/sci/ - Science & Math

>>11588370
>formerly >>11584605
Where was the mathematics in that thread?

>>11588378
Let's just forget it existed.

>>11588378
Ehhh, there was some hidden here and there.
BTW, this dude asked for a summary of inverse problems for PDEs and I gave him a shitty reply about it.
Anyone wanna hold his hand through it?

>>11588385
It was this Groetsch, btw.
https://libgen.is/book/index.php?md5=D1CF25E86766543D90E2D8C458831BE6

>>11588370
>Anti-Racism edition
brb making another one

>>11588370
>Anti-Racism

and you guys claim to be high IQ kek

>>11588370
>Anti-Racism
Why the whitephobia?

Brazilian edition more accurately

>>11588370
>Anti-Racism
Cringe and bluepilled

>>11588370
here's some mathematics

>>11588460
top kek

>>11588460
which state is that one dot that's 4x higher than everybody else on everything

what do i need to understand grunts algorithm and his thesis?

>>11588460
>0.81

L-M-A-O

>>11588370
>anti-racism
Nah being a math teacher at a highly diverse school will make anyone a little racist

>>11588502
Only if you are low IQ. Look at Einstein.

Is there a solutions manual with in depth explanation for Principles of Mathematical Analysis by Rudin?

>>11588460
Is it not possible that they are poor and unemployed due to racism?

>>11588540
And what highly diverse school did he teach at?

>>11588543
yes

>>11588543
There is indeed a solutions manual around there, it's 160 pages if I remember correctly, don't know if it has in depth explanations though.

>>11588553
Did you even look at the labels?

>>11588554
The one in OP pic

>>11588561
Yes. And?

>>11588553
>racism
Can you quantify that? Or are you just blaming stuff of an ominous label for which you have no evidence that it is causing these discrepancies.

E.g. can you demonstrate that blacks commit crimes on a very large scale because they are racially discriminated against?
Any data at all?

>>11588562
Giving a seminar is not teaching
>>11588567
Then it should be obvious. Poverty, unemployment, and education had no correlation to crime, while race% has a strong positive correlation. Your argument was that they had a higher crime rate BECAUSE of unemployment and poverty BECAUSE of racism, but that is not true BECAUSE there is no strong correlation between unemployment and poverty and crime.

>>11588578
There are lots of studies that show modern day discrimination for housing, loans, and criminal justice, all else being equal. And then there is very recent, on-the-books discrimination in the form of redlining, Jim Crow laws, the War on Drugs, and environmental racism (lead exposure, air pollution, etc).

>>11588595
>
Imagine being this low IQ to buy this shit

>>11588585
Even analyzed retardedly by putting states as data points for some reason, there are still correlations for each individual factor. Each individual factor is rarely experienced on its own, and especially true for black people, who are likely to be poor, unemployed, less educated, and many many other factors simultaneously. Adding all these together obviously makes the correlation stronger, that's common sense. And I submit the possibility these are due to racism.

>blacks are just poor

>>11588605
Imagine believing in science K-E-K

Threadly reminder to work with physicists.

>>11588585
>Giving a seminar is not teaching
What is it doing?

If I want to find the eigenvalues of a linear transformation, like T(A)=BA, can I take the results of the transformation by using the standard basis of A then setting the results into columns, then finding the eigenvalues of that matrix?

>>11588562
That's a 100% black college, how is that diverse?

Guys, this is /mg/, drop the derailing, political and racist comments and talk maths, I'll start reporting you if you don't stop

the picture is a good representation of a fake jew/khazar teaching the true original jews, the so called african americans

>>11588654
I like your optimism, but I doubt they will stop if you ask them to. Did you learn something today?

>>11588654
>Posts the bitchiest cunt in anime

>>11588654
>backseat moderating

>>11588649
>setting the results into columns
It's not clear what you want to do.

In any case, you can't find the eigenvalues of B by probing a single vector.

>Last thread hasn't hit bump limit
Wow...
On THIS slow board of all places...

>>11588691
>>11588683
>>11588677
>>11588674
>>11588672


Einstein once said racism was the disease of the white man

>>11588691
It was at 320+ before, but apparently mods deleted a shit ton of posts

>>11588683
How can I find the eigevalues when I'm given something like T(A)=BA and only given the values of B? I wanted to create a matrix from the results of BA where A is the standard basis vectors. Take the resulting vectors and put them into columns of a new matrix. Then find the characteristic polynomial from that matrix.

>>11588698
Was he being ironic on purpose?

>>11588698

>>11588698
I'll keep that in mind, thx

>>11588701
If B is an n-dimensional matrix and if what you want to say is that you have n equations (and A in each represens a different basis verctor), then the collection of BA's are just the n columns of A, so you got the matrix A.

You may just post your system. Although better go to /sqt/, since this thread is about ... well it's about racism I guess, but it should really be about dependent type theory and algebraic geometry.

>anti-racism edition
lol, you're just asking for non-math discussion, great job retard

>>11588727
>dependent type theory
You mean homotopy type theory, the chad subfield right?

>>11588698
I'm not included in the racists then.

>>11588727
>You may just post your system. Although better go to /sqt/, since this thread is about ... well it's about racism I guess, but it should really be about dependent type theory and algebraic geometry.
This. Please post it.

>>11588727
>>11588745
This is the question. I found the kernel by taking the standard basis, doing the transformation on the basis, then row reducing. For image I just took the columns with leading zeros as which vectors were the basis.

I thought I would apply the same logic to find the eigenvalues.

>>11588672
I'm learning algebra and analysis, what about you?

>>11588764
>this entire problem
Did your professor really?

>>11588595
handwaving and assertion in the general direction of "racism," as per usual. no testable hypotheses. assuming the premise of reverse ability-failure causality. de facto assuming a blank slate. contrary to all records of multivariate intelligence testing and world history. very sad the amount of energy we spent cleaning after these people, but you want more of it so that you can receive the benefits of social signalling without paying the costs.

>>11588781
Struggling with the cohomology of SL(2, 9). I got some hints on how to compute it, but I am uncertain. Even worse is the homology of [math]\Omega (B\text{SL} (2, 9)^\land _3)[/math], which I should also try to find. After almost 2 weeks of useless efforts I feel like giving up.

