New courses in Mathematicshttp://ocw.mit.edu/OcwWeb/Mathematics/index.htm2009-11-19MIT OpenCourseWare http://ocw.mit.eduen-USContent within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htmThis course introduces students to probability and random variables. Topics include distribution functions, binomial, geometric, hypergeometric, and Poisson distributions. The other topics covered are uniform, exponential, normal, gamma and beta distributions; conditional probability; Bayes theorem; joint distributions; Chebyshev inequality; law of large numbers; and central limit theorem.http://ocw.mit.edu/OcwWeb/Mathematics/18-440Spring-2009/CourseHome/index.htmDudley, Richard2009-08-21T05:31:44-04:0018.440en-USMathematicsMathematical Statistics and Probabilityand central limit theorem.law of large numbersChebyshev inequalityjoint distributionsBayes theoremConditional probabilitygamma and beta distributionsnormalexponentialUniformPoisson distributionshypergeometricgeometricBinomialdistribution functionsrandom variablesProbability spacesMIT OpenCourseWare http://ocw.mit.eduContent within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htmA broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics: hypothesis testing and estimation. Confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, and correlation. Treatment more oriented toward application and less toward theory than 18.441.http://ocw.mit.edu/OcwWeb/Mathematics/18-443Spring-2009/CourseHome/index.htmDudley, Richard2009-08-20T03:52:09-04:0018.443en-USMathematicsMathematical Statistics and ProbabilityStatistics, GeneralBayesian statisticsdecision theorycorrelationregressionanalysis of variancenonparametric statisticschi-square testsconfidence intervalshypothesis estimationhypothesis testingMIT OpenCourseWare http://ocw.mit.eduContent within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htmContent varies from year to year. Topic for spring 2003: Introduction to integrable systems, with connections to loop groups and harmonic maps. Further topics may include a discussion of recent results on special Lagrangian submanifolds.http://ocw.mit.edu/OcwWeb/Mathematics/18-969Spring-2009/CourseHome/index.htmAuroux, Denis2009-08-20T11:32:17-04:0018.969en-USMathematicsAlgebra and Number TheorymatricesK3 surfacessubmanifoldsSYZ conjecturehomologylagrangian floer theorypicard-fuchsmonodromyyukawacohomologygromov-wittenpseudoholomorphichodge theorydeformationmirror symmetryMIT OpenCourseWare http://ocw.mit.eduContent within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htmStudy of an area of current interest in theoretical computer science. Topic varies from term to term.http://ocw.mit.edu/OcwWeb/Mathematics/18-409Fall-2007/CourseHome/index.htmKelner, Jonathan2009-07-17T04:25:21-04:0018.409en-USMathematicsComputer and Information Sciences, OtherFritz John’s theoremCheeger inequalitiesGraph LaplaciansLPs and SDPs for approximating NP-hard problemsLattices and basis reductionConvex geometryIterative methods for linear algebraSpectral graph theoryMIT OpenCourseWare http://ocw.mit.eduContent within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htmA first-year graduate course in algorithms. Emphasizes fundamental algorithms and advanced methods of algorithmic design, analysis, and implementation. Data structures. Network flows. Linear programming. Computational geometry. Approximation algorithms. Alternate years.http://ocw.mit.edu/OcwWeb/Electrical-Engineering-and-Computer-Science/6-854JFall-2008/CourseHome/index.htmGoemans, Michel 2009-07-17T10:18:08-04:006.854J18.415Jen-USElectrical Engineering and Computer ScienceComputational Mathematics18.4156.854Data StructuresNumber-Theoretic AlgorithmsPlanarity Testing of GraphsApproximation AlgorithmsNetwork FlowsLinear ProgrammingMathematicsMIT OpenCourseWare http://ocw.mit.eduContent within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htmThis course explores the basic concepts of computer modeling and simulation in science and engineering. We'll use techniques and software for simulation, data analysis and visualization. Continuum, mesoscale, atomistic and quantum methods are used to study fundamental and applied problems in physics, chemistry, materials science, mechanics, engineering, and biology. Examples drawn from the disciplines above are used to understand or characterize complex structures and materials, and