/mg/ maths general: Corollary 3.12 edition

[Anonymous No.10305931]

Talk maths, formerly >>10289246

Mochizuki proceeds to update IUT, re-writing step (xi) in Corollary 3.12 which is a major point of contention for Scholze and Stix
http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20III.pdf

[Anonymous No.10306011]

>>10305931
Mochizuki will never recover

[Anonymous No.10306067]

>>10305931
it's been a long time since I last laugh, now I'm enjoying this picture

[Anonymous No.10306112]

third for reddit graffiti

[Anonymous No.10306236]

Two lineraly independent vectors can be used to deacribe any vectors.
v = Ax+By
How is this possible?
x plus y will always give vector in one direction and we can control only the lenght of it by varrying A and B.

[Anonymous No.10306258]

>>10306236
>Two lineraly independent vectors can be used to deacribe any vectors.
[citation needed]

[Anonymous No.10306265]

>>10306236
what about 2x+y? that doesn't sound like it goes in the same direction as x+y

[Anonymous No.10306377]

>>10306236
If we have 0<=A, B >=1 then all vectors are within the parallelogram spanned by two vectors. If A and B are greater or negative vectors can go outside the parallelogram.

[Anonymous No.10306389]

Is the boundary of the mandelbrot set (colored modulo some base b) normal in that base? By normal, I mean in an analogous way to normal numbers, only for a two-dimensional grid of m*n lattice points instead of one-dimensional strings of k digits.

[Anonymous No.10306396]

What is the proper term for a time series, but generalized to some distribution which is changing in time. Instead of a scalar that varies through time, it would be a function representing some distribution.

[Anonymous No.10306459]

Can we just take a second to pause and think about the fact that last general died at 219 posts?

[Anonymous No.10306463]

It's been months since the last time I browsed /sci/, what happened to this board?

[Anonymous No.10306473]

>>10306463
the great quantity of low iq posters couldnt find their way to 4channel from 4chan

[Anonymous No.10306477]

>>10306463
Race bait and IQ threads finally took over and the mods are complacent about it, actively working on demolishing the quality of this board by keeping shit threads up and only enforcing rules to things like career advice threads which are objectively much better than what we currently have. Those get immediately 404'd.

[Anonymous No.10306491]

>>10306477
Career advice threads are trash and objectively worse than IQ threads. The latter can still be called /sci/.

[Anonymous No.10306492]

Does (IA)^-1 equal to IA^-1?

[Anonymous No.10306495]

>>10306492
What do I and A mean in your case?

[Anonymous No.10306497]

>>10306492
A's an operator, right? Then yes.

[Anonymous No.10306498]

>>10306459
general is very slow. It took 2 hrs 20 mins for three post after mine to show up.

[Anonymous No.10306501]

>>10306492
If A is a matrix and I is Identity matrix of compatible order then yes. Both are same. And by ^-1 I assumed inverse operation.

[Anonymous No.10306509]

>>10306498
Yes, obviously, but it's slower than ever before, even summer, to the point that we get archived before the bump limit

[Anonymous No.10306516]

>>10305931
>arithmetic holomorphic structure
http://thatsmathematics.com/mathgen/

[Anonymous No.10306522]

>pick up a Riemannian geometry book
>five thousand theorems bounding relations on top of boundaries on curvature
>weird-ass formulas like Santalo's
Honestly, how do I memorize this stuff?

[Anonymous No.10306575]

>>10306501
Yes, I meant that. Thanks.

[Anonymous No.10306890]

>>10306236
If A and B are linearly independent, any vector in the plane containing both A and B can be expressed as Ax+By. For N dimensions, you need N linearly-independent vectors.

[Anonymous No.10306901]

>>10306477
I hate them as much as anyone else, but there are only a few and certainly no more than there used to be. Take off the rose tinted glasses.

[Anonymous No.10307001]

>>10306522
you understand it

[Anonymous No.10307315]

>>10306236
You must mean a vector space of dimension 2 or your assumption
>Two lineraly independent vectors can be used to deacribe any vectors
makes no sense. For simplicity, when talking about vector spaces you also must specify over which field, so I take you to mean R^2 over the reals. To your question you can easily change the direction of a vector by multiplying it by the scalar -1.

[Anonymous No.10307647]

>>10306522
>you study 100 hours a day for three years
>in the beginning, you will wish you were dead
and so on

[Anonymous No.10307665]

>>10307647
>100 hours a day

[goes in all fields No.10307955]

>>10307647
....?

[Anonymous No.10308073]

Post Wikipedia banter

[Anonymous No.10308083]

Rings, Fields, Group ; Do they have practical application?

[Anonymous No.10308084]

>>10308083

Cryptography

now go away

[Anonymous No.10308092]

Loday defines [math]S^1]/math]-equivariant homology of [math]X[/math] as the homology of [math]ES^1\times_{S^1} |X|[/math] without specifying the theory. Should I just consider it to be singular homology?

[Anonymous No.10308100]

>>10308083
Are you serious?

Group theory/Field Theory incredibly useful in Physics. For example, group theory was pretty much the language of quantum physics in the 20th century, and you know what quantum physics has done to the 21st century technology.

[Anonymous No.10308108]

>>10308092
Yes.

[Anonymous No.10308111]

>>10308108
Thanks.

[Anonymous No.10308254]

>>10308083

[Anonymous No.10308301]

>>10308100
The field theory >>10308083 is referring to has little to no use in physics.

[Anonymous No.10308316]

>>10308254
I remember that shitpost.
>>10308301
>that's the joke
>>10308083
Functional analysis.

[Anonymous No.10308355]

>>10308316
>I remember that shitpost.
i mean, mate, it was 2 /mg/ threads ago

[Anonymous No.10308360]

>>10308316
Well yea, but it's weird as group theory is actually fundamental for physics.

[Anonymous No.10308418]

I just came up with what seems to be a useful logic for what I'm working on.

It's based on the idea of a Boolean ring except it's actually a semiring and there are three elements: 0, 1, and ω. 0 and 1 interact with * and + like you'd expect, and ω is an annihilating element for both (except that ω * 0 = 0). Now, this semiring is well known to linear logicians but I haven't seen it used in the way I'm proposing. In the logic, conjunction corresponds to * and disjunction corresponds to +. 1 is true, and 0 and ω are both false. So when you have a clause like A + B + C then for it to be true exactly one of A, B, or C have to be true. Indexed disjunction is of course uniqueness quantification ∃!. Conjunction and universal quantification are standard. It seems to be an intuitionistic logic since there is no clear choice between 0 and ω for interpreting ⊥ and ¬.

Does anybody know if this is some established system so that I can look into it instead of having to figure more stuff out myself?

[Anonymous No.10308461]

>>10308418
Equivalently, it's the natural numbers semiring where ω stands for any natural number besides 0 or 1.

[Anonymous No.10308557]

I had to do a dumb exercise for my discrete maths class that involved looking at the remainders of 2^(n-1), for 2<n<20 and finding patterns
Obviously for primes the remainder would be 1 and for powers of 2 it would be 0.
Then I noticed that for composite numbers of the form 2p, p prime the remainder would always be 2. I proved it using FLT
Similarly for numbers of the form 4p, the remainder would always be 8
I decided to look at numbers of the more general form (2^k)p starting with k=3. I checked that for p=3 and 5 the remainder was 8 and set out to prove the general case but couldn't go far. I realized that the case k=3 wasn't so regular as for p=7, the remainder is 16. I tried k=4, 5 next and it seemed like there was no regularity in the remainders
So I decided to write a code that would print all the remainders given a k and for all primes between 2 and 217
For k>3 there didn't seem to be any patterns at all but pic rel is what I got for k=3
modular arithmetic is weird

[Anonymous No.10308787]

Say I've got a family of six sets that satisfy the following:
1. the intersection of any two sets is non-empty
2. the intersection of all six sets is empty.
Pic related is an euler diagram of the family. Is there a name for something like this?

