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# /sci/ - Science & Math

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think outside the box edition

 >> Anonymous Wed Jan 20 11:40:23 2021 No.12605557 File: 200 KB, 1440x1080, 1563641895581.jpg [View same] [iqdb] [saucenao] [google] [report] NO!!
 >> Anonymous Wed Jan 20 11:41:15 2021 No.12605562 does anyone remember which german uni had a good set of algebraic geometry notes?think it had an -eide- or a -burg in the name
 >> Anonymous Wed Jan 20 11:42:55 2021 No.12605569 That's inflation not expansion
 >> Anonymous Wed Jan 20 11:46:16 2021 No.12605584 File: 88 KB, 996x720, 99s1q.jpg [View same] [iqdb] [saucenao] [google] [report] >>12605562Heidelberg? Regensburg? Those would be two quick guesses.
 >> Anonymous Wed Jan 20 11:57:36 2021 No.12605618 >>12605584might have been bielefeldsome kind anon posted a link to their notesquite a long time ago
 >> Anonymous Wed Jan 20 12:04:21 2021 No.12605637 >>12605618Bielefield*
 >> Anonymous Wed Jan 20 12:08:15 2021 No.12605650 File: 42 KB, 770x400, suspecious_activity[1].jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Wed Jan 20 12:09:55 2021 No.12605661 File: 39 KB, 657x527, 1610511423816.jpg [View same] [iqdb] [saucenao] [google] [report] retarded anon here, just finished College Algebra 1 with an A, do I progress next to Pre-Calculus or can I jump straight into Calc 1 without being too lost? Don't shit on me please I never applied myself in high school and am doing my best to relearn all the math I've forgotten or never learned.
 >> Anonymous Wed Jan 20 12:14:57 2021 No.12605669 >>12605661you HAVE to start calculus, NOW, ANON NOW! DON'T LOOK BACK
 >> Anonymous Wed Jan 20 12:15:17 2021 No.12605670 >>12605661what the hell is 'college algebra 1'?
 >> Anonymous Wed Jan 20 12:16:56 2021 No.12605672 >>12605670x * x = 2x
 >> Anonymous Wed Jan 20 12:17:19 2021 No.12605674 >>12605670The first level of college algebra I don't know anon, it wasn't hard but I also took it at a juco.
 >> Anonymous Wed Jan 20 12:19:29 2021 No.12605675 >>12605661americans really are fucking their young adults into a life of debt servitude
 >> Anonymous Wed Jan 20 12:20:17 2021 No.12605677 >>12605661You go at it step by step. Obviously, pre-calculuscomes before calculus so try for it. For me, Ijumped to calculus at college after doing the preat high school.
 >> Anonymous Wed Jan 20 12:22:58 2021 No.12605682 >>12605675My college is free, I did my time with el Army and now I get my bennies>>12605677Ok I'll enroll into pre calculus. I bought a Ti Nspire CX before my Algebra because I found a used one for \$60 and it worked well.
 >> Anonymous Wed Jan 20 12:24:13 2021 No.12605687 Another retarded anon here. After a book like Dummit and Foote, should one read Lang's algebra or go right to a commutative algebra text like Atiyah? I frankly don't really understand how these things fit together. My university's grad program for example starts with commutative algebra, so I'm not sure why other programs have year long abstract algebra courses.>>12605661Go to Calc 1. I believe in you anon!
 >> Anonymous Wed Jan 20 12:26:00 2021 No.12605695 >>12605689np anon, actually the only deployment I went on was a peace keeping mission between Israel and every country around that hates them so I unironically did serve Israel :^)
 >> Anonymous Wed Jan 20 12:28:28 2021 No.12605700 >>12605695did you get your foreskin back at the end of your service?>>12605687did your uni recommend any supplementary mats? or is there at least someone there you could ask?it largely depends on the content of your grad course
 >> Anonymous Wed Jan 20 12:47:15 2021 No.12605752 >>12605682>>12605677I had a TI-89 Titanium for a good while until I lostit for some damn reason. I now work with thenon-graphing Canon F792-SGA which worksjust fine for me.
 >> Anonymous Wed Jan 20 13:51:07 2021 No.12605967 File: 1003 KB, 1589x1627, 1611168635082.png [View same] [iqdb] [saucenao] [google] [report] What's the deal with Aluffi?Is it a good intro to abstract algebra or is it a meme?
 >> Anonymous Wed Jan 20 13:53:35 2021 No.12605971 >>12605967kurisu is the answer
 >> Anonymous Wed Jan 20 13:56:45 2021 No.12605981 File: 832 B, 153x87, math is solved.png [View same] [iqdb] [saucenao] [google] [report] Why do people have hard time grasping this?
 >> Anonymous Wed Jan 20 14:02:06 2021 No.12605998 >>12605981What is there to grasp?
 >> Anonymous Wed Jan 20 14:04:10 2021 No.12606004 >>12605998Grasp THIS*unzips*
 >> Anonymous Wed Jan 20 14:07:37 2021 No.12606014 File: 19 KB, 400x400, e736b127e4ac0a1f605c74e53038ba56.jpg [View same] [iqdb] [saucenao] [google] [report] >>12605971You answered the wrong question!
 >> Anonymous Wed Jan 20 14:13:21 2021 No.12606024 >>12606004I think that's too small for me to have any grip.
 >> Anonymous Wed Jan 20 14:15:13 2021 No.12606028 >>12605998nothing, math is religion, no knowledge only belief (unlike the superior observational science of biology, the true meta-science).
 >> Anonymous Wed Jan 20 14:15:28 2021 No.12606029 >>12605998That you will never be a whole number.
 >> Anonymous Wed Jan 20 14:39:08 2021 No.12606107 >>12606024You talk a lot of shit online but I bet you wouldn’t say that with my cock in your face.
 >> Anonymous Wed Jan 20 15:49:27 2021 No.12606376 >>12605569kinky
 >> Anonymous Wed Jan 20 15:51:35 2021 No.12606383 >>12605538>be me>hate math >always get A’s in math classes >tell people that I hate math >”you must just be bad at it”Why are mathfags like this?
