New courses in Mathematicshttp://ocw.mit.edu/OcwWeb/Mathematics/index.htm2009-07-02MIT 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.htmThe main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.http://ocw.mit.edu/OcwWeb/Mathematics/18-727Spring-2008/CourseHome/index.htmKumar, Abhinav2009-04-20T03:24:01-04:0018.727en-USMathematicsAlgebra and Number TheorybiellipticKodaira dimensionellipticK3classificationalbanesepicardrationalitycastelnuovo's criterionlinear systemsrational surfacesruled surfacessurfacesmapsrationalbirationalnumerical equivalencealgebraic equivalencenear equivalenceMIT 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 a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications. Note: This course was previously called "Mathematical Methods for Engineers I". http://ocw.mit.edu/OcwWeb/Mathematics/18-085Fall-2008/CourseHome/index.htmStrang, Gilbert2009-03-31T10:33:33-04:0018.085en-USMathematicsEngineering mathematicsMathematics, Generalconvolutiondiscrete Fourier transformFourier seriesboundary-value problemspotential flowLaplace's equationdifferential equations of equilibriumLagrange multipliersnetworkslinear 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/OcwWeb/web/terms/terms/index.htmThis is a new course, whose goal is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.http://ocw.mit.edu/OcwWeb/Mathematics/18-712Fall-2008/CourseHome/index.htmEtingof, Pavel2009-03-03T04:16:43-05:0018.712en-USMathematicsSystems Science and TheoryBurnside’s TheoremFrobenius divisibilityFrobenius-Schur indicatorMaschke’s TheoremKrull-Schmidt theoremJordan-H¨older theoremdensity theoremTensor productsLie algebrasrepresentation theoryfinite groupsseries RepresentationsQuiver Representationsfinite dimensional algebrasMIT 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.htmThe basic properties of functions of one complex variable. Cauchy's theorem, holomorphic and meromorphic functions, residues, contour integrals, conformal mapping. Infinite series and products, the gamma function, the Mittag-Leffler theorem. Harmonic functions, Dirichlet's problem. Description from course home page: This is an advanced undergraduate course dealing with calculus in one complex variable with geometric emphasis. Since the course Analysis I (18.100B) is a prerequisite, topological notions like compactness, connectedness, and related properties of continuous functions are taken for granted. This course offers biweekly problem sets with solutions, two term tests and a final exam, all with solutions. http://ocw.mit.edu/OcwWeb/Mathematics/18-112Fall-2008/CourseHome/index.htmHelgason, Sigurdur2009-02-06T03:02:10-05:0018.112en-USMathematicsMathematics, GeneralAnalysis and Functional AnalysisThe Riemann Zeta functionThe Riemann mapping theoremDirichlet's problemHarmonic functionsthe Mittag-Leffler theoremthe gamma functionInfinite series and productsconformal mappingcontour integralsresiduesmeromorphic functionsholomorphic functionsCauchy's theoremfunctions of one complex variableMIT 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 is an introduction to differential geometry. The course itself is mathematically rigorous, but still emphasizes concrete aspects of geometry, centered on the notion of curvature.http://ocw.mit.edu/OcwWeb/Mathematics/18-950Fall-2008/CourseHome/index.htmSeidel, Paul2009-02-04T01:38:09-05:0018.950en-USMathematicsGeometry/Geometric Analysisgeometry of lengths and distanceshypersurfacesgeometry of plane curvesdifferential geometryMIT 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.htmIn this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory.http://ocw.mit.edu/OcwWeb/Mathematics/18-705Fall-2008/CourseHome/index.htmKleiman, Steven2009-02-25T03:38:22-05:0018.705en-USMathematicsAnalysis and Functional Analysisnullsetellensatznoetherzerodivisorsnakayama's lemmaartin ringnormalizationDVRhilbert theoremZorn's lemmadimension theorytensordedekind domaindecompositionlocalizationintegralchain conditionsmodulesidealsringsMIT 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.htmIn this undergraduate level seminar series topics vary from year to year. Students present and discuss the subject matter, and are provided with instruction and practice in written and oral communication. Some experience with proofs required. The topic for fall 2008: Computational algebra and algebraic geometry. http://ocw.mit.edu/OcwWeb/Mathematics/18-704Fall-2008/CourseHome/index.htmKleiman, Steven2009-02-17T04:38:10-05:0018.704en-USMathematicsAlgebra and Number TheoryGeometry/Geometric AnalysisProjective Algebraic GeometryInvariant Theory of Finite GroupsGeometric Theorem ProvingRational FunctionsPolynomial FunctionsAlgebra-Geometry DictionaryElimination TheoryGroebner BasesAlgorithmsAlgebraGeometryalgebraic geometryComputational 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/OcwWeb/web/terms/terms/index.htm