complement experimental observations.http://ocw.mit.edu/OcwWeb/Materials-Science-and-Engineering/3-021JSpring-2008/CourseHome/index.htmBuehler, MarkusThonhauser, TimoRadovitzky, Raul2009-07-13T02:57:44-04:003.021J22.00J18.361J10.333J1.021Jen-USChemical EngineeringIndustrial EngineeringEducational Evaluation and ResearchApplied Mathematicsfinite elementFEMstructural mechanicsgasmeltingevolutionfractalheatfluid dynamicsapplied mathematicsbiologymaterials sciencemechanicschemistrycomputational physicscontinuum methodmesoscaleMonte Carlomolecular dynamicschemicalquantum methodquantumvisualizationdata analysisstatistical samplingcontinuum fieldcontinuumdiscrete particle systemcomputer modelingNuclear Science and EngineeringMathematicsMaterials Science and EngineeringCivil and Environmental EngineeringMIT OpenCourseWare http://ocw.mit.eduContent within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htmThis is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected.http://ocw.mit.edu/OcwWeb/Mathematics/18-312Spring-2009/CourseHome/index.htmMusiker, Gregg2009-11-04T04:03:52-05:0018.312en-USMathematicsAdjacency and Laplacian Matrices of GraphsRadon TransformRecurrence RelationsRational Generating FunctionsMIT OpenCourseWare http://ocw.mit.eduContent within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htmAdvanced introduction to applications and theory of numerical methods for solution of differential equations, especially of physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. Topics include finite differences, spectral methods, finite elements, well-posedness and stability, particle methods and lattice gases, boundary and nonlinear instabilities.http://ocw.mit.edu/OcwWeb/Mathematics/18-336Spring-2009/CourseHome/index.htmSeibold, Benjamin2009-10-06T08:15:22-04:0018.336en-USMathematicsApplied Mathematicsmultigriddirect and iterative methodsparticle methodslevel set methodsprojection approaches for incompressible owsspectral methodsENO/WENOfinite elementsfinite volumesfinite differencessaddle point problemsKrylov spacesmultigridpreconditioningfront propagationshocksstaggered gridsFourier approacheserror analysisLax equivalence theoremconvergencestabilityconsistencyinterface problemsNavier-Stokes equationsStokes problemPoisson equationhyperbolic conservation lawsKdV equationconvection-diffusion problemsAiry equationwave equationheat equationadvection equationMIT OpenCourseWare http://ocw.mit.eduContent within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htmThis is a undergraduate course. It will cover normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of L-p spaces; Hilbert space; compact, Hilbert-Schmidt and trace class operators; as well as spectral theorem.http://ocw.mit.edu/OcwWeb/Mathematics/18-102Spring-2009/CourseHome/index.htmMelrose, Richard2009-10-21T12:40:59-04:0018.102en-USMathematicsAnalysis and Functional AnalysisLebesgue integrable functionsLebesgue integrabilityBanach spacesnormed spacesmetric spaceslinear spacesMIT OpenCourseWare http://ocw.mit.eduContent within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm
In these times of economic and environmental uncertainty, you may wonder how you can make a difference in the complex issues affecting your world. Knowledge truly is power, and OCW puts MIT’s world-class knowledge in the hands of individuals and organizations around the world seeking solutions to our most difficult challenges. By supporting OCW, you support a world of change. Please donate today and help keep OCW going and growing.]]>http://ocw.mit.edu/OcwWeb/web/donate/invest/index.htm?utm_source=RSSMIT OpenCourseWare2009-10-20T11:59:59-04:00en-USMIT OpenCourseWare http://ocw.mit.eduContent within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htmThis course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry.http://ocw.mit.edu/OcwWeb/Mathematics/18-726Spring-2009/CourseHome/index.htmKedlaya, Kiran2009-10-02T12:28:34-04:0018.726en-USMathematicsAlgebra and Number Theoryetale cohomologyriemann-rochcohen-macaulay schemesserre dualitygagahilbert polynomialsprojective spacesquasicoherent sheavescohomologyalgebraic geometryhomological algebradivisorsdifferentialsprojective morphismsmorphismsshcemesabelian sheavessheavescategory theoryMIT OpenCourseWare http://ocw.mit.eduContent within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/OcwWeb/web/terms/terms/index.htm