/sci/ - Science & Math

>>11784117
Mathematics? More like Mathemagics. Boohoo.

>>11784125
Sub 135 IQ "people" like you ought to be sterilized.

>>11784117
can sci help me with my homework:

what is 2+2

>>11784117
/mg/ suggested Tu's differential geometry book. Just got to characteristic classes and so far I'm happy with it.

Who else dreams with doing math sometimes?

I just woke up and I feel like Ive been dreaming all night about doing the same math formula again and again.

Its good because I was trying to remember that shit now its real ingrained in my mind.

>>11784186
>r*ddit spacing
Fuck off n**Rotypical!

>>11784130
Somewhat impolite.

>>11784186
I call those nightmares.

>>11784173
2+2, because addition is commutative

>>11784223
arnold bls

>>11784173
22 I think

>>11784186
>YES BIG FORUMLAS BIG MAFFS!! :D:D:D

How to become algebraic wizard?

>>11783043
Alright neat. Thanks.
>>11783250
>>11783252
I know literally no combinatorics so I'll search for something then.

>>11784284
read Lang

>>11784357
LIAM

What is /gnmg/ and /gmmg/?
Geanological math general?
Gaming math general?

>>11784130
>sub 135 iq
>he thinks anything below 3 sd is useful
just lol

the ramanujan of triple integrals

>>11784529
Gay nigger math general

>>11784765
what happened to GNAA? I remember: are you gay? are you nigger? are you gay nigger?

>>11784765
>gay nigger
why the homoraciphobism?

>>11781581
>>11780012
I didn't even think about the rope having slack. Jesus.
Maybe I should prepare my own rope

>>11784173
What have you tried?

>>11784800
make sure to leave some slack

>>11784117
>tfw scholarship runs out in 2 months and desperately need more results
I hate waking up in the morning

>>11784130
sure, that includes the likes of you

I'm doing Calc 2 and had a thought:
So for any polynomial f the roots obviously lie on the curve or curves Re(f)=Im(f). Is that curve always a closed loop? Can you integrate the area inside? If so, does it have any special connection to other properties of the polynomial? How does that change for Re(f)=|Im(f)|, |Re(f)|=Im(f) and |Re(f)|=|Im(f)|?
No doubt this has already been studied, but what topic is it a part of?

How would you prove that the mobius band is not homeomorphic to the regular, orientable band?

1/0 = +- infinity

>>11785529
Take a vector in its tangent space, transport it across a closed loop. In the regular band, the vector will have the same orientation. In the mobius, it could have opposite orientation (of course, depends on the loop, but it is enough to show one exists).

More rigorously, show that any section of the tangent bundle (ie a vector field) has a zero.

>>11785525
>So for any polynomial f the roots obviously lie on the curve or curves Re(f)=Im(f)
the polynomial [math]x-1[/math] has a zero at [math]1+0i[/math] so not sure how this is obvious.

>>11785529
mobius band has connected boundary, regular band has two component boundary. you have to prove that a homeomorphism takes boundary to boundary though.

>>11785551
this uses smooth structure so it works only for diffeomorphisms imo

>>11785556
I think all topological 1- and maybe 2-manifolds are smooth (although of course that's a harder theorem)

>>11785556
>>11785560
Also, regardless, we don't need smooth structure, we can just work with a vector bundle and achieve the same result (which in the 1d case it's just the tangent bundle again I believe)

>>11785551
I'm talking about Re(f(z)) and Im(f(z)), not Re(z) and Im(z).

>>11785551
>so not sure how this is obvious.
If f(x) = 0 + 0i, then Re(f(x)) = Im(f(x)) (=0).

Not him btw.

>>11785565
>we can just work with a vector bundle and achieve the same result
can you describe the argument in detail please?

>>11785576
Choose a point, take the tangent vectors at that point when you move on one side and then on the other side. Compare orientations.

>>11785584
Normal vectors*

>>11785576
M is the mobius bundle, which you can just take to be the mobius band if you just care about orientability

>>11785584
this proves they're not diffeomorphic

>>11785587
this proves they're not isomorphic vector bundles

>>11785525
>Re(f)=Im(f). Is that curve always a closed loop?
Of course not. Conside polynomial [math]P(z)=z.[/math]
[math]Re(P)=Im(P) \iff z=x+x*i[/math] (straight line)

>>11785593
It's still a jordan curve, so it almost counts as a closed loop.

>>11785591
The argument works similarly anyway - partition the mobius strip by cutting the line through the middle. Take a point thats not on the centre, and draw a loop around the band to show it is path connected still. The normal band will be disconnected.

>>11785598
yeah true. so >>11785587 works, >>11785584
does not I think

>>11785595
:sigh: Consider [math]P(z)=z^2[/math] then. Re(P)=Im(P) for two straight lines. [math]z=x+I*(-1-\sqrt2)x and z=x+I*(\sqrt2-1)x[/math]

What data do I need to be able to estimate, or even pinpoint, Ronaldo's semicircle's area, radius and circumference?

>>11785603
a goat, some rope and some stakes

G'day /mg/. It seems they were only striking for a day at the arXiv HQ.

>>11785612
Would you let your goat anywhere close to a man as creepy looking as Ronaldo?

>>11784800
>my own rope
Depends on your age. If less than 24, there is still hope, otherwise there is only rope.

>>11784282
Hahaha why are you studying maths? We already have calculators haha!

>>11785634
any other animes as comfy as NNB?

>>11785650
The comfiest I can think of are probably Kimagure Orange Road, Yuyushiki, Plastic Neesan and Ookami to Koushinryou.

Can anyone help me solve this word problem using polyas process?

Four children, Amy, Susie, Tessie, and Eddie are lined up according to height, each holding a balloon. The child in front (the shortest) is holding neither a red nor blue balloon. Susie is holding a red balloon. Tessie sees exactly two balloons in front of her. The child holding the blue balloon is right in front of the child with the yellow balloon. Amy is in front of Tessie. One child is holding a white balloon. Determine the arrangement of the four children (from shortest to tallest) and the color of the balloon they are holding

>>11785683
I can't help with Polya, but the order is Eddie the White, Amy the Blue, Tessie the Yellow, Susie the Red.

>>11785702
This with the assumption that Amy in front of Tessie means directly in front of Tessie. Otherwise there is now way to distinguish between Amy and Eddie.

>see professor staring at nothing
>can't tell if he's doing research or just relaxing

>>11785105
that's a pretty girl

>>11785702
thank you brother
is there a solution that helped you solve it? I need to show a plan and a solution as part of polkas process..

>>11785762
After a quick nap I realised I was wrong. I got this:
>The child in front (the shortest) is holding neither a red nor blue balloon
This eliminattes those two, and moreover
>in front of the child with the yellow balloon
this tells us that yellow can't come first either. The only possibility is white first!
>Tessie sees exactly two balloons in front of her
Tessie is third. Combining this with
>Susie is holding a red balloon
Susie is second and then the last two balloons are blue and yellow, or Susie is last and the balloons are WBYR.

