/sci/ - Science & Math

at what point do I "get" the web of maths?

>>11753103
Combinatorial matrices edition

>>11753103

> omg that is literally me

/mg/ is with antifa!

>>11753147
what do you want to achieve?

>>11753230
they don't seem to stand for much. nothing they don't root for themselves

>>11753230
Fuck off, /mg/ supports law and order!

>>11753230
>tfw based centrist

can I / how do I, express the area of a triangle in terms of its hypotenuse, irrespective of its side lengths. as any unordered set of side lengths always produce a unique hypotenuse, it is possible?

>>11753314
>as any unordered set of side lengths always produce a unique hypotenuse
but you can't go the other way around. one hypotenuse length can come from many different triangles, all of which have different areas

>>11753282
Anyone who doesn't stand against fascism is silently consenting with it.

>>11753352
Anyone who doesn't stand for fascism is silently against it, you mean.

>>11753314
0 < area ≤ (hypotenuse^4)/4

>>11753314
If you have a right triangle with hypotenuse [math]c[/math], then the other sides would be [math]a = c\cdot\cos (\alpha), b= c\cdot\sin (\alpha)[/math], and so the area would be [math] \frac{ab}{2} = \frac{c^2}{2}\cos (\alpha)\sin (\alpha) = \frac{c^2}{4} \sin(2\alpha)[/math]. In this way you could write the area as a function of the hypotenuse and an angle, but you would still have two pieces of information.

Do you need to study number theory to come up with this kind of trick?
https://cs.stackexchange.com/a/2586/121950
I understand the proof but I couldn't know how did he come up with it.

>>11753314
The area of a right triangle with hypotenuse H is at most (1/4)*H^2, which is the case when the triangle has equal legs, but could be any smaller positive value.

>>11753103
Does anyone here have interest in chern-weil theory? No one at uni ever seemed to. It seems deep and fascinating, but I don't know if that is because brainlet.

>>11753669

If you're talking about using curvature to compute characteristic classes, that's all I ever see re: char classes.

>>11753683
What field of research? My advisor (QFT) was the only other physics enthusiast who had any clue about it.
>physics
I know, I know

>>11753687

Diff geo. It's great to be able to compute something (geo/analysis/physics) which you know is invariant under stuff (top).

>>11753698
Super! Any books you'd recommend? I have some lying around, but I can never have enough resources.

>>11753705

Yeah, maybe only intro stuff though. Of course it depends on what you know already. I liked Tu's (newest) book just titled Diff Geo, very friendly. But that also has a lot of other stuff about principal bundle and riemannian geometry stuff. (which could be either interesting or boring to you).

I think Milnor/Stasheff has an appendix about it too if you just want to get to the point, and everyone loves that book. But I haven't read that yet.

I'm sure to get more into it you'd need to look into the pure topology side.

I like physics too. Does it come up at all in your work?

>>11753729
I have the background, mostly; I did a math MA before joining "the dark side" as the department called it (all in good fun, obviously). My focus was combinatorial group theory, i.e. abusing the properties of covering spaces, so I know enough topology not to cringe, though I only really know the algebraic side of K theory.
>I like physics too. Does it come up at all in your work?
Not a professional physicist. I am a midwit who left academia after getting what he wanted. And yes, it does come into my work. I was a uniquely 'topologically minded' physics student. My research heavily focused on topological obstructions in field theories, especially in curved spacetimes. The whole time I couldn't help but think "man, there has to be a math nerd who could do this better than me if they knew the topic." Because of that, I taught myself the basics of lie groups/algebras, fiber bundles, and associated bundle constructions. Differential geometry is so fucking cool that I jumped a little when I found out someone connected it to the algebraic topology I already liked.

>>11753705
If you want to have a reference for bundles in general, then Husemöller's book could be good. Also Rudyak's book on spectra has an extensive chapter on all sorts of facts related to those.

/gnmg/

>>11753744
Sounds cool

If you also know how to work with smooth mfds, I think you should be able to run through Tu's book pretty easily (hopefully that doesn't jinx it), it does all the associated bundle stuff again.

I just remembered that the whole theme of Tu's book is that chern-weil / characteristic class theory extends the Gauss-Bonnet theorem, and there's a lot more to learn there.

>>11753103
replying from last thread, >>11743843 is me:

original post:

>im writing an essay which touches upon the phil of math.

>historically, a lot of the "foundations" or methods of math were justified by intuition, such as infinitesimal calculus i believe. it was only until much much later that naive set theory, and ZFC took over.

>did we "lose anything" by switching over to an axiomatic foundation? are there issues in ZFC that "intuitive math" doesn't have?

>>11743860
by intuitive math i mean math in like the 18-17th century didn't have an axiomatic foundation, and thus lemmas like the IVT were used without justification

>>11747465
i do not understand what this essay is trying to suggest, but if physics is a part of math, then why does R fail to be a perfect characterization of spacetime? *dunks on youu*

also random question, but what does it actually mean/feel-like/require to discover/create/(wink) new math? is it supposed to be something that would be obvious to someone who is actually inspired?

Just saw the parents for the first time post-Corona and I finally got my birthday presents: Apollonius' Conics and Bourbaki, Topology 5-10. Feels good man

>>11753357
okayy tooky

Are /mg/ mostly undergrads?

/gmmg/

>>11753860
>what does it actually feel-like/require to discover/create/(wink) new math?
No idea about reaching some big result, but small things new to everyone don't differ much from small things new to the person in question. What I mean by this is the following: suppose nobody had told you that (for a fixed angle) sin^2 + cos^2 = 1, but you knew the Pythagorean theorem. You would then derived that as a corollary, and it would be something new to you, and you found it out yourself. Then imagine doing the similar thing in some other context, but this time your conclusion would be new to everyone, but not really super important. The feeling is pretty much the same, at least for me, but maybe a bit stronger. It probably depends on the person, but for me it's a lot of self doubt at first and a small smile later. What it requires is patience, dedication and playing with ideas until eventually you initiate a required chain of thoughts. Is this anything like the answers you were looking for?

>>11753864
Nice. Happy birthday, a bit late. I hope it wasn't your 24th...

>>11754043
Yes.

If I aldo avatarfaging, does it elevate my status to be the same as Yukarifag?

>>11754129
no, you would also need to be an obnoxious faggot

>>11753860
In the fields that are not directly 'about' foundations, such as Algebra/Geometry/Topology, very few people care about ZFC.
Axiomatic foundations are only really used to make proofs consistent, but mathematicians have an intuition about the objects they study outside of those proofs.
Most math is still 'intuitive'.

Finding math so very pretty yet being a brainlet is the ultimate suffering.

>>11754358
Math is an ugly beast. It is my job to tame it.

>>11754339
>In the fields that are not directly 'about' foundations, such as Algebra/Geometry/Topology, very few people care about ZFC.
This. Things work well enough for them to be intuitive. And when you for some reason need to deal with something big like the whole category of modules or based spaces w/e, you dodge problems by using Grothendieck universes or the Bernays-Gödel-von Neumann axioms and say that the objects give you a class in the sense of that triumvirate. Hardly ever should there be a situation where one actually has to consider the actual axioms, other than maybe AC if one wants to dispute it or to give a content warning to people allergic to it, when doing stuff.

>>11754358
Overcoming the "i am stupeed" is an exercise of butt muscles. You sit, you study, you learn, you start to understand, you appreciate even more.

>>11754367
It is unironically a hydra. Every time you learn something, new questions pop up. Then you keep chopping the new heads and more grow to replace them.

>>11754372
>It is unironically a hydra. Every time you learn something, new questions pop up. Then you keep chopping the new heads and more grow to replace them.
But that's not bad.
Unless you think you should know everything.
In this case, just read Faust!

>>11753860
>but if physics is a part of math
Not what he's saying - read the sentence again.

I don't think the
>did we "lose anything" by switching over to an axiomatic foundation?
has a clear cut answer.
The Begriffsschrift is 140 years old today, the breadth of mathematics is also much broader. Math is different, and formalization surely was a big part of it. We gained things - e.g. the field of computability and naturally specialized and also broadened the views on math. And old perspective and specialization and back-then-relevant knowledge is not present anymore.

Galois died at 21, Gauss had a full book of results written down by the time he was 21. I mean, no pressure, they were geniuses, so it's okay if you take things a bit slower. But at 24, you should have a PhD, or at least some papers published, right?

i just finished my undergrad exams and i'm due to start my masters next year.
what should I read over the summer? i was thinking of picking up Leinster's Basic Category Theory per a tutor's recommendation

Why is math so fucking lame? The way mathematics is represented is extremely boring and uninspired. I really don't get it. I did an entire B.Sc. in math and was bored all throughout. The only time it was genuinely fun was when geometric examples where introduced in analysis classes. Most mathematics is visualized in the abstract or through analogy anyhow.

Why the perceived need to leave out this important element of mathematical thinking? In philosophy, this need was already recognized: the result was philosophical fiction and literary presentation (e.g. Nietzsche's writing) as opposed to Scholastic systematic and dull philosophy.