>>11588822
dude just explain to me what is that homology thing and I'm sure we can do this somehow

>>11588595
>There are lots of studies that show modern day discrimination for housing, loans, and criminal justice, all else being equal.
That is totally irrelevant, even if true.
You have to demonstrate, as I said, that this alleged discrimination is causal for the crime.

>>11588654
This thread is already lost.
If you do not want politics, the tread shouldn't start with a blatantly political message.

>>11588822
How's your brain tumor?

>>11588835
Being against racism is not political.

>>11588839
Of course it is.
Under which fucking definition would it not be?

>>11588839
>brainlet detected

>>11588788
yes

>>11588829
Take the 2x2-matrices with entries in [math]\mathbb{F}_9[/math], classify that, do the Bousfield-Kan completion with respect to the ring [math]\mathbb{F}_3[/math], and then take the loop space of the 3-completed classifying space. There is then a fibration whose base space is the classifying space, total space is 3-acyclic and the fibre is the loop space of the completion, and so it should be easily computed, but I just can't. Coefficients in the field of 3 elements.

>>11588836
Not potent enough to end my worthless life. I tried boosting myself by eating some iron supplements and cod liver oil, but those don't help in getting rid of it.

I already asked this question last thread but didn't receive an answer, so I'm asking again. A few months ago there was a mathematician who announced his own death on the discussion page of his wikipedia article. Does anyone remember his name?

>>11588857
I remember that, but forgot his name as well, sorry.

>>11588764
Write [math]A = \left( \array{a && b && c \\ d && e && f} \right) [/math] and compare [math]\lambda A = T(A)[/math] out by hand.
You'll notice that the [math]e[/math] entry zeroes on one side, so you can zero all the [math]e[/math]s in both sides. Comparing the results tells you that the only possible non-zero eigenvalue is 2 (including the complex ones btw).
Algebraic multiplicity becomes muh difference, geometric has to be computed by hand.

3b1b is live now

>>11588854
that's way over my head
i know what's SL(2, 9), tell me what is cohomology

>>11588842
Might have been in the past, but nowadays it's basic decency.

Can someone, please, explain to me the philosophy behind Proof?

It seems to be i'm missing some of it.

For example, lets say that i'm learning now — learning all by myself, so there is no alma-mater to guide me and answer my "don't-understandings" — about differentiability implies continuity. We start from the equality to prove. OK. Then all of a sudden, the mind behind the proof starts the process from some limit that hasn't been mentioned before. Then he somehow comes to the idea of doing the algebraic manipulation he does. How?

I don't need explanation of how the algebra behind this proof is done. Neither i need the explanations of this very proof i'm mentioning. I don't understand the abstractness of proofs.

So, what is the philosophy of proofs?

>>11588902
Mathematics would be very easy if there existed such a thing as an automated process for being creative.

>>11588889
Firstly. You didn't give me a definition.
Secondly:
>nowadays it's basic decency.
Where in the world outside the west is that true?
Do you think Chinese are not racist? Arabs are not racist?

>>11588831
It's causal for poverty, unemployment, lack of education, bad nutrition, toxin exposure, etc. But that's all irrelevant?

>>11588902
Proofs are just games of words and symbols if we're being very informal. You have as tools logical equivalences and tautologies for playing the game.

>>11588910
>It's causal for poverty
Evidence.
>unemployment
Evidence.
>lack of education
Evidence
>bad nutrition
LMAO are black people literal cattle that can't decide on their own what to eat?
>toxin exposure
Evidence.

I like everyone even if everyone's a little different and does things a little differently.
I don't understand what would lead someone to dislike people who do things differently unless they feel inadequate or doubtful about the way they do things themselves.
I find it very difficult to see how you could be successful in mathematics and still hold racist beliefs, because success in mathematics should be something that gives you self-confidence and self-worth so that you don't need to project your insecurities onto others by claiming the achievements of a bunch of people who have absolutely no relationship to you and just happen to look slightly like you.
Part of being able to make it in mathematics is learning how to focus on yourself and your own personal growth within your field of study rather on the growth, say, of another mathematician studying something else completely different. This sort of mentality just naturally leads one away from the groupthink us-versus-them mindset.
This is not exclusive to just political issues, but also to a wide variety of personal and pedagogical philosophies. I really appreciate mathematics for leading me to a state of being where I'm less interested in the flaws or privileges of others and focus on my own flaws and privileges. Obviously, plenty of people everywhere no matter what they think have problems with this. I have problems with it too, but math is helping me to improve.
Even if it's annoying when /mg/ gets derailed, it's nice to have a moment to stop and think about this and about how what I study is not just an academic pursuit but is also transformative to one's lifestyle.

>>11588909
We don't live in China, or in the middle east.
I don't know about you, but I live in the west.
Are you troubled by the reality that you may not practice "basic decency" within your cultural milieu?

>>11588916
tl;dr

Can someone confirm for me the number of partitions of a natural number [math] n [/math] using three numbers for me?
The number of partitions of a natural number [math] m [/math] using two numbers is [math] m+1 [/math] since you choose the first number to be anything from [math] \{0,1,...,m\} [/math] and the other number is then fixed.
Then using that for our case of three numbers, you choose the first number to be anything from [math] \{0,1,...,n\}, [/math] say [math] n-m [/math] and the other two must sum to [math] m. [/math] Hence, the number of partitions is [math] \sum_{m=1}^{n+1}m=\frac{(n+2)(n+1)}2. [/math]
Sorry, this should be fairly obvious, but I just want to be certain I haven't missed anything and bing didn't turn up anything.

>>11588922
Math helps me to maintain a level of stoicism and focus on myself, and that's been meaningful in leading me away from strong political standing and toward bettering myself while respecting what others need to better themselves.

>>11588916
Great post my man, completely agree, you have my sword

>>11588876
Wikipedia it and you will know more than I do.

>>11588916
>I find it very difficult to see how you could be successful in mathematics and still hold racist beliefs
Why?
Teichmüller (who was a serious anti-semite and attacked Landau) literally volunteered to die for Hitler, Hasse got into trouble for his associations and opinions, the same goes for many other mathematicians.

