/mg/ = /math/ general

My favorite math is probably the IQ difference between blacks and whites.

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>>9023625
Really good.
>>9023629
Do you have any particular kind of blacks in mind?

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>>9023625
A+ image

>""""""""""math"""""""""" general

more like let's have another thread where we pretend to be anime girls and act gay as fuck general

go back to /g/ kids /sci/ is for manly geniuses only

>>9023629
define blacks and whites

>>9023640
Not him, but I think by "blacks" he means something like this >>9023633

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>>9023636
>>9023636
>more like let's have another thread where we pretend to be anime girls and act gay as fuck general
What's the matter, couldn't find anything math-related to post about?

>>9023636
>pretend to be anime girls
>pretend
What did she mean by this?

>>9023625
Personally I find astronomy to be extremely fascinating. Since it delves into so many aspects of abstract math, physics and theories about the universe and our excitence. I remember in astronomy class where we tried to complete a formula of how many other possible intelligent lifeforms there could be in the milkyway. But astronomy is also the forefather to all science. If we didn't live on a planet where you can, at some point in time, see the night sky without clouds in the way, we surely would have never tried to do anything related to some of the most simple geometry and math. If you're looking for something to read I can recommend Stephen Hawking, since he is good at explaining things in a modern way, instead of using a lot of academic terms, and he has more humor than most books on the matter. But anything you can read on astronomy should be good. You'll end up looking at the night sky a whole new way.

>>9023673
>astronomy
stopped reading right there

>>9023625
>/math/ general
>10 posts in and no math
If you're looking for beautiful math then knot theory has you covered, a seemingly banal subject that turned out to have great physical, theoretical, and biological application.

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Stop bullying the gorilla and prove that for any [math] n \geq 2 [/math] the general linear group [math] GL(\mathbb{Z}^n) [/math] is generated by the diagonal embedded groups [math] {\Delta}_{1,i}GL(\mathbb{Z}^2) [/math], with [math] 1 \leq i \leq n [/math], where [math] {\Delta}_{i,j} : GL(\mathbb{Z}^2) \longrightarrow GL(\mathbb{Z}^n) [/math] is defined as
[math] {\Delta}_{i,j}\left( \left(\begin{array}{cc} a & b\\ c & d \end{array}\right) \right) = \left( x_{u,v} \right)_{1 \leq u,v \leq n} [/math] with
[math] x_{i,i} = a [/math], [math] x_{i,j} = b [/math], [math] x_{j,i} = c [/math], [math] x_{j,j} = d [/math],
and [math] x_{u,u} = 1 [/math] when [math] u \neq i,j [/math].
All the other entries in the matrix are [math] 0 [/math].

>>9023673
At first I was excited since I did my undergrad thesis (we have to write a thesis to graduate here) on astrodynamics (it was about the behaviour of periodic dynamical systems under perturbations of parameters with applications in celestial mechanics, to be more specific) but then I read the rest of your post and it's just a shitpost. Astronomy and Classical mechanics were surprisingly popular in my department, since they can be approached in an axiomatic, purely mathematical context (as per Clifford Truesdell and others).

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Prove that [math] \textbf{Ab} [/math] and [math] \textbf{Mod}_R [/math] have no subobject classifiers.

https://ncatlab.org/nlab/show/subobject+classifier

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Finally, for what values of [math] k [/math] is [math] x(x^2 - 4) = ky(y^2 -1 ) [/math] an elliptic curve?
These 3 problems should keep you busy for a while.

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>>9023781
>Finally, for what values of k is x(x2−4)=ky(y2−1) an elliptic curve?
over what field?

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>>9023781
also did you mean ky(y-1)?

>>9023784
[math] \mathbb{R} [/math]
>>9023785
Nope.

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>>9023786
>[math]\mathbb{R}[/math]
No such thing, anon.

Get laid losers.

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>>9023786
>Nope.

>elliptic
>cubic in y

>mfw I started a math major and was really happy about it
>mfw the professors were shit with the exception of one
>mfw I gradually starts to become uninterested in it
>mfw I start watching game of thrones for entire days until I finished it
>mfw I start to ignore the classes
>mfw my grades were awful in every class except for one
>mfw I get dismotivated and stop going to college
>mfw I'm too scared to say anything to my family about it
>mfw I keep lying to them and go out every morning saying I'm going to college but instead I just go to a park where I just wait for some hours to go back home
>mfw I'm doing that for 2 years now and no one suspects anything

Can I still unfuck my life? Don't get me wrong I still love mathematics but I think I just fucked up the little potential I had to make a good career. I just don't know what to do and I'm extremely tired of wasting my days.

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>>9023807
>for 2 years now

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>>9023625
well I'm not smart or good in maths but I found a book about surreal numbers and the idea of a different way of representing numbers is cool

>>9023803
Yes. Cubic in [math] y [/math]. I'm not sure what is it that confuses you. Do you need hints?

>>9023807
I hope this is LARPing and no one is actually pathetic enough to go to a park every day to pretend you're in college

>>9023807
I bet this guy is asian.

>>9023819
>no one is actually pathetic enough to go to a park every day to pretend you're in college
Asians are.

>>9023819
I'm serious, I know I'm fucked up and I'm pathetic, I'm 20 right now, is there still hope for me to have a good mathematical career or should I just give up?

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>on stack exchange
>after asking so many brainlet questions, decide to give back to the community
>spot a hard question that I could answer
>spend a couple hours on it, texing it up takes a good 30 more mins
>my solution is complete, and parametrises all the answers to a particular diophantine equation
>post my answer
>somebody with shitload of rep points already posted a shitty answer, just gives a condition for a solution, posts a couple of trial and error solutions, and it was already marked by the poster as the definite answer

should i just kys?

>>9023830
dawg if you're only 20 you still have your life ahead of you, but you should get your standing with the university sorted out

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>>9023830
Are you even any good at math? Something tells me you're not being honest (not even with yourself). In any case, none of us here knows you or the full extent of your circumstances. How in the world are we supposed to advise you?

You blame your professors but maybe you lost interest because you're no good at it. I too barely went to classes during my undergrad. Because I practically lived inside the university's library. There is really nothing in your story I can relate to so I can't even begin to guess at why you fucked yourself up like this and how to fix it.

>>9023855
Like, you say you're willing to apply yourself if there's still a chance you might "make it". But do you really mean it? Did you study any math by yourself during these 2 years? (I suspect you did not.)
And why in the world didn't you take a gap year?
Your issues run deeper than your mathematical potential, that much is clear.

>>9023855
I have a problem with procrastination, that's just it, I really like maths. The problem is that I barely opened any books during the classes. Had I studied correctly everyday, then I would have got good grades.

About the professors, one of them just walked into the class with his clothes and a pen on his hands, the fucker didn't even bring any books or papers, he just walked in and started writing things off his head, sometimes he even forgot about explaining some subjects. Once my friend even asked him when was going to be the days of the tests and he said something like 'just decide among yourselves and give me a date', everyone in the room just laughed. There was also another one, a woman, who had barely any idea of how to teach. There was another who prefered to talk about soccer everyday than teaching his class.

>>9023863
I didn't ask anything about your professors. It's not just that I don't care at all about them, but also that it doesn't in the least matter how they conducted themselves. This is [math] your [/math] problem.
From my end, your whining about fuck all. What's so odd about the students deciding the date of the exams anyway? It's common practice here. Professors that fixed the date themselves were the exception, and they did it mostly due to extraneous circumstances, like having to leave for some conference after a certain date etc.

If a right triangle existed with a hypotenuse of 10 and an altitude of 6 (I know this can't happen), would the area of the triangle be complex?