 >> Anonymous Wed Jan 20 16:11:36 2021 No.12606485 >>12606383same feel anon
 >> Anonymous Wed Jan 20 16:13:07 2021 No.12606496 >>12606383>Why are mathfags like this?because most of the time, people hate math because they're bad at it
 >> Anonymous Wed Jan 20 16:13:38 2021 No.12606502 >>12605538If I was doing summer undergrad research, what would be better, something something in know theory or Bass-Serre theory?
 >> Anonymous Wed Jan 20 16:14:46 2021 No.12606506 >>12606502excuse my brain melting, *something in knot theory
 >> Anonymous Wed Jan 20 16:17:02 2021 No.12606524 File: 11 KB, 275x183, schlop.jpg [View same] [iqdb] [saucenao] [google] [report] >>12605538based largo
 >> Anonymous Wed Jan 20 16:18:35 2021 No.12606533   I have an algebraic curve C over the field of complex numbers and n given points, not necessarily distinct. Is there a general way to prove that the sum of these n points is a canonical divisor? I'd need a nonzero divisor of a differential form that is this sum plus a principal divisor. I know that there are exactly n points outside of each affine chart and I know how they look like, not sure if this helps.
 >> Anonymous Wed Jan 20 16:42:34 2021 No.12606651 >>12606383>always get A’s in math classes>thinks that makes him good at mathPathetic. Math is for the chosen few. 170+ IQ or gtfo.
 >> Anonymous Wed Jan 20 16:43:25 2021 No.12606654 >>12605967Aluffi is good for a first text on abstract algebra, and also it teaches category theory along the way. I'm not sure why it isn't more widely used in undergrad. Pinter is also good according to anons, although I'm not sure because I've not tried it myself.
 >> Anonymous Wed Jan 20 16:45:44 2021 No.12606661 >in online classes>doctor says we don't have to take notes, he will send the board after class>o-ok>can't concentrate if I don't take notes, end up watching memesb-bros, I may be retarded
 >> Anonymous Wed Jan 20 16:50:17 2021 No.12606676 >>12606651It means I’ve been successful with every bit of mathematics I’ve been presented with, so...
 >> Anonymous Wed Jan 20 16:51:57 2021 No.12606681 >>12606661You may be, but at least we are both retarded
 >> Anonymous Wed Jan 20 17:17:06 2021 No.12606793 anyone have a nifty derivative/integral to solve that requires some creativity but let's limit it to college level and not grad level?had a professor who knew a lot of these but I don't know where he got them from.
 >> Anonymous Wed Jan 20 17:24:15 2021 No.12606826 >>12606793$\int_0^1 1\ dx$
 >> Anonymous Wed Jan 20 17:45:07 2021 No.12606901 >>12606502these seem to be fairly disparate fieldswhich do u like more? what classes have u taken?
 >> Anonymous Wed Jan 20 17:46:09 2021 No.12606907 >>12606793look at the previous years of the putnam exam my friend, plenty of interesting integrals and ODEs
 >> Anonymous Wed Jan 20 17:50:09 2021 No.12606919 Candidate for the lowest bar of a meaningful proposition: the ability to decide it given halting oracles of arbitrarily high complexity.Exercise: find math problems that don't fit this criterion.
 >> Anonymous Wed Jan 20 17:52:26 2021 No.12606929 >>12606793The ones Michael Penn does, maybe?
 >> Anonymous Wed Jan 20 17:59:58 2021 No.12606929,1   >>12606654Aluffi is a memePinter is a meme>anyone who disagrees is wrong
 >> Anonymous Wed Jan 20 18:25:33 2021 No.12607030 >>12606901Some algebra, some algebraic topology, I mean, I'm an undergrad. I haven't taken a dedicated course in combinatorics though, just the basics which were taught in a 1st year class, so that kinda worries me about bass-serre
 >> Anonymous Wed Jan 20 18:26:35 2021 No.12607032 >>12607030>some algebraic topologywhich I'm in rn
 >> Anonymous Wed Jan 20 18:31:52 2021 No.12607045 >>12607030im also currently an undergrad in topology, i think knot theory might be the way to go then
 >> Anonymous Wed Jan 20 19:06:56 2021 No.12607246 Apparently I proved impossible what my professor is asking on an exercise.Consider the algebraic curve $C := \{ (x:y:z)\in \mathbb{C}P^2\, ;\ x^4+y^4+z^4=0\}$, and let $P_1, P_2, P_3, P_4\in C$ be points, not necessarily distinct (they are more specific, but the data doesn't matter). He asks to show that $D := P_1+P_2+P_3+P_4$ is a canonical divisor of $C$.What I did (in brief):1. This is equivalent to the existence of $g\in \mathbb{C}(C)^\times$ with $\text{div}(g) + \text{div}\left( d\left(\frac{x}{y}\right)\right) = D$;2. $\text{div}\left( d\left(\frac{x}{y}\right) \right) = -2(P_{2, 0}+P_{2, 1}+P_{2,2} + P_{2,3})$ where $P_{2, j} = (1 : 0 : \mu_8^{2j+1})$ for each $j$;3. Taking degrees of both sides in 1 and using 2 we get the impossibility 0 - 8 = 4.What am I doing wrong here?
 >> Anonymous Wed Jan 20 20:10:27 2021 No.12607505 >>12606826$\int_0^1 1\, dx=x\,|_0^1$$\int_0^1 1\, dx=1-0$$\int_0^1 1\, dx=1$$QED$
 >> Anonymous Wed Jan 20 20:20:09 2021 No.12607528 >>12606661lmao I probably played 100 hours of hype rouge while my professors were lecturing last semester. It was sick.
 >> Anonymous Wed Jan 20 21:01:21 2021 No.12607651 >>12606661take lighter notes and also focus more on synthesise.g. note down the general approach of a proof and which parts you find difficult / don't fully understand, relate what's being said to earlier material / other courses, etc..at least for me this helps me stay focused while not merely copying everything on the screen
 >> Anonymous Wed Jan 20 23:17:55 2021 No.12608119 >>12607246Update. Apparently I am indeed wrong, the degree of the canonical divisor should be 2g-2 = 4. The first item should be correct, so d(x/y) should be canonical and thus have degree 4, so the mistake should be on the second item. But I can't see how my calculation of that divisor is wrong. I used $d(x/y) = -(x/y)^2 d(y/x)$ and local parameters. Help plz
 >> Anonymous Thu Jan 21 00:40:51 2021 No.12608293 >>12605967what the fuck is that thing between the numbers? why do mathematicians just make shit up man, it’s not helpful
 >> Anonymous Thu Jan 21 02:46:20 2021 No.12608563 >>12605538i would have given them credit for that kek.