[Anonymous No.10308789]

>>10308787
scratch that euler diagram part, I think I fucked that up.

[Anonymous No.10308790]

>>10306477
>Race bait and IQ threads

And what it your issue with them. At least meaningful discussion is possible within them.

[Anonymous No.10308952]

>>10308790
No, it isn't.
Please provide evidence that these threads are worthwhile.

[Anonymous No.10309111]

How do I write that set contains all combinations of {0, 1}, for each length from one to N?
Like,
0, 1, 01, 10, 00, 11, 100, 010, 011, 001, ...

[Anonymous No.10309122]

>>10309111
[math]
\{ z \in \mathbb{Z} | 0 \leq z \leq 2^N - 1\}
[/math]

[Anonymous No.10309395]

>>10308083
Shoo shoo appliedfags

[Anonymous No.10309409]

>>10308952
Kek, what do you want, a study? Those threads are always the most lively and active, meaning it’s a topic people care about to discuss

[Anonymous No.10309421]

Should I just stick with my computation heavy Linear Algebra text (Lay) for my class, and then go rigorous afterwards, or try to do both at once? If so what book?

[Anonymous No.10309435]

MATHEMATICS IS INVENTED BABY

[Anonymous No.10309561]

>>10309409
Yes but the people in them are morons.
Furshit threads may be lively on /v/, does that mean they're good for discussion?
Racebait threads are pretty much the same thing, because no matter how often you explain to people the simple sociological fact that race is a social construct, people continue to shitfling like the troglodytes who still don't understand evolution.
The board should purge all threads about race and iq, because they're made by self serving /pol/tards and kill other productive threads. Remember, this is a slower board, so threads on the last page are not dead. And shitty new threads often last for more than a week.

[Anonymous No.10309567]

>>10309122
Incorrect, identifies 0 and 00.
>>10309111
The union from n=1 to N of {0, 1}^n

[Anonymous No.10309572]

>>10309421
Does your school offer a proof-based linear algebra course that you will be taking?
If not, that depends on your workload for the semester.

[Anonymous No.10309618]

>>10309572
I'm a brainlet CS major, but I like math (and am starting to do research in some graph theory stuff with network epidemics) so I like to be somewhat stronger on the fundamentals. I started to read Axler and struggled, so I wonder if I should just get through this book first then do a rigorous book. Thats sort of what I've seen people say online

[Anonymous No.10309651]

>>10309618
Yes, that makes more sense. Axler is generally a good choice. There are others, but they won't be any easier. Wait until you get deeper into the content though, because a lot of theoretical linear algebra intuition is built on the stuff in your class.

[Anonymous No.10309658]

I'm here to report that the representation theory book by Fulton and Harris is a [math]MEME[/math].

This is much better. Fulton and Harris is not even readable.

[Anonymous No.10309667]

>>10309618

[Anonymous No.10309765]

>>10309667
If he struggles with Axler what makes you think he can follow Hoffman and cunt

[Anonymous No.10309803]

>>10309658
rep theory is a meme to begin with

[Anonymous No.10309810]

>>10309765
It's better written

[Anonymous No.10309915]

>>10309810
retard

[Anonymous No.10309916]

>>10309915
no u

[Anonymous No.10309953]

>>10306396
An idea. Like a post but without a third eye.

[Anonymous No.10309985]

Is it bad practice to call most of your results corollaries instead of, say, propositions or theorems?

Most books usually trivialize their theorems by proving lemmas beforehand, so they turn out to be corollaries.

[Anonymous No.10309995]

>>10309985
I usually consider that theorems are worth memorizing, lemmas are stepping stones to theorems, and corollaries can be proved in two lines max from theorems.

[Anonymous No.10310005]

>>10309995
It's just that the book I'm reading right now has like 6-7 corollaries stringed in a row, although you are right, they do follow trivially from the theorem before it. But also there's like a discussion, then a definition, then a corollary following from definition. Why not just call it a proposition or lemma?

[Anonymous No.10310014]

>>10308787
Don't know the name but here is an example of the situation: 5 disks have a non empty union (they share the star) and the yellow ring have a non empty union with every disk.

[Anonymous No.10310015]

>>10310005
>corollary of the definition
Surreal. I've honestly never seen such a thing.

[Anonymous No.10310016]

>>10310014
Forgot the image...

[Anonymous No.10310017]

>>10310015

[Anonymous No.10310020]

>>10309985
Nobody cares what you write on your homework, no

[Anonymous No.10310024]

>>10308787
If I had to name it, I'd call it a collar.
So solid 40% chance that's the name, 40% it has no name, and a final 20% that it has a stupid name.
>>10310017
>the set S(E) of d+1 dimensional subspaces of E
The Grassmanian?
Honestly what book is that?

[Anonymous No.10310025]

>>10305931
hi anons, im a complete brainlet when it comes to math, i find force memorizing algorithms boring, is there any materials you guys could point me to to get a good solid idea of what math is about

[Anonymous No.10310033]

>>10310020
I've already submitted my master's thesis but thanks
>>10310024
>The Grassmanian?
you could call it that, yeah
>Honestly what book is that?
Analytic projective geometry by Casas-Alvero
>>10310025
Ian Stewart Concepts of modern mathematics

[Anonymous No.10310046]

>>10310033
>I've already submitted my master's thesis but thanks
>lying on an anonymous undergrad board

[Anonymous No.10310058]

Hey guys, what do you think about Flammable Maths?

https://m.youtube.com/watch?v=WP8JMVGuOD8

Do you know some other nice channels like this one?

[Anonymous No.10310060]

[Anonymous No.10310062]

>>10309667
This looks like a linear algebra bumper sticker

[Anonymous No.10310066]

>>10310058
it's sort of funny, but too much calculus
like what engineers think is cool math

[Anonymous No.10310068]

>>10308787
The graph is a cycle graph aka a circular graph.
The graph is called the intersection graph of that collection of sets, so you could say it's a collection of sets with a cyclic intersection graph. There's probably a proper set theory name for it.

[Anonymous No.10310088]

>>10310046
I didn't get my transcripts for my last year (masters) cos it costs money to get them, so those are the ones i used for my PhD application after my 3rd year.

Grades that are not shown:
Project: 78
Topics in alg+geom: 63
Riemannian geom: 98
Analysis IV: 88
Alg. top: 93

[Anonymous No.10310109]

>>10310088
lmao posting your grades on 4chan, are you fucking 10 or something

[Anonymous No.10310113]

>>10310109
The guy didn't believe me, so I posted proof. Would you not ask for tits if I claimed to be a girl?

[Anonymous No.10310116]

>>10310088
>no algebra
Weird. Any reason?
>Riemannian
That's the fun shit. You used Chavel?

[Anonymous No.10310132]

>>10310116
I started doing physics but hated it and loved math instead. Still i couldnt switch fully to math. So in second year (when you get to do optionally algebra) I had a clash with a physics course and had to do it instead. I ended up taking algebra on my own during the summer and tested it during the resit period. Got 93% so they let me take courses with algebra as a prereq.

Also the 3rd year number theory is actually algebraic number theory, topology III also had intro to fundamental group, and topics in algebra and geometry was algebraic and elliptic curves. So I did do plenty of algebra.

