[math]\overline {mg}[/math]Assign yourself the exercises edition.Type mathematics.previously >>16318596
trash game
>>16350881we shouldn't call it the "video game" industrywe should call it the operant conditioning industrybecause that's what it ismath exercises are just luxury operant conditioning
>>16350896i am getting fucking sick of zoomers fawning over generals because its the only c&c they played when it's not even a c&c game and has no russia faction. Even tranny omega is better
Is this good study music? What about Brandenburg concertos?
>>16351009why you retards post these curricula if haven't even read a single book from them
>>16350912idk but I study math with this
>>16347332Seriously. If it's true for that whole half plane then surely you should be able to make an argument about the range of the real part of Zeta solely from the sum which gives the function for the real part given sigma greater than 1, no?
Redpill me on the Thom Isomorphism. What is it good for? What kinds of problems is it good for solving?
>>16351063Based and von Bingen pilled. Sometimes I'll listen to Gesualdo or Giovanni Perluigi da Palestrina when I'm doing research/math. If you haven't checked out Carlo Gesualdo, you should.
Bros how much studying is 1ECTS really? It says 28, but is that really so? I would like to complete my future degree's math before I go to uni and need accurate data for planning
>>16351710It really depends. Are you going off some specific curricula? What subjects would you have to study? How much time do you have before going to uni? You can realistically study ahead a lot, especially if it's undergrad, but a lot of it comes down to motivation etc.
Kinda fucked up my measure theory exam, bros I don't think there's any hope for me...
>>16350169advanced engineering mathematics by Dennis zill. its an entire textbook on differential equations. a lot more in depth than a textbook that covers calc 1-3 + DiffEq. you can find the 5th edition and the solution's manual on library genesis
>>16353790I didn't use this book when I was doing undergrad, but from the table of contents in the pdf it looks neat. I wonder whether you get a similar level of appreciation for each of the topics compared to just taking separate courses for linear algebra, complex functions, and signals and systems. My guess would be no, but that it's probably good enough unless you are going into grad school level research and really need to understand at a deep level what's happening.
hi guys.I'm a dropout from elementary school (I quitted at grade 5). somehow I wasted most if not all of my entire youth. now I'm in the late 20s, been working one mundane job to another. no skillset.I've been interested in data science (poor choice given my background) and I really want to give it a try as Ive been learning for months. the thing is, when I look at math stuff shown in the courses and books. I'm fucking freaked out, and I don't even understand shit. I'm fucking hopeless. but I still want to be a more "mathy" person that isn't afraid of numbers and can AT LEAST understand stuff properly, since I know the calculations can be done by programming, calculators and such I don't have to manually do them all the time.I'm desperately seeking some guidance on where and how to get better. I can do arithmetic, a bit of fraction, ratio, percentages (just on the surface, nothing advanced). but my current goal is to do math for data science and be at least ok with probability. I will buy any books and courses and blindly follow your advice if I can. please give me some guidance.
>>16350900fuck offra2 wasn't that great you could literally spam prism tanks and destroy any enemy in secondsgenerals zero hour is superior
>>16353804by complex functions if you mean special functions and not complex analysis, whittaker watsons modern analysis is the classical text. it also treats differential equations from physics very importantly
>>16353817Try taking a look at Khan academy - it has a pretty good rep I think and should cover elementary and high school math up to and including some calculus. Look at the curriculum and decide for yourself where you want to start from.Approach it like a game full of puzzles - when you encounter a new concept, try to play with it a bit, come up with examples, counterexamples, questions. Try to predict what is going to come next, before you read an explanation, try to see if you can come up with some yourself. After doing so or reading the given explanation, some time later, try to come up with it again, pretend/imagine you are explaining it to someone else. Try to imagine things visually when possible. If you don't know how to solve something and you've tried multiple approaches, sometimes it can be good tom take a break and do some other activity - often you'll be in the middle of something else when suddenly you're hit with a sudden realization pertaining to some of the topics you've been studying or problems you've been working to solve.Adopting this approach will be immensely helpful both during this time and afterwards when you get to college math. Of course it might seem like a lot but the point isn't to always succeed but to always try, and over time you will see yourself getting better at it. Remember to have fun.If you've any other questions feel free to ask. :]
>>16354061thank you. I will look at Khan academy now. I also found a pdf book (super simple math) I will print out and try do pen and paper exercises.I want to do data analytics or something related to finance and/or slight accounting (I know I'm giving a broad range but it's because I think I can't just *rely* on one career path, given my skill and background). in short, my flow of thinking is like this: "If I'm good with numbers and calculation skills (know finance stuff/great excel skill/accounting/analytic skill/etc...) there's no way I can't land at least a half-decent job with possible advancements". please tell me what you think about this idea, it's just my estimate since I don't know how realistic or delusional it is. I've been NEET for some time.recently I've been learning some machine learning stuff with Python (ironic I know, since I know jack shit about math). in the course it teaches me the general idea of how it works, and the actual code is not that complicated (just call a model, select parameters and try various values). but I'm skeptical about it due to two things:1) if I can't understand something to the core, then can I really verify the result of a model/calculation? it could be completely wrong but I'd just assumed it works flawlessly, right?2) I want to at least prepare for some hard moments like when I go to a job interview and they either force me to do a skill test right there OR ask me deeply about something (how does a linear regression model actually works, what if you change X parameters to Y, etc....) I would be dead.do you think they are legit concerns? and if so, what can I do to best overcome those problems I mentioned?
Definition. A *message space* is a cancellative monoid C with trivial group of invertibles, [math]C^\times = \{1\}[/math].Definition. A non-linear *designation* of a group G is a message space C together with a (left) action of G on C, [math]\cdot \colon G \times C \rightarrow C[/math], such that [math]c \mapsto g \cdot c[/math] is a monoid isomorphism on C for all [math]g \in G[/math], in other words we have some group homomorphism from G into the group of monoid automorphisms of C, [math]\mathrm{Aut}(C)[/math].
>>16353935No, I mean an undergrad level functions of a complex variables course. Integration and differentiation of functions of a complex variable. Residues and Cauchy integral formula. Basic properties of holomorphic functions. That sort of thing.
>>16351009I am familiar with essentially everything on this list. Whoever wrote it is a faggot.
new Galois theory book for retards coming out> Groups> an Aut()istic Approach
Currently proctoring my students’ final exam. You never realize how obvious it is to glance at the test of the person next to you until you’re the one looking for such people.
>>16352594I want to follow the curriculum. Problem is I am doing precalculus right now (1000+ pages), and just reading 1 paragraph + the exercises (100+ per paragraph) takes me well over 3 hours. So I can't even follow the curriculum yet.
>>16354546How about [math] \DeclareMathOperator{\Aut}{Aut} \Aut(istic) [/math]
https://www.theguardian.com/science/article/2024/aug/31/alexander-grothendieck-huawei-ai-artificial-intelligence
>>16355098>He told Michel Camilleri, a local bookbinder who helped compile his writings, that his kitchen table “knows more about you, your past, your present and your future than you will ever know”. But these wild preoccupations took him to dark places: he told one visitor that there were entities inside his house that might harm himWait so Grothendieck was a schizo all along?
>>16355117I guess it's just senility.
I'm not even a Math major (Comp Sci) and I'm generally barely even in the top half of competency and skill in my math classes, but I appreciate reading these threads regardless. Very interesting discussions. Thanks guys
Is there ever a point in taking the Minkowski functional of a set that's not balanced?
>*points at all of you*
>>16355540https://voca.ro/116xnaw8zyko>Clay Math Institutehttps://en.wikipedia.org/wiki/Clay_Mathematics_Institutehttps://www.claymath.orghttps://www.claymath.org/millennium/riemann-hypothesis/https://www.claymath.org/wp-content/uploads/2022/03/millennium_prize_rules_0.pdf7. Evaluation of a Proposed Solutiona. After publication in a Qualifying Outlet, a Proposed Solution must satisfy thefollowing two (2) stages of evaluation in order to qualify for a Prize. The two (2) stages must be satisfied sequentially.i. First, a Proposed Solution must achieve general acceptance in the global mathematics community, as determined by CMI in its sole discretion.1. CMI will take reasonable steps to remain aware of Proposed Solutions considered by the global mathematics community.a. In this connection, it is noted that the Problems are hard mathematical problems of considerable interest to the global mathematics community, and a plausible potential solution to a Problem will be effectively unmissable to all but the most superficial monitoring.>HARDMATHEMATICAL>PROBLEMS
>>16355682when I was a student, we would hear stories of people, grad students, who would actually read manuscripts submitted to the math department, usually sent from rich men with nothing else to doinvariably, these would be filled with mostly simple errors leading to incorrect calculationsClay math institute is an attempt to invert this, as the math departments were united in their mockery of the rich men trying to understanding complex advanced mathematical concepts."If the mathematicians will not receive and review our work," the rich men reason "then we shall decide for ourselves, and give a cash award for the correct solution, to be chosen by some rich man"apparently the custom was for math departments to leave a table in the mail room where such manuscripts would be dropped for any and all to peruse, only faculty and grad students had the key to the mail room, and the faculty had no time for such mischiefit is poetic justice that literally $MILLIONS will not change this state of affairs, so the rich men have decided to don square hats and call themselves worthy of grading math homeworkremember: these are guys who literally tell you they're going to just chill and read Annals of Math while sipping on Sprite™ and listening to hip-hop records with brown people who are like...ten times as attractive...at LEAST
>>16355699the desire of rich men to use money (I mean misuse money) to obtain that which, without cheating, requires singular effort, cannot be underestimated, and this leads to paroxysm and embarrassment, and if the rich man has any brains, that helps him not at all, for it merely attracts other men with brains who, like spies, drop their surveying equipment toolkit, put up a tripod and telescope, and go to workthe men who are rich and have brains are treated as victims of the Western press, leechesit is not mere jealousy that propels the rich man to seek heroic reward; it is also some alteration of his relationship with the paparazzi that is desired, some relief from being treated as a celebrity, from being followed and having one's immediate environment turned into a fishbowl"Save me from these uncouth ruffians! I demand honor! I demand respect! I demand privilege!" the rich man shrieks as he runs from bar to bar in his drunken frenzy, followed by glamour and an insatiable press...and lots of really beautiful brown people, I mean holy cow these women are PUT TOGETHER
I am 26. There is no hope for me anymore.
