MIT OpenCourseWare: New Courses in MathematicsNew courses in Mathematics from MIT OpenCourseWare, provider of free and open MIT course materials.
http://ocw.mit.edu/courses/mathematics
2016-02-04T13:00:00+05:00MIT 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/terms/index.htm18.S997 The Polynomial Method (MIT)This course offers an introduction to the polynomial method as applied to solving problems in combinatorics in the last decade. The course also explores the connections between the polynomial method as used in these problems to the polynomial method in other fields, including computer science, number theory, and analysis.
http://ocw.mit.edu/courses/mathematics/18-s997-the-polynomial-method-fall-2012
Fall2012Guth, Lawrence2015-12-22T21:16:21+05:0018.S997en-USpolynomial methodcombinatoricsKakeya ProblemIncidence GeometryAlgebraic StructureCell DecompositionsRuled SurfacesProjection 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/terms/index.htm18.304 Undergraduate Seminar in Discrete Mathematics (MIT)This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.
http://ocw.mit.edu/courses/mathematics/18-304-undergraduate-seminar-in-discrete-mathematics-spring-2015
Spring2015Tamuz, Omer2015-12-17T16:51:46+05:0018.304en-USdiscrete mathdiscrete mathematicspresentationsstudent presentationsoral communicationcombinatoricsgraph theorydiscrete mathematicsProofs from the Bookmathematics communicationMIT 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/terms/index.htm18.443 Statistics for Applications (MIT)This course is a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, correlation, decision theory, and Bayesian statistics.
http://ocw.mit.edu/courses/mathematics/18-443-statistics-for-applications-spring-2015
Spring2015Kempthorne, Peter2015-12-14T18:32:13+05:0018.443en-UShypothesis testinghypothesis estimationconfidence intervalschi-square testsnonparametric statisticsanalysis of varianceregressioncorrelationdecision theoryBayesian statisticsMIT 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/terms/index.htm18.385J Nonlinear Dynamics and Chaos (MIT)This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with emphasis on geometric thinking, computational and analytical methods and makes extensive use of demonstration software.
http://ocw.mit.edu/courses/mathematics/18-385j-nonlinear-dynamics-and-chaos-fall-2014
Fall2014Rosales, Rodolfo2015-12-03T18:34:47+05:0018.385J2.036Jen-USchaosFloquet theoryPoincare-Bendixson theoryphase planelimit cyclestime-dependent systemsPoincare mapsstability of equilibrianear-equilibrium dynamicscenter manifoldselementary bifurcationsnormal formsMIT 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/terms/index.htm18.409 Algorithmic Aspects of Machine Learning (MIT)This course is organized around algorithmic issues that arise in machine learning. Modern machine learning systems are often built on top of algorithms that do not have provable guarantees, and it is the subject of debate when and why they work. In this class, we focus on designing algorithms whose performance we can rigorously analyze for fundamental machine learning problems.
http://ocw.mit.edu/courses/mathematics/18-409-algorithmic-aspects-of-machine-learning-spring-2015
Spring2015Moitra, Ankur2015-12-03T15:15:21+05:0018.409en-USMachine learningnonnegative matrix factorizationtensor decompositiontensor rankborder ranksparse codingsparse recoverylearning mixture modelmatrix completionMIT 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/terms/index.htm18.S997 High-Dimensional Statistics (MIT)This course offers an introduction to the finite sample analysis of high- dimensional statistical methods. The goal is to present various proof techniques for state-of-the-art methods in regression, matrix estimation and principal component analysis (PCA) as well as optimality guarantees. The course ends with research questions that are currently open. You can read more about Prof. Rigollet's work and courses on his website
http://ocw.mit.edu/courses/mathematics/18-s997-high-dimensional-statistics-spring-2015
Spring2015Rigollet, Philippe2015-11-10T17:50:26+05:0018.S997en-USHigh Dimensional StatisticsRandom VariablesLinear RegressionMisspecified Linear ModelsMatrix EstimationMinmax Lower BoundsSub-GaussianMIT 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/terms/index.htm18.354J Nonlinear Dynamics II: Continuum Systems (MIT)This course introduces the basic ideas for understanding the dynamics of continuum systems, by studying specific examples from a range of different fields. Our goal will be to explain the general principles, and also to illustrate them via important physical effects. A parallel goal of this course is to give you an introduction to mathematical modeling.
http://ocw.mit.edu/courses/mathematics/18-354j-nonlinear-dynamics-ii-continuum-systems-spring-2015
Spring2015Dunkel, Jörn2015-10-30T17:15:40+05:0018.354J1.062J12.207Jen-UScontinuum systemsmathematical modelingdiffusion equationequations of motionnonlinear partial differential equationscalculus of variationsBrachistochrone curvesoap filmshydrodynamicsNavier-Stokessolitonssurface tensionwavesconformal mapsairfoilsMIT 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/terms/index.htm18.445 Introduction to Stochastic Processes (MIT)This course is an introduction to Markov chains, random walks, martingales, and Galton-Watsom tree. The course requires basic knowledge in probability theory and linear algebra including conditional expectation and matrix.