[Anonymous No.10310134]

>>10310116
why would anyone bother with algebra?

[Anonymous No.10310138]

>>10310132
and Riemannian geometry used Do carmo*

[Anonymous No.10310140]

>>10310066

What's wrong with calculus/analysis?

[Anonymous No.10310158]

>>10310058
Why did he do a Laplace transform to solve an ODE with constant coefficients? You can surely just solve it using the usual method....

[Anonymous No.10310185]

>>10310158
>tfw variable separation, power series, Laplace and Heavyside are the only methods of ODE solving you still remember so you throw them at everything and hope at least one works
>>10310138
Chavel's "Notes and Exercises" are absolutely beautiful.
>remember this extrinsic definition? Gaze upon the intrinsic one.
>also vice versa
>check this dude out
>check this other dude
>prove this random old theorem
>lemme introduce you to length spaces for jokes
>>10310134
For fun.

[Anonymous No.10310187]

>>10310140
/sci/ thinks its not real math unless your transforming homophobic rainman surfaces

[Anonymous No.10310208]

>>10310187
>rainman surfaces

[Anonymous No.10310258]

>>10310140
analysis is beautiful and wonderful, but it's not just "lol what's this sum or what's that integral"
the theory of analysis is what's beautiful, single evaluations are boring and typically woefully unmotivated
>>10310187
fuck off, do not ever speak for me again. analysis is basically the only real field of math. and no, that's not a fucking pun. algebraists are all morons who play with building blocks, logicians are masturbating each other furiously, number theorists are long fucking gone, etc.
>>10310185
here's your typical algebrashit, their only justification for algebra is "it's fun." imagine being so mathematically immature you literally just play with toys all day.

[Anonymous No.10310264]

>>10310258
graph theory master race

[Anonymous No.10310269]

>>10310264
graph theory and combinatorics are arguably as beautiful as analysis due to the beautiful and colorful variety in the ways one can approach the theory
algebraic "combinatorics" is a blight on the entire field

[Anonymous No.10310296]

>Initial Theta Data - part 01 - Some Prerequisites, and The Easy Part of Initial Theta Data
https://www.youtube.com/watch?v=FTv5TnXR1HQ

[Anonymous No.10310300]

>>10310258
>lol what's this sum or this integral
Absolutely undergrad, zero respect for the special functions, incredibly shameful and embarassing.

[Anonymous No.10310307]

>>10310296
>epileptic curve over uhhh uhhh uh uh uhhhhhhhhh L is uhhhh is a....is...was..uuhhhh curve over l naught

[Anonymous No.10310341]

>>10308083
Solve a rubix cube with group theory

[Anonymous No.10310367]

>>10310300
those of his videos which deal with special functions / cool transforms / neat ways of looking at these evaluations are great. it's when he takes 20 minutes of parts and differentiation under the integral sign when one could quickly apply the residue theorem that annoys me. that's not what analysis is like. we don't just do integrals with more and more cosines in them.

[Anonymous No.10310421]

Math is actually pretty fun.

[Anonymous No.10310532]

>>10309985
I use "corollary" only when dealing with consequences of theorems which are worth noticing but should not be included in the statement of the theorem itself. Something which has a name or that is a key point is "theorem" (except proper lemmas such as "Lebesgue's number lemma"). Lemma when an argument is often (>=2) used in other proofs, or to make easier to state and prove part of a proof (eg. when it can make the notation easier). The other results are "proposition".
I also like custom names; in latex, using ntheorem, I made a 'block' environment so that I can write things like
\begin{block}[Anon's theorem], or
\begin{block}[Properties of unuseful stuff] \
\begin{enumerate}

[Anonymous No.10310621]

>>10310532
I don't really see why some impressive results are called lemmas. Like Yoneda's lemma, Urysohn's lemma, Gauss' lemma, etc

[Anonymous No.10310632]

>>10310621
They aren't necessarily that epic themselves, but they can be applied to various cases to provide impressive results.

[Anonymous No.10310635]

>>10310621
Maybe they were lemmas in their own works, and so they were referred as such by others. Not sure about that.

[Anonymous No.10310648]

>>10310632
umm, Zorn's lemma is not epic?

[Anonymous No.10310651]

>>10310621
yoneda is a tautology. urysohn isn't particularly interesting by itself, but does a lot of interesting things.

[Anonymous No.10310657]

>>10310651
Every result is a tautology in the right setting after all, following the rules of logic...

[Anonymous No.10310663]

>>10310648
Not really. It just states that a maximal element exists. What is epic is when you apply that to a product of compact spaces and deduce the product is compact etc.

[Anonymous No.10310670]

>>10310663
im sorry, but every vector space having a basis is epic, as is every ideal contained in a maximal ideal, as is an algebraic closure existing, and the best part is they're equivalent (except the last one)

[Anonymous No.10310679]

>>10310670
so you're saying that zorn's lemma is not epic, but it's equivalents are.
fuck off then
in any case, it should be zorn's axiom, though lemma sounds better.

[Anonymous No.10310695]

>>10310670
>but every vector space having a basis is epic
This is only true if you assume it to be true.

[Anonymous No.10310700]

>>10310621
>Urysohn's lemma
Pretty sure I usually see it as theorem.
Also, it builds up to the T classification "theorem".
Also, lemma sounds nice attached to Urysohn-chan's name.
>>10310657
Really weird to say that about existence theorems, but sure.
>>10310679
>zorn's axiom
"Zorn's equivalence theorem".

[Anonymous No.10311026]

Does anyone know what the author means by this? "Exhaustive". Does he mean surjective? The author is possibly italian or spanish so perhaps someone that speaks them natively might know.

[Anonymous No.10311050]

>>10311026
>two sequential commas
Solid 60% chance his first language is either portuguese or spanish.
Anyhow, it means it's either the only morphism from P_n -L to T or that it's surjective.

[Anonymous No.10311060]

>>10311050
Yeah, it's surjective. I read a bit further ahead and there was an argument where he used it again and it was obvious that it meant surjectivity. Weird, because this is 30 pages into the book, and has used "onto" every other time before.

[Anonymous No.10311140]

>>10309561
>no matter how often you explain to people the simple sociological fact that race is a social construct

Ah, of course. Naturally someone like you would be against 'race bait' threads, since you'd rather ignore the evidence that there is likely a significant genetic factor to IQ and that this can be demonstrated with studies showing differences between various ethnically differentiable sub-populations (regardless of how much of an arbitrary social construct 'whiteness' or 'hispanicness' is). You genuinely are simply against people with different views than your own since you suck at arguing against the more substantial positions and want to ban shit that bothers your feelings. You are an anti-science knucklefucker.

[Anonymous No.10311512]

>>10311140
Name the gene(s). Otherwise you have no argument.

[Anonymous No.10311524]

>>10310670
Which is an example of how to use the lemma to get something nice. Read >>10310679 and die.

[Anonymous No.10311531]

>>10305931
What is standard basis of non euclidean space?

[Anonymous No.10311535]

>>10311531
(1, 0, ..., 0), (0, 1, ..., 0), ..., (0, 0, ..., 1).

[Anonymous No.10311556]

>>10311535
What is space dimension? R infinite?

[Anonymous No.10311563]

>>10311556
Does that look infinite to you?

[Anonymous No.10311566]

>>10311563
How many axes does that ... represent?

[Anonymous No.10311569]

>>10311566
As many as there are.

[Anonymous No.10311572]

>>10311569
how many are there?

[Anonymous No.10311576]

>>10311572
However many dimensions you have -3. This would be obvious unless you are an idiot.