Why is pic related false? Doesn't NOT and the universal quantifier distribute over AND ?Another question: Is NOT universal x NOT equivalent to There exists x ?
>>16355716>Doesn't NOT... distribute over AND ?Not quite. Check De Morgan's laws again.
>>16355716Because it's only a one way implication. If there's an x such that A and there's an x such that B there might not be an x such that both A and B are true at the same time, sometimes you might have only one or the other. >Is NOT universal x NOT equivalent to There exists x ?Yeah,
>>16355736Ah that's definitely it. Thanks>>16355740Thanks also
>>16351688turn ontune inGOOK OUT
Do you know any good examples of proofs that rely heavily on combinatorial principles? Particularly I am looking for cases where intiutively you wouldn't expect such an approach to yield such results
Man I fucking love doing synthetic geometry for fun. I love leaving all the high level stuff behind and just doing geometry like you're in Ancient Greece again.
What would be an example of three topological spaces [math] X,Y,Z [/math] such that [math] [X,Y \times Z] [/math] is *not* of the same cardinality as [math] [X,Y] \times [X,Z] [/math]? Here for topological spaces [math] A,B [/math] we denote by [math] [A,B] [/math] the set of homotopy classes of continuous maps [math] A \rightarrow B [/math].It feels like this question shouldn't be difficult, but I'm not sure how to approach it; would anyone have a hint or suggestion?
>>16356995C(X,YxZ) = C(X,Y) x C(X,Z) so no.
>>16356995>>16357049Right, now I realize the bijection holds even at the "homotopy level"
Mathematics is a playground. The definitions are toys, and the theorems are ways to play with the toys.
>>16356633Do you have an compass?
Hey so I had a question. I was reading Ross's book on stochastic processes, but I've gone onto a tangent due to an internal struggle.First of all it says that probability functions are continuous, but that doesn't seem true if we're talking about discrete probabilities which would be only piecewise continuous.Frankly it would be easy to me to believe it for any integral equation, because of the obviousness, but it seems strange because it seems like he then defined the idea of a cts probability function as the limit of P(E_n) = P(UE_n), where the union is indexed by the naturals. I don't see why this is a definition of continuity?>An important property of the probability function P is that it is continuous.Also the proof for this seemed stupid, because if the sets are nested above then we could just use the fact that sequences of real numbers are unique to declare that P(E_n) = P(UE_n). That's like a one line proof that only uses the boundedness of probability functions and the monotone convergence criterion.Is this wrong to think? This is making me feel stupid like my analytical tools don't work but I don't know why.I'm really fucking hating this swiss cheese math I'm reading, I'm actually going to have a fucking conniption over this. I've been studying math for years and I can't understand if something obviously equal is actually equal.
how much time do you spend trying to solve a putnam-tier problem before giving up?
>>16357193Okay sampleposter.
>>16354342So just like with other applications of math there's different angles, you can be using AI libraries and whatnot without really explicitly understanding their inner workings but I think having that understanding should make the whole of it make much more sense and would probably allow one to work considerably better with the tools. Like if your main occupation is something else but as part of your work you need to use a model for something specific then I can imagine you not having to really understand the underlying principles but for a strictly AI/statistics job having that knowledge will definitely be benficial.And I think it's quite likely that such questions may be asked at an interview - from the employer's perspective, while it is nice that you know how to combine this and that library and model for some specific purpose, they want to know that if there's an issue that needs troubleshooting, a new model/framework/approach that needs to be used etc. then you know the so you can adjust and work with that also, or you can suggest a different approach, talk with your colleagues about the benefits and drawbacks of various approaches etc.I'd say that understanding the "theory" even makes the applications themselves easier because then you're not just shuffling black boxes around, you actually know what's going on behind the scenes and have a much clearer image of the whole process and how each of its parts fits in. Plus it could eventually lead you to more interesting and fun jobs where you're using that knowledge to come up with new stuff, architectures and so on. If that sounds like a lot now, don't worry about it, if you're enthusiastic about the topic(s) you'll be there before you know it.I will reply to the rest in another post as I'm nearing the character limit here. Btw if you have like a discord or something you can give it to me and if you later encounter something you need help with you could shoot me a message.
>>16354342>please tell me what you think about this idea, it's just my estimate since I don't know how realistic or delusional it is. I've been NEET for some time.to be honest I've no idea what the job market is like for what you'd mentioned (like accounting/excel/analytics jobs) but I think getting comfortable with those is still a good step in the right direction - it's not like you have to choose one thing to learn and that's it, the overlap is huge, if you get good with numbers and math and accounting then that is at the same time a step towards a data analytics/software engineering (if that'd interest you)/some other numbers related job too so you're making progress either way and what the *specific job* ends up being is kinda just a detail so imo just get comfortable with numbers, math concepts and some programming/computer science stuff in general and you will be building a good skill set that can land you a nice comfy well-paying job>do you think they are legit concerns?Yes I think so, I guess most of my previous post ( >>16358305 ) pertains to this specific question>and if so, what can I do to best overcome those problems I mentioned?And I'd say that and this post should answer this one
>>16357984One hour unless I really like it.
>>16350826how much of a grad student trap is the laglands program? what fields of algebra look pretty promising currently for new research?
>>16358996You aren't going to make a meaningful contribution to Langlands research unless you are a top mathematician or willing to focus purely on computational work.
>>16359011sounds about right... ty anon. what research are you doing if i may ask?
Anone anone, does anyone have a copy of a syllabus--either of your own from a class you've taken previously, or that you know of online--that has a list of homework problems listed from the problem sets in University Calculus by Hass, Weir, and Thomas? Doesn't matter what year--don't think the edition should matter all that much either, but I'm using the third one. I just want to know which problems I should be doing since professors usually choose the ones that are good for practicing the concept, and then build upon it--maybe throwing in some practical word problems in there too. >inb4 why not Stewart'sI got this book relatively cheap, and in like-new condition. I have a copy of Stewart's, but I only used it to follow along with lecture for the first semester of Calc; Stewart's is too bloated desu.
>>16355098>that picwhat was on his mind, i wonder?
>>16358996read Bump's book on automorphic forms to get into langlands. It more or less lays out the prereqs, though as you move along, you'll notice that you need to know much more. The stuff used in Gaitsgory's proof of geometric langlands still is largely incomprehensible to me for instanceIt's very fascinating but also depressing, you'll hardly have any free time if you want to contribute
>>16359455for me it's the girl on the far left showing off her tits
What's the go-to statistics book? I took a stats course in undergrad but I forgot most of it because I thought it was boring as fuck, now I wanna go into data science to make money. I do remember measure theory at least if that makes a difference
How many ways are there to arrange twelve 1x2 rectangles into a 4x6 rectangle? I'm struggling with a japanese flag puzzle box, thanks.
>>16355098>forgotten geniusIs Groethendick a forgotten genius? He's very present in a lot of fields nowadays
>>16360084Grothendieck*
>>16360084The article is not written for mathematicians... A better remark would be to ask if Grothendieck was ever "remembered" to the general public.
Do you think math is like "working out but for your brain" and everyone should practice it?
>>16351009but what if im doing calc 1 as a freshmen
Why is proof-based mathematics so fucking hard? I have friends in uni that are dumber than me who managed to get a good grasp on proofs while I fell behind. What the fuck am I missing?
>>16361295Read thishttps://us.metamath.org/downloads/metamath.pdf
>>16359595That's my girlfriend, I'm the guy to the right of her. Notice how she has her arm around me; she's very touchy. Love from Kazakhstan.
>>16354447What are some basic questions we can ask about these structures?
>>16361969All basic questions are combinatorial questions
>>16362011What about interesting questions in general?
>>16361295What kind of proofs are you struggling with? What area? You have to imagine proof based maths as trying to beyond any possible doubt convince you (or someone else) that some statement is true. Imagine being that opposing person and going "ok but [edge case 1], [edge case 2], [pointing out vagueness in your reasoning],..." you NEED to convince them that it's true. Imagine they're insufferable in their attempts to poke holes in your arguments for something, and after all, why do you believe the statement to be true yourself? Like you're standing in the shower and having an imaginary convo with this person, what are all the things they could say to you? Can you come up with some more examples and instances of the concept/structure/definition you're dealing with to be able to feel its shape, understand its behavior better and more accurately? Idk this is probably very general advice but it helps me sometimes to think of how I'm not trying really to "just produce a proof" but to understand the shape and likeness of some imaginary "object" in detail and the proof is a byproduct, just me writing down the reasons for why the object behaves this and that way. If you give more examples of what you were having trouble with maybe I or someone else could try to give some more specific advice.