Now, if Susie is the second one, we know the balloons WRBY. Moreover, we have 1ST4, and then
>Amy is in front of Tessie
gives 1=A and 4=E, and thus
ASTE
WRBY
If Susie is the last one, then we know
12TS
WBYR,
but there is no way to decide whether Amy or Eddie comes first. If this is supposed to have a solution, then the order is A&W, S&B, T&Y, E&Y.

I have no idea what this plan is supposed to be, but maybe trying to eliminate wrong options.

Should I continue math?
I failed my first year calculus course becuase I overslept and missed the online exam.

and I also linear algebra due to not studying enough, I studied a total of 40 hours for the entire course.

Should I give up on mathematics?

>>11785816
AAARGH! AW, SR, TB, EY I meant.

>>11785823
>Should I give up on mathematics?
If you have no real motivation, then yeah. Otherwise no.

>>11785823
regardless of your course, you should learn linear algebra properly. work on proofs, try to develop some intuition, understand the geometry behind etc.. if either you can't do this, or you can but you don't see any appeal, then math isn't for you.

>>11785598
So the way I understand you, you want to show that every image of the circle disconnects the normal band, but there is an image of the circle that keeps mobius band connected.
How do you show that any loop in the normal band disconnects it?
In the plane you have Jordan's theorem, which is already quite heavy machinery. How do you apply it to a band (if it's even possible)?

>>11785829
https://youtu.be/eBmVv2P-v2s

>>11785864
Why should I watch that?

>>11785844
you don't need to know that every loop disconnects the cylinder, only the loop which corresponds to the center circle of M. this loop must be a generator of the fundamental group, in particular the projection from the cylinder to S1 restricted to this loop is surjective. it's easy to show that such loop must disconnect the cylinder.

>>11785864
>PragerU
L
M
A
O

>>11785880
>it's easy to show that such loop must disconnect the cylinder
ok so how do you do it?

>>11785888
it's actually a good video though

>>11785870
>>11785888
Chop your balls off.

>>11785915
Not science or maths.

>>11785888
This

>>11785928
>>11785955
The enemy wakes up at 2:30am ready to chop your balls off. Are you gonna give them the satisfaction?
Get after it.

I... have been doing maths... for a single minute today... bros...

What happened to `hopf`?

>>11785529
If two topological spaces are homeomorphic, then a subspace of one is homeomorphic to the image of that subspace under the homeomorphism in the other. i.e. homeomorphisms restrict.
Consider the (open boundary) mobius strip with its center loop removed. It is easy to see that the result is still connected. Indeed, it is path connected by taking a path which goes first above the center loop and then below it, winding around the mobius strip twice, and then drawing lines from any point to a point on this path without crossing the center loop.
On the other hand, say there is a homeomorphism to a cylinder. Remove the image of the center loop from the cylinder. We are not removing a point, since the homeomorphism is a bijection. If you remove any nontrivial loop from a cylinder, you disconnect it: either you create a small circle on the surface of the loop which is disconnected from the larger loop, or you wrap all the way around and split the loop into two (or more) loops with any point just above the loop in a different connected component from any point just below it.
This is a contradiction, the subspaces obtained by removing the loop and its image are not homeomorphic.

>>11785959
The enemy is free to try. If the enemy is so fond of balls, maybe the enemy should give them a big squeeze and non-trivialise their homotopy.

>>11784117
Here's my quick proof that a linear map between normed vector spaces is bounded iff it's continuous (normed vector spaces are first countable so continuity <=> sequential continuity):
=>Let x_n->x. Then setting y_n=x_n-x, we see that y_n->0. By boundedness, there's a C>=0 so that |Ty_n|<= C |y_n| -> 0 => Ty_n->0 (norm is 0 iff vector itself is 0) => Tx_n->Tx by linearity.

<= If T is not bounded, then there's x_n with |x_n|=1 such that |Tx_n|>n^2. Set y_n=(1/n)x_n; then |y_n|->0 => y_n -> 0 but |Ty_n|>n so Ty_n does not go to 0.

Is this correct?

>>11785977
>either you create a small circle on the surface of the loop which is disconnected from the larger loop
What larger loop? What do you mean by "the surface of the loop"?
>or you wrap all the way around and split the loop into two (or more) loops
how do you split a loop into more loops? What are you even talking about?

>>11785890
>>11785977
I see you've already worked to the point of being pedantic about showing loops disconnect things. These are manifolds, they're not random topological spaces. You shouldn't worry about proving things like that, they are proven in some book for you.
Either way, you can prove this sort of thing by using, say, the intermediate value theorem. Consider a loop that goes above the center loop on a cylinder, map both to the mobius strip, cut the mobius strip into two and unwrap it. You get two functions. All that matters is their topology so if they're not "functions" and go over certain points more than once, whatever, just nudge those bits until they don't. The two functions are defined on an interval, one is above the other at the startpoint, and they switch positions at the endpoint. By the intermediate value theorem they must intersect. This is a contradiction.

>>11785998
I'm not going to draw the pictures for you, dude, but I didn't know you were whining about shit like Jordan curve theorem so it doesn't matter. That proof won't satisfy you.
This one should bypass that by using intermediate value >>11786002 but maybe you have issues with that too.
There I'm talking about how every closed loop on a cylinder either encloses some open set homeomorphic to a circle, or wraps around the cylinder splitting it into two thinner cylinders. But I'm not formally proving it like an autist.

>>11786002
not that anon but I could never quite figure out how to prove that the mobius band is a manifold
(Lee chapter 10 exercise 1)

>>11785964
Kill yourself.

>>11786002
I think that works.
>All that matters is their topology so if they're not "functions" and go over certain points more than once, whatever, just nudge those bits until they don't.
> just nudge those bits until they don't.
What do you mean by that? How do you nudge them while making sure the curves are kept separated?

>>11786022
I... have been doing... maths... on how to... kill myself... for the past... 3... minutes.... bros....

Is it really that hard to prove that the mobius band is not homeomorphic to the normal band?
So far nobody's been able to do it.
Of course, intuitively it's obvious they aren't. If all I wanted was an intuitive informal argument, I wouldn't have asked. It's funny how not being satisfied with a non-rigorous, informal argument gets you called an autist on /mg/. Really sheds light on what kind of people come here.

>>11786063
>It's funny how not being satisfied with a non-rigorous, informal argument gets you called an autist on /mg/.
It's because rigorous topology proofs are extremely nasty unironically

>>11786019
What? It's obviously a manifold, it's locally R^2. What do you mean "prove it's a manifold?"

>>11786046
We've localized the topological nastiness from >>11786075 into an extremely particular and uninteresting situation. Such is the goal of topology.
>>11786063
No, if you wanted a proof of Jordan Curve Theorem you would have asked for it. Here's the secret: no topologist gives a single shit about rigor and you fucking morons belong in algebra.

>>11786077
It's not obvious in any sense to me, at least not in the way Lee puts it (1/2)

>>11785959
>The enemy wakes up at 2:30am
My enemies are boomers, niggers, trannies and jannies.
None of the wake up before noon.