 >> Anonymous Thu Jan 21 02:47:22 2021 No.12608566 >>12606383you're still bad at math
 >> Anonymous Thu Jan 21 03:07:58 2021 No.12608598 I'm trying to read some math textbooks by myself. But they are hard af, a few pages on number theory took me hours. Should I keep grinding proofs or just skimming through theorems to help my cs major?
 >> Anonymous Thu Jan 21 03:12:17 2021 No.12608610 >>12605670Something like 2x + 8 + 12x - 4x = 7>Find X
 >> Anonymous Thu Jan 21 03:38:09 2021 No.12608682 >>12608610>Find XIt isn't in there, please, I've looked as much as I can, I just want to pass!
 >> Anonymous Thu Jan 21 04:33:37 2021 No.12608786 >>12608598What number theory book are you using? I don’t think there’s any reason to read number theory theorems without going through proofs
 >> Anonymous Thu Jan 21 04:43:17 2021 No.12608804 >>12608598Sheldon Axler used to say that for students it is not only normal but also desirable to spend ~1 hour on some of the heavier pages. But once you git gud you will speed up naturally
 >> Anonymous Thu Jan 21 05:04:57 2021 No.12608849 >>12608804>Sheldon Axler used to say that for studentsit's also written in his>Measure, Integration & Real Analysispdf of which is freely available on springer
 >> Anonymous Thu Jan 21 06:03:05 2021 No.12608960 >>12605538Here's a question for /mg/ historians>>12608951
 >> Anonymous Thu Jan 21 07:26:13 2021 No.12609089 >>12608960It's all true
 >> Anonymous Thu Jan 21 11:14:10 2021 No.12609571 >>12608804>>12608598https://mathwithbaddrawings.com/2015/03/17/the-math-major-who-never-reads-math/Kinda liked this take on it.
 >> Anonymous Thu Jan 21 11:28:29 2021 No.12609612 Any math undergrads here? How does something like Calculus 1 - 2 -3 compare, in terms of difficulty, to other classes you guys have?
 >> Anonymous Thu Jan 21 11:55:09 2021 No.12609665 File: 1 KB, 300x300, 5x5-grid.png [View same] [iqdb] [saucenao] [google] [report] Is it possible to remove one square from 5x5 grid and then cut remaining squares into three congruent parts?
 >> Anonymous Thu Jan 21 11:56:25 2021 No.12609668 >>12609612All equally easy.
 >> Anonymous Thu Jan 21 12:08:33 2021 No.12609706 >>12605661I'll give you some actual advice instead of these muh anons "math is joke".The entirety of Calc 1 only requires a few things to be known:- Functions- Knowledge on factoring- Exponents, logarithms, properties of each- Some trig (unit circle)Basically if you know at least 50% of the stuff posted on this website you are prepared to do Calc 1, albeit with a little more difficulty than if you had taken PreCalc: https://www.mathsisfun.com/algebra/index-college.htmlYou should only take PreCalc if you have little/no idea what the above topics I listed are.All in all, as long as you have access to Khan Academy to explain some stuff that is new to you, you'll be more than ready to go to Calc 1.
 >> Anonymous Thu Jan 21 12:09:55 2021 No.12609709 >>12605661Precalc is literally a meme. I'm not joking, I took it and it was just a refresher on algebra 2. DO CALCULUS ANON YOU'LL THANK YOURSELF YOU DIDN'T WASTE A SEMESTER.
 >> Anonymous Thu Jan 21 12:22:28 2021 No.12609744 Is calc course the circumcision of mathematics?It's the first encounter with "serious" maths (like first sexual experience of the rabbi sucking out the blood), permanently traumatises the youth with shockingly nonsense axioms and constructions (like permanent brain trauma from shock during circumcision), and those who fail, can never do maths again (like a botched surgery, rendering unable to ever have sex). Those who take it, are forever going to only see the world like this, and do weird, increasingly degenerate, constructions with sets when a simpler, potentially constructive, alternative exists for those intact (think how circumcised men masturbate and have sex).When it comes to teaching the youth analysis again, they'll do the same as what was done to them, the analogy here is obvious. The ethno-religious background is identical too.
 >> Anonymous Thu Jan 21 12:35:08 2021 No.12609773 >>12609744dunno what schizobabble you postedbut it seems to be a non-consensual problem in americaso maybe
 >> Anonymous Thu Jan 21 12:48:35 2021 No.12609805 >>12609668This a joke or for real?
 >> Anonymous Thu Jan 21 13:04:42 2021 No.12609866 >>12609805are calc 1-3 supposed to be first year modules?
 >> Anonymous Thu Jan 21 13:11:19 2021 No.12609898 >>126098661 and 2 are first year where I study. Hence my question, does it get harder or what?
 >> Anonymous Thu Jan 21 13:15:26 2021 No.12609918 >>12609709Where I'm from, trig is one semester of precalc, and you should probably take that. (The trig functions are important in calc and there is some interesting af math to be learned) But the functions and analysis semester is garbage. Like you said, it's literally just Algebra 2. I skipped that and calc is no harder.
 >> Anonymous Thu Jan 21 13:18:03 2021 No.12609933 >>12609898>erdo your homeworkseriously, those exercises are there for a reason. if you don't want to go further into it later in your degree then at least you have a decent grade to showthe plug and chug parts of calculus should be very easy with sufficient practicesome people stumble a bit in anal classes, and struggle a bit with their arguments/proofs
 >> Anonymous Thu Jan 21 14:34:34 2021 No.12610221   >>12607246>>12608119Solved. Problem was, x/y - a/b is not always a local parameter for a point with non-zero second coordinate, we have to be careful with what happens in the local ring, this can become 0 there and then its order would actually be +infinity.
