/sci/ - Science & Math

Have your unis announced what they're doing in September for courses yet?
Mine just decided that everything outside of labs is going to be delivered online again

Some days I like math, other days I don't.

>>11692894
futur math major here
my uni (UdeM) announced that all my classes will be delivered online
I will take my first uni courses online. Yeurk

how do I derive a girlfriend?

>>11693303
In your parents car as an Uber driver for some Chad and his gf

>>11693308

what's Chad doing in an uber instead of driving his on truck?

>>11693324
One who doesn't live in Kansas?

>>11693303
>how do I derive a girlfriend?
What have you tried?

What are your hobbies /mg/? How good are you in them?

Mine:
>Piano (pretty good)
>Drawing (not very good)
>Literature (pretty good)

For me, it's the symplectic Clifford algebra.

>>11692894
They wanted to make everything online here as well, but some poorfags complained that they don't have internet (but somehow they have facebook, instagram, twitter), then the uni decided to no make it online, so everyone gets screwed instead of just the poorfags

>>11693607

mine are sleeping and drinking alcohol

>>11693724
What a sad life

>>11693607
I'm an irredeemable /tg/ fag

>>11693739

escapism is the only hobby I can afford

>>11693607
>posting here (decent)
>going for walks (average)
I would like to try HEMA, but lock down is sabotaging that.

>>11692929
If it doesn't hurt, it's not worth it.

>>11693779
You can escape by having good hobbies instead of just drinking

>>11693783
>HEMA
Which one?

>>11693795
I thought there is only one... fighting with langmessers and falchions and stuff. It's probably not my thing, but those would probably suit my feeble physique best and give me the hypothetically existent chance to enjoy it.

>>11693823
Why not Kendo then? Japan is better than Europe in every single way, swordfighting is not an exception, the katana are weapons better suited for true warriors

>>11693826
I've always liked knights more than samurai, besides kendo wouldn't fit the castle surroundings as well as HEMA. I like things rough!

>>11693249
oof. J'aimerais dire bon succès, mais ce que je devrais dire est bonne chance

>>11693889
Salut mon ami français, j'ai apprendend le français, c'est une belle langue

How would I model a discrete function (read: dataset taken over time) into an actual expression I could mess about with?
The only (tenuously) relevant concept I'm familiar with are power series and the like... but it wouldn't preserve any data points besides the center.

is any1 familiar with wildbergers triple quad theorem? I intuited an alternate of it. I'm honestly in a bit of shock rn. I took a different point of departure, and my substitutions took a slightly different form, but the algebra and conclusions end up being identical. if I were to post my equations side by side with his, and describe my goals, it wouldn't be immediately apparent that we were doing the same thing, but, the algebra would look very similar and the conclusion would be the same

he seems to have dedicated his life to the exploration of this method for calculating geometric relationships, and I just had an idea and worked it out. on one side I'm happy because he's done a lot of the work investigating the consequences of such a theorem, but I'm disappointed because it's not exactly mine. this is a learning experience, and I'm very happy I got to intuit and work it out for myself, but it's a mixed bag. has any1 else found this by themselves?

https://youtu.be/3GU9mGyxz04
https://youtu.be/8rjxOFAzBa4

>>11679518
https://youtu.be/soHBNEJlzL0

>>11693778
Don’t ignore me. Post soles...

bros... i dont feel like doing any maths...

>>11694670
do physics today

>>11694670
have you considered not doing math?

>>11694685
what else am i supposed to do?
and if i dont feel liek doing maths today will feel like doing it tomorrow?
>>11694683
no point...

>>11694670
How old are you? If you're over 24, just forget about math man, believe me

>>11694696
trying to turn everybody else into a lazy failure so you don't feel so bad about being a lazy failure is not a healthy coping mechanism anon
please seek therapy

>>11694707
He's always in /mg/ saying the same shit. He's just rationalizing being a lazy fucking bum and encouraging others to be one.

>>11692864
Your resume, facebook, and instagram all have the same username. Dont anger me. Post your soles now....

>>11694755
don't scare her off dude, that's probably the only female (not male) we have in this thread

>>11694755
Please, don't leak it, delete that post, I know you're better than /bl

>>11693303
Integrate a fag

>>11694803
just private everything and wait a week

>>11694828
>>11694795
simps

>>11694803
I will spare you this time, but that was not very smart to post a picture thats available online already.

>>11694831
>chickens out without his feet pic
who's the simp again?

>>11694834
I google cute feet get 1 million results

can you stop shitting up /mg/ with your drama, nobody cares

>>11694840
this is preferable to animeniggers circlejerking all thread

>>11694845
It isn't, I was just asking if the book was good and a jerk was ready to raid me for no good reason, that's /b/ behaviour, ridiculous coming from a board whose users claim to be high IQ.

>>11694859
Feet is a high IQ fetish you midwit femoid.

>>11694919
>Feet is a high IQ fetish
feet is the most basic-ass boring fetish there is
it's so vanilla it barely even counts as a fetish

>>11694859
Nature's Numbers was pretty good, I read it as an undergrad. Most are pretty bad though. GH Hardy's book is a must read.

>>11694859
>that's /b/ behaviour
The b stands for based.
>>11694919
>feet is high IQ
Feet is the definition of a middlebrow fetish.

>>11694986
Ok nerd tell me what you think a high IQ fetish is so I can laugh at you.

>>11695002
https://www.thedailybeast.com/cuckolding-the-sex-fetish-for-intellectuals

>>11695017
Ok big brain let me fuck your gf then.

this /mg/ should be deleted.

>>11695002
You go after a boyish-looking girl and you let the paranoia about her actually being a boy completely consume you.
Also armpits.
>>11695017
Don't be stupid.

>>11695042
Not a single LaTeX post in 53, this thread isn't even about math anymore

A constructive mathematics professor was teaching a class on Brouwer, a known intuitionist.

”Before the class begins, you must get on your knees and worship Brouwer and accept that he was the most highly-evolved mathematician the world has ever known, even greater than Hilbert!”

At this moment, a Platonist set theory PhD student who had written 1500 unread papers about the consequences of various esoteric large cardinal axioms and understood the necessity of set theoretic reductionism and fully supported all applications of the Axiom of Choice stood up and held up the Law of Excluded Middle.

”Is this proposition true or false, pinhead?”

The arrogant professor smirked quite Jewishly and smugly replied “We cannot say, but our experiences strongly suggest that this proposition is not provable.”

”Wrong. If it were false, then there should be a proposition P such that ~ (P \/ ~P), but we know this contradictory, even in intuitionistic logic."

The professor was visibly shaken, and dropped his chalk and copy of Foundations of Constructive Analysis. There is no doubt that at this point our professor wished he had just studied model theory or some other mainstream mathematical discipline. He wished so much that he could argue for his position by first supposing that it were false, but he himself had petitioned against such modes of reasoning!

The students applauded and all enrolled in a set theory course that day and accepted the supremacy of classical first-order logic. An eagle named “Mathematical Platonism” flew into the room and shed a tear on the chalk. The axioms of ZFC were read several times, and Gödel himself showed up and established the existence of an abstract realm of mathematical entities.

The professor lost his tenure and was kicked out the mathematics department that day. He spent the rest of his life teaching numerical analysis to disinterested computer science students.

>>11693628
>Getting to go to regular classes
>Getting screwed.
Stop whining, you faggot.

>>11695058
>You go after a boyish-looking girl and you let the paranoia about her actually being a boy completely consume you.
>Also armpits.
100% this, soo fucking based

/gmmg/

>>11695131
So that's the story of the "if you are 24..." poster. Not gonna lie, I cried.