>>11786091
Here's the question I was talking about (2/2)

>>11786087
>No, if you wanted a proof of Jordan Curve Theorem you would have asked for it
Id didn't ask for proof of Jordan Curve Theorem. If you have a proof using it, please show me!
>Here's the secret: no topologist gives a single shit about rigor and you fucking morons belong in algebra.
Have you never read a topology textbook? It's all about rigor.
>We've localized the topological nastiness from >>11786075 into an extremely particular and uninteresting situation.
Yes, you reduced a problem which is obviously true to proving a lemma which is in no way obvious in general. I'm not even sure if it's even true.

>>11786097
Not that anon but I very strongly sympathize with you
I fucking hated the way topology was taught at my uni too, the prof kept waving his hands all the time and really
>>11786063
>If all I wanted was an intuitive informal argument
I wouldn't be taking his damn class, yet he and the graders had the highest standards of proofs on the exams and homework
the only math class I got a B in, I'm never ever going to touch this shit in grad school fuck topology

What's the longest time when you were stuck on a math problem? (research, assignment or homework)
I haven't been able to prove a lemma for my paper, which was supposed to be easy, for 3 weeks now.

>>11785890
let L be the loop on the cylinder. let C be any path from -inf to inf on the cylinder. L is homotopic to the "centre circle", and C is homotopic to a "straight line". the intersection number of these two new curves is non-zero (it's 1 or -1), and so the intersection number of L and C is non-zero (because it doesn't depend on homotopy classes).

>>11786116
>I haven't been able to prove a lemma for my paper, which was supposed to be easy, for 3 weeks now.
ngmi

>>11786108
I had the exact same experience. I think it's a very common situation; you either enjoy those kind of "just visualize it bro it's obvious" ersatz-proofs or they piss the fuck out of you and make you want to avoid the subject.

>>11786116
When I first chose my thesis problem I spent around 3 months literally nowhere before I made a bit of nontrivial progress into it.

>>11786122
Interesting. Where can I learn about these intersection numbers?

>>11786116
3 months now. The more I try, the more I realise how I don't know anything and how unable I am to learn anything new. If there was no corona, I'd get a real job and forget this nonsense.

>>11786133
read Milnor's Topology from the Differentiable Viewpoint or Guillemin & Pollack - Differential Topology. you're gonna love it.

>>11786122
Aren't intersection numbers a thing in differential topology? How do you apply them to regular topology?

>>11786163
firstly, any continuous map between manifolds is homotopic to a smooth map, so the smooth intersection number is well-defined even for non-smooth maps
secondly, there's a more general approach using cohomology which works for any space satisfying Poincare duality. the intersection number is basically the cup product of the (co)-homology classes represented by the loops.

>>11786091
>>11786094
That's not "show the mobius band is a manifold" though, that's "show the mobius band is a smooth rank one vector bundle over S^1 which is not the trivial bundle"
Moreover, that is a shit question like many of the problems in Lee. Literally just a computation bash.

>>11786172
Ok but how do we ensure that we don't get any new intersections when we apply the homotopy to a smooth map for our loop?

>>11786063
The Mobius band retracts to the circle, so that its fundamental group is the integers, and admits a generator [math]a[/math].
The homotopy class of [math]a^2[/math] can then be represented by a circle embedding, but independent of which generator you choose for the normal band, the square can't be represented by an embedding, as can be proved with the intermediate value theorem.

Might have made a mistake somewhere, tho.

>>11785073
kek

>>11786187
I thought of this exact proof as well but couldn't figure out how to make it work.
How do you prove that a^2 can't be represented by an embedding? I don't see how the intermediate value theorem applies here.

>>11786183
obviously the independence of the intersection number on homotopy classes needs to be proved. the idea is that you may get new intersections, but they pair-wise cancel (always one appears with plus sign and other with minus sign).

>>11786091
ok I think I'm retarded as fuck but why is [math]q|_S[/math] closed on [math]S[/math]?

Also I get that [math]\pi[/math] is well defined on each equivalence class (i.e. each element of [math]E[/math]) but why is it continuous? I'm not too sure but is [math]\pi^{-1}U=q((\epsilon\circ \pi_1)^{-1}U)[/math]? If so then by the topology induced on [math]E[/math] by the quotient map and by continuity of [math]\epsilon\circ \pi_1[/math], [math]\pi[/math] indeed becomes a continuous function

>>11786097
>I didn't ask for a proof of the Jordan curve theorem
No, but you're asking for things which are very similar, and which someone answering questions about manifolds wouldn't care about.
>Have you never read a topology book?
Of course I have. I'm not talking about fucking point set topology. We're talking about topological manifolds, which are extremely intuitive objects with almost no pathology. If you want something to be true about manifolds, it's true. Yes, proper rigor is important when your spaces don't behave locally like Euclidean space. When they do, rigor is a crutch.
>Proving a lemma which is in no way obvious
It is not obvious to you that you can deform two disjoint curves from one end of a compact rectangle in R^2 to the other, so that they are the graphs of functions and so that they stay disjoint? This is what topological intuition is for.
In fact, here's where Jordan Curve could come in handy. We've unwrapped the mobius strip, it's sitting in R^2. Consider the closed loop which follows one of our cut curves, then goes up the cut edge of the mobius strip, then goes across the top of the mobius strip, then goes down the other cut edge until it meets back up with our curve.
Removing this closed loop cuts the plane into two pieces. But the other curve now goes from the region outside the loop to the region inside the loop, and since it's inside the mobius strip and disjoint from the other curve, we have kept this whole curve intact (modulo maybe the endpoints). So there is a path from the outside region to the inside region. Contradiction.

>>11786200
Right yeah, but still the intersection number is still only defined on smooth maps no? We want to prove that our continuous maps intersect. We can prove now that every smooth pair that is homotopic to the original continuous maps intersect, but how does that guarantee that the two original maps intersect? Is there a theorem for this?

>>11786173
That's 10-1 b) and c), part a) literally asks you to show it's a manifold with a particular kind of smooth structure and I can't see how to do it

>>11784117
how do I stop being such a brainlet at math?
I hear you get worse as you get older, I am 25, is there still hope for me?

>>11786214
it's literally just asking you to show the mobius band is the manifold you get when you glue one side of a square to the other with a flip

>>11785981
bump can anyone please verify

>>11786217
No it's not, stop trying to handwave and simplify the question to something it's not

>>11786208
>It is not obvious to you that you can deform two disjoint curves from one end of a compact rectangle in R^2 to the other, so that they are the graphs of functions and so that they stay disjoint? This is what topological intuition is for.
to be fair, this is not obvious at all if the curves are not guaranteed to be smooth, and even then I would say it requires a proof.

>>11786219
That's fine. You can also just directly show the first part by showing it's Lipschitz, which is immediate.

>>11786208
I've got a simple proof that S^n is not homemorphic to S^m for every n!=m:
Every embedding of S^m in R^(m+1) obviously disconnects R^(m+1), and every embeding of S^n in R^(m+1) obviously keeps R^(m+1) connected for n<m. The power of topological intuition! No need for homotopy groups or the theory of homology. What do you think? Should I publish this simple proof? After all, we're talking about spheres now, which are topological manifolds: extremely intuitive objects with almost no pathology! If you want something to be true about manifolds, it's true!
You're a retard and should stop posting.

>>11786216
>i am 25
Sorry but no...