>>11754597
just pick whatever you're interested in

>>11754594
>Galois died at 21
Galois died at 20. He wouldn't have turned 21 until a few months after he died.

>>11754569
>But that's not bad.
Indeed it's not! There's always something to do because of that. Even solved problems can be unsolved if one changes the context. An example of this would be the classification of finite simple groups. Now that there are fusion systems, people need to classify the fusion systems of those groups, and there is also a catch: not all fusion systems come from groups. http://web.mat.bham.ac.uk/C.W.Parker/Fusion/fusion-intro.pdf

>>11754594
>I mean, no pressure
The pressure is INTENSE!

>>11754597
What are you going to focus on when you start your master stuff?

any thoughts on How to Think Like a Mathematician by Kevin Houston?

>>11754624
>What are you going go focus on
To be fair I don't know. I'm kind of dreading the whole thesis thing. I still feel like there's a lot about math that I still want to explore and I'm not sure how I'll be able to commit to one specific topic. I'm not sure if I have the academic maturity either.

>>11754691
I didn't mean your master's thesis, but the courses you would think you are going to take etc. Doing category theory like that suggests you would like to do some abstract nonsense, but without confirming this first, I don't know if it's a good idea to suggest Hatcher/Rotman as an introductory algebraic topology text, or maybe some intro to homological algebra if those are not what you want out of life. They would be good in the sense that the former revolves around different functors from categories of topological/combinatorial objects into categories of algebraic objects, and the latter would be full of examples of the stuff Leinster would show you. Or does your uni not have different master specialisation course lists like for example take these to be an analyst, take these to be an algebraist, take these to be a logician, and so on? I hope you get what I mean. The idea is clear in my mind, but I just can't turn it into words.

bros... i have been doing maths today... for the fifth day in a row

>>11754594
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

>>11754777
Keep it up and you will be able to beat even Yukari in this stuff!

bros... i forgot to do maths today... for the fifth day in a row.

>>11755057
NO!!!!!

bros......i sent some emails today........

bros... why are you... making fun of me...

>>11755095
bro.................

>>11754594
you can't seriously be comparing yourself and your life time trajectory with enlightenment era aristocrats, anon...

bros... when will i... will i be famous...

>>11755127
disprove that irrational numbers can't be represented as a quotient of other irrational numbers and double the unit cube with ruler and compass

>>11755126
Very true. With modern-era teaching tools, progress in mathematical pedagogy, and the fact that many proofs and theories have been simplified greatly, one's mathematical education should progress with speed much greater than 200-300 years ago.

>>11755130
sqrt(2)= sqrt(6)/sqrt(3)

>>11755133
>progress in mathematical pedagogy,
Lol. Pre University mathematics has been in serious decline for quite some time. University math hasn't changed, except for homework being typset more nicely.

>With modern-era teaching tools
Namely? I grant you that LaTeX made things look far more nicely, but I can't think of another thing.
Blackboards and lectures are still the way to go and every lecture I had which diverged was just worse.

Fuck your math.
How is it that if the whole universe is mirrored and restarted, that we still end up with matter instead of antimatter?

>>11755133
you can't have been brainwashed this bad right? you're not this uneducated right? you're not actually thinking our education is superior to theirs, right? you don't actually subscribe to historical progress, do you? wtf anon u r fucked in the head if u think like this

where are the composers on tier with Schubert, liszt, brahms, Mendelssohn? all same era as galois and gauss, yet no living soul has a musical understanding of their caliber, and no child prodigy has ever written like kid Mozart, or fuck man beethoven and bach even, how can u think like u do? by being so horribly uneducated about the history of thought that u are actually capable of holding a falsehood of this degree as de facto true
have u seen early art of da Vinci? nobody alive like that

>modern education
produces retards who think like you, go read a book

>>11755139
6 = 2 x 3, idiot

>>11755145
and b4 u try to say
>kid Mozart was a God blessed genius nobody can ever do it like he did
if his God blessing was his dad working his life to learn how to turn a (his future) kid into a prodigy, yeah, he was God blessed because he was his fathers son

>>11755139
that's rly clever anon
what about a cube root in terms of square roots?

>>11755145
>Schubert, liszt, brahms, Mendelssohn
Arvo Part, you fucking ignorant
>have u seen early art of da Vinci? nobody alive like that
John Baeder, you fucking imbecile
>produces retards who think like you, go read a book
Terence Tao, you fucking retard

>>11755145
based anti-whig historian rapes libtard brainlet

guys i was just making a 24-years-old joke... not a serious post...

>>11755194
>joke
Do you even know where the fuck you are? *Sigh*, I'm fucking tired of trolls like you, holy shit, these days I browsed /v/ after years of being only on /sci/ and /lit/ and I was suprised that 95% of the posts were underage edgy trolling, made me disgusted honestly, then I felt thankful that /sci/ and /lit/ has above intelligent users who are more engaged in having a meaningful discussion than trolling, but these last threads have become 50% retarded jokes like yours, WE DON'T FUCKING WANT YOU HERE, PLEASE GET THE FUCK OUT, IF YOU WANT TO VOMIT JOKES GO TO /B/ OR WHEREVER THE HELL, BUT NOT HERE, LEAVE!

>>11755166
Not possible by Galois theory (3 is not a power of 2).

>the proof is in the pudding

>>11753357
cringe poltard

>>11754372
>Overcoming the "i am stupeed" is an exercise of butt muscles. You sit, you study, you learn, you start to understand, you appreciate even more.
That may be the case when you're smart anon.

>>11755229
If you're over 100IQ, then there's no excuses.

>>11755145
>where are the composers on tier with Schubert, liszt, brahms, Mendelssohn?

come on brainlet, they would be nobodies in this day and age.. you are only taking their name because they were promoted and hyped by older generations.

>>11755235
That's an empty cliche. Noone in here really believes that

>>11755249
Believes what?

>>11755256
That being a 115 or so IQ midwit will let you be anything but mediocre at any math related pursuits.

>>11755258
>That being a 115 or so IQ midwit will let you be anything but mediocre at any math related pursuits.
Uhum, and why do you think that?

>>11755264
Because people smarter than me have shown that IQ measures something real and that you need a high score to succeed in some fields.

>>11755269
>Because people smarter than me have shown that IQ measures something real and that you need a high score to succeed in some fields.
Mhm, who are those people specifically? Could you also provide the site or paper with those researches?

>>11755127
I will mention you in my speech when I receive the Fields medal. "First and foremost, I want to thank the "bros..." poster in /mg/." That I will say.

>>11755182
I wonder how long Arvo Pärt will still be around. He's pretty old. Good stuff, though.

>>11755229
Some smart person can answer that. I just have a battle hardened butt.

>>11755277
>I receive the Fields medal.
Not refusing it liked Perelman. I am disappointed in you.

>>11755281
I promised the "maths Nobel" money to my sister.

>>11755284
Could it be that Senpai is a siscon? Pervert.

>>11755277
Your butt is probably rock solid anon I won't downplay that, but you probably have a nice amount of talent as well

>>11755126
Abel was a mega-poorfag working alone in an isolated backwater of Europe, died at 26 and still managed to make himself into one of the greatest mathematicians of all time.
No excuses.

>>11755287
You asked if anyone missed you. I never miss at close range. I actually used to go shooting with my dad. I am the master of Makarov.

>>11755294
I'm just lucky to live literally on the right side of the Atlantic ocean (unless you are using the Aussie map) and never had to pay for this, and consequently had no pressure. Doing things for fun instead of out of necessity makes them easier. It doesn't mean I'd have any other talents than to make people like me and go along with my stupid stupid plans. I'd like to see you even lie that you try.

>>11755127
>tfw no-one can answer, can answer that

>>11754601
Not your fault, for what it's worth. The way math is presented in many, if not most, traditional courses is designed to force you to push the buttons and pull the levers to get a desired result. It does nothing to inspire one to look deeper into the caverns of the cosmos and immerse oneself in the vast ocean of mathematics in a never-ending quest for truth. Math is the furthest thing from lame; it is by far the most creative human activity on the planet, and the best part about being alive. Look deep enough into anything at all, and you'll find math at its core. Reality is how math feels.

>>11754624
okay, can you quickly yellow pill me on fusion systems?

bros... can you please... stop... copycatting me...

>>11754601
looks like it's starting to be more painful to remain in slumber than it is to wake up

>>11755335
bro... doing that... is no different than... avatarfagging

>>11755182
>arvo part on tier with brahms
yikes
>John badder
yikes
>books are modern maths
go outside, read Aristotle, and bathe in the sun u spiritual dilletante

>>11755324
Okay, so just to make sure you know that this isn't a deep exposition of any sort: I haven't used them for anything myself, so I only know the basics. Anyway, the idea is that you take a finite group [math]G[/math], the order of which is divisible by your favourite prime [math]p[/math], and then let [math]P[/math] be a Sylow [math]p[/math]-subgroup. We know that every [math]p[/math]-subgroup is contained by one of the conjugates of [math]P[/math], so we get pretty much all the [math]p[/math]-data (can't think of any better word here) by looking at any one of the Sylows.