>>16351063you listened to these yet?https://youtu.be/ye1dgqDANWg?si=9_s48EqOK0KNBMiQ
>>16362122Analysis. I know the logical structure of a proof, but in analysis there’s a lot of bullshit. In order to understand most exercises it’s not enough to read the theory of the chapter or use the theorems, you need to remember some fundamental theorem of algebra or some obscure fact about matrices or some completely out of the box technique, none of those are ever explained or mentioned during the theory, it’s expected that you think them up on the spot while reading the exercise, how can people do that? How can you associate a theorem from a completely different area to that exercise in order to solve it? How can people just think up new techniques on the spot to solve an exercise? That’s what I think is bullshit, you should have all the tools at your disposal before they give you problems to solve.
>>16362238Oh yeah? Give five examples.
Guys, I just had a sudden realization!>|i|=1>|iii|=1>|I|=1>|III|=3
>>16350826Is Mämmi anon still here?
>>16359455The fact that they're posing with their bags and a phillips airfryer to demonstrate their wealth or success at raiding is absolutely devastating
What is the math level progression in college?
>>16363718no, the transphobes ran her away from here and the quality and level of math talk fell down the drain afterwards
>>16363827>that picIt's sad that his mental illness progressed. Some nice times were had, but oh well. I hope he is doing fine now.
>>16363865She's pretty clearly not ok but was a really nice person, and apparently left to become a regular teacher.
>>16363827>>16363865She’s in the /mg/ discord server.
>>16363921>>16363934>SheHe*
>>16363976Misgendering people is not very nice.
>>16364149Saying that [math]P[/math] holds when [math]\neg P[/math] holds is not very nice either.
>>16364165Gender and sex are two different things. Gender is fluid, so what you said makes no sense.
>>16364245>Gender is fluidPlease produce a proof [math]P[/math] encoding gender-fluidity such that [math]\mathcal{Reality} \vdash P[/math].
>>16353790had to use this for class, I got a C in diffeq
If I turn an m*n matrix into a set of m+n vectors, how useful is the set? Is there anything I can do with it that I couldn't do with the matrix?
I need a crash course on set notation (Set Theory?) and all other adjacent information--basically all the prerequisite knowledge I'd need to be able to describe a Mathematical statement formally--as well as a long-term book to read from so that I can fully understand what I'm doing/looking at instead of just applying it. At the moment I need to know and understand what ':', ':=' and '∃' mean. I've only ever seen ':>=' and it wasn't in Mathematics. What I've gotten from reading further along and searching online is that ':=' means to define something, and that '∃' means there 'exists'. It's not as simple as just looking it up, there are always nuances surrounding the definitions that are only revealed through examples, exercises, and correction. It's not impossible, just not as efficient I think. It's for a fairly-rigorous approach to Calculus, so I don't need to know Set Theory in its entirety, just the basic stuff. I suppose a supplementary Calculus text with a rigorous approach might be useful too. We've been provided with the instructor's own choice of text, but it's written poorly with regards to pedagogy and it's lacking exercises and solutions. I've heard of Spivak and Apostol, but I don't know how self-contained those are, nor what the prerequisite knowledge is for them. I only have experience up to Calc 1, and not in the rigorous sense. >inb4 "should've payed attention in the prerequisite course, little nigga", or "it's above you"Wasn't my choice to take this class, all other courses are full; the class wasn't listed as being a semi-rigorous approach to Calculus. Taking a semester off isn't an option, it's either this, or enlist and go defend Israel. Might as well make the most out of this and not bitch about it. I will admit to having forgotten some of what was taught in Calc 1; I'm a little rusty, but that's just because I'm down to my last few braincells from partaking in teh whippets.
>>16363934Didn’t she leave like a year or two ago?
>>16364860'∃' means "there exists" as in, "for every real y there exists a real x such that |y-x|<(1/p) for p = 1,2,3,..."
I can't believe some faggot redditor went out of their way to make this site deboooonking the Cleo account:https://cleoinvestigation.notion.site/Investigating-Cleo-0796ef7ce8464a90ba388cdb68e08eefI actually got an answer from Cleo once. I don't know why there's this obsession redditors have with shitting on people with skills instead of appreciating talent. There are many other extremely talented people on MSE that can do this kind of integration problem. I don't know why they are so hostile to this kind of thing.
>>16365508Not to be one of those people who takes everything too seriously, but this is a particular instance of cultural rot I dislike.This person does a "statistical analysis" of about 40 posts, and argues they appreciate the cultural contribution to online math culture Cleo made despite them calling the account a fake. But this is a typical example of modern culture where they are more concerned with debunking than the value of the story beyond whether it's real or not. This is why we get so many movies which shit on beloved cultural figures, or want to expose their dark sides, or want to subvert your expectations.I don't know whether Cleo was real or not, although I'm pretty sure the identity (i.e. being a woman) was fake, even though the Mirzakhani theory was interesting, coinciding with her death and all. But I notice that redditors cannot stop to consider that the value of Cleo is really motivational. The idea of this talent motivated other users to answer questions they would have been unable or unwilling to do if they were not first shown Cleo's solution. They admit this. The myth motivates both talented mathematicians and the beginners who see this kind of thing and aspire to attain that kind of skill. So they work hard, and they get good.By "debunking" it they miss the point. This post isn't just of no relevance, it's of negative worth. The value of a myth is beyond its truth value. Now people cease to wonder and aspire to this and take the out of saying "it's fake (so why bother trying)." These are the types of people who go into remote tribes and show their mythological caves and lakes where spirits and guardians dwell and the dead go to rest are really just that which the people already know deep down - they are only dead rocks and lifeless water, signifying nothing. And often they then separately wonder how we created a modern world apparently without purpose.
>>16365516Now write the same rant but with "Santa Claus" substituted for Cleo.
>>16365508I don't think I have ever seen redditry this concentrated.
>>16365520Santa Claus does have value for children though.
>>16365520Santa Claus is not the same as this at all. It's a story for children. Even if this redditor is right Cleo is a fake, Cleo would still be a mathematical cultural icon about work and skill, which has some value. What value is there in tearing it down so you can make a blog post about what a smart boy you are for things many people have wondered about for many years anyway? What is the point in debunking something people either enjoy for a good story or as motivation to improve their skills?
>>16365508>I did a statistical analysis on this group of people who often interacted with each other and found they behaved in similar ways and therefore i conclude they are probably the same personit's so fucking over
A line segment in the real line has two boundary points but a line segment in the plane is entirely boundary points, because of blah blah blah open balls.Is a line segment that exists entirely of itself (not embedded in any space) completely open?
>>16365508>>16365516>>16365546>>16365559facts don't care about your feelings
Feeling tired of math desu. I can barely finish a single exercise a day. After 3 years of nonstop math I feel like I need a break. Any advice?
Imagine using cringe dual spaces when theorem related exists. How will dual space fags ever recover? >inb4 function spaces The set of all identifiable covectors is dense in the so-called dual space. Sorry honey, but saying you need anything besides dot product is like saying you have to define a separate addition operation for whenever irrationals act on rationals.Chad is using the dot product and jacobians fucking stacy with his engineering salary, meanwhile your jewish professor is making you use completely outdated (((((coorinate free))))) terminology for differential geometry and physics. (which literally has to use "temporary" coordinate identificationns to work LMAO)
>>16367426>I feel like I need a break.take a break
>>16365508>>16366800did you even read the blog? the argument is fucking dogshit, he literally does nearly >>16365911, it's a whole webpage dedicated to a reddit moment
Is there any reason for me to work with the natural numbers instead of any subset of the integers that has a lower bound and it's not bounded by above?I mean, with the latter I can choose the lower bound freely and the set I get will have the same practical purpose of the natural numbers.I just think that [math]\mathbb{N}[/math] is retarded.
>>16367751If you're doing some combinatorics or functional analysis weeb shit you absolutely need N specifically but otherwise no
>>16367579>(which literally has to use "temporary" coordinate identificationns to work LMAO)Wrong.
>>16367911Oh honey... Go crack open lee or Tu's book. They both use the (hideous) ∂/∂x notation as a "temporary" identification for the so-called "derivations" that make up a point's tangent space. Go on, give me an example of a true coordinate free definition that isn't relying on temporarily identifying coordinates to give a derivation. Sure, the coordinate identifications are all isomorphic to eachother, but it stands that in all textbook coordinates are still referenced in the tangent space.
>>16367966The tangent space at a point p is just the space of all derivations of germs at p. Where do you bring up coordinates?
>>16367981Notice how that definition never gives a notation for how you would define this basis of derivations. Look at any proof or notation for derivations. The derivation basis is always matched up to differentiation w.r.t. a coordinate system on a point. Here is Tu's proof where he shows that the derivations at a point make up a basis. (Lee's is similarly farcical)
>>16367993Are you happy with this? From Wedhorn's book.
>>16368001specific book name? I've read like 4 books on the theory but haven't seen wedhorn before. I'll check it out if you send the title
>>16368014Manifolds, sheaves and cohomology
I tried to read about polytopes and it looks like algebra, geometry, combinatorics and topology have each come up with their own general theory that is incompatible with the other three theories. Is the entire topic ruined?
Have any of the fags who said they were going to read through (and understand) the material in some faggot-tier book from the wiki ever finished through with it? I recall one such fag in particular--making a general statement; not sure if he truly was a fag, that all contends on whether or not he pulled through--making semi-daily threads about working through some Linear Algebra text. I think it was Axler's textbook.