>>11786216
pick your parents better

>>11786228
It is perfectly obvious if the curves are continuous and compact with endpoints.
>>11786225
It is precisely that. Do you understand what these words mean?
>smooth covering map
>smooth structure
Just try the smooth structure you get from gluing one side of a square to the other with a twist, and show that q is a smooth covering map (it clearly is).
How to show uniqueness? I'm not really sure, maybe there's a proposition in chapter 5 with the covering maps which gets you that. Something about covering maps making it unique.

>>11786208
>We've unwrapped the mobius strip, it's sitting in R^2. Consider the closed loop which follows one of our cut curves
How do you ensure your curves are not as in pic related?

>>11786242
>It is perfectly obvious if the curves are continuous and compact with endpoints.
sketch the proof please

>>11786246
Sorry meant something like this (since we're talking about the cylinder here, not the mobius band).

>>11786231
Well, that's how I think of it of course. And that's also pretty much what the mayer vietoris sequence computation of the homology groups of S^n is saying. Of course it's not a publishable proof but it's the correct intuition.
The dude asked "why are mobius strips not homeomorphic to cylinders" not "give me a proof from the axioms of ZFC using complete and full rigor." If he asked "why is S^n not homeomorphic to S^m" any normal person would give the answer you just wrote out.
(Though I will say it's only completely obvious in 2 and 3 dimensions like we're talking with the mobius strip since there is "more freedom to move" in higher dimensions and the same intuition doesn't always hold. Perhaps I should have said, everything one wants to be true of topological surfaces is true.
And this really reads like a post written by someone who doesn't really enjoy topology much.

>25

>>11786019
Use the definition you're given to cover it in charts, define transition maps, and show they form an atlas.

>>11786270
I said pick ones which go around it, i.e. not contractible. Then you get one leaf of the curve going all the way across.
>>11786264
I did above, using the jordan curve theorem. Which is nothing small to prove, but I think most would also describe as perfectly obvious. It is one of the flaws of human intuition that we find the proof so nasty.

>>11786285
>I said pick ones which go around it, i.e. not contractible. Then you get one leaf of the curve going all the way across.
Prove it.

>>11786242
>Do you understand what these words mean?
To get a smooth structure, it suffices to find a smooth atlas on E. To say that q is a smooth covering map requires proving that q is a covering map which is smooth with respect to the transition maps provided by the atlas you give. Parroting definitions tells nothing

>>11786063
Just triangulate the two bands and compute simplicial homology if you want a really rigorous argument.

>>11786293
>Just do something I'm too lazy to do
These are topologists for you, everyone

>>11786002
>>11786285
Why can't the two loops on the cylinder map to the mobius band as pic related, in which case they wouldn't intersect?

>>11786213
the smooth approximation can be chosen arbitrarily close to the original. from compactness you can deduce that if the original curves don't intersect, neither do any curves sufficiently close. contradiction.

>>11786302
I just realized my drawing looks suspiciously similar to the transgender flag (not intentional).

>>11786293
>implying they have different simplicial homology

>>11786299
Don't ask me to do your homework for you. It reduces to that short calculation. I'm not going to tex row reductions for some anon who can't into topology.

>>11786311
idiot. the simplicial homology is the same for both spaces.

>>11786315
this

>>11786230
Oh, that's pretty neat thanks

>>11786308
My mistake, I was thinking of the Z/2Z in RP^2. They both deformation retract to the circle so they're homotopy equivalent. Okay, so you can show that a homeomorphism takes the boundary of one to the boundary of the other, but one has a boundary with two components and the other has a boundary with one component.

>>11786326
the argument with boundaries has been said already >>11785552. I think we're implicitly talking about open bands

>>11786303
How do you make sense of that when you're talking about mobius band and cylinder without boundaries (so that they are manifolds)?
And how do you show that if you allow boundaries, that a homeomorphism takes boundaries to boundaries?

>>11786338
meant for >>11786326

>>11786338
>How do you make sense of that when you're talking about mobius band and cylinder without boundaries (so that they are manifolds)?
sense of what exactly ?
>And how do you show that if you allow boundaries, that a homeomorphism takes boundaries to boundaries?
standard theorem in topology, use relative homology groups

>>11786303
going back to what you said earlier
>>11785880
The center circle on M disconnects M as well. So you must take your loop to be a^2 in the fundamental group, where a is the generator. Does the intersection degree still work out to be nonzero (I assume we can only work mod 2 since M is nonorientable)?

>>11786283
How do I choose the charts so that q in >>11786091 becomes a smooth covering map?

>>11786347
How do you prove that the mobius band and the cylinder as manifolds without boundary are not homeomorphic?
>standard theorem in topology, use relative homology groups
Can you point to where I can find this theorem?

how will topoloshits ever recover from this thread

>>11786358
One chart is the interior of that infinite strip, the other is a small neighborhood of the lines bounding that strip which become identified under the quotient map.

>>11786371
We're all just trying to learn friend. An expert is someone who's made all the easy mistakes before.

>>11786330
Didn't read the whole thread lol.

>>11786363
I think it follows from invariance of domain. and this is proved using homology.
>>11786357
I didn't make the argument with a^2. I'm saying that homeomorphism of the bands gives you a generator of pi_1 and this generator disconnects the cylinder because any curve connecting the top and the bottom must intersect the generator, because of intersection numbers.

>>11786374
How is that equivalent to what Lee says on page 252 (pic in that post)?

>>11786196
FUCK, I can't make it work either with just intermediate value.
If you identify all [math](x, 0) \in S^1 \times [0, 1][/math], you get a disk (might be easier to think of it as a cone), and the embedding becomes a Jordan closed curve, and then the boundary of the curve can't have winding number different from 1 around 0, so its homotopy class isn't [math]a^2[/math].

>>11786394
You're right. I think your proof works! Thanks!
>>11786399
I think this works as well, just with the minor correction that we're dealing with S^1 x R here, not S^1 x [0,1], so you'd have to identify S^1 x [a,infinity) to a point where a is such that the loop is outside of the identified area (which is possible because of compactness).

>>11786397
It's not, he's talking out of his ass
Since the smooth structure that makes the covering map smooth is unique, it would require Lee's suggested atlas (induced by restrictions of q on pi^{-1}(U) as U ranges over evenly covered subsets of S1) to be equivalent to the two chart atlas he's talking about, which is clearly false

>>11786419
if you're interested, you can think about why the winding number given by >>11786399 is actually the same thing as the intersection number given by >>11786394

>>11786439
(the arguments are different though)

can anyone refer me to a no-nonsense RIGOROUS and complete introduction to topology that starts from scratch and covers all of the stuff you see in undergrad? (i.e. up to algebraic topology) I'm sick of not being able to follow any topo discussion

>>11786439
It's intuitively obvious to me that they are but I'm not in the mood to prove it :p

Who's the most famous person in /mg/?

>>11786201
bump

>>11786453
You know the guy who makes those set theory posts? I'd say he's the number one. At least for me he is...

>>11786476
Who's that?

>>11786394
Still one thing is not clear to me. What are the exact conditions for the degree of intersection of two maps to be homotopy invariant.
For example, what is preventing pic related to happen in our situation?

>>11786478
>>11778230

>>11786426
>which is clearly false
Why?