We then define a category whose objects are the subgroups of [math]P[/math], and whose morphisms are supposed to reflect the idea of conjugating the elements. To achieve this goal, first restrict to a subset of injective homomorphisms between the subgroups that contains all the conjugation isomorphisms. Since we can restrict to the image, an injective homomorphism induces an isomorphism, and so we want both the induced isomorphism be in the set of morphisms. Furthermore, we want inclusions to be there, as well as the inverse of every isomorphism in the set. The composition is just the composition of group homomorphisms. We can have many examples, the easy ones being the one with all injective homomorphisms as its morphisms, and the one with only the conjugations (this works because the identity is essentially just conjugation with the identity element, and so you actually have a category).
1/2

>>11755425
2/2
What these are supposed to measure is the classical notion of fusion. Basically, you pick two elements [math]g, h\in P[/math], and then you ask if there is an element [math]x \in Q\le P[/math] such that [math]^xg = h[/math]. If the answer is yes, then you say that [math]g[/math] and [math]h[/math] are fused in [math]Q[/math]. If the answer is no, you check it for some [math]Q < Q' \le P[/math]. This, quite naturally, allows you to talk about two subgroups being fused (in a bigger subgroup) in the same way. I just don't know how they are supposed to measure this, as I've only been on the lectures that were on how you need to classify these guys the same way you would classify the finite simple groups. Moreover, there are the "exotic" examples that arise for example by taking maps from a space to the classifying space of a group. Also, according to the daily arxiv mails, you can drop the finiteness and replace it with pro-finite.

But yeah, I'm not too familiar with these. If it sounds interesting, please do check them out.

PS. Oh dear, I just noticed there are bugs in my lettuce. Well, I didn't want to eat it anyway...

>>11755425
>>11755429
There may be some factual incorrectness in these, but the basic idea is correct.

>>11755314
I don't deny that you probably bust ass and that circumstance is a factor. But you need talent. Do you think those people have no experience of their own? They go with your plans because they make sense on some level and you show promise. Because you're smart.

I will try harder but if I fail while giving my best I will come here and yell at any anime picture I find ITT

>>11755457
Suppose you fail, I can even come and meet you in person and give you a knife with which to stab me. I am yours to kill should that happen.

>>11755274
Cox's study of eminent scientists and mathematicians from the mid 20th century. research on the average iq of phd students and college students separated by major. decision theory, basic social psychological theory that indicates people self-sort/select their environments based on ability and maximizing gains. try studying with and tutoring a stupid person, then spend some time studying with a smart person and witness the insurmountable gap between good and bad genes.
>>11755323
you are a faggot

>>11755445
Okay, thanks. So it's looking at nice homomorphisms.
Feels vagely homotopic.

>>11755488
Then, under some conditions which I do not remember, you can define a so called centric linking system [math]\mathcal{L}[/math] (also a category) associated to your fusion system [math]\mathcal{F}[/math]. You obtain a triple [math](P, \mathcal{F}, \mathcal{L})[/math] called a [math]p[/math]-local group. Its classifying space is then obtained the following way:
(1) Realise [math]\mathcal{L}[/math] geometrically to obtain [math]| \mathcal{L}|[/math].
(2) [math]p[/math]-complete the realisation in the sense of Bousfield & Kan to obtain [math]| \mathcal{L}|^\land _p[/math].
[math]| \mathcal{L}|^\land _p[/math] is then the classifying space of [math](P, \mathcal{F}, \mathcal{L})[/math]. This was then used by Oliver to prove the Martino-Priddy conjecture which is, as you felt deep inside, homotopic. https://books.google.co.uk/books?id=GNFTDwAAQBAJ&pg=PA72&lpg=PA72&dq=martino+priddy+conjecture&source=bl&ots=SBqOq_H67U&sig=ACfU3U0pn-wb2Qsq1Jz5bC7m01Aeh0OFTQ&hl=fi&sa=X&ved=2ahUKEwi5_6-W9ePpAhWJOcAKHZIDCmQQ6AEwBHoECAgQAQ#v=onepage&q=martino%20priddy%20conjecture&f=false

>>11755483
>Cox's study of eminent scientists and mathematicians from the mid 20th century.
A 1926 study that estimates the IQ of prominent scientists of the past? Ok, since you've got nothing better, I'll accept it, so where in that study does it states an average IQ person will never amount to anything above mediocrity if they pursue a career in mathematics?
>research on the average iq of phd students and college students separated by major. decision theory, basic social psychological theory that indicates people self-sort/select their environments based on ability and maximizing gains.
Mhm, but where is it? Where's all that research? Surely you must have read a lot on the subject if you're writing with such certainty, so give us the links or books
>try studying with and tutoring a stupid person, then spend some time studying with a smart person and witness the insurmountable gap between good and bad genes.
That's not research though, just your personal experiences, it doesn't really say anything. Besides, an average IQ person (100~115) is not stupid. To be stupid is to be at 90 or below, I do not deny that those people would have a really hard time doing anything meaningful in mathematics, but a person with average IQ can very well amount to something far above mediocrity.

>>11755483
>try studying with and tutoring a stupid person, then spend some time studying with a smart person and witness the insurmountable gap
The primary reason so many students claim they're stupid all the time is because of insufficient contact with actual stupid people. Academics get to live in a wonderful bubble where the biggest dumbass you may converse with all year has an IQ of 112 and then call themselves "stupid" when their algebraic geometry homework takes 6 hours instead of 3. People have absolutely no clue what real stupid looks like. There are people in this world, normal people without medical disorders, who are literally too dumb to operate a cash register.

>>11755566
calm down, Peterson. academics cap out at like 135/140 any higher and they can't maintain emotional equilibrium in an environment with such explicit double think requirements such as pc, progress, specialization, pleasure of the mundane, lack of interdepartmental oversight, etc. you must agree with the status quo or you're gone, smart people, really smart people, are entirely incapable of that level of cognitive dissonance

>>11754601
That was sorta V.I. Arnold's point

>>11755565
Holy shit

>>11755309

he had the only rich that matter -- IQ

>>11755565
I can't really be bothered to dig through my booksmarks folders but here are two useful links:

https://www.sciencedirect.com/science/article/abs/pii/0001879183900465

https://scholar.google.com/scholar?hl=en&as_sdt=0%2C48&q=iq+and+educational+attainment&btnG=

Plomin's work on behavioral genetics was really what started to persuade me this body of ideas had some validity. I don't feel that iq is really the way to talk about it but it is the best proxy for general intelligence I've encountered besides mathematical ability.
>A 1926 study that estimates the IQ of prominent scientists of the past? Ok, since you've got nothing better, I'll accept it, so where in that study does it states an average IQ person will never amount to anything above mediocrity if they pursue a career in mathematics?
Basic inference: If people self-select into professional environments based on perceived future gains and possibility of attaining status in their field then its reasonable to assume that someone who is innately bad at mathematics is unlikely to stick with mathematics past compulsory education.
>anecdotes
Well yes there is little formalized theory behind cognitive science and behavioral biology. Besides very primitive attempts at using certain mathematical models to frame these interactions, we have nothing but raw empirical data and speculation to go off of. I have sat down and studied with, essentially tutored, groups of peers in my classes in chemistry and biology and the worst students were also the slowest learners, the least motivated and the most incurious and easily frustrated with difficult concepts.
>>11755566
The stupidity I'm talking about is an inability to internalize the basic logic of calculus and balancing chemical equations. A total lack of understanding of the difference between cause and effect. Severely stunted visualizing abilities and fairly bad working memory. For STEM fields this would constitute relative stupidity.

>>11753103
>look at /mg/
>100+ replies, looks promising
>it's autists talking about IQ

has anyone here studied/used polylogarithms of negative degree in applications or any such work? I'm currently working on something and it has a lot to do with polylogarithms of negative degree but I don't know that much about them at all.
>very vague
anymeaningful response will do

I did another 4 hours of math today we covered all the little continuity theorems and finally made it to differential Calc, which is even heavier review than the preceeding pages. very excited to finish this book off, at this rate I'm doing daily what classes did in a month. might do another few sections later, but for now, my brain needs time to distill.
need to cycle thru the trig proofs for memorizing, I have a feeling entrance exams are hyper autistic and have lots of convoluted trig identity problems to fully exam out of calculus. my goal is to just up and exam out of all JC maths and physics

>>11755566
take for instance people who post in /sqt/ that can't do basic trigonometry problems or understand freshman mechanics concepts like work and conservation of momentum. these are ideas that are ideally taught to 13-15 year olds, but the people complaining of difficulties are often 18-21 years old, being taught at universities by an instructor with a textbook, lecture notes and hw assignments to guide their learning and they seem to still remain wholly incapable of grasping why these ideas work the way that they do. This is relative stupidity. They are not idiots in the absolute sense, of course many people are literally incapable of remembering street addresses, teleophone numbers, understanding basic cause-and-effect like not drinking before a court date, not spending an entire paycheck on oxy. But, compared to the standards expected of a graduate student in a STEM field they are fucking morons.

