalog.mit.edu/mit/research/internet-policy-research-initiative/) - [Knight Science Journalism Program](https://catalog.mit.edu/mit/research/knight-science-journalism-program/) - [Koch Institute for Integrative Cancer Research](https://catalog.mit.edu/mit/research/koch-institute-integrative-cancer-research/) - [Laboratory for Financial 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Research](https://catalog.mit.edu/mit/research/mcgovern-institute-brain-research/) - [Microsystems Technology Laboratories](https://catalog.mit.edu/mit/research/microsystems-technology-laboratories/) - [MIT Center for Art, Science & Technology](https://catalog.mit.edu/mit/research/center-art-science-technology/) - [MIT Energy Initiative](https://catalog.mit.edu/mit/research/mit-energy-initiative/) - [MIT Environmental Solutions Initiative](https://catalog.mit.edu/mit/research/environmental-solutions-initiative/) - [MIT Kavli Institute for Astrophysics and Space Research](https://catalog.mit.edu/mit/research/mit-kavli-institute-astrophysics-space-research/) - [MIT Media Lab](https://catalog.mit.edu/mit/research/mit-media-lab/) - [MIT Open Learning](https://catalog.mit.edu/mit/research/office-digital-learning/) - [MIT Portugal Program](https://catalog.mit.edu/mit/research/mit-portugal-program/) - [MIT Professional Education](https://catalog.mit.edu/mit/research/mit-professional-education/) - [MIT Sea Grant College Program](https://catalog.mit.edu/mit/research/sea-grant/) - [Nuclear Reactor Laboratory](https://catalog.mit.edu/mit/research/nuclear-reactor-laboratory/) - [Operations Research Center](https://catalog.mit.edu/mit/research/operations-research-center/) - [Picower Institute for Learning and Memory](https://catalog.mit.edu/mit/research/picower-institute-learning-memory/) - [Plasma Science and Fusion Center](https://catalog.mit.edu/mit/research/plasma-science-fusion-center/) - [Research Laboratory of Electronics](https://catalog.mit.edu/mit/research/research-laboratory-electronics/) - [Simons Center for the Social Brain](https://catalog.mit.edu/mit/research/simons-center-social-brain/) - [Singapore-MIT Alliance for Research and Technology Centre](https://catalog.mit.edu/mit/research/singapore-mit-alliance-research-technology/) - [Sociotechnical Systems Research Center](https://catalog.mit.edu/mit/research/sociotechnical-systems-research-center/) - [Whitehead Institute for Biomedical Research](https://catalog.mit.edu/mit/research/whitehead-institute-biomedical-research/) - [Women's and Gender Studies Program](https://catalog.mit.edu/mit/research/womens-gender-studies-program/) - [Schools and College](https://catalog.mit.edu/schools/) Toggle Schools and College - [School of Architecture and Planning](https://catalog.mit.edu/schools/architecture-planning/) Toggle School of Architecture and Planning - [Architecture](https://catalog.mit.edu/schools/architecture-planning/architecture/) Toggle Architecture - [Architecture (SB, Course 4)](https://catalog.mit.edu/degree-charts/architecture-course-4/) - [Architecture (MArch)](https://catalog.mit.edu/degree-charts/master-architecture/) - [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/) - [Architecture Studies (SM)](https://catalog.mit.edu/degree-charts/master-architecture-studies/) - [Media Arts and Sciences](https://catalog.mit.edu/schools/architecture-planning/media-arts-sciences/) - [Urban Studies and Planning](https://catalog.mit.edu/schools/architecture-planning/urban-studies-planning/) Toggle Urban Studies and Planning - [Planning (SB, Course 11)](https://catalog.mit.edu/degree-charts/planning-course-11/) - [Urban Science and Planning with Computer Science (SB, Course 11-6)](https://catalog.mit.edu/degree-charts/urban-science-planning-computer-science-11-6/) - [School of Engineering](https://catalog.mit.edu/schools/engineering/) Toggle School of Engineering - [Aeronautics and Astronautics](https://catalog.mit.edu/schools/engineering/aeronautics-astronautics/) Toggle Aeronautics and Astronautics - [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/) - [Engineering (SB, Course 16-ENG)](https://catalog.mit.edu/degree-charts/engineering-aeronautics-astronautics-course-16-eng/) - [Biological Engineering](https://catalog.mit.edu/schools/engineering/biological-engineering/) Toggle Biological Engineering - [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/) - [Chemical Engineering](https://catalog.mit.edu/schools/engineering/chemical-engineering/) Toggle Chemical Engineering - [Chemical Engineering (SB, Course 10)](https://catalog.mit.edu/degree-charts/chemical-engineering-course-10/) - [Chemical-Biological Engineering (SB, Course 10-B)](https://catalog.mit.edu/degree-charts/chemical-biological-engineering-course-10-b/) - [Chemical Engineering (SB, Course 10-C)](https://catalog.mit.edu/degree-charts/chemical-engineering-course-10-c/) - [Engineering (SB, Course 10-ENG)](https://catalog.mit.edu/degree-charts/engineering-chemical-engineering-course-10-eng/) - [Civil and Environmental Engineering](https://catalog.mit.edu/schools/engineering/civil-environmental-engineering/) Toggle Civil and Environmental Engineering - [Engineering (SB, Course 1-ENG)](https://catalog.mit.edu/degree-charts/engineering-civil-environmental-engineering-course-1-eng/) - [Civil and Environmental Engineering (MEng)](https://catalog.mit.edu/degree-charts/master-civil-environmental-engineering-course-1p/) - [Data, Systems, and Society](https://catalog.mit.edu/schools/engineering/data-systems-society/) - [Electrical Engineering and Computer Science](https://catalog.mit.edu/schools/engineering/electrical-engineering-computer-science/) Toggle Electrical Engineering and Computer Science - [Computation and Cognition (SB, Course 6-9)](https://catalog.mit.edu/degree-charts/computation-cognition-6-9/) - [Computer Science and Engineering (SB, Course 6-3)](https://catalog.mit.edu/degree-charts/computer-science-engineering-course-6-3/) - [Computer Science and Molecular Biology (SB, Course 6-7)](https://catalog.mit.edu/degree-charts/computer-science-molecular-biology-course-6-7/) - [Electrical Engineering with Computing (Course 6-5)](https://catalog-dev.mit.edu/degree-charts/electrical-engineering-computing-course-6-5/) - [Urban Science and Planning with Computer Science (SB, Course 11-6)](https://catalog.mit.edu/degree-charts/urban-science-planning-computer-science-11-6/) - [Electrical Engineering and Computer Science (MEng)](https://catalog.mit.edu/degree-charts/master-electrical-engineering-computer-science-course-6-p/) - [Computer Science and Molecular Biology (MEng)](https://catalog.mit.edu/degree-charts/master-computer-science-molecular-biology-course-6-7p/) - [Health Sciences and Technology](https://catalog.mit.edu/schools/engineering/harvard-mit-health-sciences-technology/) - [Materials Science and Engineering](https://catalog.mit.edu/schools/engineering/materials-science-engineering/) Toggle Materials Science and Engineering - [Archaeology and Materials (SB, Course 3-C)](https://catalog.mit.edu/degree-charts/archaeology-materials-course-3-c/) - [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 Engineering](https://catalog.mit.edu/schools/engineering/mechanical-engineering/) Toggle Mechanical Engineering - [Mechanical Engineering (SB, Course 2)](https://catalog.mit.edu/degree-charts/mechanical-engineering-course-2/) - [Mechanical and Ocean Engineering (SB, Course 2-OE)](https://catalog.mit.edu/degree-charts/mechanical-ocean-engineering-course-2-oe/) - [Engineering (SB, Course 2-A)](https://catalog.mit.edu/degree-charts/mechanical-engineering-course-2-a/) - [Nuclear Science and Engineering](https://catalog.mit.edu/schools/engineering/nuclear-science-engineering/) Toggle Nuclear Science and Engineering - [Nuclear Science and Engineering (SB, Course 22)](https://catalog.mit.edu/degree-charts/nuclear-science-engineering-course-22/) - [Engineering (SB, Course 22-ENG)](https://catalog.mit.edu/degree-charts/engineering-nuclear-science-engineering-course-22-eng/) - [School of Humanities, Arts, and Social Sciences](https://catalog.mit.edu/schools/humanities-arts-social-sciences/) Toggle School of Humanities, Arts, and Social Sciences - [Anthropology](https://catalog.mit.edu/schools/humanities-arts-social-sciences/anthropology/) Toggle Anthropology - [Anthropology (SB, Course 21A)](https://catalog.mit.edu/degree-charts/anthropology-course-21a/) - [Comparative Media Studies/Writing](https://catalog.mit.edu/schools/humanities-arts-social-sciences/comparative-media-studies-writing/) Toggle Comparative Media Studies/Writing - [Comparative Media Studies (SB, CMS)](https://catalog.mit.edu/degree-charts/comparative-media-studies-cms/) - [Writing (SB, Course 21W)](https://catalog.mit.edu/degree-charts/writing-course-21w/) - [Economics](https://catalog.mit.edu/schools/humanities-arts-social-sciences/economics/) Toggle Economics - [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/) - [Mathematical Economics (SB, Course 14-2)](https://catalog.mit.edu/degree-charts/mathematical-economics-course-14-2/) - [Global Languages](https://catalog.mit.edu/schools/humanities-arts-social-sciences/global-studies-languages/) Toggle Global Languages - [Global Studies and Languages (SB, Course 21G)](https://catalog.mit.edu/degree-charts/global-studies-languages-course-21g/) - [History](https://catalog.mit.edu/schools/humanities-arts-social-sciences/history/) Toggle History - [History (SB, Course 21H)](https://catalog.mit.edu/degree-charts/history-course-21h/) - [Humanities](https://catalog.mit.edu/schools/humanities-arts-social-sciences/humanities/) - [Linguistics and Philosophy](https://catalog.mit.edu/schools/humanities-arts-social-sciences/linguistics-philosophy/) Toggle Linguistics and Philosophy - [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 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\| Core Subjects \| 36 \| \| \| Select three of the following subjects: \| \| \| \| [6\.7300\[J\]](https://catalog.mit.edu/search/?P=6.7300 "6.7300[J]") \| Introduction to Modeling and Simulation \| \| \| [15\.C57\[J\]](https://catalog.mit.edu/search/?P=15.C57 "15.C57[J]") \| Optimization Methods \| \| \| [16\.920\[J\]](https://catalog.mit.edu/search/?P=16.920 "16.920[J]") \| Numerical Methods for Partial Differential Equations \| \| \| [18\.335\[J\]](https://catalog.mit.edu/search/?P=18.335 "18.335[J]") \| Introduction to Numerical Methods \| \| \| Restricted Electives 1 \| 24 \| \| \| Choose 24 units of coursework from the list below. \| \| \| \| Unrestricted Elective 1 \| 12 \| \| \| Choose any graduate-level subject. 2 \| \| \| \| Thesis \| \| \| \| [CSE.THG](https://catalog.mit.edu/search/?P=CSE.THG "CSE.THG") \| Graduate Thesis \| 36 \| \| Total Units \| 108 \| \| \| \| \| \|---\|---\| \| 1 \| Subjects that can be repeated for credit cannot be used to satisfy multiple CSE SM requirements. \| \| 2 \| See list of [subjects offered at MIT](https://catalog.mit.edu/subjects/). \| ### Restricted Electives \| \| \| \| \|---\|---\|---\| \| [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 \| \| \| [4\.453](https://catalog.mit.edu/search/?P=4.453 "4.453") \| Creative Machine Learning for Design \| 12 \| \| [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 \| 12 \| \| [6\.7940](https://catalog.mit.edu/search/?P=6.7940 "6.7940") \| Dynamic Programming and Reinforcement Learning 1 \| 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 2 \| 9 \| \| [10\.552](https://catalog.mit.edu/search/?P=10.552 "10.552") \| Modern Control Design 2 \| 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 3 \| 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 \| \| \| \| \|---\|---\| \| 1 \| Restricted elective 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 restricted elective. See [6\.C51](https://catalog.mit.edu/search/?P=6.C51 "6.C51") for more information. \| \| 3 \| Students 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. \| [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/degree-charts/master-computational-science-engineering/#header) Print Options [Send Page to Printer](https://catalog.mit.edu/degree-charts/master-computational-science-engineering/) Print this page. 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Readable Markdown	[Computational Science and Engineering](https://catalog.mit.edu/interdisciplinary/graduate-programs/computational-science-engineering/) \| \| \| \| \|---\|---\|---\| \| Core Subjects \| 36 \| \| \| Select three of the following subjects: \| \| \| \| [6\.7300\[J\]](https://catalog.mit.edu/search/?P=6.7300 "6.7300[J]") \| Introduction to Modeling and Simulation \| \| \| [15\.C57\[J\]](https://catalog.mit.edu/search/?P=15.C57 "15.C57[J]") \| Optimization Methods \| \| \| [16\.920\[J\]](https://catalog.mit.edu/search/?P=16.920 "16.920[J]") \| Numerical Methods for Partial Differential Equations \| \| \| [18\.335\[J\]](https://catalog.mit.edu/search/?P=18.335 "18.335[J]") \| Introduction to Numerical Methods \| \| \| Restricted Electives 1 \| 24 \| \| \| Choose 24 units of coursework from the list below. \| \| \| \| Unrestricted Elective 1 \| 12 \| \| \| Choose any graduate-level subject. 2 \| \| \| \| Thesis \| \| \| \| [CSE.THG](https://catalog.mit.edu/search/?P=CSE.THG "CSE.THG") \| Graduate Thesis \| 36 \| \| Total Units \| 108 \| \| \| \| \| \|---\|---\| \| 1 \| Subjects that can be repeated for credit cannot be used to satisfy multiple CSE SM requirements. \| \| 2 \| See list of [subjects offered at MIT](https://catalog.mit.edu/subjects/). \| ### Restricted Electives \| \| \| \| \|---\|---\|---\| \| [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 \| \| \| [4\.453](https://catalog.mit.edu/search/?P=4.453 "4.453") \| Creative Machine Learning for Design \| 12 \| \| [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 \| 12 \| \| [6\.7940](https://catalog.mit.edu/search/?P=6.7940 "6.7940") \| Dynamic Programming and Reinforcement Learning 1 \| 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 2 \| 9 \| \| [10\.552](https://catalog.mit.edu/search/?P=10.552 "10.552") \| Modern Control Design 2 \| 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 3 \| 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 \| \| \| \| \|---\|---\| \| 1 \| Restricted elective 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 restricted elective. See [6\.C51](https://catalog.mit.edu/search/?P=6.C51 "6.C51") for more information. \| \| 3 \| Students 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. \|
Shard	180 (laksa)
Root Hash	10722954425220430980
Unparsed URL	edu,mit!catalog,/degree-charts/master-computational-science-engineering/ s443