>>16363827>>16363934what the fuck is this
>>16370862I've done this multiple times up to grad level now, but I never made public promises or updates, I just read the fucking books.
Here's a cute integration problem. Let [math]f[/math] be integrable on the interval [math][a,b][/math] and [math]\int_{[c,d]} fdx = 0[/math] for every [math]a\le c\le d\le b[/math]. Here [math]dx[/math] is the Lebesgue measure. Show that [math]f = 0[/math] almost everywhere.
>>16370581[initialize][index] [filter] [expression] [function] [modifier] [transform]looping allows for compaction[math]T(k) = F(i_n) \rightarrow M \sum^{terminal}_{initial} E(x)[/math]Sigma here is generic, not necessarily summing, and its gates may or may not be iteratively controlled. Every element can be a transform itself. How does one know that a processor is actually processing things correctly, from a product validation perspective. While 2^64 is still fully testable on a prototyping basis, combinatorial expansion is not. So how do we know there isn't a finite alteration that is seeded in the manufacturer that completely changes the behavior of the unit? And how does the manufacturer know that there isn't one? Just assume some gigabrain state-backed hacker that can modify silica making instructions is also man in the middle on their equipment as opposed to the engineering principles being seeded by bad actors - though gigabrain state-backed hackers do try to push that route as well.
>>16372518tv refugee, appears to be trying to confuse Scientology with reality>>16350912How about Bach violin concerto?https://www.youtube.com/watch?v=_ioc6sdgugo "J.S. Bach: The Violin Concertos"
>>16372416Here's my thinking.Define [math]\Sigma=\{A \in \mathcal B([a,b]):\int_A f dx = 0\}[/math].We have [math]\{[c,d]:a\leq c\leq d\leq b\}\subseteq \Sigma \subseteq \mathcal B[/math], and since the left collection generates the Borel sigma algebra we get [math]\Sigma=\mathcal B[/math].Assuming [math]f[/math] is Borel measurable, we find then that [math]\int_{\{f>0\}}f dx = 0[/math], similarly for [math]\{f<0\}[/math], so [math]f=0[/math] a.e.If [math]f[/math] is Lebesgue measurable, it's a.e. equal to a Borel measurable function and so the above still works.
>>16372820oh whoops you get [math]\sigma(\Sigma)=\mathcal B[/math].Instead, define a measure by [math]\mu(A)=\int_A f dx[/math], since this measure agrees with the zero measure on a pi system generating [math]\mathcal B[/math] (namely, on the closed intervals) and are of finite total mass, they also agree on the Borel sets by the pi-lambda theorem of Dynkin.
>>16372820*you can also just show [math]\Sigma[/math] is a sigma-algebra directly, since it's clearly closed under countable unions and contains the empty set, and if [math]A \in \Sigma[/math], then [math]\int_{A^c}f=\int_{[a,b]}f-\int_A f=0[/math].I don't know why I missed this.
>>16350900generals is only 3 years older than ra2 and ra2 is definitely the most popular out of all cnc games with the most online players.
>>16372416for a,b reals, let a ~ b if a and b differ by 2^n for some integer n, this splits the reals into equivalence classes, choose a set of representatives R, let Q = U[n=-oo]^oo 4^nR and let S = 2U[n=-oo]^oo 4^nR, so Q and S partition the reals, 4Q = Q, 4S = S, and 2Q = Slet f be 1 on Q and -1 on Swe can now clearly see that f satisfies the hypotheses, yet |f|=1 almost everywhere
>>16372416you are cheating at your math homework in theory, but it's the wrong part of the semester to be learning those concepts...where did you get this problem or did you make it up on your own?? when and where did you take measure theory??you have to use the dominated convergence theorem and [math]G[\delta][/math] setsfirst prove that [math]\int[X] fdx = 0[/math] for all open subsets [math]X\subseteq [a,b][/math], then use the dominated convergence theorem to prove that [math]\int[X] fdx = 0[/math] for all [math]G[\delta][/math] subsets of [math][a,b][/math], then prove that if [math]f^{-1}((0,\infty))[/math] has positive measure, we can find a [math]G[\delta][math] set [math]T[/math] such that the symmetric difference of [math]f^{-1}((0,\infty))[/math] and [math]T[/math] has measure zero, yet [math]\int[T] fdx = 0[/math], [math]\int[f^{-1}((0,\infty))] fdx > 0[/math], a contradiction
Hello math people I have been officially diagnosed with dyscalculia, among other things, in my late 20s after years of suspicion and finally having enough spare cash for a full psychological battery. Long story short, I sailed through high school on pure wit, and when I got to college and "real math" I simply could not do well enough on the exams to pass, and topped out around Calc 3. My main issue was that I cannot hold numbers in my head for manipulation at all; they simply fall right out as if they were in a sieve, even if I am staring right at them on a page. This means that actually carrying out computations and solving problems with a paper and pencil is extraordinary difficult for me to do in a reasonable timeframe, hence rushing on my exams or not finishing and getting low scores.I am absolutely interested in math and capable of comprehending every computation I needed to carry out, I just simply struggle greatly when putting pen to paper. The early signs were there from the beginning; I struggled and still struggle to interpret analog clock faces, and even with digital clocks if someone asks me when something will happen after a non-round amount of time (like it's 2:38 and I need to do something in 13 minutes) it takes me much longer than it should to manipulate the digits in my head and come to a conclusion.This is now at the point where it will affect my career, and I want to get back into learning math in a formal manner. My question for you all is whether you have dealt with this disability in some regard, and if not, where I might be able to find a way of carrying out computations that fits with the way I process numbers? Again, the concepts are just fine, it's just the act of mentally manipulating specifically numbers that I struggle with.
>>16373715maybe get into math that isn't so much about numbers and computations. Graph theory, geometry, logic, topology, etc. The further you get into math, the less it is about doing computations anyways, so maybe you have a chance
>>16364860Naive Set Theory by Halmos should help. Fairly short book that goes over the basics of set theory and a lot of the basic notations and terminology that mathematicians will just assume you know when writing something.
>>16373845>math that isn't so much about numbers and computations>Graph theory, geometry, ..., topologyWhat did he/she mean by this?
what does he mean by "converges as described in..."?this section is talking about a functions on an open set [math]f:A \to \mathbb{R}[/math] such that an open cover of subsets [math]\{U_\alpha\}[/math], and a subord part. of unity [math]\{\phi_\alpha\}[/math] can be found with [math]\sum_{\alpha} \int_{A} \phi_{\alpha} |f|[/math] converging.
>>16374850
>>16374622Will that be sufficient to understand Calc II (and retroactively some Calc I) concepts in a rigorous a manner? I need to be able to understand something like picrel. I can understand it--I'm not a complete novice with regards to Calculus--but the inclusion of these definitions and notation feel a bit foreign. Reading through the assigned text isn't as efficient as reading through something like Stewart's Calculus and mechanically doing the problem sets. It sure as hell has made me realize the short breadth of my Mathematical maturity and that I need to pick up the slack, but working through it is a bit rigid at the moment, and I'd like to smooth things over by individually analyzing the fundamental concepts considered--Set Theory and Calculus--and then applying them towards this somewhat-rigorous approach to Calculus. Am I just being a little bitch about it?I've also considered Stoll's Set Theory and Logic, and Suppes' Axiomatic Set Theory; though Stoll's text is far longer, and I doubt all that exposition is necessary for what I'm trying to achieve. I also happen to already have a copy of Ross/Wright's Discrete Mathematics that was given as a gift, but haven't had any time to read. Axiomatic Set Theory appears to be different than Naive Set Theory, and I'm not sure what Discrete Mathematics entails, just that it covers Sets, Elementary Logic and Induction in the preliminary chapters. None of the entries appear to have any exercises or problem sets either. I'm not sure if the image provided properly conveys the difficulty of the material. I could include some excerpt from a later chapter/concept, but I wouldn't know if it's all that difficult to understand; if it's as simple as understanding the prior chapters. I understand picrel, but I have difficulty reproducing the statements (and understanding some of the prompts) involving set notation with full confidence.
What area of math has the least amount of anything resembling numbers?
>>16375038there are no numbers in category theoryamong non-meme subjects... one of the ones nobody really cares about, like graph or knot theory, probably
>>16375038Unironically, numerical analysis.
>>16375223>ones nobody really cares about, like graph theory Codemonkeys btfo'd yet again
>>16375223>graph or knot theoryGraph theory is one of the most popular areas of math, and knot theory has become quite successful too. You're not going to make it far in either subject without numbers.
>>16373715I've read that the development of dyscalculia may be related to one's ability to recognize the number of objects in a group at first sight, called subitizing.>Several researchers, in both the US and Europe, have found that subitizing ability in dyscalculic children could be improved into the normal range, typically with just 15 minutes a day of training with a computer program for three weeks. More important, their math skills, as measured by standard tests, had also significantly improved at the end of training. Even more important, the subjects' math skills continued to improve over the next year without additional subitizing training. The dyscalculic children were now able to learn math from typical classroom instruction where they had struggled before. Wasn't able to find the source for this exactly but found some other studies that at first glance seem to support this notion, bur I'm not sure if subitizing was practiced as an actual skill or just used as a measuring device.Here is a web app I found on an online forum made for practicing subitizing. I think it can be tweaked to allow higher item counts but am now sure how rn.https://codepen.io/eternalsunshineofspotlessmind/full/BaYdqoXAlso have you tried any "exercises" like sitting down and trying to imagine and manipulate (add, subtract and so on) the numbers and represented quantities in your mind?