>>11755592
keep coping brainlet

>>11755642
Nice going Apostol-friend. Is this your first brush with Calc?

>>11755642
Just don't forget to add the constant if you have integrals in the entrance exam. I did and didn't get in the first time I tried, I had one point too few, and forgetting the constant was -1... Me in the pic.

>>11755644
Hah! I'm one of those.

why do people get defensive over IQ? Most times people aren't even talking about the test itselft but use it as an umbrella term for general brain power

>>11755650
coping that I am incapable of a level of two faced deception that hamstrings myr
ability to participate in a creative process? that structure is for people like you to wall people like me out because the sight of someone as smarter than u as this thread has been speaking, but now the interval between u, who" gets maths easily", and someone like me, who can just look at something and understand it and instantly utilize it in all of its potentiality in an enormous variety of media; the very concept of this difference between people is even worse for you than the double think, because you're pathological narcissists in the most precise sense of the term.
academia reproduces in its members a neurosis of a certain kind, u must be either blind to it, or stupid enough to stomach it, to be capable of participating within it
it's why talent is so shilled and feared, it doesn't even exist and you cling to it so u can justify you're being a talented one. until you see you're not, so you've create an closed artifical ecosystem of 2nd rate cowards to, in a grotesque positive feedback loop, prove your value to one another prima facie.
this is the conclusion I'm at currently, prove me wrong faggot

>>11755680
The problem is people using IQ to justify their own failures and to tell others that they can't do anything if they're not high IQ.

Any good geometry book in which the focus is polygon?

>>11755565
You could just prove him wrong by citing some studies which show that e.g. a large percentile of mathematics researchers have IQs below 120.

It's always a sign bad sign if your argument is "prove that my claim is wrong" instead of "this is the evidence your claim is wrong".

>Besides, an average IQ person (100~115) is not stupid.
Oh anon...
The engineer unable to grasp a proof by induction after 5 years of education is in that range.

>>11755688
>writes an essay in response to a shitpost
keep
coping
brainlet

>>11755653
i took Calc 1 and 2 about 4 years ago. this is my first encounter with a real proof based approach, and it's so much faster I can't believe it. so I've seen a lot of this material, but not like this.
any1 have recommendations for after apostol for multivariable? I want to do, preferably rigorously, e&m asap.. and it looks like I need multivar for orbital mechanics as well
im really enjoying this proof based approach but a lot of the physics books I've seen gloss over the math

>>11755715
Never seen that actually happen.
Some people are just bad at things, that is life.
There is nothing wrong with being bad at certain things, I am terrible at nearly everything.

>using IQ to justify their own failures
It is just being realistic, not everybody has the talent to become a world-class mathematician, certainly I don't.

If you want to succeed in life you have to aim to a point which you can actually reach...

>>11755737
>and it's so much faster I can't believe it
Don't trick yourself into thinking it's somehow faster because it's being done rigorously. It's faster because you're still reviewing things you already know but from a slightly more sophisticated perspective.
Doing things rigorously from scratch is quite a bit slower than the handwavey "for-engineers" method.

>>11755748
I prefer the, to aim for the moon and if I miss ill land among the stars, approach

>>11755759
I am not an insane optimist, so I really do not like that strategy.
Usually repeated failure will only end up pushing you down further then you actually belong.

Aiming for the moon usually means landing on the ground, your body totally crushed.

>>11755737
Neat. My first ever look at Calculus was proof based. It was quite a bump in difficulty, but I enjoyed it.
>>11755753
I agree with this but
>Doing things rigorously from scratch is quite a bit slower than the handwavey "for-engineers" method.
My first ever math class for engineering (yes I'm a tourist no bully) started with constructing the reals and went from there. We proved everything pretty rigorously, though we weren't required to use the theorems for anything math-y sadly.
It wasn't Rudin or anything but it was there

>>11755626
>I can't really be bothered to dig through my booksmarks folders but here are two useful links:
>https://www.sciencedirect.com/science/article/abs/pii/0001879183900465
Holy kek, did you think I wouldn't read the first one? It has absolutely nothing to do with IQ at all.
>Plomin's work on behavioral genetics was really what started to persuade me this body of ideas had some validity. I don't feel that iq is really the way to talk about it but it is the best proxy for general intelligence I've encountered besides mathematical ability.
Sure, I agree that IQ is the best approximation for intelligence that we have, but that's not what the discussion is about at all. It's clear that you haven't read enough on the subject to go around saying anyone with an average IQ will amount only to mediocrity in math, I lost my interest in keeping this up, but thanks for your time, even though it didn't convince me at all.
>>11755731
Huum, you got it wrong, I'm not trying to prove him wrong, I just wanted to know if he actually had sources backing him up or if he read enough about the subject to justify his claims about IQ and mathematical success.
>It's always a sign bad sign if your argument is "prove that my claim is wrong" instead of "this is the evidence your claim is wrong".
I wasn't the one making big claims in this thread without providing anything to back me up. Besides, a real bad sign would be to trust anyone in an anonymous board without questioning any of their reasoning just because it fits into one's preconceived opinion of a certain subject.

>>11755748
Being realistic is not the same as being pessimistic which is just as bad as being deluded.

>>11755753
Im finding, especially with YouTube, that good pictures finish the situation for me every time. I have this visual intuition that I can combine with a given sequence of strict logical operations. and math has this way of always working like this
for example I much prefer line alg done wrong to the other more traditional alternatives I scouted, and none of that is review
but yes it's not always like that, but glancing thru those handwavey textbooks is always an option. it's harder to find the rigor

>>11755825
Almost nobody becomes a successful mathematician, it's extremely reasonable I won't be either.

>>11755832
A-are you perhaps 2* years old? But yeah, it is unlikely that anyone of us becomes. However, it is certain that the ones who give up don't become that.

Do any of you use Adderall? What about coffee?

>>11755847
Literally all I drink is coffee and occasionally alcohol.
Never tried Adderall.

>>11755847
What the fuck are you doing, delete that post please, the less people who know about it the better, but for gods sake delete the post and stop spreading this info to other people

>>11755853
Why?

>>11755853
take your meds schizo

>>11755832
Life's not that simple, you won't know until you try and to be honest, it's not about being successful, it's about trying, if you tried your hardest and still couldn't make it, then you'll have no regrets because you did all you could, but if you give up without ever trying, you'll always be haunted by the feeling of 'what would have happened if I tried when I was younger?'.

Why is the height of a prime ideal in a noetherian ring finite? It's supposed to be obvious but I can't see the reason.

>>11755856
It's the only weapon that we have to fight against the geniuses, but if everyone knows about it we'll have nothing anymore, so please delete that fast, please man

>>11755539
I felt it deep deep inside me.

Speeking of deep, I'm now through the paper >>11731439
i.e.
https://arxiv.org/pdf/1712.01815.pdf
>Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm

Here's some related video links I that looked interesting:

https://youtu.be/Fbs4lnGLS8M
>(Fullstack Academy: "Monte Carlo Tree Search (MCTS) Tutorial")
https://youtu.be/l-hh51ncgDI
>(Sebastian Lague: "Algorithms Explained – minimax and alpha-beta pruning")

https://youtu.be/qv6UVOQ0F44
>(SethBling: "MarI/O - Machine Learning for Video Games")

https://youtu.be/ikDgyD7nVI8
>(Jeff Heaton: "How Alpha Zero used Reinforcement Learning to Master Chess (12.5)")
https://youtu.be/uPUEq8d73JI
>(Lex Fridman: "David Silver: AlphaGo, AlphaZero, and Deep Reinforcement Learning | AI Podcast #86 with Lex Fridman")

>>11755862
Nit him, but that mentality is great until you think
>I could have done something fitting with my ability instead of wasting 5 years for this
It really depends on your mindset. If it's healthy then all that depressing thought doesn't really happen.

>>11755863
Anon, write the definitions next to each other...

>>11755873
It's not like you'll become a homeless if you can't win a fields medal, you can still get a job in a math related field without being successful in it.

>>11755798
it's no option, you must gamble. u can diversify and hedge with several moons and ensure some of your paths to mooning have security options along the way. talebs barbell approach.
either I can be successful as a classically trained jazz pianist, or I can do actuarial science, or be Java drone/it fag, or a signal plant engineer, or I will invent or find something spectacular and become unimaginably wealthy due either to some genius award and subsequent grant or a business or a market capitalization, or network and get venture capital
vertical and horizontal diversification anon, technical knowledge can be leveraged in a myriad of ways that are intimitly connected by some magnificent tree of probabilities and god. u must expose yourself to this potential and trust yourself to see it and act properly to actualize it when the time comes. always being vigilant while working to build some kind of momentum thru effort in acquiring a leveragable asset, in this case technical, imperative, knowledge

>>11755824
>I wasn't the one making big claims in this thread without providing anything to back me up. Besides, a real bad sign would be to trust anyone in an anonymous board without questioning any of their reasoning just because it fits into one's preconceived opinion of a certain subject.
To any claim you can take three different stances:
- It is wrong
- It is true
- I do not care
If you don't agree with it and care, then you obviously disagree.