[Anonymous No.10311723]

>>10311512
https://www.newscientist.com/article/2163484-found-more-than-500-genes-that-are-linked-to-intelligence/

You know damn well that I can't gives you specific, isolated genes that specifically make population x more intelligent than population y, but also that this isn't necessary and that lack of specifics doesn't refute the idea of g-loaded intellectual ability differing meaningfully between groups of people, or that genetics are likely a significant factor. I don't believe that you are arguing in honesty and simply want to feel superior to all the shitheads on /pol/ via any means you can.

[Anonymous No.10311825]

Not sure if this is the right thread for such a question, but is there a need for mathematical rigor in physics?
It seems that physicists are often criticized for overuse of approximation or a lack of rigorous methods.
I personally have an easier time understanding mathematical abstraction than physical phenomena, but I still aim to study physics. Am I setting myself up for disappointment?

[Anonymous No.10311865]

literal retard question but does [math]\frac{\Delta TR}{\Delta Q}=\frac{d}{dQ}TR(Q)[/math]

[Anonymous No.10311883]

>>10305931
>she

[Anonymous No.10312022]

What is the most underrated or unpopular field in math?

[Anonymous No.10312042]

>let [math]\mathbb{K}[/math] be a field ([math]\mathbb{K} = \mathbb{R}[/math] [math]or[/math] [math]\mathbb{C}[/math])

[Anonymous No.10312055]

>>10311865
Nah.
>>10312022
Classical Microeconomics.
>>10312042
Who are you quoting?

[Anonymous No.10312067]

>>10312055
retards who can't understand a proof if the field isn't a subfield of [math]\mathbb{C}[/math]

[Anonymous No.10312070]

>>10312067
Are you sure the proof didn't use completeness and characteristic 0?

[Anonymous No.10312092]

>>10312070
no, the course was about polynomials and most theorems were true even when considering an integral domain.

[Anonymous No.10312149]

>>10310341
does group theory really help you solve a rubix cube better than just memorizing algorithms

[Anonymous No.10312155]

>>10312042
>let [math]k[/math] be a field of characteristic coprime to [math]6[/math]

[Anonymous No.10312168]

whats the abc conjecture

[Anonymous No.10312178]

>>10312168
>whats the abc theorem
FTFY.

[Anonymous No.10312208]

>>10311512
you dont understand genetics

[Anonymous No.10312230]

>>10311723
>You know damn well that I don't have an argument.
I am aware.

[Anonymous No.10312251]

>>10312055
>Microeconomics.
But it doesn't look like math.
Pls anon tell about underrated math.

Secretly I like probability but it is not math and too overrated. It will be fine without brainlets like me.

[Anonymous No.10312286]

>>10312149
Well, group theory helps in developing the algorithms in the first place. If you define "better" in terms of speed, clearly using memorised algorithms is going to be faster than devising a solution from basic principles.

[Anonymous No.10312367]

>>10311825
Physics is for morons and shitheads.
>>10311140
Listen, I don't give a shit what you think or how oppressed you seem to think you are because of scientific taboos. This is the math general. I apologize for bringing that into this thread, and I'd appreciate it if you'd stop, because it's just obnoxious.
I really don't care at all who is "right." I just don't really see why it matters so much to some people.

[Anonymous No.10312381]

>>10312367
>Physics is for morons and shitheads.
Your source for that being?

[Anonymous No.10312406]

>>10312381
>Your source for that being?
Reality.

[Anonymous No.10312513]

>>10312381
physishits study literal meme science and pull trash out of their asses
mathematicians respect rigor and truth

[Anonymous No.10312538]

>>10312513
>pull trash out of their asses
Like what? What is it about physics that lacks so much rigor?

[Anonymous No.10312546]

I have an exam tomorrow on algebraic topology.
Time to rethink my life choices.

[Anonymous No.10312553]

>>10312538
why are you here? isn't there a physics general open?
honestly, my field is fucking PDEs, so i have to interact with physics research on the regular. it's embarrassing.
>>10312546
algebraic topology is a trivial consequence of category theory.

[Anonymous No.10312574]

Let [math]X[/math] be a Banach space and [math]\phi \in X^*[/math] a continuous functional in the dual space. Is the set [math]\{ x \in X : \phi(x) \leq 1 \}[/math] weakly compact? If not, what do I need for weak compactness here?

[Anonymous No.10312575]

>>10312574
I meant [math]|\phi(x)| \leq 1[/math] of course

[Anonymous No.10312577]

>>10312553
I didn't have category theory. It's embarrassing I already failed functional analysis. Should probably review my notes instead of posting here rn.

[Anonymous No.10312594]

>>10312574
if it's reflexive then alaoglu

[Anonymous No.10312602]

>>10312553
>my field is PDEs
Honestly why did you do this to yourself?

[Anonymous No.10312686]

>>10312602
cause they're fun

[Anonymous No.10312774]

Am I correct in saying that the character of any irreducible representation of this group should be constant because it's an abelian group and has only one conjugacy class?

Am I correct to think of this this group as m by m matrices with +/- 1 valued diagonals?

I am not confident this construction is irreducible because that would make the trace take more than two values.

[Anonymous No.10312824]

>>10312553
>it's embarrassing.
You still didn't say why.

[Anonymous No.10312865]

>>10312824
Because physicists are egoistic dumbasses who just assume their bullshit math is correct without justifying it properly. Everything a modern physicist does is pure empirical speculation. Newton, gauss, and lagrange did more than enough for physics, no one else should have bothered afterward. And they did it correctly.

[Anonymous No.10312881]

>>10312774
>Am I correct in saying that the character of any irreducible representation of this group should be constant
No
>abelian group
>only one conjugacy class
not happening

>Am I correct to think of this this group as m by m matrices with +/- 1 valued diagonals?
Yes

[Anonymous No.10313073]

>>10312022
Algebra
Algebraic Number Theory
Algebraic Geometry
Several Complex Variables
Category Theory
Knot Theory

[Anonymous No.10313131]

>>10312251
You don't think probability is math? Do you know measure theoretic probability?

[Anonymous No.10313141]

If we have a default orthonormal basis {i, j, k}, can a vector be represented with reals? Like, v = 0.5i + 0.01j + 3k?

[Anonymous No.10313168]

>>10313073
algebra isn't underrated, it's shit
algebraic geometry is literally the current overrated meme field
any number theory is also an overrated meme, though i'll admit algebraic number theory is less common than other forms
several complex variables is the only correct one on that list

[Anonymous No.10313171]

>>10313141
yes of course
what do you think a basis is?!
every vector can be represented uniquely as a linear combination of the basis

[Anonymous No.10313181]

>>10313171
Well, I am brainlet, thought that coefficients could only be in N.

[Anonymous No.10313187]

>>10313181
oh, no. that is an important subject though! in linear algebra, we only care about coefficients in a field though (like R). coefficients in a ring (like Z) are a different object.

[Anonymous No.10313197]

>>10313168
Why algebra is shit though? Why's algebraic geometry a meme? You just make those baseless claims but provide no arguments whatsoever.

[Anonymous No.10313198]

>>10313141
Depends. Is the vector space over the reals?

[Anonymous No.10313263]

>>10313197
algebra is shit because it's not real math, it's just children playing with building blocks.
"wook mummy! a commudadive wing! pwime ideals, mummy!"
algebraic geometry at least applies algebra to something respectable, but it is by no means overrated. it's the current popular field for undergrads to go "im gonna be an algebraic geometer when i grow up!" and it will be oversaturated in 5 or 6 years. it's not a bad meme, but it's a meme.
it's also a meme because of this guy. i mean god damn. how can something that started so concrete become so fucking abstract.

