/sci/ - Science & Math

what's the answer to [math]\displaystyle \int_{ \{ |z-i|=1 \}} \frac{1}{(z^{2}+1)^{3}}dz[/math] .

Trying to show that [math]\mathbb{C}[/math] contains all its limit points. Suppose [math]z_{n}[/math] is a convergent seqeunce of complex numbers. Then [math]\lim z_{n} = L[/math] If [math]L[/math] was not in [math]\mathbb{C}[/math], then [math]L\in \mathbb{C}^{c}=\emptyset[/math] which is a contradiction. So [math]L\in\mathbb{C}[/math]. Is this reasoning sound?

>>11070072
>>11070091
>>11070097
>>11070102
>>11070943
No comment needed.

>>10959925
>>10959949
>>10959957
>>10959969
>>10959975
>>10960002
>>10959982
>>10960014
>Literally discussing muh universe is a simulation meme.
>quantum physics and energy stones and shiet.
>actually believing in any of these.

>>10811840
buuurrr..
ffffuubbubub...

>>10759823
>cope
>cringe
>have sex
There is no quicker way of outing yourself as a redditor than using these words. Loser.

>>10758104
>humans aren't dependent on nature

>>10569308
>hey! HEY! LOOK THIS GUY'S SUPPOSED TO BE REALLY SMART OR SOMETHING AND HE DISAGREES WITH THE SCIENCE SO THE SCIENCE IS BULLSHIT!!!

In engineering, is there any advantage/point to trying to learn calculus/lin alg/stats/etc. at a more fundamental level than what is usually done in practice, i.e. maths as in maths degree, not as in engineering degree? I'm going into my final year of engi undergrad and I swear the math curriculum in high school in eastern europe was more rigorous than what I've done so far in a fairly good western uni. Other than "for interest", would it be a total waste of time spending the summer on some /sci/ meme lists?

how do I parameterize the surface given by [math]z=1-x^{2}-y^{2}[/math] and [math]x^{2}+y^{2}\leq 1[/math]. I thought it would be [math]r(u,v) = \left<u,v,1-u^{2}-v^{2}\right>[/math] but on plotting this parameterization I cannot figure out what the bounds should be.