 >> Anonymous Thu Jan 21 14:40:29 2021 No.12610241 >>12607246>>12608119Solved. Problem was, x/y - a/b is not always a local parameter for a point with non-zero second coordinate, we have to be careful with what happens in the local ring, this can become 0 modulo the square of the maximal ideal there, so its order at P would be greater than 1.
 >> Anonymous Thu Jan 21 15:35:00 2021 No.12610451   File: 101 KB, 1918x928, 1583550619216.png [View same] [iqdb] [saucenao] [google] [report] How do I make this fuction go to (1,1) in the same way as it's coming from (0,0)?Point symmetry around (1/2,1/2).Think of -a instead of -0.21 with 0
 >> Anonymous Thu Jan 21 16:22:19 2021 No.12610600 >lol just ignore additive constants>lol just ignore constant factors>if I write $\ll$ everywhere no one will question my arguments>bro ur cauchy schwarz?Why is analysis and analytic number theory in particular such a farce?
 >> Anonymous Thu Jan 21 16:25:44 2021 No.12610609 >>12610600just feel and experience the size of the quantities with your intuitionno one gives a shit abour rigor
 >> Añonymous Thu Jan 21 16:31:23 2021 No.12610627 >>12605672>x * x = 2xwrongx * x = x^2
 >> Añonymous Thu Jan 21 16:32:26 2021 No.12610631 >>12608610x=-1/10did i win?
 >> Anonymous Thu Jan 21 17:05:40 2021 No.12610755 >>12605569That's not inflation, that's gaping.
 >> Anonymous Thu Jan 21 17:09:01 2021 No.12610770 >>12609744Calculus is actually pretty simple to understand if you ignore delta-epsilon proofs, or ignore all the "proofs" that are usually beyond the scope of an undergrad course. All the constructs are very intuitive and based on simple geometric concepts. To me, it's other math fields like discrete or probability that are impossible to grasp.
 >> Anonymous Thu Jan 21 17:56:10 2021 No.12611002 >>12609898I've never heard of a math major taking calculus 1 and 2. Are you using Spivak or Apostol at least?
 >> Anonymous Thu Jan 21 17:57:22 2021 No.12611005 File: 154 KB, 1920x1080, WIN_20210117_06_47_46_Pro.jpg [View same] [iqdb] [saucenao] [google] [report] Proof that the sum of 1/n^a for all Z+ a is 1/(n-1):Take some dots.....Cross out the first dotThats 1/nTake the second dot and expand it into more dots.....Then cross out one, thats 1/n^2Keep doing it at all layersAt all layers you have 1/(n-1) plus the excluded dots fraction which is fractalSo you have a sum of 1/(n-1)s at each layer, giving by distribution a total as so.I cant tell if this is a geometric or symbolic proof.
 >> Anonymous Thu Jan 21 18:03:58 2021 No.12611050 >>12611005it's not a proof it's schizo rambling
 >> Anonymous Thu Jan 21 18:08:21 2021 No.12611071 >>12611050Low IQ post, unironically
 >> Anonymous Thu Jan 21 18:10:27 2021 No.12611078 much better without all the animefags spamming
 >> Anonymous Thu Jan 21 18:12:39 2021 No.12611093 >>12611078Yeah but now its just us retards left so were gonna have to learn advanced math on our own.
 >> Anonymous Thu Jan 21 18:15:24 2021 No.12611107 thank you anon. I literally came here to ask what I needed to know to not be lost in my calc class since it has been a while since I have done any math.
 >> Anonymous Thu Jan 21 18:16:26 2021 No.12611113 >>12609706>thank you anon. I literally came here to ask what I needed to know to not be lost in my calc class since it has been a while since I have done any math.
 >> Anonymous Thu Jan 21 18:17:14 2021 No.12611120 ▲▲ ▲
 >> Anonymous Thu Jan 21 18:55:53 2021 No.12611270 Why dont alt keys work on my computer ▲▲ ▲Copypastaing the unbreaking space dont work eider
 >> Anonymous Thu Jan 21 18:58:13 2021 No.12611275 File: 25 KB, 641x530, 1609459437226.jpg [View same] [iqdb] [saucenao] [google] [report] What in the fuck is this thread
 >> Anonymous Thu Jan 21 18:58:33 2021 No.12611276 ▲▲ ▲
 >> Anonymous Thu Jan 21 18:59:47 2021 No.12611282 ▲ ▲▲It works on d?scord y not here
 >> Anonymous Thu Jan 21 19:04:46 2021 No.12611297 >>12611005there is no proof, 1/nᵃ is not 1/(n-1) while a ∈ ℕ.and please learn to write mathematical expressionsretard
 >> Anonymous Thu Jan 21 19:06:42 2021 No.12611302 >>12611297No the sum I meant
 >> Anonymous Thu Jan 21 19:11:40 2021 No.12611318 ▲▲ ▲
 >> Anonymous Thu Jan 21 19:17:10 2021 No.12611334 File: 758 B, 73x99, TriKraft.png [View same] [iqdb] [saucenao] [google] [report] ▲▲ ▲
 >> Anonymous Thu Jan 21 19:19:57 2021 No.12611351 File: 207 KB, 1250x870, 2tukky.jpg [View same] [iqdb] [saucenao] [google] [report] ▲▲ ▲I vent my spleen at the lord
 >> Anonymous Thu Jan 21 19:21:45 2021 No.12611358 $\ ▲$$▲$$▲$
 >> Anonymous Thu Jan 21 19:23:12 2021 No.12611366 >>12611358How do you do it anonThe alt key on my windows pc isnt working so alt 255 does nothing and theres no num lockHilf mir
 >> Anonymous Thu Jan 21 19:23:57 2021 No.12611374 >>12611358Noice. $\LaTeX$ never disappoints.
 >> Anonymous Thu Jan 21 19:24:30 2021 No.12611379 >>12611358Element untersuchenMathjaxAhaha Nw I know
 >> Anonymous Thu Jan 21 19:24:38 2021 No.12611380 >>12611366Git gud$\ ▲$▲▲
 >> Anonymous Thu Jan 21 19:25:12 2021 No.12611381 >>12611366Used $\TeX$. Just right click and see the commands.