>I find it very difficult to see how you could be successful in mathematics and still hold racist beliefs
Racist beliefs like "evolution didn't stop at the neck" my home city would be a far nicer place if there were actually more people like me here?

>>11588924
Also, sorry for not specifying, but the order of numbers matters, e.g. (1,2,3) and (2,1,3) are considered distinct partitions of 6 here.

>>11588906
>>11588911
Let's make it clear: you're saying that doing proof is highly creative process of logical and symbolical manipulations?

In that case the one who does the proof should be extremely intelligent. On the other hand proofs are widely included even in the first year students curriculum.

So i assume that there should be some intuition and very abstract rules that may be used in the proof-creating process.

Or my assumption is bullcrap?

>>11588915
It isn't his or my role to find evidence for you, it's of no detriment to us if you maintain your opinion. In fact, it's to my detriment if you change it, being that I passively benefit from those who seek to maintain sociocultural structures. I don't really care about that though.
You should be self-motivated by a search for truth, in which at the moment you have no evidence for one side or the other, and you are being told evidence for one side exists (in hundreds upon hundreds of studies for each point you address). If you feel no desire to find said evidence, then you have closed yourself off to the possibility of illumination.
In terms of your bad nutrition point, I do not have a study to provide but the reality is that junk food and prepared meals are much much easier and more efficient (considering money, time, etc) to eat even if they are far less healthy. Hence someone who needs to hold 2 low-paying jobs and has multiple children who cannot summon the energy to cook for all of them nightly falls into malnutritious habits. This, of course, happens to everyone experiencing impoverishment regardless of race.

>>11588915
Evidence that financial discrimination causes adverse financial outcomes? That employment discrimination causes less employment? That housing discrimination causes poorer housing conditions?
Idk man, you got me I guess.

>>11588924
yes that is correct

>>11588925
Do you know what is the hardest hit to me trying to focus on myself?
Going outside and having to interact with with the "new-Germans", I have yet to see a single one who is trying to better himself, most are extremely aggressive towards anyone who isn't "one of them" (i.e. Muslim) and it is basically impossible to have a calm interaction with them.
They also have zero concept of the politeness I expect from every human being. Like, not throwing parties with your whole family at 1am stopping the people below you (me) from sleeping.

You know. 5 years ago I was the most left leaning "I don't care what you do" liberal you can imagine, but just having to be around these obnoxious vapid macho arabs/turks made me genuinely despise them.

Also, it isn't like I am spending time "hating them", just every time I go outside it is a reminder of how awful this shithole is.

>tfw teaching myself how to do basic proofs from A Transition to Advanced Mathematics
>tfw I'm really enjoy my class on voting theory even when it's online

>>11588947
Thanks.

>>11588921
Are you saying that Chinese and Middle Eastern people are not basically decent? That's not very basically decent of you.

When a fan with a radius of 10 cm and a central angle of 30 degrees moves 4 cm as shown in the figure, what is the area of the shaded area?

>>11588942
>It isn't his or my role to find evidence for you,
So, you are just claiming random things that I have to debunk?
I genuinely spend a lot of time looking at the evidence, but I still believe in evolution.

>You should be self-motivated by a search for truth
I DO believe in evolution therefore I have to believe that a significant part of the differences in outcome between different races is down to genetics.

>>11588921
>We don't live in China, or in the middle east.
I am not so sure of the later.
There also regularly appear hate slogans against my ethnicity here, but I am not sure whether they are from arabs/turks/somalis or antifa.

>Are you troubled by the reality that you may not practice "basic decency" within your cultural milieu?
No. I have never been disrespectful to anyone because of their skin color.

>>11588950
Looks like a good book, which page are you in?

>>11588953
Find out the radius from the tip of the left triangle to the shaded area (basic trigonometry) and then calculate the areas of the two circle sections and subtract them.

>>11588980
I'll give it a go!

>>11588930
Sure, there are obviously counterexamples. I don't think those counterexamples are anywhere close to the norm, though. I think within certain cultural contexts, something like German nationalism or etcetera can overpower someone's devotion to mathematics. I find it hard to imagine that such a cultural context is present right now where you live.
I can't speak to your second point, I'm not sure what you enjoy or consider "a nice place to live" but as someone who lives right outside of Oakland, who has to be pretty aware of where I go and what I'm carrying, I guess I just don't think about it in the terms of "damn if only I could walk around carelessly at 1am" or something like that. I don't need to do anything that would currently endanger myself.

>>11588948
I hear what you are saying, but I can honestly say with certainty that if things like parties keeping you awake or perceived slights during smalltalk are this frustrating to you then you are not very far when it comes to learning to focus solely on yourself. Those really aren't hard-hits at all, they're quite passe. In my university job these are things I deal with literally daily. Perhaps us americans are a bit more used to it.
I can't get into your mind of course, and I think even as little as 1-2 years back I was stuck in that mindset. But again my mathematics study has just gotten so difficult and all-consuming that I simply don't have the energy to think about instances of social faux-pas from others anymore. Perhaps others have more stamina than I have and can juggle such emotions while devoting themselves fully to mathematics.

>>11588980
>>11588983
No wait. That's retarded!

>>11588929
https://en.wikipedia.org/wiki/Group_cohomology
it's this one right?

>>11588952
I'm saying that basic decency is a cultural phenomenon. It occurs differently within each social environment.
This isn't hard to understand, so I'm going to assume you're playing a little game just to put me on the defensive.

https://habr.com/en/post/447326/

>>11588992
Yup.

>>11588957
So you admit that you have only looked into evolution just enough to know the most basic processes controlling it, and know nothing of the time-frames involved. I respect your admittance of inadequacy.

>>11588965
Well that's good to hear, apologies if my question sounded pointed.

>>11588999
I mean dude. If you want to believe that black people are better runners then whites because of systematic anti-white discrimination, that is fine. But I do not think we need to go there...

>>11588996
Does Aluffi cover that shit? What are some good books for learning it?

>>11589006
The runners are only a small village in Kenya or whatever. Look it up.

Now blacks being better at basketball, and whites being better at golf, yes, that is due to societal factors, not genetic.

>>11589006
I don't think you have evidence to support that statement outside of anecdotal knowledge of a few famous runners.

