/sci/ - Science & Math

>>16138801

>>15977499

I've already taken a differential geometry course, I know about tensors, connections, curvature, metrics, differential forms, integration (not an expert here but still), etc. I was diving through wikipedia today and found shit like this
>Cartan connection
>Solder form
>Connection forms
>Spin forms
>Klein geometries
>Absolute parallelism
>Principal bundles
Then I got to Ehresmann connections and gave up. While I feel like I have the basic knowledge to understand what all this shit is if I read the article over and over, I feel like I would be better off reading a book that introduces this stuff properly. Any recommendations for this?
Pic unrelated

What books are key to getting started learning physics with a rigorous approach?

This one’s a classic

>write long as fuck technical paper over course of 2 years
>finally done
>time for final, forth, recheck
>nothing works suddenly
>kill_me(2).tiff
after a few hours of suffering I found that shit is still in order, just fucked up some exponent in maple when checking some symbolic calcs h-haha...

>>12077488

>>11864635
Ah ok thanks again then!
>>11864654
see pic. Also no.

>>11066202
functional analysis and differential geometry are very very important
functional analysis is the math behind quantum mechanics. differential geometry is the math behind relativity.
algebraic topology is not that important but it's useful for differential topology/geometry and anything with manifolds. i wouldn't prioritize it but it's fun.
galois theory sounds worthless to what you're doing, but you should do things which interest you.
i would recommend looking into proper PDE theory and dynamical systems theory after doing some measure theoretic real analysis and some functional analysis. ideas like distribution theory, ergodicity, and unbounded (differential) operators on hilbert spaces are really central to much of mathematical physics. DEs at this level are not "lol solve le equation," it's much more like normal analysis.

Sci bird meme thread? I know that there are more other than this, in particular I remember one about vector calculus vs differential geometry

A classic.