 >> Anonymous Thu Jan 21 19:26:28 2021 No.12611386 >>12611358genius of /mg/king of /sci/owner of the /tri/force
 >> Anonymous Thu Jan 21 19:27:36 2021 No.12611392 $\hspace{1cm}$▲▲ ▲
 >> Anonymous Thu Jan 21 19:28:47 2021 No.12611402 $\hspace{0.2cm}$▲▲ ▲
 >> Anonymous Thu Jan 21 19:29:48 2021 No.12611405 File: 33 KB, 477x165, 4chanada.png [View same] [iqdb] [saucenao] [google] [report] >>12611402>0I am a King
 >> Anonymous Thu Jan 21 19:31:18 2021 No.12611414 _/\/\_/\
 >> Anonymous Thu Jan 21 19:42:28 2021 No.12611473 File: 110 KB, 600x450, Uusi%20kirkko%2018.12.2009%202[1].jpg [View same] [iqdb] [saucenao] [google] [report] >>12611078Sorry, I was busy.>>12611351Whatever that building is supposed to be, it is nothing compared to the church in Hyvinkää, the temple of the Space Messiah.>>12608960I was going to say it has to be Cox-Zucker because C precedes Z, but the set theory axiomatisation isn't BGN but NBG. I conclude that it is intentional.
 >> Anonymous Thu Jan 21 19:44:35 2021 No.12611483 >>12611473Hey anime tranny add me on discord and teach me fourier convergence theorems pwetty pweaseMultimorph 4167
 >> Anonymous Thu Jan 21 19:49:18 2021 No.12611512 File: 98 KB, 1200x675, 1601920023924.jpg [View same] [iqdb] [saucenao] [google] [report] >>12611483Hi! Sorry but(1) I don't use discord.(2) I don't remember much anything about Fourier stuff.
 >> Anonymous Thu Jan 21 19:49:55 2021 No.12611517 >>12611483Someone who uses discord add me and teach me fourier convergencce
 >> Anonymous Thu Jan 21 19:57:14 2021 No.12611560 File: 116 KB, 1200x1200, die wissenSCHAFTEN.jpg [View same] [iqdb] [saucenao] [google] [report] https://www.youtube.com/watch?v=Wdk5yuLvRCADoes anyone else get math obsessions? Whenever I dont understand a concept I get agony. I try to reframe all concepts in terms of pure axioms and ssince the universe runs on void energy I just go in spirals. When I look at a object I create alternatives and theyre endless. The combinatoric possibilities exponentially spiral out and my brain melts. How do I do math without getting overwhelmed?
 >> Anonymous Thu Jan 21 20:15:01 2021 No.12611632 >>12605538Very funny. 0 points.
 >> Anonymous Thu Jan 21 20:17:05 2021 No.12611640 >>12609665Yes. Remove the 5x5 square and the remaining null set divides evenly into 3
 >> Anonymous Thu Jan 21 20:23:38 2021 No.12611661
 >> Anonymous Thu Jan 21 20:26:59 2021 No.12611675 >>12609665Depends on your definiton of cut bt 24 give a gihting chance. But if you want us to do it in 2 slices, then we need each group to be 8, so think not by intuition but unsure
 >> Anonymous Thu Jan 21 20:29:37 2021 No.12611683 >>12611661Counting down to 0 by intersecting endsegments can only happen in steps of one natural number per endsegment because from the definition Ek \ {k} = {k, k+1, k+2, k+3, ...} \ {k} = {k+1, k+2, k+3, ...} = Ek+1 we find the bijection subtract({k}) = Ek+1 . (3) But no endsegment can be defined that contributes to reduce the intersection from an infinite set of (1) to the empty set of (2). Only undefinable, so-called dark, endsegments with indexes not subject to universal quantification in (1), can produce the empty intersection in (2) by deleting the infinite set step by step or one by one – if (3) holds, i.e., if mathematics is valid for all steps
 >> Anonymous Thu Jan 21 20:30:39 2021 No.12611684 >>12611683"k œ Ù: E1 … E2 … E3 … ... … Ek = Ek ∫ « where |Ek| = ¡0 . (1)
 >> Anonymous Thu Jan 21 20:31:41 2021 No.12611689 File: 5 KB, 861x50, Peeoga.png [View same] [iqdb] [saucenao] [google] [report] >>12611684 But no endsegment can be defined that contributes to reduce the intersection from an infinite set of(1) to the empty set of (2). Only undefinable, so-called dark, endsegments with indexes not subject touniversal quantification in (1),
 >> Anonymous Thu Jan 21 20:34:28 2021 No.12611700 Or maybe recursion doesnt work sequentially at the edge infinity, instead acting as an omnipresent chain fully loaded in one instant
 >> Anonymous Thu Jan 21 20:43:40 2021 No.12611731 File: 167 KB, 120x120, Tetraeder.gif [View same] [iqdb] [saucenao] [google] [report] Polygon john signing off for the night. Post tetraeder facts to feed our flight.
 >> Anonymous Thu Jan 21 22:42:25 2021 No.12612035 >>12605538F(x) = 2(x)^2 G(x) = a+bJust started pre-calc, tell me how wrong I am.
 >> Anonymous Thu Jan 21 22:59:38 2021 No.12612075 >>12612035it's asking for 2(a+b)^2 =2*(a^2 + 2ab + b^2) =2a2+4ab+2b2
 >> Anonymous Thu Jan 21 23:31:11 2021 No.12612146 >>12612075Noice, yeah I suppose that makes sense.Been 5 years since I was in college, and last did math in HS, I’m a little rusty on my terminology & skills.
 >> Anonymous Fri Jan 22 00:24:36 2021 No.12612255 I've self-studied math up to Tao and Baby Rudin. The problem is I lack geometric intuition, I haven't taken any geometric class. How can I embrace the arnoldpill/sovietpill and dab on bourbakist trash?
 >> Anonymous Fri Jan 22 00:44:50 2021 No.12612302 File: 12 KB, 480x360, hqdefault.jpg [View same] [iqdb] [saucenao] [google] [report] >>12612255>bourbakist trashknowing high school level maths does not mean you're qualified to make such a value judgment
 >> Anonymous Fri Jan 22 01:17:37 2021 No.12612374 File: 174 KB, 610x600, medium.png [View same] [iqdb] [saucenao] [google] [report] Why does every element of a residue-class ring mod n have a multiplicative inverse for prime n? Is there some sort of intuition behind this or is it just a fact of numbers I need to accept?
