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18 937: Topics in Geometric Topology
3.00 Credits
Massachusetts Institute of Technology
Content varies from year to year. Introduces new and significant developments in geometric topology.
Prerequisite:
Prereq: Permission of instructor
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18 937 - Topics in Geometric Topology
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18 950: Differential Geometry
3.00 Credits
Massachusetts Institute of Technology
Introduction to differential geometry, centered on notions of curvature. Starts with curves in the plane, and proceeds to higher dimensional submanifolds. Computations in coordinate charts: first and second fundamental form, Christoffel symbols. Discusses the distinction between extrinsic and intrinsic aspects, in particular Gauss' theorema egregium. The Gauss-Bonnet theorem. Geodesics. Examples such as hyperbolic space.
Prerequisite:
Prereq: 18.100; 18.06, 18.700, or 18.701
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18 950 - Differential Geometry
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18 952: Theory of Differential Forms
3.00 Credits
Massachusetts Institute of Technology
Multilinear algebra: tensors and exterior forms. Differential forms on Rn: exterior differentiation, the pull-back operation and the Poincare lemma. Applications to physics: Maxwell's equations from the differential form perspective. Integration of forms on open sets of Rn. The change of variables formula revisited. The degree of a differentiable mapping. Differential forms on manifolds and De Rham theory. Integration of forms on manifolds and Stokes' theorem. The push-forward operation for forms. Thom forms and intersection theory. Applications to differential topology.
Prerequisite:
Prereq: 18.101; 18.700 or 18.701
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18 952 - Theory of Differential Forms
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18 965: Geometry of Manifolds
3.00 Credits
Massachusetts Institute of Technology
No course description available.
Prerequisite:
Prereq: 18.101, 18.102, or 18.103
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18 965 - Geometry of Manifolds
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18 966: Geometry of Manifolds
3.00 Credits
Massachusetts Institute of Technology
Differential forms, introduction to Lie groups, the DeRham theorem, Riemannian manifolds, curvature, the Hodge theory. 18.966 is a continuation of 18.965 and focuses more deeply on various aspects of the geometry of manifolds. Contents vary from year to year, and can range from Riemannian geometry (curvature, holonomy) to symplectic geometry, complex geometry and Hodge-Kahler theory, or smooth manifold topology. Prior exposure to calculus on manifolds, as in 18.952, is recommended.
Prerequisite:
Prereq: 18.965
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18 966 - Geometry of Manifolds
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18 969: Topics in Geometry
3.00 Credits
Massachusetts Institute of Technology
Content varies from year to year.
Prerequisite:
Prereq: 18.965
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18 969 - Topics in Geometry
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18 979: Graduate Geometry Seminar
3.00 Credits
Massachusetts Institute of Technology
Content varies from year to year. Study of classical papers in geometry and in applications of analysis to geometry and topology.
Prerequisite:
Prereq: Permission of instructor
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18 979 - Graduate Geometry Seminar
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18 994: Seminar in Geometry
3.00 Credits
Massachusetts Institute of Technology
Students present and discuss subject matter taken from current journals or books. Topics vary from year to year. Instruction and practice in written and oral communication provided. Enrollment limited.
Prerequisite:
Prereq: 18.101, 18.102, 18.103, or 18.112
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18 994 - Seminar in Geometry
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18 999: Research in Mathematics
0.00 - 6.00 Credits
Massachusetts Institute of Technology
Opportunity for study of graduate-level topics in mathematics under the supervision of a member of the department. For graduate students desiring advanced work not provided in regular subjects.
Prerequisite:
Prereq: Permission of instructor
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18 999 - Research in Mathematics
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18 CME: Study at Cambridge University
0.00 - 6.00 Credits
Massachusetts Institute of Technology
Provides credit for students studying at Cambridge University under the Cambridge-MIT Exchange program. Credit may be used to satisfy specific SB degree requirements. Consult with department and CME office.
Prerequisite:
Prereq: Permission of instructor
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18 CME - Study at Cambridge University
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