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>good at math
>making no headway at solving any of the millennium problems
Honestly I'm thinking of giving up and pursuing finance
If it takes me two decades to solve even one problem (and in the worst case solving this problem does not immediately solve the other problems as a consequence) I'll be netting a measly 25,000 dollars per year, after taxes.
It doesn't take a genius to know that two decades of compounding interest could whisk me away into a world where I make that much money in a single week.

>>9023882
>If a right triangle existed with a hypotenuse of 10 and an altitude of 6 (I know this can't happen)
why not? couldn't the base just be length 8?

>>9023891
You're already in the wrong when you want to solve a millenial problem be ause of the money you'll get.

>>9023625
What's her ethnicity?

>>9023898
Is it any different from professors who solve non-Millennium problems for their salary?

>>9023898
so what noble goals do you have after spending a significant fraction of your life on something?

>>9023709
>I will hit you with this stick otherwise
How about I hit you with my penis instead?

>>9023903
>who solve non-Millennium problems
Ew...

>>9023904
I will solve a millennial problem because I want to prove to everyone that anyone, even the most ordinary of people, can do it if they put their minds into it.

>>9023625
Do you have more images of anime girls and mathematics or with books or in a library?

>>9023915
So you've got a low sense of self-worth and have invented a chip on your shoulder? That's no reason to waste your life for peanuts (and probably fail anyway, considering that the people you'd consider "ordinary" haven't solved such problems)
Maturity is realizing that everyone is ordinary, regardless of their upbringing, socioeconomic position, and intentions. We all die eventually. And more importantly, we all have to eat.

>>9023915
This is probably the most delusional and pathetic post I've seen in these threads. And that's saying a lot.

>>9023901
Lombard.

>>9023919
I will not fail.
>Maturity is realizing that everyone is ordinary
???
Gauss was definitely not ordinary, nor was Euler, Pascal, Newton, Gödel. They've been immortalized by their minds, but I'll be immortalized by perseverance and efforts alone.

>>9023920
Yeah, people said that about Cantor also, people love humiliating other people who chase their dreams.

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I'm studying real Analysis right now, but I'm mad at your suggestions, /sci/.

>hurr Rudin is the only god-tier book you need

No fucking way you disgraceful autist, it's poor in explanation, and the exercises are too hard and they'll take me a year to solve. I need a book that likes to chew and explain every single thing.

I'll use Rudin for the exercises, but that's it.

Any other recommendations? I really need this.

>>9023923
On the slim chance that you do solve these problems, you'll be immortalized for your mind, not your efforts. The computer that assisted in the proof of the four color theorem was an example of effort. The current millennium problems can't be solved through effort (you're fucking around with infinity) so your only option is to be extremely clever. You have to be more clever than any mathematician currently living. If you solve the problem, you're not ordinary. Take that as you will.
If you're trying to prove that determination [math]\implies[/math] results you will certainly fail. Everyone will misinterpret the cause of your success.

>>9023936
>you'll be immortalized for your mind, not your efforts.
No, because, different from other genius, I was nothing exceptional during school. My grades were good but I wasn't solving any IMO problems. I once even scored 10 out of 100 in a trigonometry test because I hadn't studied anything for it. I will definitely be seen as a person who persevered despite not being a genius.
> The current millennium problems can't be solved through effort (you're fucking around with infinity) so your only option is to be extremely clever.
Do you have proof of that? This sounds like a losers speech, you sound like you already give up all your dreams and expectations of solving them and didn't even try.
>You have to be more clever than any mathematician currently living.
You just have to be more determined than every mathematician currently living.

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>>9023936
>(you're fucking around with infinity)
What did he mean by this?

>>9023931
stein shakarchi
or zorich

>>9023945
Academic record depends on more than just raw intellectual ability. Since you don't seem to realise even that, there's an extremely high chance that you're a brainlet, so you will never solve any important problem.

>>9023954
>Academic record depends on more than just raw intellectual ability
But there's certainly a correletion between them, because if you read the biographies of the so called genius of mathematics you'll see that all of them had exceptional grades during their school days.

>Since you don't seem to realise even that, there's an extremely high chance that you're a brainlet, so you will never solve any important problem.
Keep 'em coming, I will just accept every humiliation, but your words will not affect my determination at all, because I'll definitely solve a millennium problem and prove to the world that anyone can do that.

>>9023948
Allow me to elaborate
If, say, you wanted to prove the Riemann Hypothesis, you'd have to prove there were an infinite number of zeroes on the critical line.
There's no way to prove this via exhaustion, because we've assumed there are an infinite number of them.
At least one person in this thread thinks that there's some way to use a proof by exhaustion and that no cleverness is needed in such a case.

>>9023945
>I will definitely be seen as a person who persevered despite not being a genius.
No, you'll be seen as a genius who slacked off in school and then read a shitload of books, filling your enormous but previously empty mind with mathematics. Assuming you solve it.
>This sounds like a losers speech, you sound like you already give up all your dreams and expectations of solving them and didn't even try
No, I definitely tried. Maybe I didn't try hard enough. But that's because the solution wasn't simple enough. I'm not exceedingly clever. Perhaps I could reach an epiphany if I buried my head in the notes of dead mathematicians for two decades, but in the meantime I would starve and become a genetic dead end. And when I inevitably failed to solve the problem I would also be a memetic dead end.

>>9023959
>I'll definitely solve a millennium problem
Hey which one are you taking? Cause I'll definitely solve a millenium problem myself and it'd pretty awkward if you and I solved the same one

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>>9023959
Just stop posting already. It's annoying. You're full of hot air.

>>9023931
try Folland

>>9023960
> but in the meantime I would starve and become a genetic dead end.
So you're OK with abandoning your dreams because you're afraid of death and that society will not see you as a prestigious person during the time you'll spend trying to solve it? Your dreams should be above anything in your life, if it means to spend 20 years trying to prove the Riemann Hypothesis while you're slowly rotting and starving , then what's the problem?

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>>9023960
>If, say, you wanted to prove the Riemann Hypothesis, you'd have to prove there were an infinite number of zeroes on the critical line.
You should know more about what these problems actually are before commenting about them, if that was the Riemann hypothesis then it was solved almost a century ago.

>>9023953
>>9023965

I'll try those, thank you :3

>>9023923
>I will not fail.
Sooner or later you'll be giving your shotgun a blowjob.

>>9023961
I have an interest in the Riemann Hypothesis, but if someone proves it before me, I'll just move onto another one.

>>9023972
I should have also included "and there aren't any that aren't on the critical line".
It should be trivially obvious that you can't prove that by exhaustion either.

But you caught me; I don't give a shit about Riemann Hypothesis. I was deep into Twin Primes and Goldbach conjectures.

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>>9023979
I told you to stop posting. It's obvious you have no idea what you're talking about.

>>9023986
don't worry he doesn't ever need to know what he's talking about
he's DETERMINED

>>9023986
Ok, I'll stop, but what do you mean with >It's obvious you have no idea what you're talking about.

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>>9023980
>It should be trivially obvious that you can't prove that by exhaustion either.
I wouldn't say that's trivially obvious at all, hypothetically someone could prove there's an upper bound on how large a non-trivial zero off the critical line could be, and then the proof could be exhaustive. Just like how the four colour theorem was reduced to looking at ~2000 maps and then proved by exhaustion despite there being infinitely many maps that the four colour theorem applies to.

>>9023990
>someone could prove there's an upper bound on how large a non-trivial zero off the critical line could be
And you wouldn't consider that to be extremely clever?
Christ, how much does it take to impress you?

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>>9023995
>And you wouldn't consider that to be extremely clever?
I certainly would, did I imply otherwise?

>>9023997
My mistake; I thought you were implicitly defending Captain Perseverance's plan to solve the Riemann Hypothesis without cleverness.

