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It's surprising how little the list has changed since then, really, at the more advanced end: at my place we still teach real analysis from Rudin, complex from
by markgall 5y ago
It's surprising how little the list has changed since then, really, at the more advanced end: at my place we still teach real analysis from Rudin, complex from Ahlfors, commutative algebra from Atiyah-Macdonold, riemannian geometry from do Carmo, alg geo from Shafarevich and Hartshorne,.. There are good competitors to some of these now but inertia is strong. (And if anyone has figured out how to teach a good intro to schemes out of Vakil's behemoth of a book, let me know...)
- ipnon 5y agoThere seems to be only so much one can cram into an undergraduate's cranium in 4 years. Consequently the average time spent getting Ph.D. is increasing.
- fspeech 5y agoVarkil himself taught a "Algebraic Geometry in the Time of COVID" last year: https://m.youtube.com/channel/UCy3u23mZE4TyW88yr6JLx9A/videos https://m.youtube.com/channel/UCy3u23mZE4TyW88yr6JLx9A/video...
- markgall 5y agoYes, it was very cool (I had a student sit in), but it wasn't anything like an introduction to schemes course. They made it to the nullstellensatz in the last lecture. I love Vakil's book but my attempt to teach out of it was not so successful, there is just too much there.