[Anonymous No.10313291]

>>10313263
>>10310258
Tooker was at least a mildly interesting schizo.

[Anonymous No.10313335]

>>10306112
Wait a second, I know that gay infinite with a hat...

[Anonymous No.10313336]

>>10313263
What the hell? If it wasn't "real" mathematics (who let you decide what real mathematics is anyway?) If Algebra was such a "children playing" thing then why there are so many algebraists? Why is Algebra present in almost all (if not all) math degrees? Your post says more about your own insecurities on algebra than algebra itself.

[Anonymous No.10313345]

>>10313291
>>10313336
you people from reddit or something? /mg/ tradition is to shit on anyone who likes what you don't like. i don't love algebra but i don't actually give a shit.
it's like it's your first day on this website.
alg geo is still a meme for the stated reasons, though.

[Anonymous No.10313359]

>>10313345
>I can complain about whatever I want, but if you call me a schizo or complain about my complaints you're clearly fro reddit

[Anonymous No.10313374]

>>10313345
I'm new to this board actually. So, in the end this is the same as /pol/ and /lit/, full of self-entitled cunts that are actually very insecure. This place should be different than the rest of 4chan, this is where the honestly intellectuals should gather to exchange their ideas in a respectful manner, not circlejerk about fields of mathematics they like and don't like.

I will change this board.

[Anonymous No.10313385]

Basically you can approximate Pi by counting collisions between billiard balls and a wall.

https://www.maths.tcd.ie/~lebed/Galperin.%20Playing%20pool%20with%20pi.pdf

Thought it was neat to know in case you need to impress some qt(#nrofcollisions) math gf.

[Anonymous No.10313480]

>>10313374
There is no "exchange of ideas" in mathematics. You're either right, wrong, or being a pedantic autist.

[Anonymous No.10313484]

>>10313263
spotted the brainlet

[Anonymous No.10313489]

Are there any math books suited for light reading? I'm looking for something to read before falling asleep, so something which doesn't make my head spin too much would be nice

[Anonymous No.10313517]

>>10313489
I was a fan of Elements of Mathematics by Stillwell, its basically an introduction to higher math.

[Anonymous No.10313537]

>>10313187
oh, sorry, let me just throw away my book on linear algebra... Doesn't the author know Ext is 0 over a field??

[Anonymous No.10313546]

>>10313374
so you want this board to be like r/science?
i am serious enough when i do mathematics, thank you very much. i don't need to bring that level of discourse to the place i go to relax and have fun. that's not what 4chan is for.
>>10313359
we're all schizos here :)

[Anonymous No.10313551]

>>10313537
you can call module theory linear algebra all you want, but the vast majority of people are referring to the study of vector spaces when they say linear algebra.
what did you think i meant in my post when i said "another object"?

[Anonymous No.10313556]

>>10313480
Solving and proving hard problems is built on the exchange and sharing of ideas between people.

[Anonymous No.10313574]

>>10313551
Regardless, you made the dumb assumption that the vector space the poster was talking about was a real vector space. It could have well been over a field of small characteristic. He didn't specify where his orthonormal basis lived so a real representation would have been utterly wrong.

[Anonymous No.10313629]

>>10305931
Is there any book which has derivation for rotation of vector about an axis without linear algebra? Like with respect to geometrical properties of vectors?

[Anonymous No.10313651]

Can you all stfu about IUT unless you actually understand it

dumb weebs you add nothing to the conversation

[Anonymous No.10313661]

>>10313629
Here, you don't need a book. Consider a vector [math](a,b)[/math]. Then [math](a\cos\theta-b\sin \theta,a\sin\theta+b\cos\theta)[/math] is its rotation by [math]\theta[/math] degrees counterclockwise. Its derivation is obvious and left as exercise.

[Anonymous No.10313665]

>>10313651
thats not the fucking point, its news that the proof is still alive
hardly any mathematicians at all know a thing about IUT

[Anonymous No.10313697]

>>10313661
In his defense, the question was stupid.
>>10313629
No.
>>10313651
No one is actually discussing IUT.
>>10313665
/mg/ collaborative effort to produce an IUT textbook with graphs, Kurisus and touhous when?

[Anonymous No.10313702]

>>10313574
anyone using fucking i j k as a basis is working with R^3 moron

[Anonymous No.10313708]

>>10313702
Let [math]V=\mathbb F^3_{3^4}[/math] and define [math]i=(1,0,0), j=(0,1,0), k=(0,0,1)[/math] as the basis of [math]V[/math].

[Anonymous No.10313710]

>>10313697
>/mg/ collaborative effort to produce an IUT textbook with graphs, Kurisus and touhous when?
shit man im down, i can supply Patchy

[Anonymous No.10313714]

>>10313710

ok but nobody knows IUT.

typical weeb do-nothings

[Anonymous No.10313720]

>>10313708
sure, but that's nonstandard notation as far as i'm aware
the standard is for ijk to live in R^3
i don't know why you're so up in arms about this, i answered the guy's question

[Anonymous No.10313739]

>>10313714
Mochizuki does.

[Anonymous No.10313773]

>>10313714
then make a thread for learning it

[Anonymous No.10313835]

>>10313773

No, dont make a thread, just stfu and learn it

[Anonymous No.10313886]

>>10313835
youre the fucking one who wants people here to know it, despite it being near useless and massively complicated even to professional mathematicians

[Anonymous No.10314091]

anyone here can explain why category theory is needed in concepts in c++?
thought i might ask here since the 2 seems to intersect.

[Anonymous No.10314198]

>>10313131
I heard about measure theory. But there are folks who write tons of papers everyday in probability section on arxiv. It is scary sempai

[Anonymous No.10314456]

>>10314091
category theory and programming are both for idiots, so you can explain to a mathematician how stupid someone would need to be to learn something like c++ by giving the example of category theory, and you can explain to an engineer how stupid a mathematician would have to be to give formalism via categories by the example of c++ programmers.
it's a useful two way analogy.

[Anonymous No.10314499]

>>10314456
>tfw physicist
should i kill myself?

[Anonymous No.10314503]

>>10314499
no, even though i'm the "schizo" who hates physishits i would never wish that one someone

[Anonymous No.10314507]

>>10314503
>i'm the "schizo"
Schizophrenia is a spook.

[Anonymous No.10314615]

1, 5, 263, 58708, 66677, 5713030447...
I created my own well-defined sequence and it's not in the OEIS, cool.

[Anonymous No.10314882]

>>10312574
Phi = 0

[Anonymous No.10315361]

Does tr(IA^2 + B^-1A^2 + IA^-1) equal to tr(IA^2) + tr(B^-1A^2) + tr(IA^-1)? Could I simply assume so for every case?

[Anonymous No.10315389]

>>10314615
Well? What does it describe?

[Anonymous No.10315501]

https://www.youtube.com/watch?v=XB-EvNfkCMM wtf is this bullshit lads

[Anonymous No.10315510]

What do I lose by using an ARMA statistical model over an ARIMA one? I mean in practical application terms: I already ubderstand the theoretical difference between the two.

[Anonymous No.10315523]

>>10315510
IIRC ARIMA works better for long term.
>>10315501
Lad, literally what are you doing watching math stuff on youtube
>>10315361
tr(A+B)=tr(A)+tr(B)

[Anonymous No.10315880]

I need your advice, /mg/.