>>9023988
What do I mean by it? Let's see: can you calculate [math] {\sum\limits_{n \in \mathbb{N}} n^{-3}} [/math]?
>>9023990
Another genius. Why are you talking about the RH when you don't even know what an elliptic curve is?

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>>9024010
>Why are you talking about the RH when you don't even know what an elliptic curve is?
What does RH have to do with elliptic curves?

>>9024014
A great many things.

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>>9024016
>A great many things.
Go on...

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>>9024010
Can you calculate this?

>>9024017
Here's two hints: Sato and Tate.

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>>9024020
>generalizations of Sato-Tate imply analogues of RH for elliptic curves
I only spent 5 seconds googling but I hope I'm missing something, I was expecting something a little more direct based on your posts

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>>9024016
I'm 98% sure you're full of shit

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I will tie anime posters of math general in chairs in a basement, and come down to feed you and inject some feminine hormones into your veins periodically. Then I will put you in girly clothes, like skirts and stripped socks, and start drilling your asses with cute sex toys of all colors and sizes, and I'd use my own penis to dig through your mouthes and asses. I'd force you to have sex with each other and then join. Then I tie you back in the chairs, leave the basement and only come down every now and then, either to feed you, inject hormones into your veins, torture you, or fuck you.

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>>9024035
please stop

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>>9024035

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>>9024035
>I will tie anime posters of math general in chairs in a basement, and come down to feed you and inject some feminine hormones into your veins periodically. Then I will put you in girly clothes, like skirts and stripped socks, and start drilling your asses with cute sex toys of all colors and sizes, and I'd use my own penis to dig through your mouthes and asses. I'd force you to have sex with each other and then join. Then I tie you back in the chairs, leave the basement and only come down every now and then, either to feed you, inject hormones into your veins, torture you, or fuck you.

>>9024035
why don't 3d women look this beautiful?

Is there any way to prove a function is surjective iff it has a right inverse without Choice?

Should I mention math general and anime in my speech when I win my fields medal?

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>>9024050
>Should I mention math general and anime in my speech when I win my fields medal?
Why aim as low as a Fields Medal? How about you give that speech when you win the first inaugural Gorilla Trophy?

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>>9024035
>I'd use my own penis to dig through your mouth
Feel free to try. I'll bite it off.
>>9024029
>I was expecting something a little more direct based on your posts
Why?

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>>9024057
>Why?
Because you randomly brought up elliptic curves when the topic was RH, and then claimed they were related by referring to an conjecture which remains to be connected to RH in any way

>>9024035
This is some pretty decent fanfic.

>>9023948
Don't fuck wid Infinity he a hardass nigga.

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>>9023709
i don't get it.
how can these diagonal embedded groups generate GL(Z3) if entries like x3,2 are always zero?

>>9024057
Then I'd remove your teeth one by one and replace it with a silicone prothesis so it looks like you have teeth but can't bite. I'd do it in the most painful way possible so you can learn your lesson.

>>9024035
>>9024037
>>9024040
>>9024057
I have a serious question for you anime posters. Are you virgins? Have you ever gone to parties or had any friends? I won't make any fun of it. I'm just curious.

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>>9024068
Don't you have
[math]\Delta_{3,2}(\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix})=\begin{bmatrix} 1 & 0 & 0\\0 &1 & 0\\ 0& 1 & 1\end{bmatrix}[/math] which has non-zero x3,2?
?

>>9024060
What I was getting at is that the RH is a much more difficult problem than the one posted upthread (which for whatever reason tripped you up), yet you opine on it anyway.

>>9024068
>how does matrix multiplication work?

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>>9024077
>I have a serious question for you anime posters. Are you virgins? Have you ever gone to parties or had any friends? I won't make any fun of it. I'm just curious.
Is it possible to go through college and still be a virgin?

>>9024086
I suppose for anime posters who choose MATH it is. Im serious though. I'd like to read it from them.

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I thought we had already established that mathematicians are pure. Why all these pointless questions?

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>>9024085
>What I was getting at is that the RH is a much more difficult problem than the one posted upthread (which for whatever reason tripped you up), yet you opine on it anyway.
It's been a few years since I've worked with elliptic curves, they already come in a nice Weierstrass form™ on LMFDB whenever I needed them

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I want to do this to some of you.

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>>9024101
>I want to do this to some of you.
Is this the best general on all of 4chan

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>>9024102
Was until you found out about it.

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>>9024101
You want to, but can you? Let's go back a few steps: how are you even going to get me inside your basement in the first place? You've never thought about that, eh?

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>>9024119
Let's say I'm really rich. I can bribe a mod to tell me your IP and ISP. Then I bribe the ISP to tell me your address and personal details. One of these days, when you're sitting on your chair and making these cute posts of yours on /mg/, you'll be spooked to see someone right behind you. The next thing that happens is you wake up tied to a chair. Then you can choose to never see sunlight again or become my cute maid. I'd rape you in either case.

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Let's talk about math stuff.

>>9024077
i'm not even a regular animeposter but I still got caught in your (You) dragnet
To answer your question: no I don't go to parties, but I used to trade homework answers for two blowjobs, half paid upfront and another on completion. Got 11 succs that way. And by current standards I'm a daterapist.

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>>9024134
Shouldn't you have an even number of succs? What's the story behind the one that didn't complete?

>>9024101
This image will be used for the next thread.

>>9024140
>the one that didn't complete
actually five didn't complete
I'm not sure you have time for me to explain the intricacies of this tale of woe

>>9024143
Please go ahead.

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>>9024145
>calling my bluff
Shit, I wasn't prepared for this.
The truth is that if I told you how it all went down you'd be able to find out who I was with a little digging. Thus, I don't want to.

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>>9024082
[math] {\Delta}_{3,2} [/math] is not necessary. The groups given by the [math] {\Delta}_{1,j} [/math]'s suffice. The general linear group is a multiplicative group. It doesn't matter that [math] x_{3,2} [/math] is always [math] 0 [/math] for a matrix in the image of the embedding if you can multiply the 3rd line of one of them through the 2nd column of another and get something there.

Is it clear now?

>>9024082
those are some ugly thighs

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>>9024086
Yes if you realize sex is for subhumans.
The greatest people who ever lived - Jesus, Newton, etc, were all virgins. Sex is a sin in every single religion. It is a tool of mass control for the slave class. You feel pleasure from it so you can breed more slaves to the slave masters. You're wired, programmed to enjoy such a thing. Sometimes I feel bad for non virgins, they unknowingly live as slaves and in the end are refused salvation for their impurity, but then I remind myself it's not my fault I'm not inferior.

>>9024010
Just to make it clear, my plan to solve the Riemann Hypothesis is a long term project, I plan to work on it for 10~15 years and prove it with pure determination. I will work on it for as long as I live.

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>>9024156
If I own and regularly fuck sex dolls, does that make me unvirgin?

>>9024163
Sure you will. Just as I expected, you didn't even notice that the first term in that series is [math] \frac{1}{0} [/math]. Brilliance right there.
The only fruits of your determination seem to be shitposts.

>>9023709
im not doing ur 5th grade homework for you kid

>>9024177
[math]0\notin\mathbb{N}[/math] everyone knows that

>>9024196
Ok then. Calculate the series.

>>9024199
no need to calculate the answer is well known [math]\zeta(3)[/math]

>>9024177
Well what were you expecting? I'm only 19 and I said I was an ordinary person. I have a lot of time to learn high level mathematics and the subjects required to solve the Riemann Hypothesis.

And shitposting? All I have done in this thread was answer people humiliating me and trying to crush my dreams and I'm the one shitposting?

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>>9024222
>series
>high level mathematics

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>>9024235
>zeta function
>low level mathematics

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>>9024238
I didn't even ask him to calculate Apéry's constant though, remember?