http://ocw.mit.edu/courses/mathematics/18-445-introduction-to-stochastic-processes-spring-2015
Spring2015Wu, Hao2015-08-20T16:53:50+05:0018.445en-USprobabilityStochastic ProcessesMarkov chainsrandom walksmartingalesGalton-Watsom treeprobabilitylinear algebraMIT 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/terms/index.htm18.310 Principles of Discrete Applied Mathematics (MIT)This course is an introduction to discrete applied mathematics. Topics include probability, counting, linear programming, number-theoretic algorithms, sorting, data compression, and error-correcting codes. This is a Communication Intensive in the Major (CI-M) course, and thus includes a writing component.
http://ocw.mit.edu/courses/mathematics/18-310-principles-of-discrete-applied-mathematics-fall-2013
Fall2013Goemans, MichelRuff, SusanOrecchia, LorenzoPeng, Richard2015-07-27T16:48:49+05:0018.310en-USprobabilityprobability theory countingpigeonhole principleVan der Waerden's theoremChernoff boundscountingcodingsamplingrandom samplingCatalan familiesgenerating functionschord diagramslinear programmingsimplex methodZero-Sum matrixnetwork flowsmaximum flow problemsorting algorithmsQUICKSORTmedian findingsorting networksBatcher's algorithmEuclid's algorithmChinese Remainder TheoremcryptographyRSA codeprimaility testingFFTFast Fourier TransformShannon's coding theoremsLempel-Ziv codeslinear codeshamming codeMIT 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/terms/index.htm18.311 Principles of Applied Mathematics (MIT)18.311 Principles of Continuum Applied Mathematics covers fundamental concepts in continuous applied mathematics, including applications from traffic flow, fluids, elasticity, granular flows, etc. The class also covers continuum limit; conservation laws, quasi-equilibrium; kinematic waves; characteristics, simple waves, shocks; diffusion (linear and nonlinear); numerical solution of wave equations; finite differences, consistency, stability; discrete and fast Fourier transforms; spectral methods; transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion, and group velocity.
http://ocw.mit.edu/courses/mathematics/18-311-principles-of-applied-mathematics-spring-2014
Spring2014Rosales, Rodolfo2015-07-08T16:40:32+05:0018.311en-USpartial differential equationhyperbolic equationsdimensional analysisperturbation methodshyperbolic systemsdiffusion and reaction processescontinuum modelsequilibrium modelscontinuous applied mathematicstraffic flowfluidselasticitygranular flowscontinuum limitconservation lawsquasi-equilibriumkinematic wavescharacteristicssimple wavesshocksdiffusion (linear and nonlinear)numerical solution of wave equationsfinite differencesconsistencystabilitydiscrete and fast Fourier transformsspectral methodstransforms and series (Fourier, Laplace)sonic boomsMach conecausticslatticesdispersiongroup velocityMIT 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/terms/index.htm18.303 Linear Partial Differential Equations: Analysis and Numerics (MIT)This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat / diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems. The Julia Language (a free, open-source environment) is introduced and used in homework for simple examples.
http://ocw.mit.edu/courses/mathematics/18-303-linear-partial-differential-equations-analysis-and-numerics-fall-2014
Fall2014Johnson, Steven G.2015-06-25T13:46:19+05:0018.303en-USdiffusionLaplace equationsPoissonwave equationsseparation of variablesFourier seriesFourier transformseigenvalue problemsGreen's functionHeat EquationSturm-Liouville Eigenvalue problemsquasilinear PDEsBessel functionsORDSMIT 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/terms/index.htm18.783 Elliptic Curves (MIT)This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.
http://ocw.mit.edu/courses/mathematics/18-783-elliptic-curves-spring-2015
Spring2015Sutherland, Andrew2015-06-17T14:06:41+05:0018.783en-USelliptic curvesnumber theorycryptographypoint-countingisogeniespairingstheory of complex multiplicationinteger factorizationprimality provingelliptic curve cryptographymodular curvesFermat's Last TheoremMIT 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/terms/index.htm18.440 Probability and Random Variables (MIT)This 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/courses/mathematics/18-440-probability-and-random-variables-spring-2014
Spring2014Sheffield, Scott2015-05-14T13:12:51+05:0018.440en-USProbability spacesrandom variablesdistribution functionsBinomialgeometrichypergeometricPoisson distributionsUniformexponentialnormalgamma and beta distributionsConditional probabilityBayes theoremjoint distributionsChebyshev inequalitylaw of large numbersAnd central limit theoremMIT 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/terms/index.htm18.325 Topics in Applied Mathematics: Waves and Imaging (MIT)This class covers the mathematics of inverse problems involving waves, with examples taken from reflection seismology, synthetic aperture radar, and computerized tomography.