 >> Anonymous Fri Jan 22 01:35:51 2021 No.12612421 Imagine there is no multiplicative inverse for some a
 >> Anonymous Fri Jan 22 01:36:53 2021 No.12612425
 >> Anonymous Fri Jan 22 01:44:36 2021 No.12612451 How do I motivate the study of PDE without knowing physics? More abstract stuff like sobolev spaces is fine and interesting in its own right, but all the concrete examples seem to relate to the modeling of physical phenomena (which I don't understand or care about at all).
 >> Anonymous Fri Jan 22 04:45:30 2021 No.12612793 >>12612451Study classical mechanics. Even if you don't "care" about it. Also readuni-muenster.de SLASH Physik.TP SLASH ~munsteg SLASH arnold.html
 >> Anonymous Fri Jan 22 04:52:46 2021 No.12612808 Ship sails downstream from city A to city B. It takes two days. Same ship sails upstream from city B to city A. It takes three days.How long will it take for a raft to sail from city A to city B?
 >> Anonymous Fri Jan 22 04:58:45 2021 No.12612822 >>126128082 days, if we are assuming the original question posits the ship which made the journey in 2 days downstream, simply rode the current and didn’t utilize other techniques to enhance its arrival time.
 >> Anonymous Fri Jan 22 05:03:34 2021 No.12612832 File: 56 KB, 810x458, b3c84bfea39aeb6ba8e48e4a9607853d82d69ce9.png [View same] [iqdb] [saucenao] [google] [report] >>12612302> bourbak*st
 >> Anonymous Fri Jan 22 05:23:30 2021 No.12612868 >>12611560>How do I do math without getting overwhelmed?try stop smoking weed
 >> Anonymous Fri Jan 22 05:28:59 2021 No.12612879 >>1261280812 days.
 >> Anonymous Fri Jan 22 06:14:52 2021 No.12613031 >>12609665I have a proof, but it's late, so I'll type it tomorrow.The answer is no.
 >> Anonymous Fri Jan 22 06:28:02 2021 No.12613095 >>12612822>if we are assumingTip: Don't. Ever. Assume.
 >> Anonymous Fri Jan 22 06:52:41 2021 No.12613168 >>12612255Read Arnolds books and try stuff yourself, with just pen and paper, no books, no computer, no nothing, just math. Trust me, your brain works different with no outside bullshit.
 >> Anonymous Fri Jan 22 07:21:11 2021 No.12613246 >>12610627x*x*x = 3x
 >> Anonymous Fri Jan 22 07:22:32 2021 No.12613251 >>12613246No: x x x x x = 5x
 >> Anonymous Fri Jan 22 07:24:30 2021 No.12613256 >>12613251wait let me expand this so you can grasp it x * x * x = 3x
 >> Anonymous Fri Jan 22 07:26:08 2021 No.12613264 xxxxx****
 >> Anonymous Fri Jan 22 07:33:22 2021 No.12613283 >>12613256Ok, I groped it now: so x^x^x = x^3.
 >> Anonymous Fri Jan 22 09:37:35 2021 No.12613649 I want to die
 >> Anonymous Fri Jan 22 09:43:15 2021 No.12613666 >>12613246x*x*x = *(*(x, x), x)
 >> Anonymous Fri Jan 22 09:46:07 2021 No.12613674 >>12613283now you get it. x+x+x = 3+x
 >> Anonymous Fri Jan 22 09:48:22 2021 No.12613683 >no anime posters>the quality of posts plunges to lows never seen before
 >> Anonymous Fri Jan 22 09:48:34 2021 No.12613686 >>12605538>think outside the quadrilateral parallelogram editionFixed
 >> Anonymous Fri Jan 22 09:53:06 2021 No.12613701 File: 223 KB, 1335x2048, ayano.jpg [View same] [iqdb] [saucenao] [google] [report] >>12613649Same, but we have work to do first. The merciful bliss of death must be earned.>>12612374It's because of this https://en.wikipedia.org/wiki/Fermat%27s_little_theorem>>12613683Totally not my false flag, btw.
 >> Anonymous Fri Jan 22 10:06:50 2021 No.12613767 >>12611402>▲>▲ ▲
 >> Anonymous Fri Jan 22 10:07:52 2021 No.12613782 >>12612374Holy fuck I just did this problem in my linear algebra book. SPOOPY AF
 >> Anonymous Fri Jan 22 10:08:50 2021 No.12613788 >>12612868Weed isnt implicaeted>>12612808W+C = dist/2W-C= dist/3RearrangeCurrent gives velocity of dist over 12Bit odd to say you can add velocities like that but if we consider each force as contributing a velocity vector that reaches equilibrium, if the force to velocity function is linear, it makes sense (which it is for non equilibrium force vectors, and if equilibrium is a sum of force plus its resistance I think it checks out but resistance can vary due to environment). Also we would assume the wind blows/harnessedgets the same on both direction
 >> Anonymous Fri Jan 22 10:10:17 2021 No.12613800 >>12613649Why do you want to die anon? What dreams may come in the sleep of death?
 >> Anonymous Fri Jan 22 10:13:26 2021 No.12613809 File: 496 KB, 521x324, coin.png [View same] [iqdb] [saucenao] [google] [report] >>12613782The actual problem was pic related. Which I think sets it up enough for you to figure out the problem.
 >> Anonymous Fri Jan 22 10:14:40 2021 No.12613817 >>12613800Death would be better than forever being a burned-out failure
 >> Anonymous Fri Jan 22 10:16:04 2021 No.12613821 Why is there a standard math curriculum? Why arent students educated by just having them work on new problems and see what they branch into, with some methods and tools given as needed
 >> Anonymous Fri Jan 22 10:17:06 2021 No.12613823 >>12613817Then go and win at something.
 >> Anonymous Fri Jan 22 10:20:53 2021 No.12613834 >>12613823Like what? The paper I'm working on is fucking horrible
 >> Anonymous Fri Jan 22 10:35:46 2021 No.12613896 >>12613821That would require more teachers and money. But it would make way more sense.