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Is there any machine learning MOOC that doesn't pussy out on the math? The guy teaching the Stanford one on Coursera is almost too scared to even say the word subspace

>>9024281
>Is there any machine learning MOOC that doesn't pussy out on the math?
No. All but two courses on Coursera pussy out on the math.
There is https://ocw.mit.edu/courses/mathematics/18-657-mathematics-of-machine-learning-fall-2015/index.htm though

btw Galois Theory on coursera starts tomorrow

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>>9024294
>Galois Theory on coursera starts tomorrow
Is there a new one? I already took both the ones they had up (one in English one in French) like a year ago

>>9024281
Machine learning has been downgraded from being a specialized research topic at top CS schools to a subject taught at "coding bootcamps" to aspiring "data scientists".

This is what happens when you simplify your field to make it digestible for the masses.

>>9024301
No, it's the old one

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>>9024294
>All but two courses on Coursera pussy out on the math.
Also what are the two you mean (I would guess Jacobi forms and the french Galois theory class)?

>>9024308
yep those ones

>>9024222
>people humiliating me
It's called beating some sense into you, you little shit-for-brains. You haven't the foggiest clue what you're talking about yet come riding in spilling your brain vomit all over the place and implying the Riemann hypothesis is still unsolved because no one so far has been DETERMINED enough to do it. Fuck you.

If I could trade my determination for more intelligence I would do it in a heartbeat.
Idiot.

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>>9024310
I only opened this one up for 1 second but it looks not so pussied (is it fair to call GR math?)

https://www.coursera.org/learn/general-relativity

>>9024315
>If I could trade my determination for more intelligence I would do it in a heartbeat.
Me too. Although then I'd be in determination debt

>Coursera
>opencourseware
>etc
I don't get it. Why not just read a textbook?

>>9024325
There are textbooks used as resources in many (most?) Coursera and opencourseware classes

>>9024328
So what is the point of the lecture then? You do realise that lectures are entirely useless and are only held as a matter of tradition, right? It all goes back to the fact that universities were founded by the Church and the professors were clergy, with the lecture following the format of a sermon.

>>9024345
>So what is the point of the lecture then?
To do things not in the textbook

>>9024345
I mean I get it when you're enrolled in a university and attendance is mandatory or something like that, but for these free online courses that don't give you any certificate/proof of graduation?
You guys sure love to waste your time.

>>9024349
what kind of daycare-tier university takes attendance?

Can you define a homomorphism from a group to another in this "cheaty" way?

Let [math]A,B[/math] sets and [math]A\coprod B[/math] their disjoint union. Let [math]F(Z)[/math] be the free group on the set [math]Z[/math]. Suppose there are homomorphisms [math]f_A: F(A)\to G[/math], and analogous for [math]B[/math], to a set [math]G[/math]. We have some natural injections [math]j_A:F(A)\to F(A\coprod B)[/math], analogous for [math]B[/math].

Can I define a homomorphism [math]\phi :F(A\coprod B)\to G[/math] by [eqn]\phi(x)=\phi\left(\prod_{g\;\mathrm{ a\;generator}} g^i\right):=\prod_{g\;\mathrm{ a\;generator}} \phi(g)^i[/eqn]
Which obviously is a homomorphism by construction, and makes the diagram commute?

>>9024349
also nearly every online class does give you a certificate

>>9024347
Such as?

>>9024354
>Such as?
Whatever's not in the textbook... it obviously depends on the class and the textbook being used

For example the Jacobi forms class on coursera doesn't even really have a textbook, most of the references are the professor's own published papers in journals and you can't find any textbook comparable to the material in the videos anyway

>>9024345
>universities were founded by the Church and the professors were clergy, with the lecture following the format of a sermon.
Galileo, Giordano Bruno and other middle age scientists wouldn't agree, christfag.

>>9024351
Is there a typo somewhere in there? What is the value of phi on the generators? You're going in circles.

>>9024351
Oh and obviously [eqn]\phi(g)=\begin{cases} f_A(g) & g\in A\\
f_B(g) & g\in B\end{cases}[/eqn]
>>9024364
forgot

>>9024361
I am not a Christian. I don't even believe in God.
What I said is a matter of historical fact. It's unfortunate that it ruffled your feathers, but you'll have to deal with it.

>>9024370
Oh, ok then, I just don't like christians revisioning history and trying to picture the church as something good when in fact all it bring were years of scientific deve Lorena thrown into the garbage. Thought you were one of them.

>>9024379
Development*

>>9024379
You have issues.

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Help me out bros. I'm hurting in a bad way.

>graduate high school
>only take the minimum math classes to graduate
>join the army as a medic
>do that a long time
>get out
>go to university
>take placement test to know what math to be put in
>beginning algebra
>my teacher teaches the same shit to her middle schoolers at her other job
>don't remember how to do anything
>get a C

I've forgotten everything over these years, and I just can't grasp it. The classes are so condensed that they teach everything as fast as possible and move on to the next section. How the fuck can I get good at math?

>>9024412
khan academy
algebra by gelfand and shen

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>>9023931
Analysis I & II by the Shogun in the realm of maths; Terrance Tao!

>>9024345
>So what is the point of the lecture then
i didn't need a textbook or notes for my first year because i went to every lecture. still got an A in each class
i don't know if i can repeat this stunt in the second year.

>>9024412

What is your IQ?

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>>9024351
>>9024365
>is this a homomorphism?
Nope. Let's say [math] a \in A [/math]. What guarantees you that its inverse in [math] F(A) [/math] is the same as its inverse in [math] F(A \amalg B) [/math]? As given, nothing. [math] A \amalg B [/math] is an entirely new set of symbols you use to generate a free group.
Or in short, [math] F(A \amalg B) \neq F(A) * F(B) [/math].

The hack you're looking for is the pullback of [math] f_A [/math] and [math] f_B [/math].

>>9024318
id say so, isnt GR just magic complex analysis?

For programming, there's plenty of small exercises like "project euler", where you'll solve a problem, or a handful of them, every day if you wish. Other than perusing textbooks, is there a similar place to do so online? Ideally something where I could limit my questions to topics I've studied. I was thinking about making a program that would do this for me if not (it would just spit out a random problem from all the reading I've done, or something).


Also, any tips for a self taught mathematician? I am taking classes as well, but teach myself a lot of material and was wondering it there's areas where I can find expert guidance beyond #math IRC and math.stackexchange/mathoverflow.

>>9024446
what do you mean? I'm pretty sure F(A u B) = F(A) * F(B)

>>9024454
>I'm pretty sure F(A u B) = F(A) * F(B)
Prove it.

Anime is cringey and disgusting.

how to learn math, physics and chem outside of school?

>>9024466
Just like the average mathematician desu

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>gone for half a day
>new thread already half over
Guys please.

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you know, total differentials suddenly make a lot of sense once you really got tangential spaces

>>9024412
Start from the ground up anon, even Witten was a History major at first. Khan academy might work for you, though I'd personally go with the immaculate 3 volume series complied and edited by kolmogorov.
>>9024450
It's (pseudo)riemannian geometry
>>9024452
You could try brilliant, they have Olympiad style math and compsci problems. As for experts, barring math stacks, you'd just have to contact a professor directly.
>>9024477
Start from the ground up, what's your baseline knowledge

Also guys, why have things gotten so aggressively sexual in these threads as of late?

>>9024412
Study outside of the classroom too anon, don't be afraid to use external resources

>>9024477
please dont ignore me

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>>9024446
>>9024454
>>9024464
this is the proof that it is true

now prove it in less abstract settings

>>9024521
oh someone replied before it could be post.
whoops

>>9024512
>Start from the ground up, what's your baseline knowledge
pretty basic, but i know i can learn math/physics easily, i was tutored in 10th grade because i needed the grades in highschool (although it didnt matter in the last two years, due to the nature of the school, so i didnt care unfortunately) and i picked it up quite easily. as far as chem goes i was interested until 11th grade but missed a couple of classes and didnt understand anything from then on. the question is where do i start? internet is a vast ocean of information, how do i sail through it succesfully?

