/mg/ - Mathematics General

[Anonymous No.12166538]

Someone please kill Nikolaj edition

Previous Thread: >>12157556

[Anonymous No.12166985]

>>12166538
kys OP. We treat our /mg/ friends right.
all fields

[Anonymous No.12166986]

>>12166985
You can pay respects to his grave that's fine by me.

[Anonymous No.12167017]

Is anyone here studying numerical analysis?

[Anonymous No.12167028]

>>12167017
> is there anyone studying a based field?
No, go study physics.

[Anonymous No.12167049]

>>12167028
W-why?

[Anonymous No.12167053]

Here are some differential geometry exercises that are actually worth attempting.
Also what math do I need to understand elliptic curves?

[Anonymous No.12167080]

>>12167053
>differential geometry
2. Compute [math]0 = \frac{d}{dt} \langle \alpha (t_0) , \alpha (t_0) \rangle = 2 \langle \alpha '(t_0), \alpha(t_0) \rangle[/math].
3. Velocity vector is constant, so that's a straight line.
4. [math]\frac{d}{dt} \langle \alpha(t), v \rangle = \langle \alpha '(t), v \rangle = 0[/math]. Since the function is constant and zero at one point, it's zero everywhere.
5. [math]\frac{d}{dt} \langle \alpha(t), \alpha (t) \rangle = 2 \langle \alpha (t), \alpha ' (t) \rangle[/math]. One side zeroes if and only if the other side does.

[Anonymous No.12167158]

what do you think about this /mg/?

[Anonymous No.12167194]

I want a nice example of non-surjective epimorphism in a 'full' concrete category of well known structures, like R-modules or whatever. Preferably one closely related to algebra. (I know there's an example for topological coverings or something, I don't care.)

With 'full' I mean really including all the structures, because taking cheap small subcategories is lame.

For instance, for a non-injective monomorphism we can take the inclusion of [math]\mathbb{Z}[/math] into [math]\mathbb{Q}[\math] in the category of rings. Something simple and mundane like that.

[Anonymous No.12167202]

>>12167158
Can myostatin and actin fiber bundles be formalized in Topological K-Theory?

[Anonymous No.12167413]

>>12167053
>differential geometry exercises that are actually worth attempting.
you should look into Spivak or Lee

[Anonymous No.12167905]

>>12166594
Can anybody solve this, I think someone tried but all the variables x y a b c q and r are integers so their solution didn't work

[Anonymous No.12167981]

Jason needs to buy new carpet tiles for his kitchen. A plan of the kitchen is shown as 5m, 5m, 7m and 3m. The tiles Jason has chosen are 0.5m2, how many tiles will he need to cover the entire kitchen floor?
Jason must store crates measuring 6m wide, 8m long and 4m high. What is the max number of crates Jack can fit into the storeroom?

[Anonymous No.12168016]

>>12167981
Is the first question for all possible quadrilaterals with those edge lengths or just the convex ones?

[Anonymous No.12168224]

>Topos Theory

[Anonymous No.12168281]

>>12167194
Anon, the inclusion [math] \mathbb{Z} \to \mathbb{Q}[/math] in the category of rings is a non-surjective epimorphism. This is because for any ring R, there can be at most one ring homomorphism [math]\mathbb{Q} \to R [/math]

[Anonymous No.12168332]

>>12167053
>Also what math do I need to understand elliptic curves?
Complex analysis, algebraic geometry and group theory if you mean elliptic curves over C, throw in algebraic number theory if you mean over number fields.

[Anonymous No.12168352]

What is the most poggers field?

[Anonymous No.12168373]

>>12168224
Based Based

[Anonymous No.12168657]

>>12168352
The integers mod 2

[Anonymous No.12168769]

F

[Anonymous No.12169006]

>>12167202
Good wordplay.

[Anonymous No.12169010]

>>12168352
The field with one element

[Anonymous No.12169260]

>>12168281
Sorry I swapped the two things.
I knew this non-surjective epimorphism, what I want is a non-injective monomorphism instead.

I now there's one example with coverings involving the category of topology or something related, and also one with the category of divisible abelian groups. I'd like to see a more familiar and simple one, but maybe there isn't.

[Anonymous No.12169269]

>>12169006
No it isn’t you fucking brainlet

[Anonymous No.12170140]

>>12169260
iirc if you have a concrete category where the forgetful functor is representable, then every mono is injective. So, there are no examples in "nice" categories

[Anonymous No.12172410]

>>12170140
I see.

This seems to be an assimetry. Is that related to the assimetry between direct images of functions and inverse images, pull-backs and push-forward(if I remember the correct terminology) etc? I remember a short explanation of this in a differentiable manifolds book, attributing it to the assimetry of domain and codomain of functions - each element is mapped to a unique one inside the codomain, but an element in the image can be the image of more than one.

[Anonymous No.12174219]

why did it take so many years for humanity to say that there is nothing

[Anonymous No.12174240]

>>12174219
because god. there can't be nothing if your basic axiom is that god is everywhere.

[Anonymous No.12174258]

>>12167413
make sure to check the erratum on Lee's book, some (critical) exercises were simply wrong

[Anonymous No.12174264]

>>12174258
you got example?

[Anonymous No.12174273]

>>12174264
yeah, give me a sec

[Anonymous No.12174290]

>>12174264
>>12174273
Ok I had Lee's "Riemannian Manifolds. An Introduction to Curvature" in mind, and apparently missed that there's a corrected 2nd edition now. The error I was thinking about was • Page 63, problem 4-3. See https://sites.math.washington.edu/~lee/Books/Riemannian/errata.pdf for the correction. Nevertheless it's a great book, just pointing out that this is kind of a "bad" error.

[Anonymous No.12174303]

>>12174290
>missed that there's a corrected 2nd edition now
you should definitely check it, tons of new material