I'm a second year mathematics major (i.e., I've finished the undergraduate curriculum in mathematics) and I am supposed to spend a semester abroad. However, I don't know enough about foreign schools to make an intelligent decision. These are my options:
>Australia National University
>Kyoto University
>University College Dublin
>University College London
>University of Edinburgh
>University of Glasgow
>University of Melbourne
>Uppsala University
>Waseda University
>ETH Zurich
>A bunch of nowhere schools in Latin America and the Third World

Where should I apply?

[Anonymous No.10315949]

>>10315880
Wouldn't it be best to look at the homepages of those universities and look which ones have the most researchers in areas you like?
That said, you could always go to some Third World place and shitpost about it

[Anonymous No.10316118]

Hi boys, is there a name for a transformation from R3 to R2 where one would "unfold" the shape ? For example, a square would become pic related. Apologies if I don't have the correct terminology.

[Anonymous No.10316130]

>>10315880
Which nowhere third world schools? Some of them aren't so much nowhere as you would like to think.

[Anonymous No.10316138]

>>10316118
A chart.

[Anonymous No.10316161]

>>10316118

This is called a "net"

[Anonymous No.10316192]

>>10315880
Go to Kyoto university so you can be /mg/'s IUT correspondent

[Anonymous No.10316238]

Why are you using wolfram when you have sage

stop using wolfram

[Anonymous No.10316240]

>>10316192
This.

[Anonymous No.10316246]

How hard is multivariable cuckulus ?

I'm kinda worried about it because i'm also taking a math class called "Math foundations"

I thought it would be easy because I have a substantial discrete math background "off the books"

[Anonymous No.10316271]

>>10316246
do you have a brain? yes ? then no

[Anonymous No.10316285]

>>10316271

Ummm sweetie that was not a yes no question

[Anonymous No.10316307]

>>10316285
guess you dont have a brain

[Anonymous No.10316439]

>>10316246
It's easy. It's just normal calculus with more numbers. Hell, series was easier.
But the nicest thing about multivariable calc is that there once was a man named Cartan who got so mad at having to memorize Kelvin-Stokes that he created an entire new formalism that lets you generalize it, Green's, and higher dimensional analogues to [math] \int _{\partial D}f= \int_D df[/math].

[Anonymous No.10316464]

>>10316246
it's very very easy if you know your calc 1 and parts of 2 well and you can visualize stuff.
the only conceptually nontrivial bit is the very end with vector calculus, which is still pretty simple.

[Anonymous No.10316476]

The Kodaira Kombo for Komplex Analysis.

[Anonymous No.10316487]

>>10316476
The Daoist Disciple of Dynamical Systems.

[Anonymous No.10316621]

>>10316192
I am entirely too much of a brainlet for that.

>>10315949
A good suggestion, but I don't know what I like. Even if I did, I don't have the knowledge required to assess the schools in comparison to each other.

>>10316130
They are
>UNIVERSIDAD TORCUATO DI TELLA - Argentina
>BOND UNIVERSITY - Australia
>PONTIFICIA UNIVERSIDADE CATOLICA DO RIO DE JANEIRO - Brazil
>UNIVERSIDADE FEDERAL DE MINAS GERAIS - Brazil
>UNIVERSIDADE FEDERAL DO RIO GRANDE DO SUL - Brazil
>PONTIFICIA UNIVERSIDAD CATOLICA DE CHILE - Chile
>FUDAN UNIVERSITY - China
>TSINGHUA UNIVERSITY - China
>UNIVERSITY OF TAMPERE - Finland
>MICEFA - France
>CHINESE UNIVERSITY OF HONG KONG - Hong Kong
>UNIVERSITY OF HAIFA - Israel
>HANYANG UNIVERSITY - Korea
>INSTITUTO TECNOLOGICO AUTONOMO DE MEXICO (ITAM) - Mexico
>ITESM CIUDAD DE MEXICO - Mexico
>UNIVERSIDAD NACIONAL AUTONOMA DE MEXICO (UNAM) - Mexico
>AL AKHAWAYN UNIVERSITY - Morocco
>PONTIFICIA UNIVERSIDAD CATOLICA DEL PERU - Peru
>UNIVERSIDAD DE CANTABRIA - Spain
>UNIVERSIDAD DE SEVILLA - Spain
>UNIVERSIDAD PONTIFICIA COMILLAS - Spain
>THAMMASAT UNIVERSITY - Thailand
>BOGAZICI UNIVERSITY - Turkey
>SWANSEA UNIVERSITY - Wales

[Anonymous No.10316627]

>>10316621
is there a place you want to go in particular?

[Anonymous No.10316628]

>>10316627
No.

[Anonymous No.10316636]

>>10316621
Don't come to Brazil. Specially if you're studying maths. Our curriculums are trash for undergrad. Unless you're american, then they're normal.
China is also an absolutely horrendous idea.
I imagine Chile is comfy. Spain is probably also comfy, but I'd try for 'Straya in your shoes.

[Anonymous No.10316694]

>>10316621
Spanish guy here
>UNIVERSIDAD DE CANTABRIA - Spain
Meh. Very mediocre, if not terrible. Worst weather in Spain, however, also best food in Spain.
>UNIVERSIDAD DE SEVILLA - Spain
Probably one of the best in your list if you're after a good time. Education-wise probably not so great, but so are the others. I've never heard of anyone saying they regret going to Sevilla
>UNIVERSIDAD PONTIFICIA COMILLAS - Spain
DO NOT GO HERE if your skin colour is something other than white, as well as if you don't speak Spanish. Well, don't go here if you're a foreigner, period. I have a good 5-6 friends that go there and say exchange students have the worst time. Everybody that goes here is at least a mild xenophobe and racist, and they're mostly kids that got in through their connections (daddy), and are very posh and preppy.

[Anonymous No.10316731]

>>10313168
real anal*st spotted

[Anonymous No.10316895]

Brainlet here, give me an equation where a modified version of y=26x can have 5 taken away for every 3 numbers within x, rounding down to a whole multiplicity of 3 (ei if x=1, 2, 3, 4 ,5, 6, 7 then y=26, 52, 73, 99, 125, 146, 172), preferably something that can be done on a conventional scientific calculator.

[Anonymous No.10317116]

>>10313263
based

[Anonymous No.10317262]

>>10316238
This

[Anonymous No.10317345]

>>10316731
Got a problem with that, shithead?
The continuum is easily the most interesting space one could deign to study.

[Anonymous No.10317363]

>tfw going to have my first real analysis lecture today

[Anonymous No.10317384]

>>10310113

[Anonymous No.10317446]

>>10315880
I would say do this, are there any branches of math or topics that you'd like to study but aren't served at your uni? If so, figure out which ones those are and which schools serve those courses during you semester abroad and that should narrow down your choices. If you're more interested in the different cultures, however, then I'd say ETH Zurich (certain areas of Switzerland are beautiful) or Kyoto (haven't been to Japan but I always wanted to go). Also, personally, I would front end my classes so that all my lectures and uni business would happen during three to four consecutive days, and then spend the rest of the week taking various mini trips. A small country with great transit like Japan is perfect for that stuff. Don't go to Australia. England is fine, but you need to know where to go, there are some great places to visit like Cotswold, but they're usually fairly far away. Other factors include the weather and city, if the weather and cities are shit it'll make the whole experience more miserable to say the least.

I would also say this, one great thing about study abroad is that you'll be able to make connections, I would say, once you find something you're interested in, contact one of the people at the university who does that (and ideally is teaching a course about it) and strike up a conversation. Just talk to them and mention you're interested in taking the class and what have you. The prof will know you at the beginning of the class and it'll help you stand out more. This is the place to try and build relationships with profs who can vouch for you later on if you make enough of an impression.