 >> Anonymous Fri Jan 22 10:40:43 2021 No.12613924 >>12613834There will be more papers in the future. Plus Im sure its not that bad. Youre most likely just experiencing burnout, why not go for a few days of fresh air outside>>12613896Maybe it could be feasible if students were taught to be more self reliant from elementary school. To ask questions and seek answers on their own. The internet as a mega library helps and professors can act as loose guides
 >> Anonymous Fri Jan 22 10:45:00 2021 No.12613948 >>12613924>self reliant>ask questions and seek answers on their ownAh yes just derive all human knowledge on your own whilst living alone in a forest
 >> Anonymous Fri Jan 22 10:49:51 2021 No.12613970 >>12613948>The internet as a mega library helps and professors can act as loose guidesI wish you didnt have ADHD
 >> Anonymous Fri Jan 22 10:51:08 2021 No.12613975 >>12613948Also nice clock dubs
 >> Anonymous Fri Jan 22 10:52:39 2021 No.12613979 File: 524 KB, 1200x1800, 1200px-Ilmatar_ja_sotka[1].jpg [View same] [iqdb] [saucenao] [google] [report] >>12613948You mean you are not guided by the ancestral spirits and the Airress? NGMI, sorry.
 >> Anonymous Fri Jan 22 11:04:07 2021 No.12614004 >>12613979Ancestral spirits told me that addition and multiplication arent the only meaningful operations
 >> Anonymous Fri Jan 22 11:26:57 2021 No.12614091 File: 112 KB, 750x750, aw0va.jpg [View same] [iqdb] [saucenao] [google] [report] Higher homotopical structures https://sites.google.com/view/hhs2021-opening/homeInterviews about maths and life and what have you https://www.muramatik.com/math-life-balance/ & https://www.youtube.com/channel/UCYRR0SgbYH59htIHkwTbqMw>>12614004You have a good bloodline, my friend. I can see a hint of Atlantean origin.
 >> Anonymous Fri Jan 22 11:36:54 2021 No.12614137 File: 86 KB, 640x541, mg.jpg [View same] [iqdb] [saucenao] [google] [report] >>12614091Thanks for the youtube link bitch. Do you have good heritage or do you look like a mongol?
 >> Anonymous Fri Jan 22 11:38:07 2021 No.12614143 >>12614137wow me on the right
 >> Anonymous Fri Jan 22 12:03:31 2021 No.12614239 >>12614137right
 >> Anonymous Fri Jan 22 12:10:51 2021 No.12614264 >>12611517no Fourier analysis for you
 >> Anonymous Fri Jan 22 12:22:11 2021 No.12614302 >>12614264Multimorph 4167
 >> Anonymous Fri Jan 22 12:23:39 2021 No.12614305 >>12614302>>12614137>>12614143Clamped, vaccinated, circumcised, halogenated
 >> Anonymous Fri Jan 22 12:24:59 2021 No.12614310 Chapter 11 Thirty spokes are joined together in a wheel, but it is the center hole that allows the wheel to function. We mold clay into a pot, but it is the emptiness inside that makes the vessel useful. We fashion wood for a house, but it is the emptiness inside that makes it livable. We work with the substantial, but the emptiness is what we use. Alan Watts once said in an object there is inside and outside. But what about klein bottles? Are they just like a piece of paper?
 >> Anonymous Fri Jan 22 12:26:05 2021 No.12614315 But pieces of paper have edges and kleine has keine
 >> Anonymous Fri Jan 22 12:26:44 2021 No.12614319 File: 400 KB, 699x922, siis omg.jpg [View same] [iqdb] [saucenao] [google] [report] >>12614137No problem, my friend. I think I have fairly good genetics, no mongol face or anything like that. That's like tooooooootally me on the right uwu <3
 >> Anonymous Fri Jan 22 12:27:58 2021 No.12614325 >>12614319Clamped.
 >> Anonymous Fri Jan 22 12:46:26 2021 No.12614395 >>12614325based, redpilled, keyed, schway
 >> Anonymous Fri Jan 22 12:51:25 2021 No.12614420 Is Vladimir Zorich's Mathematical Analysis a good book? I heard it has a lot of application for an Analysis textbook, so I am quite tempted to switch into it.
 >> Anonymous Fri Jan 22 12:52:13 2021 No.12614424 >>12614420Clamped.
 >> Anonymous Fri Jan 22 13:16:24 2021 No.12614536 Got an optimization problem for you guys:I want to find the best armor combo to use in Dark Souls 3. There's four slots (chest, head, legs, gloves), and each piece of armor has an armor value and a weight value. You cannot wear two helmets, or two sets of gloves at the same time. You want to maximize armor while not going above a weight limit. How would you choose the best set?>inb4 g2/g/This question is not about the discussion of gaming keyboards or graphics card companies so /g/ would be clueless.
 >> Anonymous Fri Jan 22 13:20:33 2021 No.12614555 What does a course in analysis entail? I have a book called Introductory Real Analysis by kolmogorov but its basically just random math bits to define measure theory then define integrals. Feels kinda pointlessIs regular analysis just integrals or wut I relly dont know
 >> Anonymous Fri Jan 22 13:58:07 2021 No.12614737 File: 126 KB, 1920x1541, fad.jpg [View same] [iqdb] [saucenao] [google] [report] >a tensor is an algebraic object that describes a relationship between sets of algebraic objects related to a vector space. Objects that tensors may map between include vectors and scalars, and even other tensors.what does this even mean? who the fuck comes up with this cryptic shit?
 >> Anonymous Fri Jan 22 14:18:57 2021 No.12614868 >>12614737it's a useless sentence that one puts as an introduction for the sake of introductionjust scroll down in whatever you are reading
 >> Anonymous Fri Jan 22 15:39:12 2021 No.12615175 File: 56 KB, 720x410, 190214100031_1_900x600.jpg [View same] [iqdb] [saucenao] [google] [report] how do 'you' read math books /mg/?
 >> Anonymous Fri Jan 22 15:40:26 2021 No.12615182 How do ‘you’ get a cute gf (male) /mg/?
