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Anonymous Sat 09 Jan 10:00:05 2021 No.12561334 View Reply Original Report

Quoted By: >>12561346 >>12561442 >>12561509 >>12561515 >>12561531 >>12561586 >>12561790

Any thoughts on differential geometry?
I mean the real shit, dealing with manifolds

Anonymous

Anonymous Sat 09 Jan 2021 10:03:47 No.12561346 Report

Quoted By:

>>12561334
no

Anonymous

Anonymous Sat 09 Jan 2021 10:51:55 No.12561442 Report

Quoted By:

>>12561334
Start with 2D surfaces embedded in 3D space and dont bother with higher dimensions if you dont get it.

Anonymous

Anonymous Sat 09 Jan 2021 11:22:00 No.12561509 Report

Quoted By:

>>12561334
fractal geometry is king.

Anonymous

Anonymous Sat 09 Jan 2021 11:24:51 No.12561515 Report

Quoted By: >>12561527 >>12561529

>>12561334
the mathematical discipline of manipulating indices

Anonymous

Anonymous Sat 09 Jan 2021 11:29:08 No.12561527 Report

Quoted By:

>>12561515
you know nothing

Anonymous

Anonymous Sat 09 Jan 2021 11:29:22 No.12561529 Report

Quoted By:

>>12561515
fuck indices, all of my homies use differential forms

Anonymous

Anonymous Sat 09 Jan 2021 11:29:45 No.12561531 Report

Quoted By:

>>12561334
it's nice to know

Anonymous

Anonymous Sat 09 Jan 2021 11:55:14 No.12561575 Report

Quoted By: >>12561790

Thing is, I'm pretty sure, I wanna do the course(for mathematicians) next semester. Just wanted to hear some opinions.
But I'm a retard and can't express myself.

Anonymous

Anonymous Sat 09 Jan 2021 12:05:52 No.12561586 Report

Quoted By: >>12561601 >>12561781

>>12561334
What is manifold?

Anonymous

Anonymous Sat 09 Jan 2021 12:10:00 No.12561601 Report

Quoted By: >>12561610

>>12561586
Its too advanced for most of us. It was too advanced for most great mathematicians until Riemann gave an intuitive introduction to the topic. Stick to 2D surfaces and curves in 3D space like everyone did until late 19th century. A lot of general concepts will still apply, its a good stepping stone.

Anonymous

Anonymous Sat 09 Jan 2021 12:15:01 No.12561610 Report

Quoted By: >>12561619 >>12561822

>>12561601
That didn't answer my question.

Anonymous

Anonymous Sat 09 Jan 2021 12:20:34 No.12561619 Report

Quoted By: >>12561781

>>12561610
Its a surface or a curve, if you are in 3D. Like a sphere, a loop, a torus, cylinder, a plane, a deformed plane, etc.

Anonymous

Anonymous Sat 09 Jan 2021 13:58:23 No.12561781 Report

Quoted By: >>12561806

>>12561586
something that looks like R^n when you zoom in and flatten it.

>>12561619
these are examples of 2D manifolds. this anon choose to embed them in 3D space but this isn't really necessary to do.

Anonymous

Anonymous Sat 09 Jan 2021 14:04:27 No.12561790 Report

Quoted By:

>>12561334
>>12561575
it's fun. might even come in handy to know. can recommend.

Anonymous

Anonymous Sat 09 Jan 2021 14:15:18 No.12561806 Report

Quoted By:

>>12561781
Dont care, start with them. Do not bother with higher dimensional intrinsic manifolds as a newbie.

Anonymous

Anonymous Sat 09 Jan 2021 14:24:58 No.12561822 Report

Quoted By:

>>12561610
To keep it short : manifolds are general surfaces. They are a kind of subspace in higher dimensional spaces.
Most common example : the already mentioned sphere. It's only the surface of a ball, so kind of 2D, but lies in the 3dim space.

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