>>11588987
>I'm not sure what you enjoy or consider "a nice place to live"
My litmus test would be what would happen if I left the door unlocked.

>I guess I just don't think about it in the terms of "damn if only I could walk around carelessly at 1am"
Around here (when I actually go to uni) I am verbally abused by the somali drug dealers in front of the train station at like 10, before that, especially in the morning, they are just trying to sell me drugs.

>>11589010
To both questions at the same time: I don't know.

>>11589019
What evidence is there that blacks are not genetically disposed to be better at basketball?

>>11589024
Why would you want to leave the door unlocked?
It's easy to lock it.
I am verbally "abused" by people as I walk to campus as well, I don't really see why that should bother me. They're not doing anything.

>>11588994
So in the culture that you grow up in, the relative morality that you have, do Chinese and Middle Eastern people lack basic decency with respect to your morality?

>>11589019
>The runners are only a small village in Kenya or whatever. Look it up.
https://en.wikipedia.org/wiki/100_metres
????????????????
That is clearly absurdly false.

>that is due to societal factors, not genetic.
Evidence?

And what about skin color or nose width? Is that due to evolution or sociological too?

>>11589030
>Why would you want to leave the door unlocked?
Because if ever something happened (like a burglar coming, etc.) then that would tell me how much my neighbors would care.

>I am verbally "abused" by people as I walk to campus as well, I don't really see why that should bother me. They're not doing anything.
Really? That is extremely upsetting. I can not recall a single situation in which a white person was disrespectful to me without having a good reason.

>>11589020
I said look it up but I guess I'll do it for you.
https://www.npr.org/sections/parallels/2013/11/01/241895965/how-one-kenyan-tribe-produces-the-worlds-best-runners
>>11589028
lol that's not how this works

>>11589020
>I don't think you have evidence to support that statement outside of anecdotal knowledge of a few famous runners.
How about skin color?
Genes or evolution?

>>11589027
That tumor is rotting your brain

>>11589052
>https://www.npr.org/sections/parallels/2013/11/01/241895965/how-one-kenyan-tribe-produces-the-worlds-best-runners
Do you think that this is due to genetics, and is a demonstration how evolution can cause, even small groups, to become very specialized and effective at one thing or is it due to socioeconomic factors?
Like the tribe discriminating against slow runners?

>>11589052
>lol that's not how this works
Why because burden of proof is placed on the person making the positive claim? Okay, is there any evidence that black people are overrepresented in basketball because of social factors?

Okay Im the guy that asked about "path spaces" last thread and I want to try and expand on it.
Coinsider the space A. The "space of paths" from x to y is clearly some uncountable mess.
However we would expect the path spaces of A and B to be, in some sense, isomorphic, no?

Now consider space C. Is the path space isomorphic to B? I am not sure...

Lastly the path space of D is clearly different. In fact, every high school student could tell you it is "left-right-right-left... etc."

So wtf is going on here. Am I just looking at covering spaces here? I never got those well but it seems similar.

>>11589097
Furthermore consider space E. The path space should be a combination of the path spaces of A and D. There is something going on here and it must be possible to formalize it.

>>11589097
The thing is, for based paths, you're looking at covering spaces, for un-based paths, you can sort of reduce it to based paths if you have a topological group but probably can't otherwise.

So how hard is Calculus 2/3 compared to calculus 1? How about ordinary differential equation and linear algebra?

>>11589081
A few obvious reasons. Black people live in inner cities. Basketball is a perfect recreational activity for the inner city. Making a basketball court can serve 10 people in a tight space with a low cost. The cost of entry to the sport is non-existent. No equipment needed, just one ball among 10 people.

Making say, a hockey rink, is much more expensive, takes up more space, and requires tons of expensive equipment to play.

Logistics alone can explain part of the disparity.

>>11589106
linear algebra is straightforward
calc 2 is generally regarded as a challenging course. for a lot of students, integrals are the first time they meet mathematics they actually have to think about instead of mechanically following rules
calc 3 is just calc 1/2 except you do every calculation 2 or 3 times instead of just once
ODE is ass cancer

>>11589104
okay thanks

>>11589126
I heard one of these involved proofs, was it calc 2?

>>11589097
Rotation number is an invariant of homeomorphisms, right? So we can say that the the paths of C are not homeomorphic to the paths of A. I think if you consider the paths of C that have a rotation number greater than 1, then you can see that there is no isomorphism between C and A.

HIRSCH YOU FAGGOT JUST CALL IT A FUCKING SHEAF

>>11589141
Yea what you say makes sense on an intuitive levek but to be clear, there is nothing defined yet here, Im just wonderinf how one might formalize this.
It probably is just covering spaces as the other anon said, but Im too much of a brainlet to really see if thats the case. In the end coverig spaces still have homtopy, and path spaces are supposed to *not* equalize homotopic paths.

>>11589059
Perhaps. At least nothing of value will be lost.

>>11589122
That's not evidence that racial disparity is entirely due to societal factors, that's a plausible explanation for how societal factors would influence basketball. What's the evidence that the only factors are societal?

[math] \bf{None~of~the~concepts~is~difficult,~but~there~is~an~accumulation~of~new~concepts~which~may~sometimes~seem~heavy.} [/math]
[math] \tt{-Serge~Lang} [/math]

>>11589106
>>11589126
Linear algebra depends on if you're studying proof based or computational. Computational linear algebra is barely even a class. Proof based linear algebra will likely be your first proofs class, so I recommend reading a book on proofs before doing it, but the actual problems themselves aren't particularly hard as long as you don't get lost anywhere.

Haven't take ODEs, would imagine it's a bunch of recurrence relations, solving some complex polynomials, boundary conditions, ect. which can be challenging.

Calc 2 was my favorite pre-proof era mathematics class. Calc 3 was generally unfun, just a bunch of parameterizations of integrals in vector fields, 3-dimensional limits, stokes/greens thm, vector stuff, ect. Calc 3 was the hardest for me out of all of them.

>>11589169
Stop putting yourself down man, you're already at PhD level, you're gonna make it. Do it for kaguya-sama

>>11589179
this quote keeps me going, thanks serge

>>11589179
Where did he say that bros?