>>11786449
Munkres's Topology

Say you have the vector space [math]l^p(\mathbb{R}), p\in[1,\infty )[/math] consisting og series [math]\left \{ x_i \right \}_{i\in\mathbb{N}}, \left \| x \right \|_{l^p}<\infty [/math]. How do you prove [math]H(x)=y[/math] for [math]x\in l^p(\mathbb{R})[/math] where [math]y_i=sin(x_i)[/math] is Frechet differentiable with [math]H'(x)(r)=\left \{ cos(x_i)r_i \right \}_{i\in\mathbb{N}}[/math]. I have tried to solve [math]\lim_{r\rightarrow 0}\frac{\left \| H(x+r)-H(x)-H'(x)(r) \right \|}{\left \| r \right \|}=0[/math] but i don't know what [math]H(x+r)[/math] is. Anyone have any suggestions?

>>11786506
damn it must suck being a retard

bros...

>>11786516
Whats the answer then?

>>11786527
It's true of course
It amazes me that you talk about the concept of "Frechet differentiable" without even knowing elementary trigonometry

>>11786533
Can you read? I fucking know its true retard.

>>11786533
:(

>>11786527
Have you tried using a sum of angles trig identity?

>>11786538
Don't give energy to unpleasant people.

Why are Indian professors so comfy? they're always very wise and pleasant

>>11785650
Aria

>>11785844
Let [math]X=S^1\times [0,1][/math] be a description of the regular band. Let [math]L=S^1\times \{\frac 12\}[/math] be the line through the middle of the band. Then [math]X - L=S^1\times [0,\frac12)\coprod S^1\times (\frac 12,0][/math]. The latter is a disjoint union by considering [math]X[/math] as a square embedded in [math]mathbb R^2[/math] and applying the intermediate value theorem, and path connected is equivalent to connected in Hausdorff spaces - in particular [math]X-L[/math] is disconnected, since it is a union of disconnected open sets.

>>11786538
Oh, my apologies, here's the answer to "Anyone have any suggestions?": kill yourself. I'm not giving you shit for tips because you're a cumbrain who didn't even pass trigonometry in high school. Clearly the big books you've been reading are too much to handle considering your room temperature IQ. If you're this retarded then you should just fuck off

What percentile does your IQ have to be to study pure mathematics at a top 25 university?

Top 0.5%?

>>11786567
Do you have any friends you can talk to about these feelings?

>>11786583
Fortunately they aren't clinically braindead illiterates, so it never comes to euthanasia

>>11786590

Pretty much every mathematics we use was discovered by absolute breeders like Euler and Gauss ... none of them if born nowadays would be lolifags like us bros ... we're frauds ...

>>11786611
shutup faggot, you really want dumbfucks to shit up this thread with their garbage questions? He's either an underage who went "ooOoo Frechet differentiable BiG wordzzz!" on wikipedia and looked up some trivial examples only to scratch his head when he couldn't figure them out or is just fucking lazy and didn't even think about the problem for 5 seconds before posting
Low effort and low iq posts don't belong here

>>11786622
In fact I'd wager he's an underage considering he felt the need to be needlessly redundant with
>>11786506
>vector space lp(R),p∈[1,∞)lp(R),p∈[1,∞) consisting og series {xi}i∈N,∥x∥lp<∞{xi}i∈N,∥x∥lp<∞
Retards shit out clues everywhere

>>11786621
newton was a virgin till the day he died

>>11786640

I used to say that too, it's just gasping at straws because he's a point out of the curve

>>11786506
Something something compute the Gateaux differential in all the obvious directions, something something show it's bounded and use that to reconstruct the Fréchet differential, something something this is not just stupid, it's also boring, ask in >>>/sci/sqt

>>11786640
>till the day he died
so.. sex killed him?

>>11786292
Yes, you're right. Are you just saying you don't know how to write maps from a square / from R^2 to E then?
Perhaps you need to go back to chapter 2 and check some of the examples and exercises there.

what's the point bros...

>>11786302
Because you specifically choose your first loop on the cylinder to be the one that maps to the center loop on the mobius band. When you pick the other sure it could wrap around twice like that, but it doesn't because the fundamental group is a functor from Top to Grp and so the map drops to an isomorphism of the pi_1's, hence sends generators to generators.
>Why is pi_1 a functor
FUCK OFFFF!!!!!!

>>11786622
I'm glad there is a lot of high IQ dialogue in these threads otherwise.

>>11786330
Add a distance metric, arbitrary one, and take metric completions. Homeomorphic metric spaces have homeomorphic completions.

>>11786673
There is none.

>>11786686
Reminder that the sphere with both poles removed is homeomorphic to the open band.

Ladies of /mg/, I have to ask... How do you feel about the [math](n+1)[/math]-th publication of Maryam Mirzakhani in "people/women in mathematics"

>>11786539
>Have you tried using a sum of angles trig identity?
not the anon who asked but what do you mean?
[math]H(x+r)-H(x)-H'(x)(r)=a[/math] where [math]a_i=\sin x_i (\cos r_i - 1) + r_i \cos x_i((\sin r_i)/r_i -1)[/math] and this goes to zero as r does but how does this help? We need to see that [math](\sum a_i^p)/(\sum r_i^p)[/math] goes to 0

>>11784117
Lads, what do you reckon I should do? In order to finish my thesis I need to finish a problem I'm working on. However, when I was working on it I've found a bunch of inconsistencies in a previous result which my own advisor refuses to consider. I won't be too specific for obvious reasons, but the basic idea is that he's published something very hastily thrown together claiming a proof that a certain function is always positive whereas I've come up with an example that seems very obstinately bounded above by 0.
This would be fine if I were independent already. I'd just publish the counter example. But because I'm still a PhD student I've basically been told that no results of mine should contradict him because it would look bad for us both, and the last time I brought up this topic to explain why the research is hitting a wall he flew into a massive rage.
What do here?

>>11786780
how old are you?

why aren't you abusing the most overpowered aid for memory - anki

>>11786793
Because I want to forget.

>>11786793
Because the effort it would take me to actually set up a reasonable database for a course is far too large.

>>11786651
What are you even talking about
We have to find an atlas wrt to which the covering map q is smooth. (I can see that it's a covering map by taking restrictions to small enough neighborhood classes.) Lee has specified the candidates. The question is how to prove the details, namely that q restricts to a homeomorphism from [math]\Tilde{U}\times \mathbb{R}[/math] to [math]\pi^{-1}(U)[/math] and that the induced local trivializations are smoothly compatible.

>>11786780
>What do here?
Personally I would try to speak to another professor about the subject.

And honestly, you not "correcting" him will be what looks worse for you both.

>>11786793
anki doesn't work

>>11786806
but you can forget things by remembering other things (buffer overflow in a way)
>>11786814
but i would argue even tho effort might be larger you multiple dip (which i dont think so it is) on that effort since then you have a program taking care of when and what to test yourself in the future
>>11786830
why it doesn't work?

