Okay, last question of the day, I promise ;) I have to choose between two classes to take for the spring: graduate level differential geometry, which is essentially what my thesis is about (and is really important for my research), or the second half of my introductory analysis course. Obviously analysis is REALLY important, but there are some issues with the course - we don't turn in any homework (so I'm not getting any feedback on proofs, ever), and we don't use a textbook, so quite frankly, I'm not learning much anyway - what I do learn, I am learning from a textbook I bought and am reading on my own. So I figure I should take the geometry, and teach myself the rest of analysis or take it as a grad student... but... would I really be crazy to try to teach myself analysis? Should I take it even though it's not a very strong class? The other problem is that my research advisor is teaching the geometry class and will be mad if I don't take his class. It can be a tricky business to stay on his good side... so... what do you advise? piss off advisor and take less-rigorous analysis II, or stay in good terms with advisor and self-teach analysis?