What are some good math-related accounts to follow on twitter?

Also feel free to follow me, although I only use it to practice my japanese
https://twitter.com/KahlerManifold?s=09

>>11695279
twitter is a cesspool with zero content of value to anyone

>>11695282
Not true, those are good math-related accounts that I follow:
https://twitter.com/matthen2?s=09
https://twitter.com/johncarlosbaez?s=09
https://twitter.com/fermatslibrary?s=09
https://twitter.com/CardColm?s=09

>>11695279
The picture you are using reminds me of the library I used to frequent.

>>11695324
It's a random pic that I found comfy as fuck

>>11695328
It is!

>>11694687
>and if i dont feel liek doing maths today will feel like doing it tomorrow?
Not necessarily, but it will feel even more repulsive if you force yourself to do it today. Are you physically well?

derp when is it too late to git gud at math

>>11695454
never

>>11692887
2+2=4?

>>11695454
Don't try to git gud and instead try to git better

Crossdressing is the highest IQ fetish

>>11695933
Show us a picture of you in a dress!

sorry, if this question may seem a bit autistic but what should I write in an email to a professor if I want to write my bachelor's thesis under his guidance?

>>11696268
Dear Professor [name here],

I would be interested in having you as my bachelor's thesis supervisor. I have taken the [relevant courses and their grades], and would like to keep going in that direction. In particular, I have been thinking about [your ideas here] as potential topics. Your expertise on the subject would make you an optimal supervisor, and I would appreciate it a lot.

Best regards,
Frog poster

>>11696308
>their grades
Is this necessary?

>>11695131
>is not provable
>Wrong. If it were false
Why did the professor forget, from one second to the next, that "not provable" is very different from "false"?

>>11696321
Not necessarily, but good grades would make things go more fluidly, bad grades should probably be left unmentioned. I'm not necessarily the best guide, since I just marched into my supervisor's office and asked if he supervises stuff. "Yes", he said, so I came close to him. "Would you... want to do that with me?" I asked, and he asked what i wanted and what grades I had. "I want you... to supervise my thing on group theory, I got 5 from the algebra course" I replied and he told me to read Herstein's book and base my things on that. Later, I marched into my master's thesis supervisor's office, asked if she supervises stuff, received a "yes", told her I want her to supervise my stuff on category theory and she was like "OK let's do it" She didn't ask for my grades because she had taught me directly an knew the 5/5's already.

On the other hand, the thing I wrote to you is pretty similar to what I sent to my current supervisor with the slight difference that instead of listing any courses I had attached an official copy of my certificate, but yeah. It worked. he became my sugar daddy.

>>11696357
>I got 5 from the algebra course
5 out of 5? I also got a 5 on my algebra course, a 5 out of 10, oh shit i dont think i can make it anymore, supervisors will probably laugh at my grades

redpill me on fixed-point index
https://en.wikipedia.org/wiki/Fixed-point_index

>>11696424
Then you don't mention them. Keep them hidden, keep your mouth shut, only speak of them if you are asked.

>>11696428
Remove a point from the Euclidean plane to get a space homotopy equivalent with the unit circle. Do the same for the complex plane and a neighbourhood of a fixed point containing no other fixed points. Restricting to the boundary of that nbd, you get a map from to the unit circle, and then you just count how many full laps you make and in which direction. Excluding Lefschetz, I can't think of many uses for this. I guess you could use it to distinguish between different maps sharing a fixed point if they have different indices, or if the index is 0 then you don't go around the circle (and thus your map g is null homotopic). Can you make any conclusions out of these?

>>11696456
Addendum: the fixed point is isolated, so you can take a ball whose centre it is with a radius sufficiently small. Then the boundary is, up to scaling and translation, the [math]S^1[/math]. Then you can just think of the map as a self map of the circle, and so the degree corresponds to the integer such that the induced homology morphism would be the "times this integer" homomorphism from integers to integers.

>>11696325
wow you sure BTFO'd that copypasta with facts and logic

>>11696487
somebody has to get their fingers dirty

>>11696491
I hope you have less than 24 fingers, anon. Otherwise you will not make it...

Algebraically closed fields were a mistake.

>>11696518
Prime characteristic or bust!

>>11696456
What happens if I lie about my grades?

>>11696546
It's a gamble. If you lie and they find out the truth, you're going to look terrible. Sometimes they will ask for a transcript, one of my rec letter writers did. But I had a research assistant and teaching assistant position, and not a single soul asked for my transcript or about my grades, which was ideal because I was quite average. I did very well or very poorly.

>>11696546
Why would you lie about them? Not mentioning they aren't stellar is not the same as lying. If the professor asks, you can try to come up with an excuse or just say you were going through some personal stuff or whatever, but don't lie. Even better, you can be honest and say you were bad back then but now you have restudied the things you were struggling with and that sparked your interest (depending on the prof, you could want to be ready to provide evidence for this!) and show that you are motivated to learn! Consider the following chain of events: You go to the prof, lie about your grades, get accepted as his student, do what you were supposed to do, receive your degree, stay in the same uni, get a master's degree/go directly for a phd whatever is the way to go in your country, graduate, apply somewhere for a phd or a postdoc position depending on your current highest degree at that point, get rejected because you got caught lying and the prof told you are not trustworthy. Do you want that to happen? Remember, you are a student. Your mission is to learn, and failing is a part of that. If you can show that what you used to be is not what you are now, I see no reason why the prof wouldn't accept you.
tl;dr:
>don't mention your grades unless asked and then show that you have improved from those days but don't lie

>>11696456
>>11696476
somehow, i understand and don't understand at the same time
fuck topology, i'm supposed to learn lefschetz-hopf theorem and more, and I'm getting btfo'd

>>11696640
Try it out with something tolerably easy like [math]f(z)=-z, f(z)=z^2[/math].

https://youtu.be/XMAl15VHMpg
>Jade Master: The open algebraic path problem
t - 15 mins

In what way does studying modules over a ring help study the ring itself?

Parsing through my commutative algebra textbook, the only theorems I saw that were explicitly about the module structure having an effect on the ring were:

>For a commutative ring with unit, the ring is noetherian if and only if every module of finite type is noetherian (resp. artinian, coherent)

But this doesn't seem particularly illuminating, let alone a feasible way of saying anything about the ring, especially given the fact that the ring is of finite type over itself as a module so clearly the right hand side already assumes this.

>>11697013
Isn't the modules exactly all linear representations of the ring? Ask differently, what does it mean to study the ring "in itself"?

>>11692887
What is the difference between probability and geometry? They seem be different ways to describe the same thing or is there something deeper going on here.

>>11697029
Well, I'd say finding out properties of the ring to be studying the ring in itself. For example, Noetherian, artinian, coherent, local, flat, UFD, PID, ED, DVR, its ring extensions and prime properties, integral, finiteness, etc are all things that I'd want to find out about a ring, in some setting or another.

Right now, I'm reading about quasicoherent modules over a scheme, and I have a feeling that a similar sort of conclusion is going to come out of it, that is, studying qc modules over a scheme is a way to studying the scheme itself . But already, over an affine scheme, studying qc modules is like studying modules over a ring, so I have trouble seeing what exactly am I going to learn from looking at them over a scheme if I can't even see what's the benefit over an affine one.