What's a good source of algebraic review? Lowly undergrad here who just finished calc series (including vector calc), and will start linear algebra and diff eq this fall.

I relied a lot on computer algebra systems to do it for me, but I "know" most of the concepts, and don't really want a book that teaches that, I more so just want a book/text with tricky algebra problems, and perhaps another with some very algebraically sticky calculus problems.

>>9024535
If you want to learn college level general physics I perosnally found walter lewin's lectures to be good while also supplementing them with the feynman lectures (all of it is pretty basic but the point is to get a solid foundation, this is key to getting far in math/physics) You should also be ready to do a lot of problems, this is pretty much the only way forward in math/physics, read about topic, do problems till you've gotten good at said topic, repeat. If you aren't familiar with calculus mit has some good videos and notes, so does khan academy and coursera, again, all very basic but it'll get you the necessary info and provides problems and solutions. These sites also cover other basic topics that you might need a refresher on. After getting through that I need to ask what your specific goal is, do you plan on getting a degree or is this purely for fun? What topics do you want to know?
>>9024542
Do you mean high school algebra? If so go to khan academy, brilliant, or coursera. If you mean college algebra you'll want dummit and foote

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>>9023625
Hey guys I'm kind of a math/cryptography noob but I've recently been tasked with writing a graduate-level paper about RSA encryption using Hurwitz primes. I have probably a year and a half to work on this and I would be incredibly happy if anything were to come from my research, but I was wondering if any of you might have any tips about complex/quaternionic analysis that I should take into consideration before diving in? I appreciate any help I can get, as I know many people here know mathematics far better than I do.

>>9024464
>>9024522
Two things. First, that's not a proof. Second, I'm sure the exercise is talking about [math] the [/math] free group, i.e. ignoring the representation since all free groups over a given set are isomorphic.

The rub:

Let [math] A = {1,2,3} [/math] and [math] B = {a,b,c} [/math].
Let [math] \langle\ A \mid 1' = 3,\ 2' = 2\ \rangle [/math] and [math] \langle\ B \mid a' = c,\ b' = b\ \rangle [/math] be representations for [math] F(A) [/math] and [math] F(B) [/math], respectively.
Let [math] \langle\ A \cup B \mid 1' = a,\ 2' = b,\ 3' = c\ \rangle [/math] be a representation for [math] F(A \cup B) [/math].
But [math] F(A) * F(B) = \langle\ A \cup B \mid 1' = 3,\ 2' = 2,\ a' = c,\ b' = b\ \rangle [/math].

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>>9024546

>>9024546
What's your background?

>>9024545
By "college algebra", do you mean abstract/linear?

I'm just looking for a text full of those really tedious problems that come up every now and then, for both plain algebra and calculus (ideally in that order). I feel I should never struggle "solving for x" and taking some tricky derivative/integral, but I found that due to relying on a computer, this happened far too often on exams.

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>>9024501
also, am I mistaken or does it make no sense at all to call the function corresponding to a chart differentiable because charts define what differentiability is on a manifold?

>>9024572
>>9024545
Just to expand a bit, I'm not looking to relearn the rules that I already know, so I feel Khan would be a huge waste of time. I just need to get my hands dirty in some algebra and calculus, but don't want to review my book because finding the specifically sticky questions isn't obvious until you begin solving them, and I am completely fine with the concepts and cut and dry problems. The only I things I have trouble with are solving convoluted algebra and tricky integrals / derivatives (integration by parts, and within that, u-substitution, etc)

>>9024572
Check out Polya's Problems and Theorems in Analysis

>>9024568
I graduated from Yale's Philosophy and Mathematics (undergrad) double major program which put a lot of emphasis on logic and number theory in the area of math and I think that might have hurt me in the long run as I'm not too incredibly familiar with complex analysis at this point - I got on board with this paper after I wrote a piece about k-theory and I thoroughly believe I'm in over my head but I'm really happy to work through it.

>>9024545
>what your specific goal is
i hope i get on a competitive enough level to apply for mech school. in most europe countries you dont pay for a seat in uni, you sit through an exam

>>9024578
Also "Larson. Problem-solving through problems"

>>9023931
Rosenlicht is very good. The only annoyance is that he insists on proving many results for Rn asap. I would rather relegate them to their own chapter. You'll like Rudin more later, long after you've learned analysis.

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>>9024535
A good place to start is the Landau-Lifshitz series.
1. LL classical mechanics + Goldstein
2. LL E&M + Jackson
3. LL QM + Sakurai
I'm sure you can get through this over the summer.

>>9024572
And another one to check out is Demidovich's "Problems in Mathematical Analysis"
just found out it's translated into English, the book has a meme status in Russia

>every other student is working on a project with their favorite professor
>I'm too shy to ask professors if I can work with them
>I'm halfway through college and have done shit yet
>Think that everyone hates me and that they think I'm pathetic
I want to stop being a bitch so bad, but they look so aggressive.

>>9024617
Talk to a therapist, you may have a paranoid personality disorder (I'm not diagnosing you over a 4chan post - just informing you that that's a possibility).

>>9024559
1', 2' are not elements of A, what the hell are you doing? what do you even mean? it's clearly true, stop writing nonsense

>>9024635
' is obviously used to denote the inverse of an element. 1' = 3 means that 13 and 31 reduce to the empty word.
>it's clearly true
In a categorical setting (up to isomorphism)

>>9023807
>>9023830
>>9023863
Woah, this is almost exactly what I've been doing. I'm a little older than you though, I'm 22.
I've been working odd jobs and shit while I pretended to be in school, nothing enough to actually sustain myself though.

I wish I had some advice to give. Pay your student loans on time I guess. I'm thinking about becoming a navy rescue swimmer, I'm really out of other ideas and I can't keep living like this

>>9024642
then you're simply wrong
<{1,2,3} / 1' = 3, 2' = 2> is NOT a representation of <{1,2,3}>
(unless you're being facetious and hit me with "hurr they're still isomorphic" in which case go away)

>>9024648
><{1,2,3} / 1' = 3, 2' = 2> is NOT a representation of <{1,2,3}>
huh?

>>9024572
>>9024576
Yeah, by college algebra I meant abstract/linear algebra, if you're looking for a ton of problems then dummit and foote has them. But if you're looking for HS algebra for solving tricky integral problems then some problems solving books may do you well, two mentioned so far are >>9024578 and >>9024587, though various texts on olympiad problems will teach you the various tricks and give you practice problems, books art/craft or problem solving have a lot of good techniques to solve tricky integrals. Other places to find problems are brilliant, khan academy (don't watch the videos, just do the problems), coursera, MIT opencoruseware, and the like.
>>9024585
A good book for complex analysis is ahlfors, it covers complex analysis with a view towards number theory, another book that does this as well is stein/shakarchi complex analysis. At least if you're doing cryptography this should help.
>>9024586
If it's for mech E then what I suggested should be enough to start. The math covered for mech E is usually Cal (single/multi var, vector analysis), Linear algebra, ODE's, PDE's, maybe some complex analysis, a math methods book will usually have everything you need (>>9024576 these books will also have the kind of problems you're looking for) (like hassini, strang applied math, here's a good link to some sources and videos https://ocw.mit.edu/courses/mathematics/18-086-mathematical-methods-for-engineers-ii-spring-2006/readings/)

There may be a few things I'm leaving out, what else do you guys need or do you want to me to go into more depth on any of the things I've suggested or want alternatives

>>9024602
>Landau-Lifshitz
>For someone who has basic knowledge in math/physics
Not saying they aren't fantastic books, nor that someone could reasonably get through the 6 books you mentioned over the summer (as long as put a decent amount of time in it's not too difficult) but I don't think it's a good choice for someone who doesn't already have a basic understand of the covered concepts, nor who's trying to go into engineering.