I did a bit of research:
https://doi.org/10.1038/213441a0 was quite interesting. It obviously has enormous problems when it comes to sample size, but apparently the range of IQs of mathematicians in Cambridge who took part in the study was between 124 and 136.

>>11755863
Ok so I looked it up and turns out this is not obvious at all and the proof is pretty lengthy. Don't know why the author didn't mention that.
>>11755881
Go to hell.

>>11755844
I am not saying that you should give up and work at McDonald's, but if becomes clear that success is impossible, you should take a different route.

>>11755873
>instead of wasting 5 years for this
What do you mean "waste"? Even if you totally flub out as a mathematician and never even get a postdoc, you're getting paid to spend 5 years exclusively pursuing mathematics. That seems like a pretty good deal.

If 5 years of studying the math you enjoy most is "wasted" time to you because you don't get to be famous afterward, do you really like math that much?

>>11755847
Water and juice during day time, something to help me sleep in the night. No time for coffee. It's making me chubby...

>>11755863
Ascending chains + Noether < [math]\infty[/math]

>>11755871
Good gut instincts.

>>11755898
>Ascending chains + Noether < ∞
What?

>>11755862
But I am not arguing against trying. IAM arguing against trying when you know failure is inevitable.

At some point you have to accept that when your parents told you that "you can become whatever you want" they lied.

>>11755896
>success is impossible
But you can't be certain of that unless you try your hardest, to the point where you can feel satisfied with your attempt and ready to move on.

>>11755898
>Ascending chains + Noether < ∞
It's not as simple as that.
Noetherianity trivially gives you that there are no infinite chains of ideals, but it's not obvious at all that you can't have unbounded finite lengths. That takes work.

>>11755897
>>11755883
That's now how I think, but I used to think like that because I had a lot of anxiety and depression. You are both right.

>>11755884
>u can diversify
You really can not. You can't pursue a PHD in Chemistry, mathematics and physics at the same time. Specialisation is inevitable.

>either I can be successful as a classically trained jazz pianist, or I can do actuarial science, or be Java drone/it fag, or a signal plant engineer, or I will invent or find something spectacular and become unimaginably wealthy due either to some genius award and subsequent grant or a business or a market capitalization, or network and get venture capital
But you *got to make a choice* which will inevitably change what paths are open to you.

>thru
Nobody who writes "thru" has a correct opinion about anything.

>>11755865
>>11755853
Erdős being high off his tits on meth is already common knowledge

>>11755905
Sure, but you actually *have to move on* at that point. Trying to force something you know is not going to happen isnot helpful.

>>11755909
That's not how I think now*

>>11755918
Didn't he only start using it later in life, after he had already achieved great success in maths?

>>11755903
So have you really tried your hardest without any regrets? What's your life story. I'm sorry, but from the way you post it sounds like you're not satisfied at all with your attempt, if so, then you need to keep going for it, you haven't reached the point where you're satisfied with your attempt and ready to move on.

>>11755871
I'm a chess brainlet but I find it neat on some level. AlphaZero is very interesting. It's really cool to see the strategies it uses, very alien.
>>11755922
Yep, but still

Next time make the pic Serre page 2.

>>11755932
Within maybe a bit over a year we could read the entire Course in Arithmetic if we kept that up

>>11755896
You have already given up. I can see it in your eyes without having to even see your eyes. Maybe it's temporary, maybe it's permanent. I'd suggest you go get some sleep and look at the world and its darkness with new eyes.

>>11755897
Yep. I know I'll probably be doing something else in a few years, but at least I got a little bit of extra time to play around with this stuff. It will leave some smile inducing memories, and that's what I want. Begging to get some grant, crying blood when all the applications come back rejected etc., bleh no thanks.

>>11755902
Ascending chains with proper inclusions are finite in Noetherian modules, in particular rings.

>>11755908
Ah yes true! It's a supremum, silly me. Sorry about that.

>>11755937
That would be tres bon.

>>11755954
>Ascending chains with proper inclusions are finite in Noetherian modules, in particular rings
Yes, that's the definition. How does that help at all?

>>11755958
It doesn't. I forgot how suprema work.

>>11755924
I am getting towards the end of my masters now.
I am not sure if I have tried enough, but certainly that will show fairly soon.

>>11755954
>You have already given up. I can see it in your eyes without having to even see your eyes. Maybe it's temporary, maybe it's permanent. I'd suggest you go get some sleep and look at the world and its darkness with new eyes.
I don't feel I ever felt as awake as I do now. I did some sports and went for a walk in the woods...

>>11755918
>>11755922
Erdos started popping pills in 1971 after his mom died.
People've actually analyzed charts of his publications. He did definitely write more papers after he started taking stimulants, and since he was getting old you can probably conclusively attribute that to meth letting him focus 18 hours a day.
They generally weren't as important as his earlier ones though (if you click through the "stuff named after Erdos" page on Wikipedia, you won't find a lot he did after 1970). But I don't think you can really place causality there, since most old mathematicians tend to no longer care whether or not they're doing "important" work.

>>11755954
>doing something else in a few years
Math related? What are your plans if you fail in the academy? Although I doubt you'll fail at all, we're in a much worse situation than you.

>>11755968
>I am not sure if I have tried enough, but certainly that will show fairly soon.
No, that's not it, you're not putting up a fight, you're just raising your arms to defend yourself and now you're just waiting for the match to be over, if you want to succeed, you have to really fight and you have to stop thinking a out winning or losing and just keep fighting until you can no longer, if failing at a masters in your prime years is enough to make you give up then you haven't tried hard enough.

>>11755987
>failing at a masters
As if. No, the question is whether I get a PhD position or not ...

>>11755989
I have a feeling you're gonna make it.

>>11755989
I have a feeling you're not gonna make it.

>>11755997
>>11755998
Now what?

>>11755483
>you are a faggot
Brilliant reply, smoothbrain. I'm enthralled with your scintillating acumen.

>>11756000
Now you choose what you want to believe in.

>>11756002
I choose to believe in going to sleep, right now.

>>11755968
Lucky you, I miss good and long walks in the woods. Nothing like a stroll in the sylvan shadows amidst the fog of an autumn morning.

>>11755975
I used to be an inspector of incoming goods for a company selling medical equipment. The boss sent me a few requests to come back, but I had to reply him that I don't have such an amount of free time to come even for the summer, and the lock downs would be making it even more difficult to get back. I'm fairly sure I'd get back if I told him that's what I want. It was nice, a lot of exercise, nice people and sufficient salary. When I'd get home, there would be no work in my mind until the next morning when I'd go to the bus stop and wait for my ride. Something similar is my plan after I get my degree or run out of time (at the moment). Obviously, things can change and maybe I will find a reason to try become a post doc. Who knows?

>>11756006
Good night.

>>11756006
Study while they sleep and then live what they dream.

>>11755914
under that circumstance, yes, but u chose that position
>consider the following
buying a few acres in the middle of nowhere, dedicating a few years of your life to building a castle, and then be Dr Frankenstein and do whatever u want with math

Ahlfors, Conway or Kodaira? Which one is the greatest Complex Analysis book?

>>11756053
Conway is much better written than Ahlfors. I actually read Conway instead in a course using Ahlfors because Ahlfors is so obtuse about everything.

Kodaira is different. I doubt it would work as a textbook that well because it barely has exercises. It also doesn't really contain that much of what most people would call "complex analysis"; it does the really basic stuff quickly and then rams balls-deep into Riemann surfaces for the last couple hundred pages.

>>11756076
Ok, but Conway is graduate level, do you think it's too advanced for an undergrad? So Kodaira's not a good book? It was recomended to me a while ago, I'm interested in riemann surfaces

good night /mg/!

>>11756089
i've seen some extremely simple books labeled "graduate level", so don't pay too much attention to that

>>11756089
>but Conway is graduate level
It says graduate on the tin, that doesn't mean you're only allowed to read it in grad school.

>So Kodaira's not a good book?
I can't judge the book itself, I haven't read it, but I have flipped through it.
I'm only saying it's probably a poor choice to read if your goal is to get a solid foundation in standard complex analysis knowledge. If you like Riemann surfaces you can always just take a look at those sections for interest.

>>11756029
>buying a few acres in the middle of nowhere, dedicating a few years of your life to building a castle, and then be Dr Frankenstein and do whatever u want with math
Mephistopheles, why are you tempting me?

>>11756108
Good night to you,

and to everyone else too.

>>11756108
>>11756113
Ok, I'll read conway then, thanks.