>>11697013
modules are literally vector spaces except there's a ring instead of a field, it's a really simple structure which comes up a lot naturally
as for the proposition you quoted, obviously the interesting part is
"ring is noetherian => every module of finite type is noetherian"

>>11697065
Yes, but vector spaces are interesting in their own right, just like modules are, but if didn't know any better, I wouldn't use vector space theory to study the field itself, especially [math]\mathbb R,\mathbb C[/math] - however, I do know that over smaller fields like finite extensions of [math]\mathbb Q,\mathbb F_p[/math], that actually, there's a lot to be gained from vector spaces through Galois theory. Ultimately, I want to study scheme theory, where (I assume, have yet to get there) I'll be studying schemes such as quotients of rings [math]R[X_1,...,X_n][/math], and I assume that looking at quasicoherent modules over these schemes will be a way to study them, as I mention >>11697064 .

There's a similarity between modules over a ring and quasicoherent modules over a scheme, so what I want to know is how to expect to reap the benefits of this interaction, by starting at the basics of what do modules over a ring elucidate about the ring.

>>11697013
Imagine showing that modules over a certain kind of ring have a property, pick a ring you want to study and construct a counter-example. I'm feeling silly, so I give you a very very very stupid example: the ring of integers is not a field, because [math]\text{Tor}(\mathbb{Z}, \mathbb{Z}/2\mathbb{Z}) \neq 0[/math]. You can also weaken isomorphism to Morita equivalence which is a property of rings but an equivalence between the categories of modules. This gives you more wiggle room, just like weakening homeomorphism to homotopy equivalence does in topology.

>>11697172
I see. But to be honest, I'm looking more for examples of properties that thing ring *has* rather that doesn't have. Maybe it's too much to ask for.

>>11697013
Modules give you structure theorems, they're not so good at individual properties.
Artin-Wedderburn is a nice example of this kind of thing. There's a fairly broad class of rings with a completely understood decomposition, but in order to prove (and even formulate) this decomposition you have to go through modules. If you haven't seen the proof it's probably a good way to convince yourself modules are useful.

>>11697213
Suppose every (finitely generated) module over your ring has a projective cover. Then your ring is (semi)perfect. What if I told you that if all flat left modules over your ring are projective, your ring has no infinite set of orthogonal idempotents, but it satisfies the descending chain condition on principal right ideals? Suppose that the category of f.g. projective modules over your ring is Krull-Schmidt. Then you can lift all the idempotents from the quotient ring you get by dividing out the Jacobson radical. Seem better?

>>11697172
you could have at least called it [math]\mathbb{F}_2[/math] instead of writing it as a quotient ring of the thing you're trying to prove has a quotient ring

Rate this typo.
>>11697013
Rather than giving you a good answer, I'll give a very shitty one.
Left and right ideals are left and right submodules. Subrings drool, ideals rule.

>>11697263
I was using it as an abelian group because I wanted to show that there is a module over the integers for which the Tor does not vanish. I could have called it [math]C_2[/math], though.

>>11697267
Nasty/10. Where is that from?

>>11697293
Relative Homological Algebra.

>>11697305
そうか

>>11697310
I don't speak ching chong.

>>11697316
I said 'Souka'.

>>11697318
Listen carefully, lad.
I. Do not. Speak. Nip. Nong. Bing. Bong.
Get it?

>>11697305
Thanks. I hope there's an errata correcting that.

I'm trying to get the lagrange equation for a double pendulum.
I got y=-lcosa exactly the same way this link does
https://www.math24.net/double-pendulum/
However its clear from the next question in my assignment I'm supposed to get y=L(1-cosa) like this link
https://blog.cupcakephysics.com/classical%20mechanics/2015/08/09/small-angle-oscillations-of-the-double-pendulum.html

However they both state they are taking the origin at the same place, but y=L(1-cosa) would be taking the origin at the rest position of the upper mass, wouldn't it? What am I misunderstanding here?

>>11697321
You don't need to know japanese to understand souka, it's basic anime vocabulary that everyone knows like onii-san, kaa-san, ohayou, sayonara, hayai, daijobu etc

>>11697267
explain

>>11697326
Or to be more helpful. In the first link, what happens to the "1"s when you substitute (1-(a^2)/2) for cosa1 and cosa2? They don't cancel out so what assumption is being made where cosa just becomes -(a^2)/2?

>>11697348
For literally any submodule [math]A[/math], [math]B+A = B[/math]. The condition is only meaningful if [math]B=A=0[/math], the zero module.
>what should be there
Probably [math]N=B[/math], considering the existence of Nakayama's lemma.

let C be a convex closed compact subset of a Banach space
let f:C->C be a continuous map
prove that C has a fixed point

>>11697372
https://en.wikipedia.org/wiki/Schauder_fixed-point_theorem

>>11697380
my god why is this topic such a clusterfuck literally 50 fixed point theorems each named after a different person
give me a quick rundown on the proof

>>11697389
http://people.math.aau.dk/~cornean/index.html/newindex_files/schauder.pdf
Telling you it's compact also tells you it's basically finite-dimensional.

>>11697348
>>11697367
If [math]A<M[/math] is superfluous, then [math]A+B = M \Rightarrow B=M[/math].

>>11697394
why does the projection [math]\pi_{\epsilon}[/math] exists?

>>11695131
>axiom of choice
I don't see why we need this axiom, no choosing is required even for an infinite number of sets with an infinite number of elements there exists an infinitel number of sets whose elements are combinations of 1 element of each set. the only choice to be made is which derived set is to be examined, not which set is derived.

>>11697423
>I don't see why we need this axiom
What's the current stance of the mathematical community about the validity of this axiom?

>>11697409
http://www.math.unl.edu/~s-bbockel1/933-notes/Schauder_Fixed.html
Proposition 4.1 constructs the projection for you.
Tl;dr you have the centers of the balls you covered the compact set with. If a point is in only one of the balls, you map it to the center. If it's between two balls, you map it to the line between them according to a weighted average of the distances. If it's between three of them, you map it to the triangle between them, and so on.

>>11697466
thank you
now i get it

Anyone here know Anything about littlewood Paley theory?

>>11693303
By understanding that the love and relationships are a complex dynamical system and the only way to make sense of it is to analyze nonlinear relationships by using parameter estimations of chaotic dynanical systems.

Can anyone translate this shit?
I'm assuming he means that, if [math]\oplus_{i \in I} G_i \in G[/math], then each [math]G_i[/math] is in [math]\mathcal{F}[/math]. Does that sound correct?

bros...

>>11697541
Yes.

>>11697545
Are you over 24?

>>11697551
im.... 23....

>>11697555
You can still make, but you have to be quick.

>>11697566
its too late for me....

>>11697551
>Are you over 24?
Will you keep mocking me forever, weeaboo piece of shit? Isn't my failure and unfortunes enough?

>>11697567
No, you are not 24 yet.

fuck im 24 and not sure if gonna make it

>>11697572
I'll most likely get bored in a few days, but at this moment there are pretty much only 2 things that give me joy:
>24 posting
>this picture

>>11697573
it.... literally.... is...

>>11697583
You should be ashamed of yourself, you don't know how hard it is to live knowing you'll never be able to be a researcher anymore because you're already too old, what would you know you piece of shit? You've been gifted since birth, you'd never understand true suffering, true hardship

>>11697583

>>11697598
>you'd never understand true suffering, true hardship
he'll understand in a year or two once he turns 24

>>11697587
Give up now and I will find you and show you what real failure looks like. I will tie you onto a chair, sit on your lap and whisper motivational stuff into your ear.

>>11697598
Too bad I've been mediocre at best. I know very well what it feels like to be inadequate, but I will stay leeching royalty's money as long as I can before I return home defeated for the last time. I gave it a try, and it is obvious I am going to fail. Luck and hard work take you only so far. It's bittersweet to have an office but to know I will be back in a warehouse inspecting incoming goods in a few years.