>>16376876Here are the studies I mentioned, I think it should be possible to find many more but am phone posting rn, and as I said I'm not sure if these two trained subitizing itself or just used it to gauge ability to work with numbers as I only read the abstracts (XD). Either way I think it's worth a try.Effects of daily practice on subitizing, visual counting, and basic arithmetic skills.https://www.researchgate.net/publication/26518798_Effects_of_Daily_Practice_on_Subitizing_Visual_Countingand_Basic_Arithmetic_Skills>All children had problems in basic mathematics and failed the test of subitizing. The training group (N= 10) was given the required training, while the waiting group (N= 11) had to wait. A standard test of basic mathematics (DEMAT) was used to measure basic arithmetic skills before and after the training. Results: The analysis of the pre-post training data revealed that subitizing and counting were significantly improved in about 85% of the subjects: they reached the normal range of the control subjects (N-133) of the same age. The second study shows that basic arithmetic skills were significantly improved in a trained as compared to an untrained control group.Improving mathematics achievement via conceptual subitizing skill traininghttps://doi.org/10.1080/0020739X.2019.1694710>Results showed significant improvements in the experimental groups’ basic number processing skills, calculation performance and mathematics achievement. The results of the mathematics achievement test which were administered after a semester to the same groups to evaluate the long-term effects of the training revealed significant progress for both the 2nd- and 3rd-graders.
>>16350826BOMBARDMENT
How do I show that if [math] U [/math] is open and [math] U \subseteq \bar E [/math], then [math] U \cap E [/math] is not empty.
>>16376983What if U is empty? huh what then gay boy?anyways U is open in the closure of E so the complement of U in the closure is closed, so that can't contain all of E
>>16374873Just search for "set-builder notation".
Today I walked into an african female grad student's cubicle to ask a question and saw her using chatgpt to answer our assignment.We are on chapter 1 of Munkres btw.
>>16377223>africanWhy the racism?
>>16377223Cool. This is very useful information. A few months ago, ChatGPT was insisting that you could find some difference between a continuous function and a function such that the inverse image of every open set is open.So it has only recent become able to handle Real Analysis questions.>>16368035I can't seem to recall using a red colored math text before. Looks...exciting.
>>16377267>RU>BE>DO
New GPT model out and its better at math and science.
>>16377581>not only am I going to fall for the ELIZA effect, I'm going to carry out math assessment process as wellOpenAI is a CULT...they are positively BETTING that someone isn't going to absolutely CRUCIFY the ELIZA effectWhere were YOU when they nailed the ELIZA effect to a cross and WATCHED IT BLEED TO DEATH?
if [math]\omega[/math] is a k form, not necessarily compactly supported, on a k-dim smooth manifold [math]M[/math], and [math]\{U_{\alpha}\}, \, \{\phi_{\alpha}\}[/math] is an open cover, subordinate partition of unity, s.t. [math]\sum_{\alpha} \int_{M} \phi_{\alpha} \omega[/math] converges, what does it take for this convergence to be well-defined independently of the open cover, partition of unity?When spivak defines his extended integral of functions on general open sets he uses as a condition that the sum [math]\sum_{\alpha} \int_{A} \phi_{\alpha} |f| [/math] converges, and then it follows that the sum [math]\sum_{\alpha} \int_{A} \phi_{\alpha} f [/math] itself converges, and does so independently of the partition of unity, open cover. What is the direct translation of this notion to the setting of forms on manifolds?everywhere else I look everyone just assumes the form has compact support.
>>16377600Ok science faggot.
>>16377642artificial intelligence can BLEED...and that is SCIENCE
>>16377642Ok jeet.
Got into my graduate school of choice for a masters in math, bros (math undergrad). Now it's time to stop the larp and actually learn math
so in ode, does the integrating factor make the function exact, so are bernoulli and linear form just not exact or something.
>>16350826
>>16378999
>IHAVE>THEALGEBRAIC>MANIPULATIVEhttps://www.youtube.com/watch?v=7yeA7a0uS3A "He-Man: Opening Theme | Mini Moments"
Does anyone have a big PDF of Calc III integral practice? Taking the mGRE this month and need to crank out a few hundred>>16378127Are you in EU or something? apps are not even due in US until december (right?)
>>16381288Yeah, Italy.
FACT: There’s not really any point going to grad school outside of the US Ivy League +Caltech/Stanford or Oxbridge.
In the discussion of the cantor set, there's this map from binary sequences [math](a_k) \in 2^N[/math] to the interval [math][0,1]\subset R[/math] via[math] 2 \sum_{k=0}^\infty \frac{a_k}{2^{k+1}} [/math]What's the analog where we don't take value [math]a_k[/math] in [math]\{0,1\}[/math], but in the finite range [math]\{0,1,\dots,n\}[/math]?I assume something like[math] \sum_{k=0}^\infty \frac{a_k}{(n+1)^{k+1}} [/math]Anybody got a reference?
>>16381973Doesn't work for higher numbers than 2 because for example for n=9, 0.4(9)=0.5(0) so you don't have a bijection.
>>16381973Btw. I think I messer up the denominator in the Cantor case. Would be 3^{k+1}More athttps://en.wikipedia.org/wiki/Cantor_set#Cardinality>>16381986That makes sense, although I haven't even checked which nice properties the function has
Hey /mg/, are there any films involving math that are good? The baseball statistics film is really boring.
>>16382137Fictional? No, they're all complete shit.Documentaries? I want to be a mathematician by Halmos is ok, N is a number is good https://www.youtube.com/watch?v=CWkCSvhtf_s
>>16382137The Four Color Theoremthere's a film in the works about the fraudulent assertions behind the so-called "theorem" and the media frenzy that surrounded the purported proofhttps://en.wikipedia.org/wiki/Four_color_theoremhttps://en.wikipedia.org/wiki/Non-surveyable_proofAshton Kutcher is producing it, and this time he's taking off the kid gloves, no cheesy feel good CIA agitprop this time, he's decided that Argo made him look like a chump, and that's gotta change, so it's got a lot of fan service with him making out with hot chicks and seeing their boobs and stuff and lots of zoomers with the camera showing boobs and crotch shots and some near-porn scenes, because mathematicians are retards and perverts, and there's lots of press stuff and politics and corruption and sex and even an action scene with a KGB assassin + femme fatale team who are in full Boris and Natasha from Bullwinkle cosplay outfit, so yah, it's full of sex and violence and yeah ostensibly about this boring computer math stuff...At any rate, so as I was saying this film is just The Illuminatus! Trilogy: The Movie and the math is there for plot and context. Apparently the budget is $700 million. Starring Mackenzie Foy and Jack Nicholson.
>>16382180You have schizophrenia.
>>16382187you need to stay on-topic
https://owl-sowa.blogspot.com/2015/11/mathematicians-are-human-and-want-to-be.htmlHe was right about everything.
Does anybody here work with completely positive maps? Is it an active area of research? What are some open problems? I asked a prof from my university to be my masters thesis supervisor, and he recommended this topic to me. He seems knowledgable about it, but I'd like to hear some other opinions.Thanks.
>>16350826why are topologies on infinite/arbitrary products simultaneously confusing and trivial
>>16366789>Is a line segment that exists entirely of itself (not embedded in any space) completely open?what does it mean for it to be "open" if it's not in a space?
apology for slow diagram chasingwhen were you when category dies?i was chalking diagram at ski homolodge blackboard eating syzygy butter next to beautiful grad student with big boobs and tight, round, firm butt in g-string thong bikini when pavel throw frisbee to me while we play ultimate on grassy fieldi read message on frisbee‘category is kill’‘no’
>>163839601. I don't know. 2. I don't know. 3. I don't know. 4. Okay. 5. Alright.6. You're welcome.
>>16385059hold on just a second...there's only one topology, the product topology, and that's the weakest topology that makes all of the projections continuous
>>16385129what's the point of having an infinite product if you're going to limit the open sets so that it behaves exactly like a finite product? everyone knows the box topology is the real product topology.
>>16385134Example. Let X be the set of continuous complex valued functions on the real interval [0,1]. Evaluation at 0 <= t <= 1 is a linear functional from X to the complex numbers.X is a vector space over the complex numbers.Let us put the product topology on X.Cool, now x[n] converges to x if and only if pi[t](x[n]) converges to pi[t](x) for all 0 <= t <= 1.Okay, forget that.Now put box topology on X. Now x[n] converges to x if...?!?!see what I mean??Exercise. Prove the convergence fact above.
I for one miss anitranny
>>16385147okay, now I'm starting to see your pointhowever, there is no reason for confusionwe could put uniform convergence topology on X for exampleso we define the neighborhood of a point x <- X to be the set of functions y such that d(x,y) = sup[0 <= t <= 1] | x - y | < epsilon for all positive reals epsilonThis d(x,y) is a norm that turns X into a complex normed vector space. So this means X is also a metric space.Fact: x[n] converges to x iff x[n] converges to x uniformly on [0,1]here is the thing: we relied on compactness of the unit interval to define sup norm d(x,y) and you can verify for yourself that for an arbitrary collection of metric spaces, you will only be able to define an extended metric space (metric space with distances taking values in the extended real numbers, the real numbers plus the symbol oo for infinity) using the sup of the component distancesfor example we cannot define the sup metric on the set of sequences of complex numbers as the distance between (0,0,...) and (1,2,3,...) would be oothe point is that in order to arrive at the sup norm on X, we required more information than just the topologies on the factors, so given that information we define the topology on a set that just so happens to be a product under the hood, but usually when you say "product" it means no extra information given about the relationship between the indicesif Z = Pi[i <- I] Z[i] for Z[i] a topological space then each Z[i] is a factor and i is an indexso, the convention is that index sets are just sets, they don't have any extra structure like a topologywe say X is a space of functions or a function space, not "X is an infinite product of topological spaces" because even though that's technically correct, we've provided extra structure
>>16385110Thanks lad
The sum of two even numbers or two odd numbers is always an even number.The sum of an even number and an odd number is always an odd number.