>what are you studying

I am studying for my Linear Algebra I final tomorrow. The last topic we covered were vector spaces of linear transformation, algebras (because with composition these vector spaces form unitary algebras), the dual space and the bidual space. We only went as far as constructing a basis for the dual space over an arbitrary field, and constructing a basis for the bidual space over an arbitrary field.

We didn't have a textbook though, so could anyone tell me what kinds of problems could come in a final about these topics? We never did any practice problems because these things were literally covered in the last week. I am looking for problems online but they seem to be from more advanced courses.

>>9024575
That's right. Differentiability only makes sense a priori for coordinate changes (between open subsets of R^n) between charts

>>9024648
As soon as you define the action of an arrow element-wise you lose generality. In your construction, [math] \phi [/math] is dependent on the presentations of the groups, so it's not well-defined.

>>9024576
Read "Equations and Inequalities" by Kucera et al. Taught me everything I know about basic algebra. You can even find it for free if you google it

>>9024585
can we read you k theory piece?

>>9024585
How is it possible to focus on number theory without specializing in complex analysis?

What did you do? 4 straight years of elementary number theory?

Hi. I asked a question in sqt but I would like to ask it here too since this has more activity.

Let T be in Hom V and nilpotent so that T^n=0, but T^(n-1) =/=0 and assume V has the property that any of its subspaces has a complement (in terms of direct sum to V). That is for any subspace M in V, there is a subspace N with M and N forming a direct sum for V.
Now let V_1 be the complement of the null space of T^(n-1) called N^(n-1) here. I have shown that the intersection of T[V_1] and N^(n-2), the nullspace of T^(n-2), only contains the 0 element. I have also shown that T[V_1] is a subset of N^(n-1).
The part I'm stuck on is asserting the existence of a subspace V_2 such that V_2 and N^(n-2) form a direct sum for N^(n-1) but T[V_1] is a subset of V_2.

The textbook in particular says "extend" T[V_1] to a subspace V_2 with that property. I don't know how to do this

>>9024757
>How is it possible to focus on number theory without specializing in complex analysis?
There's tons of areas of number theory that don't really require complex analysis:
>algebraic number theory as long as you stay away from Dedekind zeta functions
>cohomology of number fields
>Iwasawa theory
>p-adic anything
>geometry of numbers
>elliptic curves
>arithmetic combinatorics
>Galois representations
>dynamics
list goes on...

>>9024785
Okay true but come on... Complex Analysis is classic. Complex Analysis is THE thing for number theory. But oh well.

>>9023972
Mutable sub-frequency graduation. For there to be zeroes there must be a one.

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>>9024803
>Mutable sub-frequency graduation

>>9024785
>elliptic curves
>dynamics
kek
Besides, you can't really isolate these things from one another and some of them do require some complex analysis.

>>9024735
I'd rather not share it because my real name is tied to it.

>>9024795
It's not like I'm completely new to complex analysis, but I don't think a semester-long course gave me anywhere near enough preparation to deal with this: >>9024546 .

>>9024810
>kek
What's funny? You can easily spend a lifetime studying elliptic curves over the rationals or finite fields without needing anything more than the most basic knowledge of complex analysis, same with dynamics. Take a look at Silverman's books, 'Arithmetic of Elliptic Curves' and 'Arithmetic of Dynamical Systems'

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Theoretical physics grad here. Never felt I had a grasp of proper rigorous mathematics, like all physicists we skim over it and focus on the physics. Now a software engineer.

Anyway I've been reading a first year maths student book, really basic stuff, getting me back into the groove ready to apply to a math-phys masters.

But I'm being hit by that realisation grad students get of "holy shit there's so much I don't know". Even this basic stuff for a couple hours a night after work is taking ages, it takes maths students 3 or 4 years to learn all this studying fulltime.

Basically what's more useful to a wannabe mathematical physicist? Would I be better off with a primitive 1st or 2nd year math student's understanding of pure maths (ie. keep slogging at the fundamentals), or do I skip ahead to advanced topics and accept that I'll never have a pure mathematicians understanding on these topics (like your average theoretical physicist does in other words).

Next on my reading list at the moment is Geoff Smith Introductory Mathematics: Algebra and Analysis.

>>9024656
Hey thanks I found a high-quality copy of the stein/shakarchi complex analysis book as a pdf so I think I'll check that out. Appreciate the help!

>>9024823
It really depends on the specific field you're going into, "mathematical physicist" is very broad and for a lot of it you won't need to be at the same level as say, a 4th year grad student, but for some you will, so which field do you want to go into?
>>9024839
No prob, also if you didn't know you can download pretty much any mathematics text out there from lib gen.

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>>9024823
>like all physicists
Speak for yourself.
>useful
Why do you feel the need to be able to pretend you understand these things? What topics in mathematical physics are you even interested in?

>>9024823
you won't get anywhere without the "mathematical maturity" that you gain from working through actual rigorous proofs, not the ones you get in your physics courses.

With that said, you would probably be better suited working through a book that teaches you about proofs (How to prove it, how to prove it, etc), then get onto a relatively intuitive 'hard' topic like real analysis to get a taste of how mathematics works

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>>9024765
[math] ker(T^{n-2}) \leq V [/math] so it has a complement, i.e. [math] \exists V_2 \leq V [/math] such that [math] V_2\oplus ker(T^{n-2})=V [/math].
But [math] T(V_1) \cap ker(T^{n-2})=\{0\}[/math] so [math] T(V_1) \subset V_2 [/math], by the definition of the direct sum.

I'm running out of lewd things to say.

>>9024913
>Speak for yourself.
lmao, as if your shit isn't sloppy as fuck.

>>9024925
Thats not necessarily true and not what I'm after. Its possible for a point in T(V_1) to be in neither the kernel of T^(n-2) nor V_2 but still formed by a sum of the two elements. V_2 here is supposed to be the compliment of T^(n-2) in nullT(n-1)

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How did you get into Math? For long have you been into it? And how many hours do you study a day on average?

>>9024939
>rough ideas are sloppy
Oh wow it's as if you've never done research in your life before.

>>9024947
Oops I meant [math] ker(T^{n-1}) [/math] not [math] V [/math]. You get [math] V_2 [/math] from the intersection of its complement in [math] V [/math] with [math] ker(T^{n-1}) [/math].

>>9024948
i took an "Intro to Modern Algebra" course as a freshman, and then took every algebra offered to undergrads and grads at my undergraduate university.
i still like it, but i think there is more money in QC and Simulation, so that's what i'm doing for graduate school

>>9024973
Ok I think I see what you are trying to change, but I still dont see why T(V_1) is a subset of V_2

>>9024973
>the intersection of its complement
The intersection of the complement of [math] ker(T^{n-2}) [/math] in [math] V [/math] with [math] ker(T^{n-1}) [/math] I mean.

>>9024987
this is a little hard to keep track of at this point. could you rewrite it please

>>9024909
>>9024913
Cosmology. Relativity. String theory, quantum gravity. Stuff like that.

Differential geometry was a big stumbling block for me, really showed the gulf between being a physics student specialising in theory and suddenly hitting this wall of advanced mathematics that you can't sidestep anymore.

>>9024914
Cool I'll keep proofs in mind when choosing topics, it is an area I know nothing of.