>>11697623
Anon, this... this is some real art here. This is the thing I have been seeing in my dreams. Thank you for sharing this with me. <3

>>11697630
>Too bad I've been mediocre at best. I know very well what it feels like to be inadequate, but I will stay leeching royalty's money as long as I can before I return home defeated for the last time. I gave it a try, and it is obvious I am going to fail. Luck and hard work take you only so far. It's bittersweet to have an office but to know I will be back in a warehouse inspecting incoming goods in a few years.
We're all in this together, I wasn't even capable of putting hard work, procrastination was always in my way, it fucked me for 6 years, now at 24 I'm still and undergrad with nothing but failures under my belt, I know I should quit and find a job and live like a normalfag, but I'm still here clinging to those pathetic dreams I had when I was in high school, it's a really sad life, but it was my fault things got to this point, damn I wish I was born with the discipline of those genius people

>>11697630
i.... gave up.... long time ago...

>>11697669
Get at least your bachelor's degree before quitting. Then you get to choose between non-mathsy and at least a bit more mathsy jobs. I don't know about any academically inclined or w/e you would call those jobs, but there are several nice things to do out there. You'd be surprised by how much more fun it is to deal with all sorts of strange deliveries where the info you have been given by the system totally contradicts whatever you can guess from the pack list written in Dutch. Beats diagram chasing easily.

>>11697699
Where are you? I'm going to show you pain.

>>11697725
nowhere...

>>11697766
That's a lie. You are in my heart, now and forever.

/gnmg/ <3

>>11697786
おやすみ

What is the purpose of a commutator?

>>11697669
I went back to uni at 29 after failing spectacularly in my my second year in my early 20s. Completed my degree with top grades. Just stop making excuses dude and get on with it.

Einstein & an Indian are sitting next to each other on a long flight...

Einstein says: "Let's play a game...I will ask you a question, if you don't know the answer, you pay me only $5 and if I don't know the answer, I will pay you $500..."

Einstein asks the first question: What's the distance from the Earth to the Moon...?

The Indian doesn't say a word, Reaches his pocket, Pulls out a $5...

Now... It's the Indian's turn...

He asks Einstein: What goes up a hill with 3 legs and comes down on 4 legs..?

Einstein searches the answer everywhere possible and asks all his smart friends... After an hour he gives the Indian $500...

Einstein going nuts and asks: Well... so what goes up a hill with three legs and comes down with four..?

Indian reaches his pocket again and gives Einstein $5...

Einstein fainted.....

>>11698108
funny

>>11693953
Look up fourier trasform and fourier series. I don't know it well but the concept is really pretty. Pretty much the basis of file compression

the reality is a man isnt worth his weight in salt until 40+. this deification of youth is revolting, men aren't women

>>11698087
You're you and I'm me, we're not the same, pal. I tried for 6 years to build a studying habit, for 6 fucking years I tried beating procrastination and every single time I failed. Some men were just doomed from the start like me, even worse now that I'm already 24, I'm beyond my prime now, after this point brain activity only declines, and to make things even more terrible I would still have to do a masters and a PhD after graduating. I'm finished

>>11698108
he

I'd actually drop the last line

Can /sci/ offet some insight as to the von Neumann minimax theorem? The proof is not difficult, but rather I'm looking for some "aha; of course this should be the case" kind of understanding.

>>11698165
yep, men. got it tranny? you will only get worse >>11697786

>>11698214
Dude I completely bombed out of uni, then did a second time, and it was entirely because of habits.
>I'm already 24
Try failing at shit for another 5 years before moaning to me.
>I tried for 6 years to build a studying habit, for 6 fucking years I tried beating procrastination and every single time I failed
You don't "beat" procrastination. You just get slightly better forcing yourself to do shit. I still don't have good habits, I still leave stuff to the last minute, but I stop making excuses to make myself feel better.

If you want to quit then quit, but accept that it's because you don't want to, because you're lazy, not because you're "doomed from the start" or "past your prime". You can do this but you are choosing not to.

This thread sucks

>>11698350
Why?

maybe i should just kill myself

>>11698391
Now's the time to chose, to die and be free of pain or live and fight your own sorrow. Now is the time to shape your story, your fate is in your hands.

>>11698108
based

Is the expected value of the distance to the nearest leaf in a full binary tree given by:
[eqn]\sum_{i=0}^{n-1} (n-1-i)\frac{2i}{2^{n-1}}[/eqn]

or did i fuck up? i couldn't find this online anywhere

>>11698391
why? are you 24?

>>11699133
It doesn't look like your probabilities add up to anything near one here

>>11699172
why would they? I feel like it's wrong, but when I manually expand the summation it looks so right. I couldn't find anything on this, or what my answer is supposed to be.


>>11699134
whats the signifcance of 24 here?

>t. 24

>>11699177
>why would all possible probabilities add up to one
anon...
>but when I manually expand the summation it looks so right
What do you mean "manually expand"? Have you actually done any examples? I don't think you'll get a sensible answer out of this if you try it on the tree with 3 nodes or something else small.

I'm not sure what the answer is because I'm not completely sure what you mean by "full binary tree". That has a formal definition but I don't think you're using it with that meaning here.

>>11699203
full binary tree as in every non-terminal node has exactly 2 children. i don't see the intuition behind it summing up to 1..

>>11699203
also, my latex was wrong, the i in the numerator was supposed to be a power, 2 raised to the i. I have a reworked formula below:
[eqn]\sum_{i=0}^{n-1}i \cdot \frac{2^{n-(i+1)}}{2^n-1}[/eqn]

and yeah, I've done small examples, with n=0 to n=4. when i expand the summation, it looks exactly like an expected value summation, so it looks accurate, but i heard somewhere ese it should be nearing one

>>11699234
shit son this approaches 1, am i doing something right, oh wise condescending anon?

>>11699216
>full binary tree as in every non-terminal node has exactly 2 children.
that doesn't specify a unique tree though, and different ones are going to have different expected values. Are you talking about the perfect binary tree where all leaves have the same depth?
>i don't see the intuition behind it summing up to 1..
If I add up the probability of every single possible distance to a leaf, that's just the probability that a node has ANY distance to a leaf at all, which had better be one.
>>11699234
Well it looks much more correct when you don't botch the formula. This seems good, provided you are talking about perfect binary trees.
>but i heard somewhere ese it should be nearing one
what do you mean? that sum does tend towards one

>>11699250
where can i find this formula that I botched?

and yeah, perfect binary tree is a better word, my book just called it a full one.

>>11699257
Sorry, I don't have a source for you to check, but the second reworked formula you posted seems pretty clearly correct to me

>>11699250
>If I add up the probability of every single possible distance to a leaf, that's just the probability that a node has ANY distance to a leaf at all, which had better be one.
huh, maybe I'm answering the wrong question then. the question I'm supposed to answer is "in a PERFECT binary tree, find the expected value of the number of edges from a randomly chosen vertex to the nearest leaf". are the answers equivalent?

>>11699264
thanks anon, just couldn't find any SE answers or anything to reference, appreciate the help, bigly

>>11699267
I think you're missing what I mean by probability.
When you do an expected value, you're doing a _weighted_ sum of probabilities that looks like [math]\sum i P(x=i)[/math] . The probability is only the last bit, in your case the probability that a node has distance i is [math]\frac{2^{n-(i+1)}}{2^n-1}[/math] , and if you add all of those up you do get 1, as you ought to.

>>11699278
well, I thought this was all said and done but it's look like I still don't get it. does my formula give the appropriate expected value? I understand EV is a weighted sum of various probabilities, and that all probabilities in a sample space must add up to 1 - is it just a geometric coincedence that the expected distance to a leaf from a randomly selected node in a perfect binary tree is also 1?

all this info together makes me unsure if what I did was actually answering the question.

