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
2015-10-02T15:22:35+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.htm18.445 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.htm18.782 Introduction to Arithmetic Geometry (MIT)This course is an introduction to arithmetic geometry, a subject that lies at the intersection of algebraic geometry and number theory. Its primary motivation is the study of classical Diophantine problems from the modern perspective of algebraic geometry.
http://ocw.mit.edu/courses/mathematics/18-782-introduction-to-arithmetic-geometry-fall-2013
Fall2013Sutherland, Andrew2014-05-23T13:35:46+05:0018.782en-USalgebranumber theorydiophantine equationsalgebraic geometryplane conicselliptic curveshyperelliptic curvesabelian varietiesTate-Shafarevich groupMIT 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.htm18.821 Project Laboratory in Mathematics (MIT)Project Laboratory in Mathematics is a course designed to give students a sense of what it's like to do mathematical research. In teams, students explore puzzling and complex mathematical situations, search for regularities, and attempt to explain them mathematically. Students share their results through professional-style papers and presentations.
This course site was created specifically for educators interested in offering students a taste of mathematical research. This site features extensive description and commentary from the instructors about why the course was created and how it operates.
http://ocw.mit.edu/courses/mathematics/18-821-project-laboratory-in-mathematics-spring-2013
Spring2013Miller, HaynesStapleton, NatGlasman, SaulRuff, Susan2014-01-30T14:42:35+05:0018.821en-USmathematicsresearchcommunicationwritingpresentingLaTeXteamworkMIT 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.htm18.353J Nonlinear Dynamics I: Chaos (MIT)This course provides an introduction to nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in engineering and science.
http://ocw.mit.edu/courses/mathematics/18-353j-nonlinear-dynamics-i-chaos-fall-2012
Fall2012Chumakova, Lyubov2014-01-08T16:40:41+05:0018.353J2.050J12.006Jen-USnonlinear dynamicschaosdissipative systemsfree oscillatorsforced oscillatorsnonlinear phenomenabifurcation 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.htm18.357 Interfacial Phenomena (MIT)This graduate-level course covers fluid systems dominated by the influence of interfacial tension. The roles of curvature pressure and Marangoni stress are elucidated in a variety of fluid systems. Particular attention is given to drops and bubbles, soap films and minimal surfaces, wetting phenomena, water-repellency, surfactants, Marangoni flows, capillary origami and contact line dynamics.
http://ocw.mit.edu/courses/mathematics/18-357-interfacial-phenomena-fall-2010
Fall2010Bush, John W. M.2013-08-06T15:47:35+05:0018.357en-USfluid dynamicsfluid mechanicsinterfacial phenomenawater-repellencysurfactantsMarangoni flowscapillary origamicontact line dynamicstears of wineMIT 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.S996 Category Theory for Scientists (MIT)The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields.
http://ocw.mit.edu/courses/mathematics/18-s996-category-theory-for-scientists-spring-2013
Spring2013Spivak, David I.2013-07-02T11:29:17+05:0018.S996en-USSetsfunctionscommutative diagramsproductscoproductsfinite limitsmonoidsgroupsgraphsordersschemasinstancesdatabasescategoriesfunctorsmathematicsnatural transformationslimitscolimitsadjoint functorsmonadsoperadsisomorphismmolecular dynamicsologMIT 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.htm18.703 Modern Algebra (MIT)This undergraduate course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics.
http://ocw.mit.edu/courses/mathematics/18-703-modern-algebra-spring-2013
Spring2013McKernan, James2013-06-26T01:17:39+05:0018.703en-USalgebragroup theoryfinite groupsring theoryunique factorizationEuclidean ringsfield theoryfinite fieldsMIT 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.htm18.100C Real Analysis (MIT)This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation.
The three options for 18.100:
Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible.
Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology.
Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication. This fulfills the MIT CI requirement.
http://ocw.mit.edu/courses/mathematics/18-100c-real-analysis-fall-2012
Fall2012Seidel, Paul2013-04-11T13:35:39+05:0018.100Cen-USmathematical analysisArchimedean principledecimal expansionCauchy-Schwarzmetric spacesopen subsetsEuclidean spaceconvergent sequencessubsequential limitsinverse functionsStone-Weierstrass theoremtheory of integrationRiemann-Stjeltjes integralFourier seriesMIT 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