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Is it generally true that for US Math PhD programs, Riemannian geometry is a 2nd year grad course? I was looking at JHU, one of the PhD programs I will be applying to, and they don't require you take any prereq grad courses. And the cirriculum seems to be the standard RG cirriculum: metrics, Jacobi fields, curvature, sectional curvature, Hopf-Rinow, etc.

Some schools require that your first year of grad school is essentially Algebra I, II, Analysis I, II and Topology (with a mix of Geometry via differential forms, deRham cohomology, differentiable manifold, vector fields, tensors, lie derivatives, and so on) I and II.

What are your experiences with this? I don't see why it would be a first year course as not all students are going to be pursuing RG in graduate school anyway while all grad students should know basic grad level analysis, algebra and topology/geometry.

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# Riemannian Geometry

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