[Anonymous No.10317450]

>>10315880
>>10317446
It pains me to say this being the aspey that I am, but networking is pretty fucking useful. For me, I happen to work with an older guy who knows a ton of people and so a good chunk of the networking is done for me, but that can only last so long and at some point you have to force yourself to talk to people. Mos profs are pretty nice and willing to chat with you, just don't be too presumptuous and don't freak out if you don't get an immediate response. Worst comes to worse, you leave and never have to see those people again.

Also, you're in a new town, anon, put yourself out there (if you don't have a partner). Look my dude, you're presumably young, in a new place for a few months with no attachments, so live a little. You into European girls and chocolate? Go to Switzerland. You like anime shit and Asian girls? Japan is the plan my main man. Wanna visit some interesting historic areas and make new friends? Sky's the limit. Not saying you shouldn't be serious about your studies, but honestly, you can learn math anywhere provided you have a laptop and internet access. So take advantage of the change of scenery, nobody knows you so take a few chances, make some mistakes, really try and enjoy yourself.

[Anonymous No.10317521]

>>10317363
enjoy! real analysis is the best intro undergrad math class, hands down.
or if you don't enjoy every moment of it, go fuck yourself and switch to cs. we don't need more fucking algebraists.

[Anonymous No.10317537]

>>10317521
>real analysis is the best intro undergrad math class
I'm gonna say complex analysis is just as good, if not better, shit's magic.

[Anonymous No.10317605]

>>10317537
real analysis looks ugly but is beautiful underneath, because of how beautiful a lot of the ways we prove things end up being (and because so many of the results are just results in metric spaces / top spaces)
on the other hand, i found that complex analysis was a class with beautiful results but butt-ugly unimpressive computational proofs. i mean, as someone who took pdes before complex, yeah, we fucking get it. harmonic functions are very very nice. but it's really not that surprising that they are. and analytic functions are just special harmonic functions, so there's no reason for them to not be nice.
everything feels very trivial once you have cauchy riemann equations - cauchy's theorem, integral formula, residue theorem, laurent series decomposition, etc. and anything that isn't trivial is a fucking nightmare to prove - riemann mapping, picard's little and great theorems.
i could get my hands around everything in real analysis, but it was always fun. in complex, everything looked cool going in, but most of it turned out boring and the rest was too complicated to really get my head around. maybe i'll like it more as i get better at math and learn more nontrivial complex analysis, but for now it didn't feel like i grew at all from the class.

[Anonymous No.10317660]

Redpill me on the dark arts of recurrence relations.

[Anonymous No.10317710]

>>10316621
Avoid the Brazilian ones like the plague.

[Anonymous No.10317974]

This might be a dumb question, but is there a mathematical formalism that deals with lines connected to each other that have positive slope, negative slope, or are horizontal or vertical? I don't care about the exact slope of a line, but more about what it connects to.

[Anonymous No.10317988]

>>10317974
put another way is there something like topology where geometry sort of matters, but not really? Alternatively, I'm looking for something that lets me analyze the equivalence of 2d configuration spaces.

[Anonymous No.10318025]

>>10317974
Riemannian geometry. You'll need to know differential topology (any "smooth manifolds" or "differentiable manifolds" book works. Knowing differential geometry is nice, but not that much of a requirement (the requirements for differential topology are real analysis and topology)).

[Anonymous No.10318033]

Do numbers have an end? I have seen mathematical proofs, but they seem to rely on being able to "choose" numbers, which doesn't seem to imply that choosing numbers beyond a finite end is possible.

[Anonymous No.10318057]

>>10318033
You sound drunk and stupid.

[Anonymous No.10318097]

>>10318033

I will prove there is no largest natural number

First define the natural numbers:
-0 is a natural number
-For every natural number n, S n is a natural number

Now, let m be any given largest natural number. S m is a larger natural number. Thus we have a contradiction.

[Anonymous No.10318118]

>>10318033
>choosing numbers beyond a finite end is possible
You can't do that because of the induction axiom. If it can't be written as 1+1+1....+1 it isn't natural.

[Anonymous No.10318224]

>>10318097
You're implying that you were able to come up with that number that is larger.

[Anonymous No.10318229]

>>10317974
Can you concretize a bit more? Perhaps you're looking for projective geometry, or graph theory? What do you mean by connected? That they're incident? In projective geometry (specifically [math]\mathbb {RP}^2[/math]), every pair of lines is incident in exactly one place, and you have some sort of concept of slope that can be translated as the projective closure of an affine line.

[Anonymous No.10318231]

>>10318033
Yeah, it's called the axiom of choice

[Anonymous No.10318566]

Need some recommended literature for infinite dimensional projective spaces. Anyone know of any?

[Anonymous No.10318598]

>>10317605
Wew, I did Real analysis this past semester and really liked it, I think it's my favourite module so far. I was hoping to really enjoy complex analysis too, I hope we don't agree on that.

[Anonymous No.10318770]

>>10318598
I was hoping the same. Most people hate real and love complex. I think there's just something wrong with our heads.
After all, I love PDEs and they're awful.
Liking nice things is boring.

[Anonymous No.10319068]

Are any two n x n matrices with the same rank equivalent up to selection of basis?

[Anonymous No.10319184]

Need some help /mg/, I can't find any info on this on google and I need to know. A book I'm reading has the following:

>consider a quartic curve [math]C\subset\mathbb P^2_\mathbb C[/math] and a line [math]l\not\subset C[/math]
>[math]l[/math] intersects [math]C[/math] in 4 points (by Bezout)
Now there's the following statement:
>Let [math]C_l[/math] be the double cover of [math]l[/math] branched above the 4 points. Then [math]C_l[/math] is a smooth curve of genus 1.

I don't know any of these last notions. What is the double cover branched above the points? How is it a smooth curve of genus 1?

Please give me anything

[Anonymous No.10319193]

>>10319068
Depends on what you mean by equivalent.

[Anonymous No.10319201]

>>10319184
Should be here: https://en.wikipedia.org/wiki/Branched_covering
>>10319193
https://en.wikipedia.org/wiki/Matrix_equivalence
By the way, yes.

[Anonymous No.10319208]

>>10319201
It isn't there, I already read that. I need some construction of this double cover, and it's somehow a curve again?

[Anonymous No.10319250]

>>10313374
fuck off, no one wants you to come here and change it to what YOU feel it should be

[Anonymous No.10319253]

>>10313374
this site has always had low-quality discussion and you're delusional if you think anyone here is an "honest intellectual". As with everywhere online you'll encounter people who are quiet knowledgeable in some area but are also:
a) complete morons in any other area
and
b) complete assholes
/sci/ is especially guilty of (a) so I don't know what you're expecting to "change". You're probably a retard too, so welcome to the fray.

[Anonymous No.10319277]

>>10319253
Based, I literally know nothing about physics but I'm gonna keep calling physishits just that and BTFOing their seething little heads. At least I'm semi-self aware, unlike that guy.
Well, I don't know about self aware. But I'm not schizophrenic.

[Anonymous No.10319639]

What's your favorite ordinal, /mg/?