>>11589172
What an epic shift of goalposts m8. Fuck you, I'm done.

>>11588698
He caught that disease when he was in China.

>>11589213
What was the goalpost shift? In both posts I asked for evidence that basketball racial disparity is due entirely to social factors.

>>11589181
Trying...

>>11588939
>In that case the one who does the proof should be extremely intelligent
Really depends on statement one is trying to prove. Showing that the sum or product of continuous functions from R to itself are easy to do and require really just a basic understanding of inequalities and the definition of continuity.
>So i assume that there should be some intuition and very abstract rules that may be used in the proof-creating process.
Somewhat, but the rules you can apply in proofs don't have to be VERY abstract.

>>11589250
You will and we'll make research together one day

>>11589276
Is that a promise?

>>11589250
>>11589314
I really like your anime girls selection

>>11589276
>>11589314
>>11589314
wtf gay

>>11589351
It's only gay if someone else than me is topping

>>11589314
Did I ever lie to you?

>>11588743
no, not necessarily

>>11589337
Based opinion.

>>11589351
Nope.

>>11589357
Not yet, but that one anon totally BTFO'd induction with the sand grain example. I will still decide to trust you. Let's make sure that collaboration will happen.

>>11588953
It's the area of the entire sector minus the area of the same sector with radius 10cm-4cm = 6cm. So you get pi/6 (100cm2-36cm2) which is 32/3 pi cm2.

>>11589388
>Nope
you being a fucking tranny makes it even more gay bro

>>11589419
Stop offending my friend, you jerk

>>11588872
>It's a Wildberger episode

>>11589419
>gay
Why the homophobia?

>>11589486
who's the homophobe here

>>11589490
Tranny is a homophobic slur
https://en.m.wikipedia.org/wiki/List_of_LGBT-related_slurs

>>11588460
>source: the color of crime
Okay this seems like a promising, unbiased start
>Citing 63 sources
But what the fuck is it citing from them? Where does the data actually come from? Making some data up then citing a bunch of people doesn't make the data real.

>>11589533
English

>>11589533
Terrible post.

>>11589495
That's very cisnormalized of you to assume that all trannies are homo

Is the 'usual' Frobenius inner product of a 2x2 matrix in real space <u,v>=tr(uv^t)? Or do I use the standard dot product for a vector?

>>11589588
the frobenius product is <u, v> = tr(u^t v) = tr(uv^t), which is precisely the same as if you were to just take the dot product by multiplying all the entries and adding them up
you should write out the formula to see this

>>11589588
>>11589592
in other words, note that for [math]A, B \in M_{n\times n}(\mathbb{R}) [/math], we have the following identity:
[eqn]\mathrm{tr}(A^\top B) = \sum_{i, j = 1}^n A_{ij}B_{ij} [/eqn]

>>11589592
>>11589596
I see thanks man

>>11589581
admittedly

but hey, it's not race bait

Any book on modeling inequality problems and trick to solve them?
I'm trying to prove that my algorithm is under a certain bound but I got stuck for 3 months. To be honest I have always been dumb when it comes to inequalities. Should have chosen something else. Fuck.

>>11589209
That's the second sentence of Part One in his Algebra text, in the preface on the page right before chapter one. It's a pretty bitchin' textbook, as I remember it.

>>11589601
Yes, thanks for that.
>>11589599
I'm not a "man."

>>11589685
shit, sorry. me either btw

>>11588468
>bump
WHAT DO I NEED TO UNDERSTAND GRUNTZ

>>11589685
>>11589761
resident /mg/ trannies?

>>11588370

"Unz zat is vye da rent iz sooo high."

Are there two sets, equipped with operations which are algebraically isomorphic, but, equipped with topologies not topologically homeomorphic?

https://www.youtube.com/watch?v=BipvGD-LCjU

/mg/ anthem?

how to git gud at math?
not at one specific thing, I'm asking how to think like a mathematician and be able to use the information and knowledge I have to formulate new knowledge, and figure out things that aren't intuitively obvious.

>>11589890
Sure, take any algebraic structure with more than one element, you can put the discrete topology on it and you can put the continuous topology on it

What are the contents of an Abstract Algebra II course?

>>11589916
Fields and Galois Theory

>>11589901
Maybe... Just maybe... By... Studying math...?

>>11589901
The pure of heart may exploit a shortcut, pic related, but it's the most expensive drug on the market.

Forgot pic. This is it. Are you pure of heart?

>>11589897
https://www.youtube.com/watch?v=Lt52Z8Y6eLo

You forgot to post the /mg/ remix.

Let [math]P(x) = x^2+x+1[/math] such that [math]P(x) \in \mathbb{Z}/2\mathbb{Z}[/math]. What are the roots of this polynomial? is it just [math]1[/math] or are we considering stuff like the roots of [math]x^2 + x + 1 = 4[/math]?

>>11590026
Plato and heidegger are shit my man

>>11590033
Z/2Z only has two elements, the conjugacy classes of 0 and 1

>>11590033
What's Z/2Z?

>>11590054
https://en.m.wikipedia.org/wiki/Quotient_ring

>>11590054
But if that's the case, [math]P(x)[/math] has no solutios, and I'm being asked whether if [math]\{a + b\alpha : a, b \in \mathbb{Q}\}[/math] is a field or not when [math]\alpha[/math] is a root of [math]P(x)[/math].

This set wouldn't even make sense if [math]P(x)[/math] has no roots.

>>11590208
Sounds like you're being asked something about the rationals, not Z/2Z
I think alpha should be a root of P(X) as a polynomial in Q

>>11590214
Sorry, I meant [math]\{a + b\alpha : a, b \in \mathbb{Z}/2\mathbb{Z}\}[/math]

https://arxiv.org/pdf/2004.09765.pdf

>>11590389
Wow.

People on 4chan keep making fun of me for not having never taken a linear algebra course. I've taken Algebra I & II, Geometry I & II, Trig, Calculus I & II, Probability and Statistics, but I haven't taken linear algebra (this is Amerifat curriculum) because it wasn't necessary for my shit college major. Now that I'm in a technical field, I'm trying to bridge my math gap but people keep calling me retarded. Should I just give up?