http://ocw.mit.edu/courses/mathematics/18-325-topics-in-applied-mathematics-waves-and-imaging-fall-2012
Fall2012Demanet, Laurent2015-04-29T11:58:55+05:0018.325en-USwavesimagingradar imagingseismic imagingRadon transformbackprojectionreflection seismologycomputerized tomographysynthetic aperture radarMIT 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/terms/index.htm18.915 Graduate Topology Seminar: Kan Seminar (MIT)This is a literature seminar with a focus on classic papers in Algebraic Topology. It is named after the late MIT professor Daniel Kan. Each student gives one or two talks on each of three papers, chosen in consultation with the instructor, reads all the papers presented by other students, and writes reactions to the papers. This course is useful not only to students pursuing algebraic topology as a field of study, but also to those interested in symplectic geometry, representation theory, and combinatorics.
http://ocw.mit.edu/courses/mathematics/18-915-graduate-topology-seminar-kan-seminar-fall-2014
Fall2014Miller, Haynes2015-04-15T19:38:37+05:0018.915en-USmathematicstopologyKan SeminarDan KancommunicationpresentingMIT 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/terms/index.htm18.314 Combinatorial Analysis (MIT)This course analyzes combinatorial problems and methods for their solution. Topics include: enumeration, generating functions, recurrence relations, construction of bijections, introduction to graph theory, network algorithms, and extremal combinatorics.
http://ocw.mit.edu/courses/mathematics/18-314-combinatorial-analysis-fall-2014
Fall2014Stanley, Richard2015-03-17T13:30:01+05:0018.314en-USEnumerationGenerating functionsRecurrence relationsConstruction of BijectionsGraph TheoryNetwork AlgorithmsExtremal CombinatoricsMIT 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/terms/index.htm18.S096 Topics in Mathematics with Applications in Finance (MIT)The purpose of the class is to expose undergraduate and graduate students to the mathematical concepts and techniques used in the financial industry. Mathematics lectures are mixed with lectures illustrating the corresponding application in the financial industry. MIT mathematicians teach the mathematics part while industry professionals give the lectures on applications in finance.
http://ocw.mit.edu/courses/mathematics/18-s096-topics-in-mathematics-with-applications-in-finance-fall-2013
Fall2013Kempthorne, PeterLee, ChoongbumStrela, VasilyXia, Jake2015-01-05T16:47:35+05:0018.S096en-USFinancial termsValue at Risk ModelsVolatility ModelingRegularized pricingRisk ModelsRisk analysiscommodity modelsportfolio theoryIto calculusBlack-Scholes formularisk neutral valuationoption pricingQuanto credit hedgingRoss recovery theoremcounterparty credit riskMIT 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/terms/index.htm18.05 Introduction to Probability and Statistics (MIT)This course provides an elementary introduction to probability and statistics with applications. Topics include: basic combinatorics, random variables, probability distributions, Bayesian inference, hypothesis testing, confidence intervals, and linear regression. The Spring 2014 version of this subject employed the residential MITx system, which enables on-campus subjects to provide MIT students with learning and assessment tools such as online problem sets, lecture videos, reading questions, pre-lecture questions, problem set assistance, tutorial videos, exam review content, and even online exams.
http://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014
Spring2014Orloff, JeremyBloom, Jonathan2014-12-19T13:39:32+05:0018.05en-USprobabilitystatisticsmodelscombinatoricsexpectationvariancerandom variablediscrete probability distributioncontinuous probability distributionBayesdistributionstatistical estimationstatistical testingconfidence intervallinear regressionnormalsignificance testingbootstrappingMIT 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/terms/index.htm18.175 Theory of Probability (MIT)This course covers topics such as sums of independent random variables, central limit phenomena, infinitely divisible laws, Levy processes, Brownian motion, conditioning, and martingales.
http://ocw.mit.edu/courses/mathematics/18-175-theory-of-probability-spring-2014
Spring2014Sheffield, Scott2014-12-12T17:28:19+05:0018.175en-USLaws of large numberscentral limit theoremsindependent random variablesconditioningmartingalesBrownian motionelements of diffusion theoryfunctional limit theoremsMIT 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/terms/index.htm18.700 Linear Algebra (MIT)This course offers a rigorous treatment of linear algebra, including vector spaces, systems of linear equations, bases, linear independence, matrices, determinants, eigenvalues, inner products, quadratic forms, and canonical forms of matrices. Compared with 18.06 Linear Algebra, more emphasis is placed on theory and proofs.
http://ocw.mit.edu/courses/mathematics/18-700-linear-algebra-fall-2013
Fall2013Vogan, David2014-10-21T21:03:34+05:0018.700en-USlinear algebravector spacesystem of linear equationsbaseslinear independencematricesdeterminanteigenvalueinner productquadratic formSpectral TheoremMIT 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/terms/index.htm