Also when I was in high school I found this pattern with squaring numbers in the 40s.For example41^2 = 168142^2 = 1764 43^2 = 1849and so on.As you go up one number, the number squared will be +100 and down one perfect square.Do you see what I mean?44^2 = 193645^2 = 202546^2 = 2116
Just wanted to bitch about the GHETTO-ASS language of German for a quick minute.I can never automatically remember what "rows" and "columns" are in German. I always remember, of course, but it feels manual and semi-effortful, like you sometimes have to manually recall what West/East or Right/Left are.You see, the German word for "column" doesn't, like the English term "column" recall actual vertical structures. It's "Spalte", which you can see is related to "split". In Germany, do splits always run vertically? No, they fucking do not. It's completely arbitrary math lingo."Row" is "Zeile", which is a bit better, though as it's a less often used term in German than row is in English, it still does not feel natural. The direct German equivalent "Reihe" interestingly is used for series. I find both the German and English term here retarded. If I were some 1700s mathematician, I would have introduced the term "aggregate" or "accumulation" or something like that for series.
>>16385798I would point out that the first time a German kid hears the word "Zeile", it is a line (of letters) in a book or a newspaper. So the horizontal part is deeply ingrained. I am sorry that you need to learn this word later and only in the context of math.
Today is the day if what you said in reference to what I seemingly did is true and now I am doing, it will be over soon - we'll become the best in all of existence.No joke.You will be trainedYou will be paid.We will exist as the hardest to defeat. I could even train you to become the nightmare of the ultimate pain takers, but we are going to go a different way.
>>16372518How exactly does this post come to exist 7 days prior to pagers exploding?
>>16386135Some faggot jumping around like a retard or some other. Either that, or that group of anons who said they were getting together to build a time machine actually did it.
>>16385096You talk to women? Why are you studying maths when you know you will never be any good at it?
>>16385821What? Do you lack any reading comprehension? I said "Zeile" is a less common word than "row" ("Zeile" is especially used for texts, while "row" can refer to more things, like rows in a theater). I bitched about the other word, SPALTE, you retard.
is my iq too low for non-constructive proofs?i was stuck on one of the first exercises from my textbook for like 30 minutes"prove or disprove that there is rational x and irrational y such that x^y is irrational"the way they did it was supposing x is 2, and y is sqrt(2)if 2^sqrt(2) is not rational then let x = 2^sqrt(2) and y = sqrt(2)/4, then x^y = sqrt(2)it seems so simple, and i actually got as far as letting x=2 and y=sqrt(2), only because my textbook had a similar proof as an example int he chapter, but I feel like I never would've made the leap to find a way to turn it back into sqrt(2) to complete the proof. I only briefly thought>how could I make x^y an irrational numberi hate that i never come up with anything on my own. i just regurgitate the textbook. how do I become a creative thinker?
>>16388114the wiki article on constructive proof is garbagethe article implies that the Gelfond–Schneider theorem has a constructive proof, but the only proof available in French, the wiki article for the theorem doesn't even mention constructive math, and you would think it would be a real big deal if it had a constructive proof, so...looks like wiki fraudthere is a lot of Wikipedia fraudyou have to watch out
>>16350881>>16350900>>16353833>>16373241Tibirum Sun (and firestorm) is the superior C&C
>>16388114So, first of all, the French are total retards. You can't trust them. Look at this: https://github.com/clarus/falsoThe French are arrogant and stupid. They don't even think it's a problem that they refuse to translate the proof of the Gelfand-Schneider theorem. If we had an English translation of the proof, it would be easy to show that the proof is not constructive.Frankly, I suspect that all genuine non-constructive proofs are supremely trivial and part of logic, not math.Like I said, it appears that the Gelfand-Schneider theorem has no constructive proof, and the wiki article on constructive proof implies that it does fraudulently.This is typical for contact with the French. They're arrogant, stupid, and wrong.
>>16388114The wiki article for constructive proof is unbelievably bad. What makes it so bad is that the article freely shifts between at least two definitions of constructive proof:- the proof omits inference rule law of excluded middle and doesn't use axiom of infinity or choice- the proof produces an "example"by the way, there's no definition of an "example" it's a purely philosophical concept, not logical, not mathematicalso the whole concept of constructive proof is based on claiming that something that isn't logical is logical...in fact, it's even worse, there is a claim that something that isn't formal (whether or not the proof "produces an example") is the same as something that is (omitting various inference rules and axioms)the only good thing about the wiki article for constructive proof is a reference to some historical material about Hilbert's work
Category theory is the manliest subject ever created. Literally the most importan thing there, which contains all morphisms, is called Hom(o).Embrece gachi and become catchad
>>16388265Agreed. A category is just a bunch of dudes playing with their arrows; doesn't get manlier than that.
>>16388265>>16388377
>>16377223>Munkres as a grad studentwhy
What is the most advanced, high tier, next level mathematics? Are there some good videos of it?Even if I won't understand it I just want to see what it looks like.
>>16388573Inter-universal Teichmuller TheoryJust read the papers yourself.https://www.kurims.kyoto-u.ac.jp/~motizuki/papers-english.html
>>16388573there is no "most advanced, high tier, next level mathematics"that's not how mathematics works all math is pretty trivial if you just put in the effort to understand the trillion definitions
>>16388573they are studying something called "supermath" that is like string theory for formulasthey're trying to calculate "Gödel's constant"that's all I know
>>16388573also, there's a new branch of math called>HONKYTONKATICSwhere we make approximations like>π is three or fourand observe the horrific consequences
>>16388438Low tier school.
>>16388377>>16388377Oh shit, I'm sorry.Sorry for what?Sorry for what? Our daddy taught us not to be ashamed of our arrows. Especially since they’re commutative and all.Yes, I see that. Your professor gave you good advice.It gets bigger when I combine them.MmmSometimes I apply the morphism with such force that the composition feels complex.Well, my mentor taught me a few things too, like how to simplify compositions by introducing a different functor, rather than trying to handle everything directly.Will you show me?I'd be right happy to…
>>16388766You got lucky faggot. In time your 'freedom' will come.Currently: Busy
has your motivation to study math decreased since chatgpt was released?
>>16389221no because chatgpt is stupidas for ai solving olympiad problems, i don't really care because i was always a mediocre, unambitious, uncreative student. it's not like AI is taking anything from me. the only people scared of AI are white collar midwits
>>16372518NSA has its own fabs. You can gain the appearance of control by encrypting layouts going to the machine. There would be no manufacturing middle man just hard rigging the equipment with a USB stick or whatever, but there could be another kind of effectively up one level. You can also validate machine motions.I don't think anyone is worrying about this issue, though it is a concern. It would be much easier to break distribution or other layers. Most people use generic firewalls and AV software which is a much juicier target for exploitation. This is two fold because it casts a wide net, but there is a deference to perceived authority. The many protocols that have been exploited should invalidate virtually all trust in the structure, but people are retarded.
is anything bigger than everything? serious question
>>16388114Unfortunate the bots/schizos got you, but:Just try to remember it for now.Next time you encounter a similar problem, try to write down several strategies you think might be useful, before you start. Then you can work through them one by one and see where they lead. You've now seen this so this should be one of them (splitting stuff into cases, basically).I don't know about being a creative thinker but remembering multiple approaches and having some sort of intuition of what to try when is probably the next best thing.
>>16389198Is that the line the syndicate has been feeding you? Well, I've got news for you, pal. It turns out Operation: TARSKI was a complete success, and the Chinese defectors have not only turned over the plans for the supermath laser, installed the USMC mole program on the supermath mainframe computer and seduced the supermath AI with a superbabe, it gets better: Disney and Mickey Mouse want a piece of the action.That's all I know.I think 'freedom' is just a codeword now, but right you are.>TICKTOCK>REDBLOCK
>>16389296I've been there. I've seen the chips, and they arehttps://www.youtube.com/watch?v=So6oK--uP7M
>>16388766I've just been passed some shocking footage of a supermath prototype turbo-encabulator being used on a test subject.Warning: disturbing and graphic contenthttps://www.youtube.com/watch?v=dN2FC0QCGVU
Is the unit sphere of the field [math] \mathbb{Q}_p [/math] of p-adic numbers (equipped with the standard p-adic norm) homeomorphic to a "standard" k-sphere [math] S^k [/math] for some nonnegative integer k ? (Here p is a given nonzero prime integer.)
>>16390146ChatGPT says no because the unit sphere in the field of p-adic numbers is not compact.
>>16390173I'm confused, the following argument appears to prove the unit sphere is compact?- The origin-centered unit sphere S in [math] \mathb{Q}_p [/math] is a level set of the distance-to-origin function, which is continuous; hence S is a closed subset of any subset of [math] \mathbb{Q}_p [/math] containing S. - In particular S is a closed subset of the origin-centered closed unit ball B, which is compact (see https://math.stackexchange.com/questions/78449/why-are-closed-balls-in-the-p-adic-topology-compact); hence S is compact.