>>11698308
I guess I deserved this reminder for being mean yesterday.

>>11698391
Only if you do it in the nature so that your boy can be used by animals and plants as food.

>>11692887
What’s up guys what’s the non meme way to learn some trig. I am a senior and about to graduate and I want to get into robotics and it turns out trig is really important. Whenever I have to do some trig I flounder and can’t remember the stupid trig rules. Any sort of book to reinforce this shit? Ideally going from very basic to more advance and cement it in my mind probably some practice problems where it gives solutions for in the book too.

>>11699569
Prove the rules. It's the same for logarithms or derivatives. Prove the rules to learn the stuff, then it comes from your backbone and you will be the one unleashing Skynet upon us in no time.

>>11699177
>whats the signifcance of 24 here?
the point of no return. a good new /sci/ meme. at least /mg/ meme.

How do we know that every non-negative real number has an n-th root? I.e. how do we know that there doesn't exist some real number x, such that x^(1/n) isn't real?

>>11700099
[math] f(y) := y^n [/math] is monotone and surjective onto your domain, so if you want to speak in terms of Dedekind cuts, it's clear that the set exists.

>>11700107
How to show f(y) ) y^n is surjective though? Isn't that just restating the question. Also, is it really necessary to bring in function definitions here? Surely we would want this result to hold without having to develop a theory of functions.

I looked into it a bit, does Dedekind's fundamental theorem do it?

>>11700113
continuous + monotone => surjective

>>11700122
>continuous + monotone => surjective

>>11700113
I'm not actually using functions, I'm that as a Dedekind cut of Q, in the sense of
https://en.wikipedia.org/wiki/Dedekind_cut#Construction_of_the_real_numbers
the number you're looking for is the pair of sets

[/math] x^{1/n} := (\{ l<0 \lor l\in\mathbb{Q} : l^n < x \}, \{ u > 0 \land u\in\mathbb{Q} : u^n \ge x \}) [/math]

>>11700113
I'm not actually using functions, I'm that as a Dedekind cut into dense lower and upper halves of Q,
ie. in the sense of
https://en.wikipedia.org/wiki/Dedekind_cut#Construction_of_the_real_numbers
the number you're looking for is the pair of sets

[math] x^{1/n} := \langle \{ l<0 \lor l\in\mathbb{Q} : l^n < x \}, \{ u > 0 \land u\in\mathbb{Q} : u^n \ge x \}\rangle [/math]

>>11700113
define y^1/n to be sup{x : x^n < y}

>>11700113
I'm not actually using functions, I'm that as a Dedekind cut of Q, in the sense of
https://en.wikipedia.org/wiki/Dedekind_cut#Construction_of_the_real_numbers

the number you're looking for is the pair of sets

[/math] x^{1/n} := (\{ l<0 \lor l^n < x \}, \{ u > 0 \land u^n \ge x \}) [/math]

with l and u all in Q.

We might attempt to do the same for the Cauchy reals.
Try and post.

>>11700113
I'm not actually using functions, I'm saying that as a Dedekind cut into dense lower and upper halfs (L,U) of Q,
i.e. in the sense of
https://en.wikipedia.org/wiki/Dedekind_cut#Construction_of_the_real_numbers

the number you're looking for is the pair of sets

[math] x^{1/n} := ( \{ l<0 \lor l^n < x \}, \{ u > 0 \land u^n \ge x \} ) [/math]

with l and u all in Q.

We might attempt to do the same for the Cauchy reals. Try and post.

>>11700136
>>11700133
>>11700129
My man please calm down. I get what you mean, although you wrote it sloppily. Thanks.

>>11700099
[math]f(x) = x^n[/math] is continuous.
We also have that, for any [math]a[/math], [math]0^n\leq a \leq a^n[/math].
Intermeme value then kicks in.
>>11700122
>continuous + monotone => surjective
>>11700134
Don't you have to do a bunch of autistic shit to show that there are n-th powers arbitrarily close to y so that this proof works?

>>11700099
Intermediate value theorem.

[math]f(x)=x^n-r[/math] for some [math]r>0[/math] attains negative values, and as [math]x\to\infty[/math], it attains positive values. So it must pass through the [math]y=0[/math] line, thereby attaining your nth root.

>>11700143
Uhhh, forgot to assume that [math]a \geq 1[/math].
The other case is left as an exercise (tip: use 1).

>>11700134
>>11700143
>>11700146
I don't like how you all turned around his notation
x <=> y

textbox thinking

>>11700143
>>11700146
I don't think using intermediate value theorem works here, since you're assuming that the reals don't have gaps. I.e. (from Wikipedia): "the intermediate value theorem states that if f is a continuous function whose domain contains the interval [a, b], then it takes on any given value between f(a) and f(b) at some point within the interval.", however, since the point x^(1/n) is the one being called into question, IMV doesn't hold. You cannot prevent this by changing the interval since the point where f(x) = 0 is exactly when x = r^(1/n), i.e. it must always lie in the interval.

Like I said before, I think trying to prove this using functions is a mistake. Dedekind's fundamental theorem is the correct way.

>>11700160
Baboon nigger tier thinking.

>>11700099
[math]\sqrt[n]{x} = \sup\{ y \in \mathbb{R} \mid y^n < x \}[/math]. this is the definition. it exists and it gives x when raised to n-th power. all of it can be proved from the least upper bound property.

>>11700141
>>11700160
>>11700168

>>11700160
>however, since the point x^(1/n) is the one being called into question, IMV doesn't hold

>>11700160
lol what the fuck are you saying ?

>>11700166
>>11700172
Instead of posting memes you could point out where the flaw in my argument is. IMV requires an interval [a,b] which it doesn't have.

>>11700176
That the assumptions of the IMV doesn't hold without first presupposing what we're trying to prove. For a specific example, suppose you wanted to show that [math]2^{1/2}[/math] is a real number, using the IMV. You'd construct the function [math]f(x) = x^2 - 2[/math]. Now, by the IMV f takes all values [f(a), f(b)] on the interval [a,b]. But what a and b would you choose? Whatever interval you choose you cannot have [math]a\leq 2^{1/2} \leq b[/math] without first supposing that [math]2^{1/2}[/math] is in fact real. But then the whole argument falls apart, since your interval _must_ contain this number for the IMV method to work.

Again, just use Dedekind's fundamental theorem.

>>11700183
The flaw in your argument is that it's completely pants on head retarded.

>>11700183
>Whatever interval you choose you cannot have a≤21/2≤ba≤21/2≤b without first supposing that 21/221/2 is in fact real.
I ask this question with the utmost seriousness
what did he mean by this?

>>11700183
[math]f(0) = -2[/math] and [math]f(10) = 100[/math], therefore there exists a number [math]x \in [0,10][/math] such that [math]f(x) = 0 \in [-2,100][/math]. in other words, [math]x^2 = 2[/math].

>>11700198
100 is obviously my notation for 98

If your roots are real, then why is [math]z = e^{i\frac{\pi}{12}} \not\in \mathbb{R}[/math] but [math]z^{24} = 1[/math]? :^)

P.S. do you ever get spooked by your email beeping? That just happened to me.

>>11700200
whenever i get an email its bad news.

>>11700196
I assume he points to how formulations like pic related I would not grant you existence of merely described values
>P(u) ... true
in R. The way this is given in pic related, it assumes u is part of the interval in R and then makes a statement about continuous functions.

There's probably more autistic formulations of the theorem, tho

>>11700205
I'll send you a nice email.

