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So I'm trying to finalize my schedule for this semester. I can't decide whether I should enroll in a grad level Differential Topology (Milnor) class or just the undergrad general topology one. The reason I'm having doubts about Diff Top is because I haven't really developed my analysis and topology intuition yet since I've only started doing a course on Rudin this semester. I don't know much about important theorems like inverse and implicit functions either. So it seems like a bad idea to enroll in Diff Top. Would you guys agree?

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If you've just started studying Analysis and haven't taken General Topology yet, do it first. Differential Topology would be too early for you. General Topology will help you a lot with developing your Analysis abilities. – Ayman Hourieh Sep 11 '12 at 10:19
Nils's answer is the correct one. IMO, you really need to understand the implicit/inverse function theorem, but the professor is the best person to give you advice on what you should do. – Sam Lisi Sep 11 '12 at 21:32

The best thing to do is to ask that question to your differential topology professor. He knows maybe already which audience he's having in mind, and in particular the background he expects of every participant to have. Be honest to him about what you know and what you don't. This should give you a good idea of whether you should take this course or not.

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