>>11786780
It's not clear from your post whether it's possible for you to finish your thesis in spite of this. If that's at all possible, just drop it for now.
If you can't, compute an explicit counterexample in excruciating retard-tier detail and then bring it in and deal with it. Don't worry about "correcting" him or publishing anything right now, first get to the point where you don't disagree about whether the example works. The fact that this triggered a temper tantrum makes me think maybe you did suggest something like that; "I can't get your theorem to work with this function, can you help" is not going to immediately induce frothing rage in any human without a severe mental disorder.
The other guy's advice is more of a last resort; dragging other people into disagreements will rankle even well-tempered profs. Don't do that unless he's being so outrageously abusive you have no other options.

Funnily enough I had a pretty similar situation, although my advisor dealt with it much better. One of the objects he suggested I study (which he constructed) turned out to be explosively not-well-defined, but when I showed him he basically just said "well fuck" and gave me something else to do.

>>11786853
>but you can forget things by remembering other things (buffer overflow in a way)
I could, sure. I just can't think of anything worth learning.

>>11786622
Anger is a sign of low IQ. I am sorry anon.

>>11786871
Yes, Galois was truly low IQ anon

>>11786869
>I could, sure. I just can't think of anything worth learning.
You are just not asking the right questions.

Threadly reminder to join the physics department summer party.

>>11786875
If he was so smart why did he fucking die in a duel at age 20 lmao

>>11786869
why tf her jaw broken?

>>11786875
he was

>hmmm I'm probably going to die tomorrow better spend my last hours writing a bunch of autism rather than try to find a way to get out of it

literally nobody would even talk about him if he weren't killed at a young age. The kurt cobain of mathematicians

>>11786883
Korean sweatshop artist's finger slipped

>>11786878
But what could those be?

>>11786898
There are always questions to ask. Even Terry Tao has questions.

>>11786483
the classical condition is that the manifolds need to be closed (compact and without boundary). if they have boundary, then its only invariant under homotopies which fix the boundary and satisfy some other technical assumptions, basically exactly so that this picture doesn't happen. same goes for non-compact manifolds, but then the homotopies need to have compact support or something (it's the same idea, just treat the "ïnfinity" as the boundary).

>>11786863
>It's not clear from your post whether it's possible for you to finish your thesis in spite of this
Maybe. Considering dropping it because of this desu, his demands are "solve this" but when I point out a previous lemma doesn't seem to be as solid as thought he just seems to not remember any part of the conversation by morning.
The thing that frustrated me is that he doesn't even seem to have read the paper he referenced to base this thing off. I don't know what's going on because I brought a detail up and he had never heard of it when he cited the paper with his coauthor (who's dead now). He just kinda looked at it and started asking me what a bunch of stuff meant in the paper he'd cited to prove this thing.

>>11786910
Yes. Questions exist, but they are not mine.

>>11786942
That sounds...quite disturbing I must admit. How long has this guy been on tenure?

>>11786954
About 20 years I think

>>11786946
Then make them yours and figure out how to make your own questions.

>>11786976
Do you think he could possibly be going senile? Dementia maybe?

>>11786981
Easier to just find something else to do.

What to do after substitution for sin and cos?

>>11786780
Have you considered very, very slightly broadening the class of objects that his result works for, adding a paragraph about how his result is essential for the research of the original object, and then adding a version of his result as one of the axioms for the new object, or something similar enough?

>>11786988
Yeah I have considered it. Looking at his older work especially the stuff done in his 20 and 30s it's phenomenally different to where he is now. I actually think this probably is age related decline to some extent but that's a really sensitive thing to even touch. He does seem to heavily rely on the younger researchers now whereas he didn't in the earlier 2010s.
But it's just frustrating as fuck for me when he seems to not be aware of stuff until you mention it like 5 times while the clock keeps ticking for my funding.

>>11787001
Just expand and do term by term, it's much faster

>>11787026
Realistically, just how vital is this result/lemma to your work? How far are you done with your thesis? (% wise)

>>11786693
Yeah, I wanted to see if I could get the fucker to agree with a false proof. While I was typing, the similar counterexample I thought of was an open interval versus a circle with a point removed.

What in the fuck is an L-function, and why should I not just go ahead and kill myself?

>>11786853
>but i would argue even tho effort might be larger you multiple dip (which i dont think so it is) on that effort since then you have a program taking care of when and what to test yourself in the future
Most of my exams revolve around theorems and proofs.
Just entering the quick rundowns into Anki would take many many hours. If I spent that time just learning I am better of.

The script for my current course is 100 pages. Just reading through that will take multiple hours. I just do the system by myself and repeatedly check myself if I have remembered certain parts correctly...

>>11786827
So your issue is a slightly unpleasant children's computation?

>>11786483
Why do you keep asking about these obvious things that anyone who has taken an introductory course in manifolds knows? Read a fucking book.
You'd probably blow a gasket at Guillemin and Pollack so not that I guess. It's a bit hand wavey.

>>11786853
too many things that can't be copy pasted from memory, working memory is not the mediating factor for performance in mathematics.

>>11787028
You're joking, right? It's literally just a fucking hyperbolic trig powers integral.

>>11786780
Yiou should talk to someoned else at the department Do you have a second supervisor?

>>11787071
Depending on who you ask you get different answers. This is precisely why they're interesting.
For me they're a convenient way of recording properties of a motive.

>>11787091
Yeah they're so obvious that most proofs given ITT of the statement were completely wrong and/or nonsense.
>Read a fucking book.
What book then?

>>11787106
I can't tell if this is a serious answer or a LARP

Leading me towards the suicide option here.

>>11787131
Why are we alll so depessed? When did this stop being fun?

>>11787131
Totally serious, for the automorphic reps people they're a similar "digest of available information" but things like analytic continuation are much easier to prove. Most of the time the galois side is really implicitly restricted to galois reps of geometric origin. i.e. galois reps that can be equiped with a motive. To an analytic number theory person I suspect they're something else entirely. On some level the Langlands program is about answering the question "why does the same set of functions arise in several essentially different ways?".

>>11787142
Prime numbers haunt my dreams, and if we discover their true nature it would collapse society in an instant.

>>11787159
Thanks, that helps.. A little bit.. I need to read up on langlands I think

>>11787081
My issue is what I posted. Surely a children's computation cannot be that intricate for the budding Grothendieck here?

>>11787190
Also, you never affirmed whether that is all one formally has to do to give a rigorous answer to 10-1a). All you've said so far is "oh but it's all about that square, uhm yeah so you uh glue it with a flip, you know? Yeah you glue it and then *farts* oh sorry about that *burps* excuse me, yeah so mobius manifold there you have it hahahaha children's computation"

What's the general rule for generating permutation cycles from transpositions where 1 element is fixed? For example, a pair of such transpositions equals a 3-cycle: [eqn](1i)(1j)=(1ji).[/eqn] How about a triple of transpositions: [math](1i)(1j)(1k)[/math]? If we don't put any restrictions on [math]i,j,k[/math], will this generate all 4-cycles?

>>11784117
I'm interested in studying mathematics at a top 25 university.
How many people get into graduate school? I'm guessing the top 10%?
Based off of the assumption that gettting in to graduate school is difficult, the majority of math majors do not get into graduate school. I know that money is not everything, but the choices I make now end up affecting the rest of my life. What can you do with a major in mathematics and a minor in computer science after university? I just really, really don't want to be a high school teacher after university.