>>11700206
>"let u be a real number. since u is real..." is now circular reasoning
welp, math is over boys
time to go home

>>11700193
>>11700196
>>11700198
https://en.wikipedia.org/wiki/Intermediate_value_theorem#Relation_to_completeness

Again, I don't see how you guys aren't getting this. Without assuming completeness of the reals you cannot use the intermediate value theorem. That's why I said your interval cannot contain [math]2^{1/2}[/math]. That's why I kept repeating that using Dedekind's fundamental theorem is how you would go about it.

>>11700218
obviously IVT requires completeness, nobody claims otherwise. it's just that your reasoning is total garbage.

>>11700218

>>11700225
I don't think my reasoning is "total garbage". Regardless, using the IVT will not work to show what was needed.

>>11700227
Enlighten me, what is wrong with the argument?

>>11700218
You're understanding the IVT wrong. The IVT doesn't presuppose that [math]2^{1/2}[/math] is real. The IVT *shows* that it's real. In this >>11700206 picture, [math]u=2[/math], which is by your assumption, real. The IVT then says that [math]2^{1/2}[/math] is a value that exists.

>>11700229
>what is wrong with the argument?
it's completely and utterly retarded

>>11700229
you're saying that IVT doesn't prove existence of square roots ?

>>11700229
Do you believe the following:
>Let f be a continuous function on the reals (e.g. [math] y \mapsto y^n [/math] in our case) then for all x in R, if f is surjective, [math]f^{-1}(x)[/math] is of course in the domain of f (and thus a real number)

>>11700235
I think he doesn't want having to speak about functions, inverting them, ect. to prove existence of those

>>11700257
obviously his point is that IVT is too much machinery and he's not wrong. read his arguments though:
>But what a and b would you choose? Whatever interval you choose you cannot have a≤21/2≤ba≤21/2≤b without first supposing that 21/221/2 is in fact real.
this is just gibberish

>>11700278
>obviously his point is that IVT is too much machinery
Really? I was thinking that his point was that the IVT requires completeness, and completeness somehow assumes the existence of all n-th roots, which makes the proof circular, so the IVT literally doesn't work.
>got evidence?
Mainly >>11700218

>>11700278
I think that was forcing the inverse function perspective.

The Dedekind perspective is also far too bulky imho, I'd like to know how/if people would have answered this before Cauchy/Dedekind.

>>11700282
how does completeness "assume existence of n-th roots" ? you still need to prove it, it's not immediate.

>>11700282
That is my point, yes. I should be clear however, that when I say "completeness" I mean it in the sense of there being no gaps in the reals. The argument does seem circular to me. E.g. the IVT over [math]\mathbb{Q}[/math] doesn't hold, because [math]\mathbb{Q}[/math]
has gaps. But we do not yet know if [math]\mathbb{R}[/math] has gaps, since we don't know if [math]2^{1/2}[/math] is part of [math]\mathbb{R}[/math] or not yet.

>>11700278
How is it gibberish? You're inducing an order relation on an object of which you have no information. You cannot say that [math]1 < 2^{1/2}[/math] without presupposing that [math]2^{1/2}[/math] is real.

>>11700302
but I'm not saying [math]1 < \sqrt{2}[/math]. I'm just guessing that IF such number exists, it would probably lie in [math][0,100000000][/math]. IVT shows that my guess is correct and that such number indeed does exist.
I'm not assuming anything.

>>11700294
>how does completeness "assume existence of n-th roots" ?
Really makes me wonder why did I add that "somehow" to the sentence.

>>11700330
I don't know, why did you ? either it does assume it, or it doesn't.

>>11700302
How exactly do you think the Dedekind theorem/axiom you keep posting sidesteps this?
If "R has IVT, therefore roots exist" is circular, why is "R is Dedekind-complete, therefore roots exist" not circular despite the fact that IVT and Dedekind-completeness are provably equivalent to each other?

redpill me on tao analysis I and II
is it good for self study

>>11700373
sure

Although, ironically given this thread, he invents his own concepts to introduce the reals. I remember a LIMIT function (called LIMIT) that takes sequences to LIMITs.

>>11700373
Use Pugh, Tao's for brainlets. Pugh's for those too intelligents for Tao, but too dumb to Rudin, the perfect middle term between both.

>>11700322
>>11700345
Ah shit, nevermind, I'm retarded. I was confused about the interval. I thought [a,b] necessarily meant a complete interval, rather than just a real one. That is why I kept going on about the intervals, and no interval being small enough to be complete without including the "gap" for the IVT to hold.

Please don't bully me.

>>11692887
I'm presenting my end of year project in 20 minutes wish me luck. I've got a no-detriment benchmark of 74% so I'll get a first as long as I pass but I'm still shitting myself

Why has nobody told me about sumatrapdf before? I used to use STDUViewer for djvu files and they always were kinda blurry and unpleasant to read. Although they weren't so intolerable that I would look for another viewer (I could read the content), I thought perhaps that's just how djvu files were. When I tried sumatrapdf, it's like night and day! Pic related. Fucking hell.

>>11700414
>Please don't bully me.
Too late.

At least people were talking math for 20 posts.

On a vaguely related note, is there any introduction to algebraic geometry, maybe up to schemes, that works entirely on subsets of the rational numbers Q?

>>11700428
link?

>>11700432
>link?
Of what?

>>11700432
https://www.sumatrapdfreader.org/download-free-pdf-viewer.html

>>11700487
>Windows only
ic

>>11700428
Your fault for being too dumb for not reading /g/'s wiki

>>11700493
>Not using windows
Wtf

>>11700517
You're awful.

>>11700529
Thanks!

>>11700517
Why would anyone go to /g/?

>>11700543
>Why would anyone go to /g/?
Huh? /g/ and /sci/ are practically sister boards since their subjects are deeply interconnected

>>11699333
bump? can anyone follow up on whether or not the formula here >>11699234 represents the distance in a perfect binary tree from a randomly selected to the nearest leaf?

>>11700567
I can see why an engineer or a CS person would go there, good point.

>>11700543
To grab a pirated copy of Windows or Office from >>>/g/fwt/

>>11700576
You're welcome, it's always a pleasure to educate the unneducated

>>11700582
I wish there were pirated copies of matlab, mathematica and maple

>>11700587
use octave you rat

>>11700592
Not as good

Math textbook authors sometimes leave a large list of books at the end of their book for reference. Have they actually read all those books? It would take a ridiculous amount of time to read them all. How many books do you think experts read on a particular subject?
Also, how many times has /mg/ been banned on this website. For me now, it's like 15 times.

>>11700582
I see. Maybe I should go and check those threads if I need some software some day. Thanks 2hu.

>>11700585
uneducated*, it's always a pleasure to correct typos.

>>11700599
>How many books do you think experts read on a particular subject?
After ten books read on a particular subject there won't be much left to learn on it

>>11700599
Depends on how much of an expert. I think they skim A LOT of books related to their subject. As they become proficient the time it takes to read the books goes down very quickly. I can easily see an analysis professor "reading" most intro to analysis textbooks in less than a day, only really stopping when a novel presentation comes up, which probably sits at around one such thing per book.

>>11700624
>reading" most intro to analysis textbooks in less than a day
But anon, there are hundreds of intro to analysis textbooks. Are you saying analysis professors have superhuman reading abilities?

>>11700599
They steal cute proofs from here and there. Also, sometimes their colleagues point out some details from books they have read and the authors are like "nice I'll include that in mine". Here you can see how a friend of Rotman's dropped some truth bombs during a lunch break or something similar.

>>11700599
>Have they actually read all those books?
No, of course not. That's not what a scientific citation is. It's not saying "go read this entire book", it's saying "if you want more detail about this particular section go read 6 pages out of this book". Or "here is where I got this problem from".

