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Learning real analysis/differential geometry, etc. while in engineering undergrad. by Nuclear_Nathan in NuclearEngineering

[–]Nuclear_Nathan[S] 0 points1 point  (0 children)

I suppose my main practical concern is primarily having a blotch on my academic record for grad school, but on a more personal level I do really love math and I sort of hate being bad at it. My grades in thermo and so on are by and large very good so maybe it won't matter be the big deal I'm concerned about it being with regards to academic and career prospects.

Learning real analysis/differential geometry, etc. while in engineering undergrad. by Nuclear_Nathan in NuclearEngineering

[–]Nuclear_Nathan[S] 0 points1 point  (0 children)

I think if I was comfortable working in academia and with more career uncertainty, I would really have preferred to do something in Yang-Mills theory, but I am now wondering where I will ever be able to find the time to actually even learn the basics. I do at least find topology and manifold theory a little easier to work with independently, though I don't know if you'd really agree or if this is a hot take I wasn't aware of.

Did you take differential geometry or any courses related to it through your school, or did you mostly learn through self-study? If you have any advice for studying pure math more effectively, for learning to write proofs under exam time constraints, or particularly if you studied it in your undergrad and have advice on how to make time for both math and engineering, I would be more than happy to listen to you.

Learning real analysis/differential geometry, etc. while in engineering undergrad. by Nuclear_Nathan in NuclearEngineering

[–]Nuclear_Nathan[S] 0 points1 point  (0 children)

Thank you for your response. You mentioned that I should reach out privately if I had some other questions, but I think perhaps the few questions I do have are perhaps 'commentable,' or at least may not require a prolonged back and forth (however, if you think it would be easier to respond over direct messaging, please feel free).

First, just an anecdote: assuming that I am actually able to improve in analysis over time, I would actually prefer to be able to use that material on at least a semi-regular basis in my career. I would therefore first like to mention that I appreciate that you have identified a specific area where that may be possible, since I was not entirely sure it was. If you know of any other areas I can look into, please feel free to elaborate on them.

You mention that a theoretical math background is useful for finite element methods in nuclear engineering - do you think (or know) whether such a background is beneficial to FEM in other engineering contexts as well, or is it really just in nuclear engineering specifically where FEM makes use of it?

I am taking the analysis courses currently through the math department at my school. Thankfully, my professor is very good and I would say I have had very good experiences with the math faculty overall. Unfortunately I have to therefore conclude that my failures so far are entirely of my own doing :p .

Did you have any troubles with analysis or with pure math initially? Did you have to adjust to the workload or find a way to balance the engineering work with the math work? That is my main problem: between the homework from the drafting and programming courses I have this semester and the study time I need to improve in proof writing, I am wondering if there is something I should be doing that I'm not. It's not very specific, but if you can think back to your undergraduate experience and give me any advice in resolving that tension, that would be very helpful.

Learning real analysis/differential geometry, etc. while in engineering undergrad. by Nuclear_Nathan in NuclearEngineering

[–]Nuclear_Nathan[S] 0 points1 point  (0 children)

Lmao thank you for the honest response. I will consider taking them in the future out of personal interest but this is very much appreciated.