>>11787282
>I'm interested in studying mathematics at a top 25 university.
>How many people get into graduate school? I'm guessing the top 10%?
Why, I just found the post for you!
>>11783528

Is there a broader generalization of mathematics than systems of axioms and sets?

If a language is a syntax and a diction, and an algebra is a pair of sets of symbols and axioms, aren't they essentially the same thing? Is this concept the basis for all knowledge?

>>11787294
So you are basically saying that it is easier to get into medical school than mathematics graduate school?

>>11787039
I was at 75% but this puts me back to about 50%
>>11787142
>when did this stop being fun
I don't know, it's all just fucking exhausting. Sometimes you want to go to sleep and just dream forever, you know?

>>11787294
For admission to top schools what I've heard is:
if you get one B they ask questions, if you get two they don't.

>>11787310
>>11787329
I'm not interested in top, top schools. How difficult is it to enter graduate school for math at a top 150 university?

>>11787314
>t's all just fucking exhausting
Yes iy is.
>Sometimes you want to go to sleep and just dream forever, you know?
I know what youmean. But you have mase it so far, Please finish the figjt!

>>11787335
What's even the point in going to such a low-tier grad school? You'd be better off ordering a PhD degree from Alibaba

>>11787347
Haha these typos soon sleep

>>11787294
Do you have to literally solve some professor's conjecture and e-mail him asking for a spot to get into a top 10 program nowadays?

>>11787361
pretty much

>>11784786
people here usually don't remember them, too many zoomers I guess
to answer your question: probably grew up. even raiding and making intentionally bad Naruto subs gets old after a while I guess

>>11787363
Huh, sounds like a pain in the ass.
Thank God I do this shit as a hobby.

how to i translate "finitely many" into predicate logic?

i believe i would need a sentence in PL of arbitrary length, but i dont know how you express that non-meta-linguistically.

>>11787306
>broader generalization
assuming some statements are true, we can derive other statements
>same thing
no, the implication only works in one direction, mathematical theories model phenomena.
youre confusing the map for the territory.
read the SEP article on the philosophy of mathematics

>>11787361
yeah but after that its 200k starting

>>11787414
You nees to have a finite string of existemtoal quantfiers, one for each element, and then you put a universal quantifier and say that all x are one of the y that you quantified to exist, if I remember correctly.

How fucked am I going into an MSc after a 4 year break after my BSc?

>>11787424
oh i understand that, but then youre using "..." (or something equivalent) which isnt typically in PL, so it would be a metalinguistic statement

>>11787436
Math Msc? Very, lube up

>>11787440
I literally haave no idea sorry.

>>11787414
>yeah but after that its 200k starting
my friend who "only" did a Bachelors in computer science landed a job at Amazon straight after graduation for 170k
Even thinking of attributing a pay boost as a legitimate plus that comes from doing a math PhD at a top 10 is ridiculous

>>11787436
You'll be completely shellshocked for 2-3 weeks and then it'll be like you never left undergrad. People adapt fast.

What's a good book or lecture notes on microlocal analysis?

>>11787370
I want to do this shit as a hobby. But can I make a decent living as a B.Sc in math (with a minor in CompSci) from a top 25 school?

>>11787567
Yes.

>>11787349
Your advisor and your research is more important than the schools name to a certain extent. Obviously going to Harvard or Princeton is great but it matters more what you want to research etc. I know someone at Princeton who went to a program with a less prestegious name for the advisor.

What is the purpose of integration? If the purpose of differentiation is to find the rate of change, then why reverse that?

>>11787073
>Just reading through that will take multiple hours
And while reading that text you dont come across any striking fact/insight or question you would like to remember? If yes (if not whats the point of even reading that script) you then only have to type that into anki and you are done. You seem to extremely overestimate the time you would need to put into anki.
>I just do the system by myself
And while you have to put conscious effort into doing and remembering about doing that stuff I turn my downtime into useful time and test myself while sitting on a toilet or talking a walk.
>>11787093
>too many things that can't be copy pasted from memory
Like? Almost anything can be formulate into a Question:Answer form which then can be put into anki.
>working memory is not the mediating factor for performance in mathematics.
What does working memory have to do with anki?

>>11787642
Those cases are exceptions. In general, a shit program is likely to have advisors that are shit too (which is part of what makes the image of the program shit)

>>11787414
>assuming some statements are true, we can derive other statements
You're thinking of Noetherian proof systems I believe. That's a feature of an axiomatic system, and therefore is generalized by it, not the other way around.

>mathematical theories model phenomena
Not necessarily. You can build a system of mathematics out of any concept really. It may appear to be modeled on phenomena because there's no other source of creativity for us to build upon.

>>11787685
>It may appear to be modeled on phenomena because there's no other source of creativity for us to build upon.
This is a mere hypothesis

>>11787647
>then why reverse that?
Sometimes you already know the rate of change, and you want to figure out the _total_ change. This is when you integrate.

bros why is it so comfy to do some maths at 4 in the morning?

>>11787788
It's silent, night is comfy in general, and no percivable time limits. Wrote about 90% of my PhD-thesis between 1am and 5am.

>>11787700
Surely, but as we are bound to our human perspectives, we must be aware that we have a limited scope of visibility.

>>11787936
>we are bound to our human perspectives
that is an assumption

>>11788110
There are many things we cannot perceive. Even with our best instruments, it's a known fact that we have not observed a great amount of the universe. Why do you think we're building an even larger large hadron collider?

>>11785829
damn i need to submit it now and i checked hoping that thered be further explanation and there is thank you so much may you have a hot wife anon

>>11788140
having things we cannot perceive/not having observed the entire universe does not imply "we are bound to our human perspectives"

>>11788194
I think you're taking my meaning too literally

>>11787647
Integration is not a priori antidifferentiation

>>11788238
well I can't peek into your mind to figure out what you mean

>>11788296
>implying every anon you talk to is the same anon
you're paranoid.

>>11788335
Thank you for your diagnosis
You shouldn't reply to a chain without the obligatory "not that anon but..."

>>11788340

>>11788352
take your pills you projecting schizoid

>>11788357
neck yourself first

>>11788368
faget

>>11788374
take it easy heh

>>11788383
heh heh heh neck yourself easy eh

How do I know that I am smart enough to be a math major? I've never done a mathematics contest before. I just like learning math outside of high school? Everytime I see a proof I get excited.

New Threade: >>11788501

>>11788514
bit early anon

>>11788540
I post a new thread whenever this one reaches the bump limit.

>>11787685
>Noetherian
i have no idea what youre on about
>axiomatic system
rightly so.
i think this might still be accurate (perhaps in an equivocal way) about other proof systems as you still have to assume the truth of say the validity of certain rules of inference or schemata.

>mathematical theories
i meant to the extent that they werent mathematical theories of mathematics but of other sciences (in the broad sense).
im certainly not saying that all theories of mathematics are based on phenomena (although it might be true in some kantian sense that they are all based on the possibility of phenomena).
>theres no other source of creativity
yeah youre really going off the rails here, unless the bit about "creativity" was a goof and you really meant 'categories'

>>11788357
>>11788368
you guys stop

>>11788561
It's not reached bump limit yet.