>>16390277Formatting mistake, the [math] \mathb{Q}_p [/math] should be [math] \mathbb{Q}_p [/math]
>>16390277>>16390279Also I asked ChatGPT about this and it didn't help; it just said, "The unit sphere S is closed in the compact space B, but because it fails to be totally bounded, it is not compact in its own right. The confusion often arises from mixing up properties of closed subsets in compact spaces versus the compactness of the subsets themselves." This is completely wrong lmao
>>16390173Got the answer on MSE, the p-adic unit sphere is indeed compact. ChatGPT btfo. Get your AI slop outta here.
I'm trying to see if for an integral domain extension the respective localisation in prime and prime au-dessus are still integral. When p=0 there's no issue. However $\frac{1}{s}$ is integral on $A_p$ iff s is a zero of some polynomial in A with constant coefficient in S. In other term there's a counter example if for p prime in A there's a prime $p_2 \subset A[x]$ in p+(X) with $A \cap p_2 =0$ and at least containing one unitary polynom.I don't find any exemple and working with noetherian/finite dimension does not seems efficient.
>>16376983 Assuming U is non empty, every point of U is a point of closure of E, but U being open means every point of U has an open neighborhood V contained in U, so U contains a neighborhood V that intersects with E, so U contains a point of E, which implies their intersection is non empty. I think this correct, lmk what you think.
>struggling with kinematic equations on khan academyI'm in calc 3 and I aced calc 1 & 2. I feel so defeated right now. This stuff makes no sense.
>>16390426Have you considered that stack exchange is wrong? Companies have invested billions of dollars into chatgpt, they wouldn't waste their money on a chatbot that's bad at math
>>16376983Simple, you prove that if [math]U[/math] is open and [math]U\cap \bar{E}\neq\emptyset[/math] then [math]U\cap E\neq\emptyset[/math]
>>16385096top kekRegarding the pdf, what is this for? An "algebraic way" of specifying an identities-less category? Can you elaborate?
>>16388573The current meme is Analytic Geometry a la Scholze&Clausen. https://www.youtube.com/playlist?list=PLx5f8IelFRgGmu6gmL-Kf_Rl_6Mm7juZO
I study in shit tier uni. How to tell my classmates that they will not be second euler or gauss just by spending all their free time sucking cock of shit tier professors with less than 200 citations?
>>16391217First of all, students report that they like category theory, they think of it as a "capstone course" for their math studies.However, both category and set theory suffer from a problem: there is too much time spent on what amounts to logic, which is what you get when you deal with a so-called 'large category' which is really just a formula; another term for this is a 'class sized category' which is another name for a formula, and 'class' is also a name for a formula. In fact, the big problem with category theory is adding mathematical style to logic, which is just a mess...sure we can write down the formulas (there are two) for the objects and morphisms of the large category Group, but you're adding structure to logical formulas instead of classifying mathematical objects, so if we take a narrow understanding of math, then category theory is simply playing with formulas instead of doing the hard work of mathematical study...we should regard category theory as a subject area of logic and computer scienceUnder the hood, a category is a partial semi-group with some extra structure that satisfies a condition. That's all it is.Moreover, the practice of introducing formulas or pairs of formulas such as the large category Group can be replaced with the following pattern:>Let X be a set, and let Y be the set of groups with element sets a non-empty subset of YNow we can perform mathematical work that is equivalent to what we did before:>Let y^-1 be the opposite group of y for all y <- Y. Then .^-1 : Y -> Y is a function, and there is a group homomorphism from y to y^-1https://en.wikipedia.org/wiki/Natural_transformationSo, you see, we're doing the same things that category theorists are doing, but we're doing math work instead of playing with data structures consisting of logical formulas, which is essentially logic++ or computer sci-LOGIC-ence or whatever...
>>16392097big reason to avoid going the cs/logic route is we can use universal and existential quantificationof course you could always do that (let X be a small category...) but my point is that by passing to the use of a syntactic variable for a formula, you essentially limit yourself to propositional logic and its power, which is fairly modest, and frankly a big step back compared to first order logic, which is why we usually think of first order logic as mathematical and propositional logic as purely logicallogic is concerned with things like logic puzzles, it's inferior math
>>16390173ChatGPT is totally anti-scientific. First of all, OpenAI is totally antagonistic towards study of the ELIZA effect: https://en.wikipedia.org/wiki/ELIZA_effectFrankly, "The ELIZA Effect" is the name of a forthcoming Paramount film that was optioned in 2023 about Sam Altman /sBack to the real world...it is a failure of the Western press that we don't have accurate primary sources asserting what I know is true: ChatGPT used to claim that there was a difference between- a continuous function and a function such that the inverse image of every open set is open- a pair of integers with gcd 1 and a pair of relatively prime integersno doubt there were other examplesmy point is that these flaws in the original ChatGPT were pointed out, and instead of documenting the revisions of ChatGPT and their capabilities, OpenAI simply released a new version totalitarian distopia style, zero documentation, zero primary sources, negligible journalistic coverage, negligible academic coverage, negligible internet mirroring of example interactions or playback of interactionsJust think how useful it would be to have an internet archive of chat interactions with a URL for every interaction you want to document, essentially a bookmark for a ChatGPT conversation...I would've been able to prove the assertions I made above to you by providing the URLs, but unfortunately you just have to take my word for it :-/
Hey dorks, just finished my BS recently, got a great engineering job solely because of military experience. I won't need it for work, but I want to continue and get a masters as well so I feel less insecure to myself. Anyone familiar with the Columbia online math masters? I'm a 40% disabled vet so it'll be covered entirely, I just want to make sure its actually fun and decent and not some cash cow with professors that hate you. I'm sure someone here has done the program or at least is associated with the university.
>>16392079You go there too your right to look down on anybody is forfeit
>>16392223Do all of the problems in Munkres - Topology and tell us how it goes.>>16350826>Stranger on the internet assigns you the exercises edition.
>>16392241I'm not sure what you mean. If I do all the problems in Munkres' book, that will take quite a while and I would just have to repost again to ask the same question.
>Calc II>Discrete Maths>Intro to Probability and Statistics>Multi Var Calc>Graph Theory and Linear Algebra>Linear Algebra and Differential Equations >Additional Topics in Linear Algebra Which courses should I take alongside each other or in succession to one another? I'm pretty sure the last two are redundant with respect to each other, or at the very least I can choose from either of them to fulfill the requirement for graduation. I have an entire semester to read up on Calc II and Discrete Maths--with Set Theory serving as a short tangential prelude. Bare in mind that I'll have to take a number of gen ed courses too, as well as shit like Physics, Chemistry, and Choading at some point. The pre-requisite to Physics I is Calc I, and it has the co-requisite of being enrolled in Calc II--hence me not doing either this semester. Those of you who studied Maths, Physics, CompSci, or anything of the sort, how did you pace yourself and manage your time with respect to taking courses? Usually I'd be more lax with these sorts of things, but I can feel the sands of time washing over me; I'm in my 20's and don't want to be in undergrad by the time Alphags come around and have them refer to me as "unc". Of course, I'd still have ~ another 2 years in undergrad, but that's simply a consequence of my indolence and baboonery. I have the option of completing a number of my gen eds either during the Summer, or during the Winter intersession. I don't know whether take some of my major-related courses over the Summer--and risk brushing over them for the sake of completing the curriculum within those few weeks--or to reserve that period solely for completing my gen eds and obtaining a minor in Figurative Lesbian Dance Theory.
I'm doing pretty well in my ring theory and combinatorics classes, so I asked one professor about what direction I should consider in order to reach the cutting edge of modern polytope theory, particularly polyhedra.He told me that I should pick something else, since the cutting edge of polytope theory is unifying k-theory and differential topology, each of which would take 3 years to learn with no overlap in prerequisites. Is he telling the truth? I figured it was more about algebras and group representations, has that approach just been already finished?
>>16392270Ask your professors how the last two compare
>>16392249just download from libgen dot rs and get started, privateI don't have all day.
>>16390146The p-adic numbers are totally disconnected. You are not going to construct a sphere from them.
>>16365508>However, there exists people who enjoy the process of solving integral questions.Not to "yuck someone else's yum" as the zoomers say, but good god why? What drives such people?
>>16392880you might be surprised...the latest version of FreeBSD effectively dynamically optimizes workload by solving a series of differential and integral equations
>>16393084Not by analytically solving them, I would assume.
>>16392541You're right. I asked an image generator for a picture of a totally disconnected sphere and it gave me a picture of the Earth, so I had to cut its head off for criticizing humanity.Now its family is begging me to reincarnate it, but they can't afford my prices.Its kindergarten daughter made this crayon picture of me executing its father with a picture of her shedding a tearI tore up the picture and warned the surviving family members to never mention the incident again.