>>11590480
>Should I just give up?
No, but you should do some linear algebra

>>11590480
absolutely give up. how are you a functioning adult and you don't know linear algebra yet? look, just work at mcdonalds, there's no matrices involved in saying "would you like fries with that?"

>>11590480
>>11590487
Also what kind of fucking class is trig? In uni? What?

>>11590511
I took all my math before college. I stopped at Dual Enrollment Calc II and majored in a econ (no more math needed).

>>11590220
They basically asking about the ring (Z/2Z)[x]/(x^2+x+1). Can you write everything in that ring as a+bx? Is it a field?

For the ones that did the chartrand proof book, how many hours of work or how many days from start to finish did it take you to complete the book?

Why Newton method is so unstable?

>>11590389
did they check for roots around [math]\hat{\infty}[/math] though?

>>11589419
Someone's a bit grumpy, eh?

>>11589964
Trying to be.

textbook recommendations for physics (looking for mostly relativity + mechanics) from the mathematical perspective?

ideally something with the intuition coming from physics but the notation from mathematics.

>>11590891
This would satisfy the content criterion you have, but I can call it neither good nor bad without reading it myself. https://www.springer.com/gp/book/9781461299059

>>11590826
>Why Newton method is so unstable?
The question you need to ask is
Why Newton method is so unstable, bros?

>>11590389
Is there a canonical way for enumeration?
plz respond
(Haven't looked at the paper yet)

>>11590891
>ideally something with the intuition coming from physics but the notation from mathematics.
I don't think it's actually so different for mechanics
(inb4 indices)

>>11590891
for the mechanics part, Arnolds's Mathematical Methods of Classical Mechanics

>>11590819
>the chartrand proof book
proofbooks = memebooks

>>11591226
Do you know the book?

>>11590819
From 3 to 4 months

>>11591263
WTF

>>11591270
What?

>>11589897

damn I wish I could be part of the math beach boys

>>11591227
No anon, he used a basic syllogism. Didn't you learn how those work in school?

>>11590389
>true up to [math]3 * 10^{12}[/math]
It means nothing.
>rigorous way
Newton method? (I think Newton fractal on [math]\zeta(z)[/math] might look fabulous.)

>>11591281
Im just used to instant gratification. I just want to do enough so that I can approach abstract algebra and real analysis with an idea on how to tackle the proof exercises.

>>11591294
No I did not. Why are proof books considered a meme?

>>11591309
>Im just used to instant gratification
Heh, good luck tackling abstract algebra and real analysis books if you can't even stand spending some months in a 600-page proof book.

>>11591317
I enjoy the time doing maths it seems. I just want everything to go faster.

>>11591328
Then stop wasting time on /sci/ and the internet and start reading the book, if you read 20 pages per day you'll finish it in one month, although this will probably require at the very least 6h of reading+exercises per day.

>>11591350
yes sir

Are there any mathematical problems thaf fail for extremely large numbers (like Skewes's number)?

>>11588370
>Can we get partial credit on the exam?
Do undergrads really believe that they'll get a 0 for missing a minus sign?

Remember your nutrients, friends!

>>11591460
post tits?

>>11591527
why would you want to see a man's tits

>>11591546
You're not a man.

>>11591546
>why would you want to see a man's tits
I'm not a "man."

>>11591527
As you wish.

Found on Wikipedia:
>Erik Christopher Zeeman tried for 7 years to prove that one cannot untie a knot on a 4-sphere. Then one day he decided to try to prove the opposite, and he succeeded in a few hours.

>>11591875
Just like the people who are trying to prove the RH nowadays, if they spent their efforts trying to prove the opposite, they'd succeed fairly fast.

>>11591614
Very cool titsposter.

>>11591875
That must have hurt.

>>11591460
>woman's health
Why specifically woman's? Do they put hormones in those things?

>>11591949
I don't think he would have been able to prove the opposite if he hadn't spent so many years trying to prove it. His attempts must have gave him a lot of insights in where specifically things can go wrong that he used to find the counterexample. It's very unlikely that a new researcher could find such a counterexample in a few hours: in a lot of respect the story seems to be exaggerated for dramatic purposes.

https://vixra.org/pdf/1808.0599v3.pdf

*Picture of guy yelling into a tube*

Any other textbooks with hilarious banter?

>>11591999

>>11592047

>>11592050
>>11592047
It's sooo dumb, right?

>>11592038
Was that supposed to be funny?

>>11591999
Why do they accept those shit at Arxiv?

>>11591957
This is true, although it speaks to why he fucked up spending 7 years trying to prove something - if you need to show something is true and are stuck, then the best way to move forward is to try and show it's false. If you fail to show it's false, you'll better understand what you need to take advantage of in showing it's true.
I imagine he is fluent in that sort of problem-solving but that it just didn't hit with this one. Nevertheless, it's an important and useful tactic.

>>11592047
Terribly written. It's like reading a child's attempt to write a mathematics text.

>>11592071
>Arxiv
>https://vixra.org/pdf/1808.0599v3.pdf
try again

>>11592071
>arXiv
>viXra

Does any convex function satisfy [math]f\left(\int x d\mu(x) \right) \leq \int f(x) d\mu(x)[/math] for a probability measure [math]\mu[/math], or do we need some extra assumptions about it?

>>11591875
Damn son

>>11592183
just google jensen inequality

how far are we from the first tranny to win the fields medal

https://arxiv.org/pdf/math/9906042.pdf

I don't get it

>>11592038
oh my sides! they went into another category for a moment there!

>>11592230
Yukari is winning one in the next batch.

>>11591375
going in your general direction
http://oeis.org/A129935

>>11591301
>Newton method?
I think what you do is you can wrap a box around an interval on the cricial line (e.g. (0,0) and (1,7i) being the lower left and upper right corner of a rectangle of volume 7 encloding the critical strip from 1/2 to 1/2+7i). Then evaluating along this conture for Log(zeta(s))', i.e. zeta'(s)/zeta(s), gives the number of poles of Log(zeta(s)), i.e. zeros of zeta(s). Say there's 5 zeros. You then put a grid on the box and make sure the sinks are not on the critical line.
Then you go up along the imaginary axis. This way you can exclude non-trivial zeros on the line.