>>11756108
>>11756119
>Night
The fuck you talking about, still 8pm

>>11756128
>not going to bed at 8 and waking up at 3:30
do you even depression

How do people come up with numbers (bounds) in conjectures such as the one in Erdos-Szekeres conjecture?

>>11756186
lots of examples, usually
combinatorialists spend a substantial portion of their days playing with examples of things trying to find patterns

>>11756108
I'm taking an undergraduate course that follows that book. We're not covering all chapters though. The writing style is a bit terse and so are the exercises, but the focus in Möbius transformations and stuff is interesting if you're into geometry.
>>11756186
Since it's combinatorics, usually it follows naturally from the combinatorial structure of the problem. Can't be sure about that problem in particular but if a power of 2 shows up, then the argument for the bound likely involves taking pairs of things: http://www.openproblemgarden.org/op/erdos_szekeres_conjecture
In other fields such as analysis, bounds arise naturally from the behavior of certain functions. In any case it's usually easy to find trivial bounds first and then keep refining them until it's eventually optimal.

>>11756237 was meant for >11756089 sorry

>>11756237
>follows that book
Which one? There were two mentioned in that post.

I have tried reading a few books (Hubbard, bachman) and clicked on a lot of videos but I still cant really wrap my head around what a differential form is. Any book/video recommendations or just an explanation /mg/?

Does the Jordan Curve Theorem have any uses outside Topology? Like in Graph Theory, or Analysis?

>>11756362
Do you consider 1D complex analysis to be topology? Contour integration uses Jordan curves, although the issue isn't always brought up in every book.
It does show up in basic proofs about planar graphs, although only in the very weak borderline-obvious polygonal form. Graphs are only ever built out of straight lines, I can't imagine ever needing the big-boy version for anything.

>>11756398
Okay, thanks!

i wonder if there were ever any 55ers in these threads

>>11756539
I can transfer to a better uni to get a BA in maths or a BS in comp sci and I can’t decide. Regardless of which I choose, I’m planning on applying for a graduate degree.
Do any of you enjoy your jobs? Is the pay alright?

>my reu, which starts soon, got moved online because of corona
Feels bad, i was really looking forward to it.
Any tips on how to salvage this experience? Like how to be a productive stay-at-home research collaborator?

>>11756665
you got fucked hard
REUs are complete memes, they're literally just a vacation that you get to put on your resume
take away the social/travel aspects and there's basically nothing left

>>11756685

>>11756539

Ok /mg/ question time. I go to a small uni, and I was going to to transfer to a bigger institution to do a full "real" degree. Thing is, I...uh didn't apply in time. The deadline was yesterday. So I have two options.
1. I try to apply anyways (though I hate the school)
2. I do a smaller degree on paper, but since our schools are linked I am allowed to take courses at the bigger school, so I take the requisite courses anyway and don't count them on my final degree.
What would you people recommend? Would a (Canadian) university care about that for admission to a masters program? ty~

When you read a paper, do you try to understand the proofs line by line? Or do you skim it and only read the important parts, to understand the general idea?

>>11756823
>sorry my application was sent late, my internet went down during the riots, and also my grandpa was dying of COVID-19
They can't say no

>>11756871
haha, but I'm in Canada (no riots) and not in Quebec or Ontario (no corona)

>>11756879
How about
>I'm sorry I was late because I was bully on an image board for posting 2hu pictures

>>11756881

Are there any advanced math topics that only require logic, set theory and proofs as prerequisites?

>>11756823
One more thing to add, my backup plan from phd is teaching high school (in french, better market). Small school is french, bigger one isn't, and french is my second language (I can already feel it leaking out my ears just after 2 months away).

>>11756665
>>11756685
They are not complete memes, I did one, and I definitely learned some skills I took to grad school. They are pretty much a vacation and you get to make some cool friends, but you do get some research experience. My experience kind of felt like an internship with a mathematics professor. Maybe not all are like this, but our adviser liked to talk a lot, so she told us about the inner workings of math departments and academia. She also gave us basically workshops on how to read papers and come up with questions. We got to go to a conference in the specialty give presentations. Some people have the misconception that you're going to learn hardcore math. Most problems tend to be combinatorial in nature since you can't expect 2nd, 3rd year students to know that much machinery. It sucks yours got moved online.

>>11755824
First study is discussing somewhat related idea of self-assessment of mathematical ability and choice of college major/intensity of mathematical education in college. It wasn't meant to be directly related to iq at all. However, if you don't see a broader connection between selecting an optimal early-adulthood environment and profession and perceived ability in mathematics or the sciences given past experiences of positive and negative feedback when performing mathematics in public school you are not giving this much thought at all. Its very reasonable that at least a good portion of people's decisions to avoid math at all costs in college are informed by actual failure at mathematics and negative feedback from teachers and peers (the idea one might be stupid or quantitatively challenged if that bothers you).

I never claimed nor would I claim that someone with an iq of 110 couldn't do mathematical research. I'm suggesting that they don't attempt to do so because they already have experience failing at basic mathematics, that most mathematicians tend to be well above average intelligence scoring quite high on iq tests and that the average of math and physics grad students is well above that of the average person off the street. You are significantly less likely to be able to or to desire to perform in mathematical research environments if you are not mathematically gifted. The time lost to failure alone during childhood when others are learning at a rapid pace, accumulating familiarity with difficult mathematical concepts is very costly when mathematical research is already a game for young people and for the precocious and competitive. Add in that its entirely possible many problems in mathematics that are still worth anyone's time are heavily iq gated and it seems as if you should have low expectations of someone who cannot perform as well on an iq test as the average successful math grad.

/gmmg/

>>11756128
It was midnight.

>>11756892
>logic, set theory
Try logic or axiomatic set theory.
>proofs
All of them.

>>11756892
>>11757239
Actually now that I checked my email, this could be of interest to you: https://arxiv.org/pdf/2006.01613.pdf

>>11754597
And this one is for you to read if you want to see CT from another perspective to understand what Leinster is saying https://arxiv.org/pdf/1912.10642.pdf

>>11756362
Yes. Specifically the Jordan-Schoenflies theorem, which is found e.g. in the study of the Cheeger Problem in the calculus of variations, where a "Jordan domains without necks" (A Jordan domain is exactly what the Jordan theorem describes) is a central object which allows the generalization of solutions from the basic case of konvex domains, to which a solution formula for the Cheeger problem is well known.

what math do I need to Calc out voyager 1s kinematic quantities relative to the sun for any t during its voyage?

>>11757259
>>11757269
Very curious that both of those are dated to yesterday - how did you come across them?

>>11757397
he said it himself, you can subscribe to stuff on arxiv

>>11757397
Arxiv mailing list. It's nice.

>>11753103
I am interviewed for two academic positions in maths. How bad will they laugh at my brainlet abilities (I do """""effective""""" stuff) ?

>>11757397
>>11729920 <- read this

>>11757408
cool

>>11757391
ODEs and numerics of ODEs.

>Don't want to jump into a book full of stuff I've already done
>Books with stuff I haven't done casually refer back to things I've never done before
How do I overcome this?

[eqn]e^{i\pi}+1=0[/eqn]

>>11753103
I hate maths why the fuck am I forced to study it in a computer and communications masters degree?

>>11757477
because we hate you

bros... i forgot to do maths today... for the sixth day... bros...

>>11757479
there's still time bro...

>>11757477
>computer
Computers function based on mathematics.

Study theatre if you do not want mathematics.

>>11753352
Ok? *Not standing against fascism*

>>11757536
>study theatre
>don't know how to make change at starbucks
>get fired

hey /mg/
undergrad pure student here. which one of these courses should I take? I only have room for one. I have taken differential geometry and group/ring theory courses and really liked them, so I'm inclined towards the bottom option. but I also love philosophy and want to know what exactly I'm working with when I use sets. any advice appreciated.

Who the fuck was Nagata and why is every single counterexample in algebra attributed to him

>>11757653
They both seem perfectly fine. It really depends on what you actually want to learn.
Personally, I would probably choose the top option, but if you are interested in "deeper" algebra the bottom one might be quite interesting.

>>11757653
Set Theory/Logic without a doubt.

>>11757653
Top one will probably be hard as fuck because the content is hard
Bottom one will probably be hard as fuck because physishits pull shit out of their asses all the time, and even some in mathphys fall into that category

>>11757653
top if you're a gigantic autist, or you want to suffer
bottom if you don't hate yourself

>>11757653
I'd take the lower route and read some set stuff on my own (for example maybe >>11757259).

>funding cancelled due to covid
Should I wait a year, kms, or just drop research entitely

>>11753103
need to find a [math]\delta[/math] such that the three following inequations:
[eqn]0<x_{0}<1 \\ 0<y_{0}<1\\ (x−x_{0})^{2}+(y−y_{0})^{2}< \delta [/eqn]

Implies that:
[eqn]0<x<1 \\ 0<y<1[\eqn]

How do i start to approach this problem? Can i really come up with a delta or shoud i learn a bunch of particular deltas for different situations? Is there abook where i can learn about those inequalities found in topology and analysis, focusing in the resolution of the inequalities and not the formal terminology?