>>9025027
>String theory
>Differential geometry was a big stumbling block for me

you ain't seen nothing yet

>>9024818
I have trouble seeing how you could study elliptic curves over Q without ever considering their complex points and their topology (I mean there are many other aspects to the study of elliptic curves, but the Riemann surface pov is pretty salient)

can someone please help me understand lie groups, and how generators are tied to the underlying lie algebra, specifically concerning the SO group, pls?

spin is a very difficult concept, and it seems lie groups are the only thing that properly describe them

>>9025031
They still have a topology when they are not over C. The Zariski topology is obvious, but the etale topology is more interesting.

>>9025030

Yeah why do you think I'm studying pure mathematics.

If I could go back in time I'd have enrolled in a mathematics course (we can't transfer about like you can in the US because our bachelors are 3 years, we specialise from the start)

>>9025035
The lie algebra is the tangent space of the lie group at the identity element.

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>>9025027
None of those are mathematical physics, except maybe for string theory which is half math half /x/. All of those are no problem for actual theoretical physicists, and there are thousands of references out there for these (written by physicists) that are rigorous.
Actual topics in mathematical physics include geometric quantization, homotopy quantum field theory and constructive quantum field theory (to name just a few). These are actual mathematical topics inspired from physics.
If you're having trouble with differential geometry you're best pace yourself first because it's still much too early for you to try to study actual mathematical physics.
>>9025035
If you want to understand spin you need to understand Clifford algebras.

>>9025027
I found a good way to learn abstract proofs from axioms (once you have the mathematical maturity as I said earlier) is to learn something like topology, and attempt every single proof to every theorem in the book before you go through the proof (maybe a book like Munkres). They are easy especially at the start of the book, although completely abstract.

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>>9025004
>>9024986
For some reason I read your exercise as "V has the property that any of its subspaces has a [math] unique [/math] complement". Vector subspace always have a complement so I didn't register why they'd mention that in the first place, it's a banal property. Anyway...
>how to extend a subspace until it has the desired property
You add new points to [math] T(V_1) [/math] and take their hull until the resulting space is large enough. (You will need to use the axiom of choice if [math] dim(V) = \infty [/math].)

I'm too sleepy to write a full sketch.

>>9025229
Oestrogen makes you stupid.

>>9025229
I want to be a cute boy, but I don't think I could ever go as far as taking hormones
I will stick to diet, exercise and proper skin care, thank you

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>>9025195
>filename
For the longest time I have thought I was posting alongside West Europeans.

>>9025244
>discount trap
Rude, I'm not trying to be any sort of trap

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There will be a /mg/ cute boy orgy within our lifetimes.

>>9025236
>dissing Latin
What an uncultured swine.

>>9025229
>>9025233
>>9025244
>>9025248
>>9025253
just kys already

>>9025255
Maybe after the /mg/ orgy I will

>>9025255
>t. mad burly hairy man

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>>9025254
I can tell it's Romanian, Spanish, Italian, or any of the hundreds of languages related to those three. You would have written it as cvlpa it if was Latin, and that's not even how you write sorry as far as I know Latin.

>>9025280
I know for a fact it's a relatively common expression in Spanish.

>>9025280

Confiteor Deo omnipotenti, beatæ Mariæ semper Virgini, beato Michaeli Archangelo, beato Ioanni Baptistæ, sanctis Apostolis Petro et Paulo, omnibus Sanctis, et vobis, fratres: quia peccavi nimis cogitatione, verbo et opere: ***mea culpa, mea culpa, mea maxima culpa***.

I confess to Almighty God, to blessed Mary ever Virgin, to blessed Michael the Archangel, to blessed John the Baptist, to the holy Apostles Peter and Paul, to all the Saints, and to you, brethren, that I have sinned exceedingly in thought, word and deed: through my fault, through my fault, through my most grievous fault.

>>9025302
>I know for a fact it's a relatively common expression in Spanish.

I'm from latin america and not a single time have I heard anyone say "mea culpa". It is not an "expression" either. At least not a popular one, perhaps if you read a novel from those cockstroking authors that love to choke on latin cock you will find it.

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>>9025280
What a dumb Murrican.

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>>9025313
>I'm from latin america
Stay away from this thread and never come back.

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>>9023625
What percent of math grads are autistic animufags?

I'm starting my PhD in the fall, and this general is seriously giving me second thoughts.

>>9025321
/mg/ is a non-representative sample.

>>9025320
Shut the fuck up retard, your tax money is paying for my education as we speak so I think I know who is the superior one here. Go clean my shoes, whitey.

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>>9025321
Stop being so squeamish.

>>9025321
Most math PhDs aren't this autistic, only the good ones.

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>>9025315
www 行ってよし
私はアメリカ人ではない
アメリカ人は野蛮人です
>ラテン
ポーランド語、スウェーデン語、ギリシャ語、と日本語は十分です

>>9025399
Holy shit. How did you end up like this? Please tell me this had nothing to do with mathematics.

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>>9025409
When you do nothing but watch anime the whole day and consume other similar medias, you start acquiring a taste for girly things. The first thing you buy is a pinky cushion, then some figures, then some body pillows. You start cosplaying and then you realize it's fun, and you want to cosplay as female characters. Months later and you're wearing skirts before you know it. I wouldn't say mathematics is a cause or an effect, it's just a symptom.

>>9025423
>When you do nothing but watch anime the whole day and consume other similar medias, you start acquiring a taste for girly things.

I agree, I have seen many times that I have a taste for girly things. Mainly because in anime I almost only see girls so I start relating a lot to girls. That said, the rest is bullshit.

>Pinky cushion
Fuck no man, I'm not gay
>Then some figures
Yes, I have figures but of sexy anime women I want to fuck.
>Then some body pillows
Yeah, I have a couple but again they are of sexy women with little clothes who I want to fuck.

>you start cosplaying
I will never engage is the mass degeneracy act that is cosplay
>cosplay as female characters
Holy fuck anime is a mistake
>months later you are wearing skirts
SHEEEEIIIIIIIIIIIIIIIIIIIT

>>9025429
Is that you? If so, please post time stamp while holding a math book. Nothing pleb though, I want to know if you are actually a mathfag or some roleplayer messing with us.

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>I want to know if you are actually a mathfag or some roleplayer messing with us.
You must be new to this website.

>>9025454
>You must be new to this website.

I've been here for 5 years now. I know about the degenerate trend that is traps but I have the firm believe that traps and people who like them are subhuman 2 digit IQ plebs.

Post a timestamp or yourself in a skirt and holding a book on anything above the undergrad level or I know you are just some /cgl/ faggot larping.

>>9023807
switch your major to something easy like accounting

>>9025429
I don't believe those are not a girl's legs.

>>9025512
Are you saying you want to see the cock and balls for... proof?

>>9025517
Y-yes. No homo, though, all for the sake of confirming that /mg/ is full of cute boys.

>>9025524
Well, now we at least now it is full of gay boys.

>>9025321
Well, you have to remember that they're only like this because they have a self esteem issues and a serious deficit of attention from other sources. They'd just come off as average quiet friendless nerds when you bump into them in the hallway.
Academics are surprisingly normal on average, what you should be worrying about are the pooinloos.

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>>9025526
Just like yourself. A gay boy amongst a sea of gay boys.

>>9025542
BUT I SAID NO HOMO!

>>9025542
Whoops, >>9025575 was actually meant for >>9025526.

>>9025399
>>9025429
>>9025517
>>9025524
>>9025526
>>9025575
This is getting a little gay...keep going. Also explicit dick isn't necessary, a skirt lift revealing a bulge is more than enough...while having it be time stamped and with a GTM book

>>9024939
She didn't say she was capable of proper rigorous mathematics. She just said she has a grasp of it, which is pretty good for a physicist.

>>9025457
>I've been here for 5 years now.
So as I said, you are new to this website.

>>9025636
>a skirt lift revealing a bulge is more than enough
>expecting these low testosterone failures of evolution to have enough dick to form a bulge

You are asking for too much.

