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
2014-06-30T17:18:06+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.htm18.782 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
Sutherland, 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.htm18.783 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-2013
Sutherland, Andrew2014-04-22T15:32:08+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.htm18.821 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
Miller, 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
Chumakova, 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
Bush, 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
Spivak, 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
McKernan, 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
Seidel, 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.htm18.S997 Introduction To MATLAB Programming (MIT)This course is intended to assist undergraduates with learning the basics of programming in general and programming MATLAB® in particular.
http://ocw.mit.edu/courses/mathematics/18-s997-introduction-to-matlab-programming-fall-2011
Farjoun, Yossi2013-01-28T16:12:18+05:0018.S997en-USMATLAB,programmingvariablesplottingscriptsfunctionsflow controlstatisticsdata structuresimagesvectorsmatricesroot-findingNewton's MethodSecant MethodBasins of AttractionConway Game of LifeGame of Lifevectorizationdebuggingscopefunction blockMIT 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.htm18.781 Theory of Numbers (MIT)This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.
http://ocw.mit.edu/courses/mathematics/18-781-theory-of-numbers-spring-2012
Kumar, Abhinav2013-01-22T16:45:18+05:0018.781en-USprimesdivisibilityfundamental theorem of arithmeticgcdEuclidean algorithmcongruencesChinese remainder theoremHensel's lemmaprimitive rootsquadratic residuesreciprocityarithmetic functionsDiophantine equationscontinued fractionsMIT 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.htm18.100A Introduction to Analysis (MIT)Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 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.
http://ocw.mit.edu/courses/mathematics/18-100a-introduction-to-analysis-fall-2012
Mattuck, Arthur2013-01-16T10:12:26+05:0018.100Aen-USmathematical analysisestimationslimit of a sequencelimit theoremssubsequencescluster pointsinfinite seriespower serieslocal and global propertiescontinuityintermediate-value theoremconvexityintegrabilityRiemann integralcalculusconvergenceGamma functionStirlingquantifiers and negationLeibnizFubiniimproper integralsLebesgue integralmathematical proofsdifferentiationintegrationMIT 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.htm18.337J Parallel Computing (MIT)This is an advanced interdisciplinary introduction to applied parallel computing on modern supercomputers. It has a hands-on emphasis on understanding the realities and myths of what is possible on the world's fastest machines. We will make prominent use of the Julia Language software project.
http://ocw.mit.edu/courses/mathematics/18-337j-parallel-computing-fall-2011
Edelman, Alan2012-12-21T14:42:47+05:0018.337J6.338Jen-UScloud computingdense linear algebrasparse linear algebraN-body problemsmultigridfast-multipolewaveletsFourier transformspartitioningmesh generationapplications oriented architectureparallel programming paradigmsMPIdata parallel systemsStar-Pparallel Pythonparallel Matlabgraphics processorsvirtualizationcachesvector processorsVHLLsVery High Level LanguagesJulia programming languagedistributed parallel executionMIT 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.htm18.330 Introduction to Numerical Analysis (MIT)This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods in linear algebra.
http://ocw.mit.edu/courses/mathematics/18-330-introduction-to-numerical-analysis-spring-2012
Demanet, Laurent2012-12-14T16:24:02+05:0018.330en-USseries expansionsroot findinginterpolationFourier transformapproximation functionsleast-squares approximationprincipal component analysisMIT 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.htm18.904 Seminar in Topology (MIT)This course is a seminar in topology. The main mathematical goal is to learn about the fundamental group, homology and cohomology. The main non-mathematical goal is to obtain experience giving math talks.
http://ocw.mit.edu/courses/mathematics/18-904-seminar-in-topology-spring-2011
Snowden, Andrew2012-12-13T09:13:53+05:0018.904en-USstudent lecturesmath writingtopologyfundamental groupcovering spacescommunicationoral communicationmathematical writingMIT 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.htm18.152 Introduction to Partial Differential Equations (MIT)This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications.
http://ocw.mit.edu/courses/mathematics/18-152-introduction-to-partial-differential-equations-fall-2011
Speck, Jared 2012-06-28T08:14:02+05:0018.152en-USdiffusionelliptichyperbolicpartial differential equationInitial and boundary value problems for ordinary differential equationsSturm-Liouville theory and eigenfunction expansionsinitial value problemswave equation;heat equationDirichlet problemLaplace operator and potential theoryBlack-Scholes equationwater wavesscalar conservation lawsfirst order equationsMIT 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.htm18.03SC Differential Equations (MIT)The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.
http://ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011
Mattuck, ArthurMiller, HaynesOrloff, JeremyLewis, John2012-02-08T14:08:08+05:0018.03SCen-USOrdinary Differential EquationsODEmodeling physical systemsfirst-order ODE'sLinear ODE'ssecond order ODE'ssecond order ODE's with constant coefficientsUndetermined coefficientsvariation of parametersSinusoidal signalsexponential signalsoscillationsdampingresonanceComplex numbers and exponentialsFourier seriesperiodic solutionsDelta functionsconvolutionLaplace transform methodsMatrix systemsfirst order linear systemseigenvalues and eigenvectorsNon-linear autonomous systemscritical point analysisphase plane diagramsMIT 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.htm18.06SC Linear Algebra (MIT)This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering.
http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011
Strang, Gilbert2012-01-24T16:18:50+05:0018.06SCen-USmatrix theorylinear algebrasystems of equationsvector spacesdeterminantseigenvaluessimilaritypositive definite matricesleast-squares approximationsstability of differential equationsnetworksFourier transformsMarkov processesMIT 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.htm18.024 Multivariable Calculus with Theory (MIT)This course is a continuation of 18.014. It covers the same material as 18.02 (Multivariable Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.
http://ocw.mit.edu/courses/mathematics/18-024-multivariable-calculus-with-theory-spring-2011
Breiner, Christine2011-12-08T10:51:15+05:0018.024en-USlinear algebravector integral calculusCalculus of several variablesVector algebra in 3-spacedeterminantsmatricesVector-valued functions of one variablespace motionScalar functions of several variablespartial differentiationgradientoptimization techniquesDouble integrals and line integrals in the planeexact differentials and conservative fieldsGreen's theorem and applicationstriple integralsline and surface integrals in spaceDivergence theoremStokes' theoremapplicationsMIT 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-2011
Sheffield, Scott2011-12-07T11:34:46+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.htm18.702 Algebra II (MIT)This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.
http://ocw.mit.edu/courses/mathematics/18-702-algebra-ii-spring-2011
Artin, Michael2011-10-28T12:57:09+05:0018.702en-USSylow theoremsGroup Representationsdefinitionsunitary representationscharactersSchur's LemmaRings: Basic DefinitionshomomorphismsfractionsFactorizationunique factorizationGauss' Lemmaexplicit factorizationmaximal idealsQuadratic Imaginary IntegersGauss Primesquadratic integersideal factorizationideal classesLinear Algebra over a Ringfree modulesinteger matricesgenerators and relationsstructure of abelian groupsRings: Abstract Constructionsrelations in a ringadjoining elementsFields: Field Extensionsalgebraic elementsdegree of field extensionruler and compasssymbolic adjunctionfinite fieldsFields: Galois Theorythe main theoremcubic equationssymmetric functionsprimitive elementsquartic equationsquintic equationsMIT 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