I know this comes from trying to show that every disc stays inside the square. I just care about the inequalities at this point, and the geometry didn't really help me to see what delta use. I only know that it may depend on [math]x_{0}[\math], [math]y_{0}[\math] or the [math]min \{ x_{0}, y_{y_0} \} [\math]. But i need a explicit [math]\delta[\math].

>>11757850
Pretty sure you're either misinterpreting the problem or delta it's infinity

How many hours does it take to master abstract algebra?

>>11757663
>>11757664
>>11757669
>>11757690
>>11757753
thanks guys. leaning towards set theory now but still unsure.

>>11757865
I know up to representation theory of groups, UFD theory for rings, a bit of basic modules shit, and still feel like I know only basic abstract algebra. I've probably put over a hundred hours in total although I really have no idea how to even begin to estimate this number. What do you even mean by 'master'?

>>11757880
Being able to teach and grade math 55a at Harvard.

>>11757865
the formula is:
[eqn]\frac{1000}{\textrm{your IQ} - 100} \textrm{ hours,}[/eqn]
if your IQ is below or equal to 100 then you will never master it

>>11757891
I'm a retard with an IQ of 65, so I already mastered it 29 hours before starting?

Is it practical to read two to three books every day? Like learning one/two subchapters per day and maybe do some problems. Or, is it more optimal to focus on one book only?

I'm trying to self study before my college classes begin. The textbooks we're supposed to use in class are Stewart's Calc, Linear Algebra by Axler, and a couple of texts for discrete math such as Book of Proof, etc. I already know Calc I/II and some knowledge about Linear Alg, but I just want to go over and review. Any tips for studying would be appreciated!

>>11757871
No problemo. Just pick the one you gravitate towards the most.

>>11757891
It's actually like this: the chances of ever mastering anything = 1 - H(y-24), where H is the Heaviside step function and y is your age in years.

>>11757898
the more books the better. Gotta confuse the brain for optimal intelligence growth

>>11757907
So you are guaranteed to master something, then the next day (24th birthday) you are guaranteed to never master anything?

>>11757925
Exactly. Isn't life just cruel?

>>11757929
You're an engineer I'm assuming?

>>11757935
I sometimes help an engineer out. Close enough.

>>11757898
Of course it is. This is exactly what you do in university. You don't spend three weeks ONLY doing linear algebra full-blast all the time, and then move to something else. You take 4-5 courses at the same time and do a bit of each every day.

https://www.muramatik.com/motives-what-not/
>Motives and What Not
>MOTIVIC ZOOM CONFERENCE SERIES
>The third edition of our mini-conference will happen on 17th June in Zoom!

>>11757935
Show some respect to the best poster on this thread, you piece of shit.

Is animuposter and 2huposter the same guy?

>>11758119
the main animeposter is an alright guy
the 2huposter is an insufferable faggot

bros... i have been doing maths today... for the six day in a row

>>11758077
Now now, anon. You are being too nice. Did you do something mentally stimulating today?

>>11758119
I don't understand geometry at all, so nope. Someone will probably tell me that neither does the 2hu poster...

>>11758156
Very good, very good. You can almost touch the Fields medal already.

>>11758156
This man doesn't stop.
This man knows what he wants and he gets it.

>>11755816
>>11755737
Wait, how did you learn proofs?
I tried taking a rigorous book like Spivak, even though I knew calculus, I couldn't prove basic shit he asks you to do in the beginning because I have no idea on how to write a proof, verify, let alone even start it
So I went back to my comfortably applied stuff

>>11757653
>>11757871
Unless they're in the exact same time slot, why aren't you just going to both for the first week and then deciding? Then you get to see firsthand what you're picking instead of guessing and using the uneducated opinions of anonymous shitposters. Tons of people do that in all courses.

whats the prereqs for probability and statistics?

>>11758219
The proofs work in a way very similar to thought experiments. I'll show you how you can do an indirect proof in a non-mathematical context and you can try to dissect it. Okay, so we want to prove that the earth is flat, and I will present you a water tight argument by deriving a problem out of the counter-assumption.

So, let's assume that the earth is round. Suppose there are two eskimos, one living on each pole. By symmetry, we can assume that the northern eskimo wants to visit the southern one. When the eskimo reaches the south pole, his feet point away from the planet, so he falls into space. Since this does not happen in real life, we conclude that the earth cannot be round. []

Can you follow the structure of my proof?

>>11753352
What is fascism?

>>11758248
wtf it was flat all along?!

I am struggling with the following result.

Consider some normed space, and let [math]f[/math] be a function which is not necessarily lower semicontinuous. Denoting an [math]\epsilon[/math]-ball around [math]x[/math] as [math]B_\epsilon(x)[/math], the function
[eqn]\lim_{\epsilon \rightarrow 0 }\; \inf_{x' \in B_\epsilon(x)} \;f(x')[/eqn]
is then lower semicontinuous, and equals [math]f[/math] if [math]f[/math] is lower semicontinuous.

I can see how f and the function will be equal when f is l.s.c., but how to show that the function defined in this way is always l.s.c.? Is there some intuition for this construction?

>>11758262
>how to show that the function defined in this way is always l.s.c.
did you try looking up the definition of "lower semicontinuous"

what's wrong with my answer? epsilon 'e' denotes the empty set here

>>11758219
Well, I knew from memes some techniques. I'm only half joking with that one.

I used Apostol as I said, the first chapter is probably easier than Spivak's. I don't know, I just sort of read the book? And followed the structure of the proofs inside.

also, this one?

>>11755199
nice, can’t wait to share this on /r/dankcopypastas

>>11758246
Basic probability/statistics? Just single/multi-variable calculus, pretty much.
The rigorous second course in probability requires measure theory but I'm guessing that's not what you're asking about.

this was my first ever attempt at a proof
>>11756560
how did I do?

>>11758416
Your basic understanding of f'(x) is incorrect.
It shouldn't really be understood as "change of y / change of x". Well, that's correct most of the case.
But the truth is, as lim dx approaches to zero, it doesn't exactly represent that anymore.
f'(x) is just the slope of the tangent at x. Nothing more, nothing less.
I don't know why you go through all that trouble when x^3 is a perfect example.

>>11757653
While learning set theory and logic are cool, anything near Gödel sucks, and they can both just be pretty painful at times. On the other hand if you don't have a lot of interest in mathpys, I don't know how useful that one will be to you.
I would recommend >>11758224 idea

>>11758270
yes

Can I learn abstract algebra just by reading textbooks?

>>11758579
If you solve the exercise problems without the use of pen and paper, then yes.

>>11758219
skimmed the first few pages of how to prove it and naive set theory for notation. I have a semi background in formal, Aristotlean, and transcendental logic. I've read hurley, the organon, and a lot of hume Locke leibniz kant hegel. I'm a logic boy and a lot of these proofs are either borderline tautological or
if p then q, p, thus q.
some of them are much more complicated than that, and I'd be lying if I said I'm currently capable of more than a few of the proof exercises left to the reader, but I can do some of them. but
most importantly, I can follow them, and the solutions given for them.
supplement some of the vagueness with pictures and YouTube and drawing them out myself, and trust that eventually I'll be able to work well in this framework.
there's also a baby inductive proof intro here
https://youtu.be/L3LMbpZIKhQ
once u get it u just kinda get it. the hardest part for me has been looking at something and saying thats just so obviously true If that's legal anything goes,and reconciling this against my ignorance of mathematical proof

if anyone wants a mindfuck of Aristotlean logic scholarship, get Aristotles categories and concerning interpretation translation with commentary by Kenneth Telford.
the biggest issue with all this set theory mathematical logic is the bedrock foundation of class inclusiveness and representation with venn diagrams. this is a patently false method of logical procedure, and it triggers me endlessly

What does submodular set function mean?
https://en.wikipedia.org/wiki/Submodular_set_function
Is it just mean that, a bigger the input set is, the smaller the value becomes?
Why is it important?

Is this the yukarifag?

>>11758461
Even people who teach it like "change of y / change of x" warn you about "paradoxes" like these.
3blue1brown does it, for example.

>>11758671
This picture nicely demonstrates the two paths to winning a putnam
you can either be so incredibly cripplingly autistic that you wear anime porn t-shirts in public, or you can be asian

>>11758842
If he wasn't standing manually, he'd be based, though.

>>11758842

>>11758842
im trying to decide if I'm Chad enough to wear an anime girl shirt like a wolf or eagle shirt, or if the stigma is so strong no Chad is Chad enough to make anime Chad. something tells me it'll be highly controversial and maybe the hottest 10% of teenage thots will surface read it as unwavering confidence sourced from absolute self certainty and relaxation and be helplessly attracted to it. the pros are it would trigger betas who would be equally helplessly motivated to make negative comments which would give me an opportunity to flex my chadness by embarrassing them, which would only serve to confirm in the hormonal mind of a thot that this guy fucks. the cons are I'd lose face with boomers

How many math problems do you do per day /sci/?

