/sci/ - Science & Math

>>10317537
real analysis looks ugly but is beautiful underneath, because of how beautiful a lot of the ways we prove things end up being (and because so many of the results are just results in metric spaces / top spaces)
on the other hand, i found that complex analysis was a class with beautiful results but butt-ugly unimpressive computational proofs. i mean, as someone who took pdes before complex, yeah, we fucking get it. harmonic functions are very very nice. but it's really not that surprising that they are. and analytic functions are just special harmonic functions, so there's no reason for them to not be nice.
everything feels very trivial once you have cauchy riemann equations - cauchy's theorem, integral formula, residue theorem, laurent series decomposition, etc. and anything that isn't trivial is a fucking nightmare to prove - riemann mapping, picard's little and great theorems.
i could get my hands around everything in real analysis, but it was always fun. in complex, everything looked cool going in, but most of it turned out boring and the rest was too complicated to really get my head around. maybe i'll like it more as i get better at math and learn more nontrivial complex analysis, but for now it didn't feel like i grew at all from the class.

>we laboriously compute
>we write out the tedium for the reader
>we include all relevant computations
>we opt not to skip steps in this result
>we take the time to build some motivating examples

>>10228031
>>10228035
Woah, now these posts are hilarious. What, do you want me to apply for jobs which won't ask me to think and engage in modern research? Sure, I'll go make fucking websites for flower nurseries like you lot. That sounds fulfilling.