In my department, we’re considering whether we have too many basic graduate courses, by which I mean courses with (mostly) fixed syllabi aimed at first and second year graduate students, as opposed to advanced topics courses which never cover the same thing twice. In geometry/topology, we have not less than 11 such one-semester courses, of which two arguably belong more to algebra:
- MATH 518 Differentiable Manifolds I
- MATH 519 Differentiable Manifolds II
- MATH 521 Riemannian Geometry
- MATH 522 Lie Groups and Lie Algebras I
- MATH 523 Lie Groups and Lie Algebras II
- MATH 524 Linear Analysis on Manifolds
- MATH 525 Topology (really, this is basic Algebraic Topology)
- MATH 526 Algebraic Topology (really, this is more advanced Algebraic Topology)
- MATH 527 Homotopy Theory
- MATH 533 Fiber Spaces and Char Classes
- MATH 535 General Topology
In contrast, my last university had just 4 or 5 such classes, and that was with the quarter system, so that’s only about 3 semester’s worth of such classes!
So I’d be curious to know how many such classes are there at your university (or any other university that you’re familiar with, e.g. where you went to grad school). Please post your data in the comments!