Mathematicians rarely read things straight through, even papers. There's just not remotely enough time in anybody's day to keep up if you read that way. You have to pick and choose which parts of the material are relevant to what you want to get out of it.

>>11700630

What am I in for?

>>11700712
why don't you read it and find out?

>>11700712
>kodaira
uh oh stinke

>>11700712
Kodaira is always the best when it comes to complex analysis and complex manifolds

>>11700722
>>11700737
which one is it? A professor (not mine, but one whom i respect) recommended it to me.

>>11700747
Are you kidding me?

>>11700774
I don't get it

>>11700797
Stop seeking validation here and start studying, Kodaira is a famous mathematician, so it should be obvious that his book is high level.

>>11700712
>>11700747
Are you sure he didn't tell you to read Complex Manifolds and Deformation of Complex Structures?
>>11700737
No, that's Grauert-kun.

How do you guys write STATEMENT (chain of only if) END-STATEMENT? I dislike starting my sentences with an equation/symbols, since it's unclear. For example "Lorem ipsum. x = 2 only if x is even." looks strange to me, because an equation follows immediately after the period. I sometimes use phrases like "We have", or something similar.

>>11700881
I can't think of an example where you would actually want to start a sentence with a symbol. The example you posted isn't something that would ever show up in mathematical writing, you wouldn't just say "x = 2 only if x is even" without any further content to the sentence.

>>11700432
You need schemes to work with [math]\mathbb Q[/math]. Well, classical AG also does work on [math]\bar{\mathbb{Q}}[/math]. Almost all books dedicate a section on rationality though. You might want to check Liu's book on arithmetic curves, relatively self-contained without prior knowledge of classical AG.

>>11700881
If A, then B, and so C, hence D, therefore E, wherefore F, consequently E, thus F, ergo G, whence H, for this reason I, accordingly J, thereupon K, that being the case L, therefrom M, correspondingly N, resultantly O, which is why P, on that Q, thereby R, so that S, subsequently T, ensuring that U, as such V, where from W, giving us X, requiring that Y, which is precisely why Z.
QED

>>11700893
It's a rare occurrence, like you say. My example was a bit contrived, but I've been in a similar situation a few times before. I'm trying to avoid posting specific examples since then I'll just get specific suggestions. I want a general methodology.

Hi, sorry for asking such a stupid question about probability distributions, but I don't know where else to ask it. I have a set of numbers, all of them very small and all positive (between 0 and 1). I can take the standard deviation of this set and its mean, and I would like to create some number that "fits in" with this set, however if I put the standard deviation and mean into a gaussian distribution I end up with a lot of negative numbers (I can obviously "clip" this by just taking the absolute value, but this leaves the distribution biased towards the values between the mean and 0). Is there some other form of probability distribution I should be using here? Again, sorry for the basic question, I'm here from /g/ just trying to implement a method for accurately guessing at missing data.

>>11700963
Subdivide the x axis into intervals of length (epsilon) to be adjusted. Make a histogram for how many points there are in every interval. Interpolate with a curve. That way you will get zero outside of where you already got the points.

>>11700925
>If A,
>then B,
trivial
>and so C,
obvious
>hence D,
exercise
>therefore E,
clear
>wherefore F,
check
>consequently E,
left for the reader
>thus F,
(why?)
>ergo G,
by definition
>whence H,
fact from highschool
>for this reason I,
skipped
>accordingly J,
easily seen
>thereupon K,
draw a picture!
>that being the case L,
similarly
>therefrom M,
iron out the details
>correspondingly N,
the observant reader should already have noted this
>resultantly O,
(tedious)
>which is why P,
like leaving a nut in water for months
>on that Q,
by construction
>thereby R,
up to a change in notation
>so that S,
reduce it to a previously known case
>subsequently T,
straightforward
>ensuring that U,
defined to be true
>as such V,
by analogy
>where from W,
think
>giving us X,
superfluous to spend more time on this
>requiring that Y,
do it
>which is precisely why Z.
omitted

>>11700982
>>11700963
Now that I think of it, there's actually no reason to interpolate it. It's way easier to integrate rectangles than other functions. You just make a histogram and that is your distribution. Now to generate a random point according to this distribution, you generate a random number x in (0,1) and then your random point in the distribution will be such a point that the combined area of the histogram to the left of the point is x (when the histogram is normalized so that the total area is 1).

>>11701000
>left for the reader
this one is honestly the most infuriating

>>11701012
Why? I like them. They're like exercises. A good math book is one that forces the reader to think.

>>11701012
>Brainlet can't prove the theorems that authors leave for readers
You realize they're left for you to prove because they're very easy, right?

>>11701021
W-wait... are you saying students are supposed to do something?!?! How dare the authors?

>>11701012
Observe:

>>11701060
Theorem 109 is not even true.
-2>=-3 but 4>=9 is false.

>>11701060
Which book is this? Why did the author(s) not just pile them all into one theorem and then go on like (a) thm 70, (b) thm 71? Quite an ugly way to do that.

>>11701082
Most true.

>>11701130
>Which book is this?
2 dollars say it's Lang's Basic Maths.

>>11701082
X,Y,Z, and U are all assumed to be positive. The author does something sort of non-standard and calls the positive integers just "integer", and then when he gets to the reals he begins by discussing negative integers and promptly renames "integers" to "positive integers".

>>11701130
Foundations of Analysis by Landau. No idea why the style was chosen as it was. Most proofs are very short, so I guess if you it that way you'd just have four theorems but each having 50 parts to them. In that case it's preferable to separate them.

>>11701142
Why the hate for Lang's basic maths? I've only ever heard /mg/ and /sci/ in general meme on it.

>>11700168
best answer

>>11700982
>>11701009
thank you very much

>>11701169
I see. Thanks for the reply.

>>11692887

This is supposedly Archimedes last words

>>11701358
Yes, and?

>>11701369
Don't disturb anon's posts!

>>11693613
fo r me its addition

>>11701393
Based.

>>11701358
was this autism?

>>11700049
>new
not sure 'bout that one boss...

>>11700049
Ok but what does it mean? Why 24?

>>11701446
From last thread >>/sci/thread/S11685818#p11686028

>>11701000
based trips

Who else
>black square qed symbol
gang?

>>11702205
That's such an insult to the intelligence of whoever's reading the proof, indirectly saying that the person can't understand where the proof ends unless there's a sign pointing to it, it's like putting a 'the end' at the end of a text.

>>11702205
what about the contradiction symbol.

Threadly reminder that if you stare into the physicist, the physicist stares back at you.

>>11702221
Wow you're such a faggot contrarian
>>11702205
white square or kys

>>11702283
He who fights physicists should be careful lest he thereby become a physicists himself, for when you gaze long into physics, the physics also gazes into you

>>11702221
I think it's useful just from a typographical standpoint. Sometimes you want to skim a paper and save the proofs for later, and the QED symbols help with that.

/hmmg/

>>11702205
I use the white square because it resembles my emptiness as a human being.

>>11702853
Yes, happy morning is what I intended...

>>11702853
>I use the white square because it resembles my emptiness as a human being.
wow this is relatable...

>>11702931
/mg/ death cult when?

bros...

>>11702957
NO!!!!!!!

Mathematics is finished, it's nothing but trash, math was a mistake

Putnam Bros ...

>>11703302
yes..?

>>11703333
Nice quads.

>>11703333

post a hard euclidian geometry problem please

>>11703420
Prove that there are no 17-side regular polygons

>>11703420
prove the Great Poncelet Theorem for the special case of two circles and a triangle

>>11703490
That's ellipitic geometry

>>11703502
what i've posted includes only circles and lines
it's euclidian geometry u monkey

I want to impregnate all the math-trannies.