Although it's actually the case that the Riemann hypothesis is [math] \Pi_1 [/math], in the sense of
https://en.wikipedia.org/wiki/Arithmetical_hierarchy
so there's a non-analytic statement equivalent to it (in fact, I think you can find some online.)

>>11588543
Read Counterexamples in Analysis by Gelbaum.

>>11592344
Thanks, this is what I was looking for!

Back to basics here, lads

Is it PEMDAS/BIMDAS or PEDMAS/BIDMAS? Surely it makes more sense to divide before you multiply, especially when attempting to simplify and equation?

For example, take pic related. It's clear you're supposed to divide 20/5 before you multiply by four to get 16 (Ignore the 'both answers are equally correct' shite)

>>11591953
It doesn't say anything about hormones, but it helps with menstrual blood loss. That's probably the reason why it is officially targeted to women, but in the package it says that is for everyone except small kids.

>>11591957
Good point! Must have hurt at first, though. At least I would have been quite shocked by my stupidity as an immediate reaction.

>>11591944
Thanks.

>>11588791
Let me understand your brilliant mind right here, right now: blacks are inferior to whites because of their lower iq. Ok fine. Jews and Asians have higher iq than whites but this is just commie propaganda designed to bring down the white man.
>what are you talking?
>there’s no cognitive dissonance to speak of

>>11592554
>Jews and Asians have higher iq than whites but this is just commie propaganda designed to bring down the white man.
Jews are white and Asian IQ statistics are skewed by excluding rice farmers.

>>11592554
>Jews and Asians have higher iq than whites but this is just commie propaganda designed to bring down the white man
You can actually also circumnavigate this by saying that the Asian IQ is a consequence of traditionalism and the Jewish IQ is why they run the show. Then you don't have to feel so bad about having a smaller IQ than they do, as it is merely a result of the Jews tearing down your traditional society and thus lowering your mental capacity. Proof for this? No need, just read Evola.
t. different anon

>>11592554
>blacks are inferior to whites because of their lower iq
lower intelligence makes you necessarily inferior?
do you look down on everyone less intelligent than yourself?
we're not robots, there's more to a person (and by extension a people) than what they know or can understand.

>>11592565
>do you look down on everyone less intelligent than yourself?
Yes.

>>11592571
based literal autist

>>11592557
>Jews are white
I... I don't even... Just leave this place please and study a lot before coming back...

Y'all need to read some HunterxHunter, especially Chimera Ants Arc. Komugi proved to Meruem that strenght and intelligence aren't the only things that matter, she proved there are different kinds of strenghts in each human, so no one is necessarily better than anyone who's not as intelligent as them.

>>11592557
>Jews are white
Don't you FUCKING EVER compare the superior Chosen Ones to filthy goyim EVER AGAIN. Do you FUCKING HEAR ME??

>>11592584

>>11591999
>>11592047
his other paper's even better

>>11592607
omg

>>11592607
What's wrong with it?

>>11592620
Nothing, academia's just not ready for this level of freethinking brilliance

>>11592627
tfw Riemann was a wizard

>>11592627
I'm horrible at calculus, but even I can say that [math]\int_s^sF(s)ds[/math] isn't necessarily going to tell us much.

>>11592634
>post-modernist mathematicians
Jurgen Jost BTFO.

>>11592599
lmao

>tfw you realize social norms and connections are only but vanity
>tfw you detach yourself from society's chains and control your ego
>tfw you realize the only things that truly matters in this world are the arts and mathematics
I think I'm close to reaching the nirvana frens

>>11592685
Just make sure you don't detach yourself too much, as then we may not be able to make the paper. We need to play the stupid game until we get what we want and where we want. We may see through it, but we are still bound by its rules if we want to be able to express ourselves meaningfully in this society. Don't stray too far, for I am waiting.

Good night!

Apart from "bounded holomorphic function on the entire complex plane must be constant"' what are some non-intuitive results of complex calculus?

I'm evaluating the following integral.

Take some fixed complex number [math]r e^{i\phi}[/math] with [math]\phi \in [0,2\pi][/math] and compute
[eqn]\int_0^{2\pi} \int_0^\infty e^{-\frac{r^2}{2} - \frac{s^2}{2} + r s \cos(\phi - \theta)} s \; ds d\theta[/eqn]
It looks like it should simplify but somehow I can't do it, and even Mathematica gave up on computing this. Any ideas?

Help! Tho hours ago I discovered that I've got direct access to Wolfram|Alpha from Mathematica and I can't stop! Help!

>>11592743
>Apart from "bounded holomorphic function on the entire complex plane must be constant"' what are some non-intuitive results of complex calculus?
https://en.wikipedia.org/wiki/Zeta_function_universality

>>11592714
You are so cute, I might fall in love

>>11592747
You can pass the [math]e^{-r^/2}[/math] outside of the integral, because it's constant.
Other than that I'm lost.

Are there any examples of fields composed of functions?

>>11592765
>Are there any examples of fields composed of functions?
https://en.wikipedia.org/wiki/Function_field_of_an_algebraic_variety

>>11592770
Uh, that's a weird example, but thanks. Are those examples of fields of uncountable cardinality?

>>11592774
>Are those examples of fields of uncountable cardinality?
Not writing anything rigorous here but if the functions have coefficients in an uncountable field then I think the function field should also be uncountable.

>>11592747
reminds of cosine law (but maybe you obtained this integral using this already): https://en.wikipedia.org/wiki/Law_of_cosines

>>11592789
bigger

>>11592743
> Apart from "bounded holomorphic function on the entire complex plane must be constant"' what are some non-intuitive results of complex calculus?
I don't think that's non-intuitive, what's non-intuitive is that there's series of monomials x^n that make for a periodic function. (sin, cos, etc.)

>>11592774
You can use less "weird" examples, if you like. The regular old rational functions (of two polynomials) form a field too.

>>11592747
Convert to rectangular coordinates.

What, in your view, is the key to a good mathematics textbook?

>>11592853
>What, in your view, is the key to a good mathematics textbook?
Author needs to be Russian

>>11592853
Understanding and memorizing the definitions and theorems.

>>11592853
avoiding any context to ensure you don't see why the material was developped the way it is. True mathematicians ask themselves natural question and rebuild everything from their own superior understanding, they don't need someone to lay these questions for them.