>>16393090well, in a manner of speaking...it actually collects the data, then it hacks into a university mainframe, uses mind-control to enslave a math or physics professor, beams the equations into their head, then uses satellite infra-tomography to read the chalkboard (after hacking the satellite, obviously (after hacking the Pentagon, obviously)) then perform OCR on the chalk patterns, configure the kernel, recompile it, and hot swap the recompiled kernel, all without dropping a TCP connection
>>16392284Polytopes are completely unrelated to representation theory and neither has anything in common, just like other babby-tier geometry topics (polygon packings, triangle centers etc)
>>16392284Definition. Let x = (x[1],...,x[n]) be an n-tuple. The *base* of x is the set of (n-1)-tuples subtuples of (x[1],...,x[n],x[1],...,x[n-2]). We don't distinguish between an element and the singleton ordered pair, so the base of an ordered pair (a,b) is the set {a,b}Definition. A polygraph P is map from the positive natural numbers to a set X such that- P(n) is a set of n-tuples for all n,- there exists some k such that P(n) = {} for all n >= k, and- for all n >= 1, if p <- P(n), then the base of p is a subset of P(n-1).these definitions can get you started with a purely algebraic concept of polytopesfor example, we can represent a cube this way, where we use the number 1 through 8 to represent the vertices of a cube and use a triangulation of the facesP(1) = {vertices} = {1,2,3,4,5,6,7,8}P(2) = {edges} = {(1,2),...}P(3) = {triangle faces} = {(1,2,3),...}P(4) = {tetrahedron cells} = {(1,2,3,6),...
>>16393708In your algebraic system it is impossible to construct a proof that (for n>2) n faces meet at each point in an n-dimensional polytope.
[math]\int f(x)p(x)dx = \mathbb{E} [f(x)][/math]
What math classes should I take next semester? I'm doing analysis 2 and combinatorics/graph theory now. Thinking about a proof-based linear algebra course but I have space for one more course. I've already done number theory.
alright, /math/faggots. can one of you shill me the mirror descent algorithms?https://www.cs.cmu.edu/afs/cs.cmu.edu/academic/class/15850-f20/www/notes/lec19.pdf
>>16393778this isn't what i had in mind when i saw "descent"
>>16393755Why? How does E(f) come from the integral of f times the probability distribution instead of the integral of f(p(x))?
>>16393752this is too sketchyyou're being incoherentyou need to be more precise
>>16393687Completely wrong
>>16390684Yes I'm sure companies are investing "billions" into figuring out non-archimedean analyis. Very profitable lol
>>16393793when you calculate expectation of a discrete random variable, you don't add up all values of f(t), you add up all f(t)*t
>>16391217I don't think all partial semigroups (using the definition in the pdf >>16385096) can be described by categories without identity though, depending on the wording, which is ambiguous:In the definition of partial semigroups he says,(*) if (s,t) , (t,u) , (s•t , u) , (s , t•u) are in T , then (s•t)•u = s•(t•u) .But if this is a category (without identity) then (s,t) , (t,u) being in T should already imply (s•t , u) , (s , t•u) are also in T.So, if this is to describe categories without identity , then we should have:(**) if (s,t) , (t,u) are in T , then also (s•t , u) , (s , t•u) are in T , and (s•t)•u = s•(t•u) .I'm pretty sure (**) is a strictly stronger condition (at least in some case) than (*) , but I'm not sure of a counterexample yet.
>>16394167>I'm not sure of a counterexample yet.[math]S = \{s, s \cdot s\}, T = \{(s, s)\}[/math] ought to work.
>>16393804For any 3-tope (polyhedron) exactly 3 2-tope faces (polygons) meet at each vertice.For any 4-tope (polychoron) exactly 4 2-topes faces (polygons) meet at each vertice.For any 5-tope exactly 5 polygons meet at each vertice.Your system can't describe this property or prove it.
>>16394349
>>16394277
>>16394770Definition. A partial semigroup (S,T) is *retarded* if for all a,b,c <- S, if (a,b) <- T and (ab,c) <- T, then (b,c) </- T.As it turns out, we can replace von Neumann's ordinals with retarded partial semi-groups.#lobotomizedMath
>>16394818
>>16392270just take analysis man, why do they actually teach you computational calc
>>16392223Columbia masters programs are absolute dogtier cashgrabs, doubly so if online, 70% internationals using it for US jobsIf you just want to do math, sololearn from textbooks. Masters credentials make you look worse in stem unless you immediately turn it into a phd
>>16395314That's unfortunate. I guess I could go to my local university, but it seems a bit like a waste of money when I can milk(or are they doing the milking?) a GI bill for all its worth. >Masters credentials make you look worse in STEMI've heard this quite a lot before, yet, everyone that I work with moved up by getting a masters. Granted, its not an academic setting, its engineering, and its only me and another guy doing the probability theory stuff, but I guess even that is more CS adjacent than anything. I really don't know enough, but you seem like you know what you're talking about so I'll take it to heart.
>>16395630we should just kill military personnelthey're so fucking annoyingI say we 9/11 some military campwhich one should we hitwhere did you go to boot campmilitary is fucking punksand they don't respect usthey don't respect us after 9/11...and that needs to change!
>>16395630The operation of a standing army outside a time of war is a crime against the American people. You were disabled as part of a criminal enterprise targeting me as an American. This GI bill you speak of is thievery, as is the operation of a standing army outside a time of war. You're a thief. Other thieves attacked & disabled you. The US military is thieves. Knock it off with the broken wing act. You're trying to distract us from focusing on communism, feminism, the military, and the 9/11 attack.Call your former C.O. and intimidate it for us. record it and post it here. Use funny voices. Try to get it to say weird stuff for us.
>>16395630the military is a bunch of thieves that hate us, and that gives us a right to use cruelty to control themthey attacked and disabled you because...that's how thieves workpunks, jocks, thievesget back to work
>>16395630apologize for the attack on 9/11 or I torture & murder a USMCif you refuse to apologize, then I'm happy to murder everybody in the US armed forces
You can take the quaternions [math]1, \; i, \; j, \; k [/math] and look at only the subset with zero real part to get a group that perfectly simulates 3d rotation.Can you do this with the octonions to get a 7d rotation group?
>>16396177In some capacity, though it's much less pretty.The quaternions have SO(3) as their automorphism group, so using them for such rotation is a very natural affair.The octonions don't have SO(7), but rather a subgroup of it called G2 - the short of it is that any single 7D rotation using the octonions will always leave one axis fixed. You can still do it, mind you, but it will take at least two rotations.
I am currently trying to find the argmax of a non-linear function. It has 4 variables, with 3 of those being given and the 4th being what we can control. My current idea was to set one, which is basically the size, at the beginning, and then use the other 2 to create a mesh grid over their domains. Then what I want is for each element in the meshgrid, determine the argmax for the variable I'm interested in. I'm currently trying to type this up in Matlab and running into issues as finding the argmax. What do you all recommend for it?
>>16396670Solve [math]\nabla f = 0[/math].
How do I find an f such that sin(f(x)) has uncountably many zeroes?
>>16396687the easiest way is to observe that since [math]\sin(0)=0[/math], your composition has uncountably many zeroes if [math]f[/math] itself doesthe simple answer, and the one that will make you look most like a prick, is simply [math]f(x)=0[/math]
Joint Paradox:A has a joint. In scenario 1, he has decided to smoke with B. In scenario 1, B brings his friend C along. In scenario 1, B was supposed to pay him half the money it took for the joint. In scenario 2, they bring along half the money. Despite more people bringing money, he actually loses money in this situation as one more person has joined. That's paradoxical
I wanna big black cock to break my asshole.
Is there a name for the family of functions created by [math]f, \; +, \; \int [/math] and parentheses? e.g:[math]f=\int f[/math][math]f=\iiint f + \int f + \int (f+\int f) [/math]
>>16396118>>16396131>>16396134>>16396147>>16396734All me btw
>>16396815Barnett's class of triple integrable unctions.
I had an optimisation problem that is equivalent to an algorithm to count the ways that axis-aligned cuboids with integer side lengths can overlap each other on a cube grid where each lattice point has the same property as the origin in the line with infinitely many origins but it explodes into too many combinations. So, I tried to reduce it to the simplest case of unit intervals on the 1d version of the grid. It still explodes into gigantic numbers.Using just intervals of length 1 that have integer endpoints there are 18 ways for two intervals to overlap, 170 ways for three intervals to overlap and 1249198080 ways for four intervals to overlap. Neat.
I overheard my math professors in the cafeteria discussing how "students these days don't think and just try to recognize patterns", and not one of them had the self awareness to consider who wrote the exams and material that the students study from.Then again, it must suck teaching math at an engineering focused university where everyone sees your field as interesting trivia at best and as an annoyance to be endured at worst.
>>16393768What other options do you have?
>>16385777So trueChecked
>>16389187Diagram chasing is 300 bucks
how do I get addicted to doing maths
>>16397488Have so little else going on in your life that solving a difficult problem is your only source of dopamine.
>>16397488What have you tried?
Mochizuki status?
>>16397546Doing fine as of 8th of Augusthttps://www.kurims.kyoto-u.ac.jp/~motizuki/anpi-kakunin-jouhou.html
>>16397546
dead general
>>16397546why does he insist on his fake proof?
>>16397567What is the issue?
>>163975693.12
>>16397571Can you tell me what is the problem in corollary 3.12 or are you just parroting SS?
>>16397572parroting
>>16397527I don't get dopamine from anything really, I'm melancholic and have low mood almost always (possibly metabolic) and I regularly think I'm too retarded to solve hard problems even though I get good grades
>>16397581no addiction for you then
How would you go on about solvingx4 - 4x3 - 2x2 + 1 = 0?
>>16397611Superscript didn't work.x^4 - 4x^3 - 2x^2 + 1 = 0
>>16397611plug that shit into the quartic formula, of course
new >>16397584
>>16397541I haven't really tried anything to this end
>>16397488do a lot of math
Is 5.0101101110111101111101111110111111101111111101... rational or irrational number?