>>9025355
Nice, broken Japanese. google translate or some other site?

>>9025764
Hah? Borukegu na Nihongo desu? Ja nai desu!

>>9025399
>thick thighs
I see you've learned to pose well. I can get the same effect from that angle with a pillow under my thighs. I will spare you the image because I don't epilate my legs.

>>9025769
If you call that thick thighs then your own degeneracy has already started consuming your brain.

>>9025457
Look at the filenames you dumbass. You're getting trolled.

>>9025775
The pictures may not be them, but they could still be traps. Just shy traps. I still want to know if they are actually math traps or if they are regular traps larping.

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>>9025770
>he likes fatties

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>>9025782
No retard. See pic related for thick. Lay off the traps for a month and you will go back to normal.

>>9025782
>He doesn't want a thicc and stronk amazonian math gf
Less competition for me. By the way, I'm still waiting on a cute boy census for /mg/. So do go on.

>>9025789
>By the way, I'm still waiting on a cute boy census for /mg/.

I second this notion. I am still waiting for the timestamped bulged panties.

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Thinkin' about math n shit. Is Lurie's book on higher topos theory a good way to introduce oneself to the world of topos homotopy?

A nice little result I came up with maybe a week ago is that if [math]\mathscr{E}[/math] is a category in which terminal objects are initial (for example an abelian category), then all its objects are initial if [math]\mathscr{E}[/math] is a topos. This follows from the fact that, in a topos, any arrow whose codomain is initial is an isomorphism. This, naturally, affects the spoopy skeletons of such categories, and thus there is only one equivalence class of abelian toposes.

On the other hand, in a well-powered abelian category satisfying a distributivity condition, there could be (I'm making this up while writing) a topos of disjoint subobjects for any object. This idea came to me from the fact that a topos satisfying certain conditions is a Heyting algebra, and so a frame. Anyone here know any conditioms for this to be true?

>>9024047
I'm quite sure this thing is equivalent to the AC, sorry.

>>9024948
Reading Logicomix and Logik, språk och filosofi by Georg Henrik von Wright. I try to spend a few hours every day thinking about mathsy stuff, even if I'm not studying.

>>9025786
That's already very thick thighs. I am not using "thick" as in the "thicc" meme garbage. All women with some feminine curves have thick thighs. Men don't. The thigh to foot muscle ratio is usually closer in men. Legs don't have the same truncated conic look, they're closer to a cylinder.

Do I really need to teach you basic anatomy and sexual characteristics?

>>9025786
>pic related
Ugly.

>>9025794
>Do I really need to teach you basic anatomy and sexual characteristics?

Yes please because I have never so homosexual as to start deepling thinking about the "thigh to foot muscle ratio" in men, you fucking homo. Please do tell because this is all new for me. How about the cock and ball ratio? What do you know about that one?

>>9023767
I need to head out. I suspect this can be proven informally using the first isomorphism theorem. A formal proof might require drawing an adjunction between $\textbf{Grp}$ and $\textbf{Set}$ to show that $\Omega$ has too many automorphisms, and so that it cannot exist in a small category.

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>>9025794
>>9025799
There's nothing homo about being observant. I really wish I were homo at times though.

I'm doing a major in math at a small state school. Part of the program is a one-semester-long seminar which entails the research, development, and presentation of a formal paper regarding some topic in mathematics.
I have no idea what to do for this course (I still have two semesters before I take it). I do not know of any purely mathematical problems that I could explore, but I know of a few applied math problems in earth science that haven't been examined yet. I would like to model the rotation of platy clay minerals under lithostatic pressure in order to determine when mud deposits become fissile (i.e., at shallow-burial or diagenetic pressure). There are many papers that venture a guess at this problem via real-world observation, but no one has modeled it yet.
That being said, should I model clay mineral rotation? Or should I do something more math related. For what it's worth, I hope to attend grad school for geology. I am doing the math major to demonstrate my ability with quantitative stuff.

>>9025808
>There's nothing homo about being observant.
Perhaps not if you are a biologist. But if you are just a casual who googled these things, or learned them by looking at other men's legs then you are definitely 100% undoubtedly gay.

>. I really wish I were homo at times though.

If you wish you were gay then you are probably gay. Being straight is literally the best. You get to naturally fuck the most fuckable creature in the world: the human female. The human female is a fuck machine specifically for the pleasure of the cock, and you want to reject that?

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>>9025815
You're projecting quite hard anon. Are you sure you're not starved for cock? There no need to try so hard to prove anyone that you're straight, you little homo.

>>9025823
Nice setup for a mindgame but I'm not falling for it. I never argued that I was straight, and I don't even need to mention if I was straight or not. I simply argued for why you are very fucking gay.

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>>9025827
Anon please...

>>9024047
No, because that's false. A morphism can be epi even if, say, no inverse morphisms exist.

>>9025814
>but no one has modeled it yet
I don't know about rock polishing stuff, but just from this I imagine it's going to be a really big challenge for you to tackle. You should ask proffessors from both the geology and the mathematics department for this stuff.

>>9025837
Well, a morphism can be epi without even being a function, so...

>>9025842
Thanks for the input. One of the geo professors has a strong computer science/mathematics background. I will see what he thinks once classes start again.

>>9025848
If you're talking about the case where all functions between pair of sets exists, then >>9025792 is right. What you're trying to show is the existence of an injection for every surjection such that the composition yields identity, which is AC.

>>9025837
Surjections are inconsistent with AC.

>>9025863
I'm not the either the guy who posted that nor the guy who replied. I'm only pointing out that morphisms and functions are different things. A morphism is an arrow between the objects of a category. These objects need not be sets, so a morphism need not be a function.

>>9025873
Rubbish. You don't need the axiom of choice to prove that surjective functions exist. You need the axiom of choice to prove that surjectivity is equivalent to right-invertibility.

>>9024424
I concur with this statement.

>>9025884
You can remove functions arbitrarily from the category of sets and still end up with a valid category.

>>9025887
He is right though. You can't prove that a function is surjective without the axiom of choice.

>>9025899
That statement cannot be true. You can always show state that an identity function is a surjection. Every identity is an isomorphism, and every isomorphism is both a surjection and an injection.

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>>9025898
You can also remove yourself from the thread and we'd all be better off for it.
>>9025899
Stop posting, brainlet.

>>9025909
He's trying to prove a statement that's ill-defined in important ways. Once he clarifies the functions that do and don't exist, it will be obvious whether or not he's trying to prove AC using ZF axioms.

You're (you) mining aren't you?

We should have a new thread soon.

>>9025908
>You can always show state that an identity function is a surjection.
Yes, assuming the axiom of choice.

>>9025909
>Stop posting, brainlet.
Says the retard who posts r*builds.

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>>9025909
He's clearly baiting, you're outing yourself as a brainlet by falling for it.

Also, the equivalence of AC and the existence of right inverses is obvious. Consider a disjoint family of non-empty sets and the function defined on their union which assigns every element to the set where it belongs. Any right inverse for this surjection is a choice function.

>>9025908
>That statement cannot be true.
It's actually true I think. Surjective functions can't be shown to exist in ZF.

>>9025919
No, even without the axiom of choice. The identity function is by definition its own left and right inverse.

>>9025924
You can't prove this statement without AC. It's certainly surjective, but there is no proof of that in ZF.

>>9025918
Why? We're barely on page 2. The weekend is almost over even on the West Coast. Monday morning in Europe. The rest of the globe only makes up, what, 10% of the posters here?
Post frequency will drop precipitously.

>>9025928
Identity: f(x) = x by definition.

Proof that f is the right inverse of f: f(f(x)) = f(x) = x. QED.
Proof that f is the left inverse of f: f(f(x)) = f(x) = x. QED.

What part of this requires AC?

>>9025921
Yes, I realised that. >>9025915