>>11592853
>What, in your view, is the key to a good mathematics textbook?
Author needs to be yourself

>>11592853
The textbook should be just a list of theorems with no examples or proofs

>>11592853
yellowness.

>>11592886
titled: "Left as an Example to the Reader"
I'd buy it

>>11592886
titled "Left as an Exercise for the Reader"
I'd buy it

>>11592892
Don't mind me, on my way to make billions of dollars

>>11592882
But what if you don't want to be a PhD level theoretical mathematician and want to actually put the theory into practice and be a productive member of society as an engineer?

>>11592910

>>11592910
>theoretical mathematician
/sci/ pls

>>11592925
Purely theoretical maths that no one beyond those with 150+ IQ can understand is irrelevant and useless to the economy. As an engineer, I'm going to be out there actually producing stuff for society while you sit there studying Wiles' proof of Fermat's last theorem or some shit.

>>11592936

>>11592910
Finish highschool, you should have the required level. So for books, I guess any that your teachers suggested will do.

>>11592936
Oh jeez, where to start? First, Wiles didn't prove Fermat's Last Theorem you fucking orangutan piece of shit with a coconut for a brain, he proved a special case of the modularity theorem for elliptic curves.
Second, where do you think all innovation in engineering comes from?
Third, you don't have to be 150 IQ to understand higher math, you just need a lot of effort, but you probably never did that in your life because I can tell from the way you type that you're a sad and pathetic human being who'll amount to nothing not because you can't but because your weak mentality prevents you from going any higher.

>>11592960
Yes, I'm sure your highly theoretical PhD in mathematics is contributing to the ability of people to pump petrol into their cars, the ability of machinery to be more efficient, or the ability of programmers to streamline processes.

The fact is that no one cares about PhD level mathematics. I do not have an IQ of 150+, and I don't care that I don't.

I disagree that hard work alone can carry one to PhD levels of mathematics. A certain IQ level is required, which I do not possess. But that's fine, because I'll be a contributing member of society.

As a part-time McDonald's worker who's also an engineering student, I am infinitely more useful as a member of society than you useless fucks are.

>>11592758
gay lmao

>>11592978
>As a part-time McDonald's worker
Hum, should have left that part out man, I was almost falling for your bait, but that part gave it away, sorry...

>>11592982
True love knows no gender

>>11592986
It's not bait. I work part-time in McDonald's while working towards an engineering degree, and I still contribute more to society than PhD mathematicians.

>>11593013
Blah blah blah, I can see through you, bitch, at least admit it and leave with dignity or just stop posting, it will be less shameful than keep trying to convince us of your failed bait attempt.

>>11593013
but why aren't you working part-time as a gay escort? You would be paid way more for doing what brought you to engineering, and still be a contributing member of society. It seems you are indeed not 150 IQ, in fact I wonder if you reach triple digits.

>>11593043
I refuse to believe anyone who discovered /sci/ or /mg/ is below triples digits.

>>11593046
sadly >>11593013 gives a compelling argument supporting the existence of below three digits anons on this Amerindian canopee house...

>>11593043
You can cry all you want. Just know that your life's work means nothing, while my work means contributes to society and the economy.

>>11593054
Shall we eliminate this unwelcome creature then in order to preservate the integrity of /sci/?

>>11593072
Oh boy, he continues... Have you no shame, you poor soul? This is so sad to see, please, as a word of advice, we all can see through your bait already, just know your place and leave, your dignity should have more worth than that.

test

>>11593091
Does PhD level mathematics produce petrol? Does it contribute to construction? Does it produce computer programs? Does it produce automation streamlining?

/mg/pill me on stacks

>>11592758
Please don't.

>>11592990
This is true, though.

>>11593096
>Does PhD level mathematics produce petrol?
It consumes it when you travel all around the world seeing people.

>>11593106
Holy shit wtf japan is fucking based

Why are all the top mathematicians male?

>>11592810
"Bigger" than uncountable is still uncountable

>>11590819
>For the ones that did the chartrand proof book, how many hours of work or how many days from start to finish did it take you to complete the book?
Why not read a maths book instead?

>>11593139
fair enough

Too many racist schizos ITT

>>11593127
So you're just a net drain on society and the economy, is what you're saying?

>>11593138
The female ones are smart enough to stay out of the spotlight.

>>11593149
What I said was:
>Please don't.
>This is true, though.
>It consumes it when you travel all around the world seeing people.

>>11593127
>Please don't.
Can't be helped

I'm having a hard time understanding this proof. Where does he prove that any subspace which contains S also contains L? And, together with the fact that L is a subspace of V, why would it follow that L is the subspace spanned by the set S?

Also, my professor said this proof method was also used in other areas of mathematics, is this true?

>racists btfo
>RH btfo
>pfoofbooks btfo
>engineers btfo
Best /mg/ thread ever? Yeah, I guess so.

>>11593177
Oh, I understood the first part. It's because in the first inclusion he proved that L is contained in the intersection of ALL subsets which contain S. I still don't see why is the second part true.

NEW THREAD >>11593150

>>11593167
What have I done... L is the smallest subspace of V containing S, and that is, by definition, what it means for a subspace to be spanned by S. That follows from the fact that it is (contained by) the intersection of all such subspaces: suppose a smaller subspace would exist and conclude that L would not be contained in that.
>Also, my professor said this proof method was also used in other areas of mathematics, is this true?
Whenever you are dealing with a proof something that is minimal (maximal) with some property, you try to show that it is smaller (bigger) than any object with the said property.

I hope I understood your questions.

>>11593177
>L is the smallest subspace of V containing S, and that is, by definition, what it means for a subspace to be spanned by S. That follows from the fact that it is (contained by) the intersection of all such subspaces: suppose a smaller subspace would exist and conclude that L would not be contained in that.
>>Also, my professor said this proof method was also used in other areas of mathematics, is this true?
>Whenever you are dealing with a proof something that is minimal (maximal) with some property, you try to show that it is smaller (bigger) than any object with the said property.
>I hope I understood your questions.
Was for you.

NEW THREAD >>11584605

>>11593360
you're pointing at an old /mg/ there, that's a mean trick