Need to choose between analysis and geometry

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The discussion revolves around the decision between enrolling in a graduate-level differential geometry class, crucial for the individual's thesis and research, or the second half of an introductory analysis course, which lacks structure and feedback. The analysis course does not require homework submissions, and the student is primarily learning from a self-purchased textbook. There is a concern about the potential negative impact on their relationship with their research advisor, who is teaching the geometry class and may be disappointed if the student chooses the analysis course. The consensus leans towards taking the differential geometry class due to its relevance to the thesis and the importance of maintaining a good rapport with the advisor, while also considering the feasibility of self-teaching analysis.
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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?
 
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kind of a no brainer to take the diff geom class
 
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