[Anonymous No.10319806]

>>10319184
So, here's the best I got, starting on page 514 of Vakil's book he talks about branched covering and explicit constructions of the curves.
http://math.stanford.edu/~vakil/216blog/FOAGnov1817public.pdf
Harris also does this in a more limited context on page 10
http://staff.math.su.se/shapiro/UIUC/curvesHarris.pdf
I think Harris illutrates the concept best, but this is the best analogy I can come up with. Take y^2-x=0 and the map that projects the curve onto the x-axis. Such a map is almost like a double cover on the interval [0,infinity] except there is a single, special point, occurring at x,y=0, where the pre-image of this point is a single point in the original curve, this is unlike the case of every other point on the interval in which the pre-image of a single point is two points (ya know, the double cover and all). The term "branch point" becomes kind of obvious looking at Harris' diagrams on page 10, they are the points from which the curve begins to branch out and the projection map finally starts acting like a double cover. So in the question at hand, what they are looking for are double covers that have that specific "branching property" at those points, i.e. if you look at the pre-image of the double cover at those points you only get a single point back and not two like everywhere else. If I were to hazard a guess, for what you're talking about, there is likely some projection map from your curve onto L that, at least to me, would be a double cover of L branched above the 4 points by construction. Gonna be honest with anon, I have absolutely no idea what the fuck I am talking about here, but I'm trying to cobble together some understanding of what your question is asking. I think these sources could help you a lot more than my hamstrung explanation. The wiki page here
https://en.wikipedia.org/wiki/Riemann%E2%80%93Hurwitz_formula
appears to make sense as well. Sorry my dude, this is the best that I can do, my field is harmonic analysis.

[Muhammed Abobou No.10319998]

>>10318033
Numbers have an end.

[Anonymous No.10320053]

>>10319184
The easiest way to think about this is using Euler characteristics.
You start with a line in P^2 (genus 0 and thus characteristic 2) you take away the four points (char = 2-4 = -2) take a double cover (char = -2*2=-4) and then put back the four ramified points (char = -4 + 4 = 0)
The cover is smooth projective and has Euler characteristic 0, which means it is a genus 1 curve.

[Anonymous No.10320112]

>>10319639
Probably Church-Kleene

[Anonymous No.10320177]

>>10318770
I love integrating random integrable functions, unless the trick is too easy too to spot, so I at least expect to like those bits in complex analysis.

[Anonymous No.10320354]

what was the source, person and/or institution that you learned the most mathematics from?

[Anonymous No.10320356]

How to study mathematics by yourself? While approaching a task, what would you do if you stuck? My level is about calculating the multidimensional limits, kind of understand SVD, maybe if I struggle hard I'm going to reminisce what is the isomorphisms.
So it's not completely zero, but not worth a shit. And I study Applied Math, didn't manage to bother and now suck dicks. Full of regrets. It's been three years already, and one year is left.

[Anonymous No.10320363]

>>10319806
I get the general gist of it, but I'd need to see some more concrete construction to understand what specifically is this curve that happens to branch over 4 points and is smooth.

>>10320053

Pretty lost here sorry

[Anonymous No.10320444]

>>10319998
>Numbers have an end.
Source?

[Anonymous No.10320451]

>>10320354
libgen.io
>>10320356
If you can't solve something, reread the theorems and examples in the chapters. Math books basically spoonfeed the reader while he complains they're hard.

[Anonymous No.10320611]

>>10320177
Oh, well I fucking hate that. Enjoy. That's what the class ends up being.

[Anonymous No.10320620]

>>10305931
(((scholze))) btfo. the jew fears the samurai

[Anonymous No.10320689]

>>10313073
>Algebra, Algebraic Geometry, Category Theory, Knot Theory
literal memes
>Algebraic Number Theory
actually underrated
>Several Complex Variables
why

[Anonymous No.10320692]

Thoughts about records? Please no meming.

[Anonymous No.10320783]

b-based?

[Anonymous No.10320806]

Is it true that the ideal generated by a polynomial in two variables is prime if the polynomial is irreducible? I know this is true for single variable polynomials, but I'm not sure for higher variable ones since there's no simple division algorithm (or rather, no uniqueness unless special circumstances).

[Anonymous No.10320819]

>>10320806
You have a commutative ring with unity, which means a maximal ideal is prime. Is the ideal generated by an irreducible polynomial maximal?

[Anonymous No.10320826]

>>10320819
>>10320806
Nevermind, I'm working over a UFD (polynomials over a field) and the answer is obviously yes

[Anonymous No.10320907]

>>10318025
shit
>>10318229
As in line segments with endpoints connected to each other. Yes I would say it could be a graph. I am doing this because I am trying to find a way to abstractly describe 2d configuration spaces and reason about trajectories upon them. Because of this requirement the graph must not have any intersecting edges. Although the graph is allowed to be placed on a cylinder or torus. I say reason about trajectories to mean, determine if a particle restricted to move on these line segments will end up at a specific location(arc or node) when a 'force' or sequence of forces is applied. For example if we apply a force positive Y, our particle can move along diagonal and vertical segments, but not horizontal ones. This might be too much to ask, but I'm also trying to figure out relative distance along Y. If I know that point a and b are connected with a line with positive slope, then I can reason about their relative positions. And maybe I can use this to determine if a sequence of lines with different slopes can connect two points seperated by a Y increment.

[Anonymous No.10320930]

>>10316487
Fun Analysis with Fredholm!

[Muhammed Abobou No.10321082]

>>10320444
I urge you, brother, to look to the forest. Do the trees grow to the heavens? No, therefore, numbers have an end. Now look to your children and exclaim "Numbers have an end", for we must be prophets of wisdom to the young.

[Anonymous No.10321090]

>>10320354
gen.lib.rus.ec
>>10320689
>why
how can you not get it

[Anonymous No.10321666]

Why are there so few women in pure mathematics relative to applied math and actuarial "math"? Are they not autistic enough?

[Anonymous No.10321707]

>>10321666
>Are they not autistic enough?
Yes.

[Anonymous No.10321734]

>>10321666
Unlike in physics, CS, and similar fields, where women are usually discriminated against, heckled, laughed at, because of their gender, because of heteronormative and patriarchal tendencies, in pure math, there is no such behaviour. Instead, they are discriminated against by their own stupidity.

[Anonymous No.10321780]

>>10321666
I know a pure math girl. She's beautiful, smart, a sweet selfless person, has the same hobbies I have. She's pretty much perfect. We see each other everyday because we're working on a project together (not math related), and as the days are passing, her place in my heart just gets bigger and bigger.
Too bad we're both in a relationship with other people.
Thanks for listening, Satan.

[Anonymous No.10321813]

>>10320783
We have daily math department tea and small catered snacks once in a while.
What does your department do to relax and take a break, /mg/?

[Anonymous No.10321823]

>>10321666
Most people in math departments are pretty old. The proportion is rising, but there's a slow turnover rate in academia.
I think this will take a few generations of mathematicians to resolve itself, but eventually the proportion will be somewhat closer to equal.

[Anonymous No.10321829]

>>10321813
That sounds comfy anon, mine doesn't really do anything like that. Or if it does I'm never invited.

[Anonymous No.10321833]

>>10321780
>he has a girlfriend but still complains
>>10321823
>a few generations
Dubious.

[Anonymous No.10321836]

>>10321829
Well, technically ours is for the graduate students and professors, but if you pretend to look like you know what you're doing no one asks.

[Jagresh Abibi No.10322020]

>>10321082
Thank you, brother. I see the light now.q

[Anonymous No.10322289]

>trying to generalize result from a paper to a slightly different case
>realize original proof contains an error
>not immediately clear if it's possible to fix or if the whole proof strategy is hopeless
what the fuck do I do now? the paper is by a fairly big name as well

[Anonymous No.10322344]

>>10322289
>realize original proof contains an error
>paper is by a fairly big name as well

be very, very, very certain you're right

[Nierja Aslaam No.10322844]

>>10321082
I have seen the light. Thank you.

[Anonymous No.10322961]

>>10321082

[Baleshk Achachachach No.10323292]

>>10321082
Blessings be upon you, brother. I now see the truth.