>>11787656
>And while reading that text you dont come across any striking fact/insight or question you would like to remember?
Hundreds of them.

>You seem to extremely overestimate the time you would need to put into anki.
Firstly ankis TeX capabilities seem to be quite limited, secondly typesetting math is fucking hard. A single page roughly takes an hour...
Setting up the around 100 question needed for it to have a chance to function would take many hours.

>And while you have to put conscious effort into doing and remembering about doing that stuff I turn my downtime into useful time and test myself while sitting on a toilet or talking a walk.
I have the script on my phone. I can do this too.
The conscious effort is near zero anyway, since I can just see if I get later sections, if I don't I need to learn things from further behind...

yo /mg/, I'm a highschool dropout. Since dropping out I've gone on to make good money (100k) at a telecom where my job is literally 'satellite controller'. Unfortunately to progress I need to have a masters. Fortunately my work will pay for it. Unfortunately I dont have a bachelors so I dont qualify for it. Fortunately work will pay for my bachelors, too. So starting next january I'll be doing a Bsc. I qualify for the Bsc because I also have a commercial pilots licence, which in my country gives you an automatic entry score into university of 92/100. However I haven't done any math more advanced than times tables since dropping out of high school 10 years ago. In order to make the transition from where I'm at now to where i'll be taking math and physics 1 at a university what resources would you recommend? I'm assuming khan academy however I would much prefer a book, even if its a pdf that I can print.

What can one actually do with a maths degree (master or doctor) if we exclude academia and anything related to programming?

>>11788752
ur mom

>>11788756
sounds like a good deal to me

>>11788756
Already done that. What else?

>>11788765
your dad

>>11788720
>what resources would you recommend?
A nice long rope

>>11788767
I did and he died. What else?

>>11788779
I think you can also kys next with that degree

>>11788788
Nice digits. Why should I do that?

>>11788791
I don't know, but it's definitely something you can
>>11788752
>actually do with a maths degree (master or doctor) if we exclude academia and anything related to programming

>>11788800
So you don't know? You could just have said so.

>>11788806
Why would I say so earlier when you never asked why you should do what you can do with that degree in the first place?

>>11788822
Why don't you just make the world a better place by killing yourself?

>>11788834
ironic words from an animenigger

>>11788853
End your pitiful existence, faggot.

>>11788752
>>11788806
Not going to be getting that masters anytime soon with logic of this tier
>>11788834

>>11788857
I already got that degree 2 years ago.

>>11788858
You should probably give it back then

>>11788864
Why would I do that?

>>11788868
you'll get it after you do it

>>11788869
So you can't even answer that What a surprise.

>>11788872
It's better to figure out some answers yourself
Glad I could entertain you, there's too much boredom in a sped's life as it is

It seems you "people" are just wasting the oxygen of people better than you. Fuck you all.

>>11788882
ya seethe bitch lmfaoo

>>11788882
>he SNAPPED
quick, call spedpatrol! Oh shit they're defunded, nvm

>>11788886
>>11788894
You bullied the tranny away. Good job.

>>11788882
>Has a mAsTeRs
>>better than you
o i am laffin

Let's just hope he doesn't come back. Annoying as fuck.

>>11788922
addicted to coming here and getting btfo, truly a tranny

>>11788933
Probably lmao. Can't wait for the posts where he cries about failing his studies for the millionth time. Assuming he doesn't 41% himself before that which would be even better.

>>11788894
CHAD posting isn't allowed in /mg/, anon
Or was it CHAZ?

>>11788960

>>11788711
>Firstly ankis TeX capabilities seem to be quite limited,
The only limited capability of TeX in anki is bad editor
>A single page roughly takes an hour...
Are you computer illiterate? Don't tell me you are unironically typing TeX without any type of macros and/or AHK scripts
>I have the script on my phone. I can do this too.
So you are just rereading/looking at the same script over and over? That's extremely inefficient
>The conscious effort is near zero anyway,
Tell me that when you are going to look on a script from a course you took a year ago

>>11788720
You need to master basic algebra and trigonometry before you do calculus. Since you will be doing physics 1, I assume it will be calculus based. Good luck.. your about to earn your money.

>>11789201
>The only limited capability of TeX in anki is bad editor
It uses the shitty mathJax, right?
The same as on 4chan.
It is basically unusable unless you want to spend a million years typing out the fucking function space a million times...

>Don't tell me you are unironically typing TeX without any type of macros and/or AHK scripts
If you are using AHK scripts you are RETARDED.
I use the VSCode autocompletion engine and snippits, implementation depending on whether it is vim or VSCode which I am using.

>So you are just rereading/looking at the same script over and over? That's extremely inefficient
So you are just rereading/looking at the same set of cars over and over? That's extremely inefficient

>Tell me that when you are going to look on a script from a course you took a year ago
I know what it covers and what theorems are in there, I don't need more.

I found a question that vould be interesting: Let [math] \mu [/math] be a measure on [math]\mathbb{R}^d[/math]. Can the shape of any set be recovered by knowing the measure of each translation? Formally, For a measurable set [math] M [/math], consider the function [math] f_M: \mathbb{R}^d \rightarrow [0,\infty)[/math] where [math] f_M(x) = \mu(M+ x)[/math].
The question is then if the assignment [math] M \rightarrow f_M[/math] is injective. This can be understood as meaning that the function determines the set.
For any translation invariant measure this is clearly not the case, as [math] f_M[/math] is always constant.
One would probably need a measure with fractal structure to make this work.

>>11790118
If you use the Lebesgue measure and let M, M' be any two countable sets, you get the same function.

>>11790124
Maybe I was unclear, but since the Lebesgue measure is translation invariant the function f_M should always be trivially m^d(M) everywhere.

>>11790141
The functions f_M and f_{M'} are the same. Translation invariance itself does not mean much, you could define an equivalence relation for your measurable sets turning any two translates of the same set equal. The problem is that you can have even non-translates like a singleton and the set of naturals both of which determine the constant 0-function.

How do you colour your pdfs for optimal viewing pleasure? Just found out about this feature, but need to test ideal colouring. Also, there's those black bars that remain on arrows. Is there any fix?

>>11790177
>Is there any fix?
Probably a big in your pdf Editor. Try out a different one.

>>11790118
The assignment is certainly injective on any collection of subsets each of distinct measure: [math]f_M(0)=\mu(M+0)=\mu(M)\neq \mu(M')=\mu(M'+0)=f_M'(0)\Rightarrow f_M \neq f_M'[/math].

Suppose [math]\mu(x)=0[/math] for all [math]x[/math]. Then any distinct pair of single singletons get assigned the 0 function, so for the assignment to be injective on all sets we would require some singleton getting non-trivial measure. Thinking a bit more about this.

>>11790177
Usability studies proved that dark grey on white or black on dark grey are the most readable combinations. Dark themes are a meme.

bros... I did maths today... for the nth day.

>>11790177
If you are using sumatra, it's the "advanced options" which opens up a text file. I use this: TextColor = #ffffff
BackgroundColor = #31343a
or a bg of #E79EDF if I'm feeling spicy. The first one is basically a blackboard color. Don't know what's with your arrows tho