>>11758591
>without the use of pen and paper
based!

>>11759014
>chad chad chad chad thots trigger betas chadness thot boomers
This post just disqualified you from ever being "Chad".
Please tell me your brain doesn't actually function like this

>>11759078
0-3. Today 2½.

>>11759079
Let's hope this reading only anon is based!

>>11759090
It almost looks like you are trying to bait that anon into posting a doomer or joker wojak. We both know he has a big folder of those.

>>11759100
Oh and stay hydrated, keeps your brain functional (at least better than writing a bunch of buzzwords)!

>>11759014
>im trying to decide if I'm Chad enough
8 words in and you've already failed

[math] T := \{n \in {\mathbb N}\mid\forall(S \subset {\mathbb N}). \phi(n, S)\} [/math]

>>11759234
I hope to find what this means in the morning.

Good night.

>>11759387
Good night. Sleep well.

Is /mg/ mostly European?
I feel like it's always dead around this time.

>>11759849
I'm Chinese.
美国是狗

Have you ever tried studying under a hallucinogenic? As I often tunnel vision and don't seem to be able to think creatively about problems I wonder if drugs can open some pathways to facilitate that

>>11759849
Mmm...Well I'm Canadian, bildschirmfoto-anon says they aren't German, but that's probably a lie, Yukari is either in the US or Japan, I can't remember, and one of the /gnmg/-anons is european I think bcuz of their sleeping time

>>11755566
Honestly I think a lot of it is that university aren't very good at actually teaching people how to solve problems. They just throw a shit load of theory at you, show the simplest example and expect the students to put it the rest all together. This is more pronounced in math and physics where the people lecturing you are good at physics/math, but not necessarily at teaching and making sure their students are capable or at communicating in general. They test rather than teach.

I got an actual math tutor for one subject and understood everything immediately because they understood how to actually "teach" rather than lecture.

Learning Intermediate Algebra here with Prof Leonard.

Hes a good professor but I feel Im lacking more exercises practice.

What are the best exercises that will train many overall Algebra skills?

>>11760125
>he thinks the purpose of university is to teach you things
oh anon...

>>11760148
I know I know.. I'm point out why people feel dumb when they stryggle at university and don't understand why. They're relying on the university to teach them.

>>11760148 #
I know I know.. I'm pointing out why people feel dumb when they struggle at university and don't understand why. They're relying on the university to teach them.

>>11755323
this but unironically

>>11758283
simplify

>>11759849
I'm Canadian.
There do seem to be quite a few yurops in here though because whenever people come and ask PhD questions, if you answer regarding the American system you will always get some shithead replying
>heh not how it works retard t. 15 average
or something along those lines

>>11760094
>Yukari is either in the US or Japan
Poland.
>/gnmg/-anon
East Europe

What do I need to learn in order to kill the putnam?

>>11760306
autism

>>11759849
Borgar here.

>>11760138
Does intermediate algebra mean high school algebra or abstract algebra?
If high school algebra then why not just move on to calculus on your own and practice it that way. You'll shoot to birds with one stone and get some trigs as well. If you don't wanna do that just get something like Axler Precalculus from libgen and do the exercises at the end of related units, there is enough and they have solutions to odd numbered problems. Not that it matters, at this stage you can enter basically all problems into something like Symbolab and get a step by step by explanation and solution.

If it is abstract algebra, I dunno.

/gmmg/

>>11759395
Thanks, I did.

>>11759849
Probably not.

>>11760094
Yukari is/was somewhere in Canada a few years ago at least. There are also several German speaking countries.

>>11760299
>East Europe
But living in the UK on the queen's money.

>>11760364
>Does intermediate algebra mean high school algebra or abstract algebra?
I'd say it's most likely the not-abstract version.

>>11760306
Systema, krav maga and ninjutsu.

bros... i forgot to do maths today... for the seventh day in the row... bros... i want to do maths... bros...

>>11760731
Let's take the bros guy as an example and motivate each other starting today. Just do math bro. I believe you can do it.
>>11760496
>I'd say it's most likely the not-abstract version.
Yeah, that's what I guessed as well but it is hard to be sure since so many names exist.
One of my friends was talking about college algebra and I thought it was abstract algebra and I was impressed since he didn't like math much but turns out it was just precalculus stuff.
Another time someone mentioned elementary algebra and what they meant was introductionary abstract algebra.

>>11753103
>solving for dt
Ugh i don't think its legitimate operation. For me d theta over t means just derivative of theta with respect to t. This is just 1st chapter of ode book. I am not comfortable with this, i do not know what is going on. Is there any other way you get the result without that stretch? Should i just stick with it and proceed or are there books which dont do that?

>>11760764
Yep. It would make communication significantly easier if algebra meant the same thing for everyone, but we know that day will never come. Never ever.

>>11760893
It isn't legitimate operation. It is shorthand for change of variables in integral:
[math] \theta '(t) = f(t)g(\theta) [/math]
[math]\int {f(t)dt} = \int {\frac{\theta'(t)}{g(\theta)}dt} = \left[^{\theta = \theta(t)}_{d\theta = \theta'(t)dt}\right] \int{\frac{d \theta}{g(\theta)}}[/math]
[math]F(t) = \int {f(t)dt}[/math]
[math]\int{\frac{d \theta}{g(\theta)}} = G(\theta)[/math]
equation [math]F(t) = G(\theta)[/math] implicitcly defines [math]\theta(t)[/math]. Now, by differentiating [math]F(t)[/math] and [math]G(x)[/math] with respect to t you get:
[/math]F'(t) = f(t) = G'(\theta)\theta'(t) = \frac{\theta'(t)}{g(\theta)}[/math]

>>11757669
This is also reason why differential equations are hard to understand formally. Sure, you can get away with 'solving for [math]dt[/math]' in this case, but you can't always guarantee that

>>11760955
Now, by differentiating [math]F(t)[/math] and [math]G(\theta)[/math] with respect to t you get:
[math]F'(t) = f(t) = G'(\theta)\theta'(t) = \frac{\theta'(t)}{g(\theta)}[/math]

>>11760899
Maybe if mathematicians take over the world and start using the proper terminology.
Algebra for abstract algebra.
Retard algebra for what is now taught in k12.
And then other adjectives can be added.
Elementary algebra = introductionary abstract algebra
College retard algebra = brainlet middle school class for retards in university.
Etc...

Does this make sense or am I sounding retarded?

>>11760974
>Does this make sense or am I sounding retarded?
It does make sense, but it is also extremely optimistic. For a while, it would make sense, but eventually this global terminology would be necessarily fall apart, I am afraid. Basically, it would be close enough to a language to suffer the fate of languages in the sense that different groups of people using it would develop their own uses for it, and then it would give rise to a bunch of different versions of what these things would mean. Maybe a bit confusing a message this one of mine, so just interpret that use difference thing as dialects of a language, language games in the sense of Wittgenstein, or both if you are really brave!
>Maybe if mathematicians take over the world
Would you like to join me in this quest? Interuniversal Hyperwar to seize power.

Anyway, my creative break is over, back to doing stuff. Adieu~

>>11759849
Rio here (not misha)

>>11760960
Thank you. I realised change of variables was going on when they showed dy/dx=f(x)g(y) to dy/g(y) =f(x) dx. I know the existence of solution theorems but what bothers me there are alot of theese shorthands left without explaination. I suspect some of then are just a lil bit more involved like here and some sit ontop of heap of other inner 'crap' not mentioned. I would appreciate they showed really what is going on with some of the differentials shuffling and the correspondence between approaches was more explicit or if some workings are more complex and beyond the scope, some info on where to look for the details. I don't know if i would be able to know all the details on first course but i would like to be informed when i dont.
So tell me do you know some books with the approach ti the topic i described? Or would you recommend to suck it up and just learn more details along the way with later math

>>11760996
Our patience has its limits. We shall rise up and add hell onto earth and subtract the heaven they don't realize they have.
Good luck anon. Make sure to study lots before the promised day comes.

>>11761347
Privet totally-not-Misha.

>>11753103
Is there a name for numbers that can't be produced by having an integer base with and integer exponent grater than 1? ex. 1, 2, 3, 5, 6...

>>11761407
I have dedicated my life to these dark arts, I know my Sun Tzu both in martial sense and as a theorem of rings, I am ready.

>>11761422
Whoops I meant to exclude 1
greater*

>>11761443
It's not about whether you are ready or not. It's about if the day is right or not.
Remember this as you continue your journey in math, grass hopper.

>>11761471
I am waiting for the sign to come.

>>11761422
Squarefree

>>11761654

>>11753749
>>11754624
>>11755425

incel detected

>>11761953

>>11761953

>>11759078
I do research so it depends whether I am reading or working. But I like to do undergrad problems from time to time regardless. Plus I have an undergrad that I am coaching, so I do his problems. On average I'd say one or two a day.