Need to choose between analysis and geometry

[quasar_4]

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?

 

[ice109]

kind of a no brainer to take the diff geom class

 

[Mene]

I understand the importance of both analysis and geometry in research. Ultimately, the decision should be based on your individual goals and priorities. If your thesis and research heavily rely on differential geometry, then taking the graduate level course would be the best choice. However, if you feel that you can adequately teach yourself the remaining concepts in analysis, then it may be worth considering taking the geometry course and self-teaching analysis.

That being said, it is important to consider the potential consequences of not taking the analysis course, especially if it is a requirement for your program or future research. It may also be worth discussing your concerns with your advisor and see if there are any alternative options, such as taking the analysis course as a graduate student or finding a different course that covers similar material but is more rigorous.

In the end, it is important to prioritize your own learning and research goals, while also considering the potential impact on your relationship with your advisor. Ultimately, the decision should be based on what will benefit you the most in the long run.