>>11703490
Judging from the wikipedia .gif, the construction is really simple. Take a point in the inner circle, and then there's a tangent line to it. This line crosses two points on the outer circle. and from either of these points, there's only one more line that's again tangent to the inner circle, and it crosses the outer circle in some point.
You add in the other tangent, and you borrow those theorems about angles on circles to show that the triangle closes.

Does this work as is or is the proof completely different?
>>11703527
Good luck.

>>11703506
>Poncelet's porism can be proved by an argument using an elliptic curve
https://en.m.wikipedia.org/wiki/Poncelet%27s_closure_theorem

Don't you quote me EVER again you disgusting fucking weeaboo

Stupid question that the other thread is too slow to answer and my laptop's battery is dying

Is learning Algebra from Apostol's Calculus a dumb idea? I know it sounds funny, but its an honest question

>>11703596
That's pretty rude, don't you think?

>>11703596
Wait a second.
Elliptic curves have something to do with elliptic geometry? I always thought elliptic curves were tori and didn't admit metrics with constant positive curvature.

>>11703630
Yes, it is.

>>11703574
I doubt you can do it just by angle chasing.
>>11703596
this says "can be proved" not "this is absolutely the only fucking way to prove the theorem"
and it refers to a general case of n-gon and arbitrary conic
that's why i dumbed the problem down to a specific case, u moron

I'm too stupid for differential geometry.

>>11703788
So am I. Do AT instead.

>>11703802
Algebraic Topology is the language of Differential Geometry, nigga...

>>11703754
>proof he knows doesn't involve chasing angles
Oof.
Well, there's not a chance in hell I'll try to solve that with analytic geometry, and I can't think of any other way to solve it with synthetic geometry, so I'll just give up.

>>11703823
>so I'll just give up.
Damn, you're such a shame to all serious mathematicians...

any cool math facts about the number 84?

>>11703831
It's the last two-digit number where its second digit is half of its first digit

>>11703821
>t. has read the Geometry of Vector Sheaves a dozen times and knows the contents frontwards and backwards
>>11703830
Yes, I am.

https://www.maths.ed.ac.uk/~cbarwick/papers/future.pdf

>>11693613
>the
is there only one?

>>11693607
>>Literature (pretty good)
what does that mean

>>11702957
It'll be fine. Learn combinatorics.

>>11703831
[math] 84 = \sum_{n\in\{1,2,3\}} 2^{2n}[/math] ?

>>11703821
Yes but it need not involve all the atlases and differentiabilty things etc. that made me cry blood. Keeping it nice and easy is the way to go, and that's my excuse for doing anything else than that.

>>11703831
84 = 60 + 24, the number of minutes in an hour plus the number of hours in a day. Furthermore, 24 is the age where you should stop trying anything.

Did anyone also have trouble understanding Equivalence Classes when they first read about it? Is it a sign of my brainletness? I read about it in several books and only after Aluffi's thorough explanation that I understood it fully. How important is it in Abstract Algebra? Should I master it before proceeding to study group and ring theory? Also, what about Quotient Set?

>>11703841
>what does that mean
Means I have enough artistic sensibility to chose only the really good books to read
>>11703842
>Marika
Best girl

>>11703848
>how important
Yes. You will often be working with various quotient structures, and the elements of those are literally equivalence classes. Normal subgroups and ideals give you quotient groups and rings, resp., and yeah.

>>11703858
Ok, what about the other questions?

>>11703848
>trouble understanding Equivalence Classes
I blame the Cantorian Revolution and its Consequences.

>>11703854
Ah, good skill.

Could have also meant you write.

>>11703858
>Koma-chan
Holy shit you have such a good taste when it comes to waifus, you only post the best, a man of culture I see

>>11703862
>I blame the Cantorian Revolution and its Consequences.
Uuhh... Ok...? How does that help me?

>>11703861
>Did anyone also have trouble understanding Equivalence Classes when they first read about it?
Yes.
>Is it a sign of my brainletness?
I don't know but I am a brainlet.
>Also, what about Quotient Set?
Path components of a space. You will specialise in homotopy theory, will you not? I dare you to say "no" to me.

>>11703865
More like agriculture. My mom comes from a farm, so I guess I inherited her peasantness.

>>11703873
>You will specialise in homotopy theory, will you not?
That is a possibility, I wanna do something revolutionary, can I accomplish it in that field?

come on lol create a new thread

>>11703880
That's not how it works around here newfag, we wait for this one to die first...

>>11703884
>almost 40 posts past the bump limit
>not dead
>calling people a newfig
sweetie...

>>11703875
I have no idea. My supervisor said that I would get the Fields medal if I proved the Moore conjecture, but I can't remember what that was about. Something about spheres having homotopy exponents, I think. Do that and become a superstar.

>>11703880
I would but I don't know how to. How about you show us how to start a new one?

Is there any (new) book on Homotopy Theory without strong emphasis on Topology?

>>11703893
Homotopical Topology

>>11703887
I would but for some reason I get a (you) notification every time somebody posts, even if theyre not quoting the OP. If you know how to turn off getting the red text after someone replying to the thread when they're not quoting me on 4chanX then I'll do it.

>>11703903
There you go >>11703907

I'd still like to know how to remove the red text for future reference, if you happen to know tho

>>11703913
I have no idea

>>11703903
But I want to give you a (you) <3

>>11703920
The problem is not that I get you's, but that I get a red text in the thread watcher (which usually implies a you) when someone replies without quoting me, which is annoying on these persistent threads

>>11703903
>4chanX
What the hell is that?

>>11703933
I got you mean.

>>11703937
An extension for Firefox, if I remember correctly.

>>11703939
>An extension for Firefox, if I remember correctly.
Holy shit that's awesome I'm gonna try it

>>11703945
On firefox you need to download violentmonkey extension, then look for the 4chanx extension on greasyfork

on chrome its on the extension store

>>11703950
I'm a chromechad thank god

>>11703899
mhm,
I'm not sure if this is either now, nor without strong emphasis on topology

>>11703968
Homotopical Topology - Fuchs-Fomenko
Its focus is on the drawing, not on topology

>>11703973
kk, but it says it's a 60's book

>>11703980
It was a joke, can't you understand a fucking joke?

https://www.youtube.com/watch?v=M6g-sR-lRCU&t=710

autism

>>11703993
What's our stance on tibee? I need to know before I decide if I like her content or not

>>117040
I like her because it's a science curiosities channel without the production value like a veritasium. She's also very serene which triggers ASMR for me.

>>11704028
>triggers ASMR
That's intentional

>>11704004
If you don't count the effort 3b1b puts into his videos, then to me she's the second second or third most interesting [math]\le 2[/math] second year youtuber.
The history stuff provides some service (e.g. the Tesla clip recently) and the semi-sad Bob Ross imitations are a plus on effort too.
I don't like how she talks, but I won't hold that against her.
That said, I don't think she's particularly good or interesting, compared to other general channels on youtube (which however aren't on math).

>>11704127
>general channels on youtube (which however aren't on math).
Which ones?

>>11704137
Do you want me to post a random youtube channel I like?

>>11704176
No, I want you to post all of them

>>11704261
Calebcity
Atun-shei
Lindybeige
Theburgerkrieg
e;r
Mox
JuliansmithTV
Leafyishere

That's every single good youtube channel

>>11704432
Didn't like any of them

>>11704471
wrong

>>11704512
I wanted math channels you idiot

>>11704517
>>general channels on youtube (which however aren't on math).
what

>>11703841

yikes and cringe

>>11704831
What's cringe about it?