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DIFFERENTIABLE MANIFOLDS

MATH 761
과목 설명

Differentiable manifolds, vector bundles, implicit function theorem, submersions and immersions, vector fields and flows, foliations and Frobenius theorem, differential forms and exterior calculus, integration and Stokes' theorem, De Rham theory, Riemannian metrics. Familiarity with basic undergraduate analysis coursesMATH 521and522orMATH 621) is strongly recommended.

선수과목

Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

충족 요건

This course does not satisfy any prerequisites.

학점

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미보고

평점
3.71

-0.77% 과거 데이터 대비

수료율
100%

1.61% 과거 데이터 대비

A 비율
57.14%

-28.78% 과거 데이터 대비

학급 규모
14

-0.4% 과거 데이터 대비

Cumulative Grade Distribution

강사 (2026 Summr)

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유사 과목

INTRODUCTORY TOPOLOGY I

MATH 751

An introduction to algebraic and differential topology. Elements of homotopy theory, fundamental group, covering spaces. Differentiable manifolds, tangent vectors, regular values, transversality, examples of compact Lie groups. Homological algebra, chain complexes, cell complexes, singular and cellular homology, calculations for surfaces, spheres, projective spaces, etc. Familiarity with undergraduate algebra and topologyMATH 541or551) is strongly recommended.

DIFFERENTIAL GEOMETRY

MATH 561

Theory of curves and surfaces by differential methods.

DIFFERENTIAL GEOMETRY

MATH 765

Covers the metric properties of Riemannian manifolds. The following topics will be covered: Vector bundles and connections, Riemannian metrics, submanifolds and second fundamental form, first variation of arc length, geodesics, Hopf-Rinow theorem, second variation of arc length, Jacobi fields and index lemmas, Bonnet-Meyer theorem, Rauch comparison theorem, spaces of constant curvature, Hodge-de Rham theory. Familiarity with the topics in a differential manifolds course (e.g.MATH 761) is strongly recommended.

TOPICS IN DIFFERENTIAL TOPOLOGY

MATH 856

The theory of differential manifolds such as differential forms and de Rham theorem, cobordism groups, Lie groups, homogeneous spaces, fiber bundles, characteristic classes.

INTRODUCTION TO MANIFOLDS

MATH 621

Integration in Euclidean spaces, change of variables, multilinear algebra, vector fields and differential forms, manifolds and tangent spaces, integration on manifolds, Stokes theorem. Classical vector analysis. Cauchy integral theorem.