 >> Anonymous Fri Jan 22 15:49:05 2021 No.12615206 how do i become a tranny girl
 >> Anonymous Fri Jan 22 15:51:14 2021 No.12615211 >>12614536Linear programming could be used but it's simpler to look at all possible combinations and eliminate the ones that exceed the limit.
 >> Anonymous Fri Jan 22 15:55:09 2021 No.12615225 If you take the infinite integer plane lattice $\mathbb{Z}^{2}$ and draw as many lines connecting vertices to other vertices as you like, including intersections of drawn lines with other lines as vertices, can you construct an intersection at every point in $\mathbb{Q}^{2}$?
 >> Anonymous Fri Jan 22 16:01:41 2021 No.12615254 >>12606383>A in math class>thinks he's good in mathkek, maths is about understanding and it's fair to assume when one understands math he'll be impressed and like it, you can get A's without even knowing you're studying maths.
 >> Anonymous Fri Jan 22 16:23:10 2021 No.12615362 >>12615182lurk /soc/
 >> Anonymous Fri Jan 22 16:23:26 2021 No.12615363 >>12614536Knapsack problem
 >> Anonymous Fri Jan 22 16:25:22 2021 No.12615370 File: 2.02 MB, 330x275, 1611287680959.gif [View same] [iqdb] [saucenao] [google] [report] Professional retard here, how the fuck do I learn calculus? I got an A in precalc but then corona hit and we switched to online for calc 1. I passed it through bullshit but understood none of it. Now Im retaking calc 2 because I couldnt bullshit a high enough grade the first time and Im still completely lost, dont get integrals or u substitution or any of that, can only make some sense of graph related problems. What the hell do I do?
 >> Anonymous Fri Jan 22 16:27:14 2021 No.12615381 >>12615370Practice. Your goal should be to have so much confidence in your knowledge that you can just google random problem and solve them without your hand being held. Doing every exercise in the textbook is a good place to start.
 >> Anonymous Fri Jan 22 16:27:24 2021 No.12615382 File: 55 KB, 600x719, 1268891287892.jpg [View same] [iqdb] [saucenao] [google] [report] >>12615370Don't listen to Stalin, there are limits in calc. https://www.youtube.com/watch?v=i83cVs03EE0
 >> Anonymous Fri Jan 22 16:35:12 2021 No.12615414 >>12607505Sauce for the first line.
 >> Anonymous Fri Jan 22 16:40:22 2021 No.12615441 >>12608293it's simply a relation defined from {(0,0),(0,1),(1,0),(1,1)} to {0,1}the problem leaves the actual mapping open to interpretation, so the problem is unsolvable but there are 2 possible solutions, so it's a 50-50.QED
 >> Anonymous Fri Jan 22 16:41:24 2021 No.12615444 >>12608598>cs majorjust learn to code brosuf give up the math larp
 >> Anonymous Fri Jan 22 16:41:23 2021 No.12615445 >>12613095The way the question was worded forces you to assume something or else it is completely unanswerable.It’s a compromise.
 >> Anonymous Fri Jan 22 16:41:27 2021 No.12615446 Dunno if I'm the only one to find this nifty, but I genuinely like to interpret [eqn]\int_{\gamma} \mathrm{d}z\, f(z)[/eqn]as [eqn]\int_{\gamma} \mathrm{d}\begin{pmatrix} x&-y\\y&x\end{pmatrix}\, \vec{f}(\vec{z})\text{, with } \vec{z} = \begin{pmatrix} x\\y\end{pmatrix},\vec{f}(\vec{z}) = \begin{pmatrix} \Re (f(x+iy))\\\Im(f(x+iy))\end{pmatrix}[/eqn]You can make it fully consistent by instead making f,z matrices, ofc, but this mixed style is more compact and yields no redundant equations.
 >> Anonymous Fri Jan 22 16:44:37 2021 No.12615457 >>12615175I have a paint application open and I prove every theorem and do every problem. If I get stuck for too long I'll drop the book usually going to an easier book in the subject I failed at and come back later.
 >> Anonymous Fri Jan 22 16:45:28 2021 No.12615461 >>12613821School isn't about teaching kids to be critical thinkers.
 >> Anonymous Fri Jan 22 16:45:51 2021 No.12615463 >>12615211>>12615363Thanks bros, I can dig around from here. I did some optimization and such in college, but I've been out for years now and had no idea where to start with this one.
 >> Anonymous Fri Jan 22 16:49:45 2021 No.12615484 >>12615381Will try, already picked up a textbook>>12615382Banger
 >> Anonymous Fri Jan 22 16:58:12 2021 No.12615504 >>12615445>t. moronThe answer is 12 days
 >> Anonymous Fri Jan 22 17:06:05 2021 No.12615531 File: 117 KB, 1280x720, awbbh.jpg [View same] [iqdb] [saucenao] [google] [report] >>12615484Yes. I have heard nothing good about Stalin vs Martians except that it has a banger soundtrack, the idea is great and that gif of Stalin dancing is awesome.>>12615175Using my eyes. Then I fall asleep because reading makes me tired.>>12615225I think it should be sufficient to show that you can get $(p, q)$ for any $p, q \in \mathbb{Q}, 0 < p, q < 1$ as such intersections. Then you can translate the line to get all the rest. Try lines that pass through $(0, 0), (p, q)$ and $(p, q), (1, 0)$.>>12615182I don't know.>>12615206Take your pills.
 >> Anonymous Fri Jan 22 17:15:06 2021 No.12615559 >>12615225>>12615531It may be even easier to construct two distinct lines that also intersect the integer lattice left and right of the point, but that's my gut.
 >> Anonymous Fri Jan 22 17:20:31 2021 No.12615580 >>12615531post face
 >> Anonymous Fri Jan 22 17:28:25 2021 No.12615607 I like math but I'm bad at it, what do?
 >> Anonymous Fri Jan 22 17:29:21 2021 No.12615611 File: 231 KB, 1920x1080, uiopl.jpg [View same] [iqdb] [saucenao] [google] [report] >>12615559You mean like taking any rational pair instead of something inside that square of mine? That would at least be quicker. Did I interpret your idea correctly?>>12615580I don't think I should. I have already ruined a few threads with one photo. I don't want to ruin more with another.>>12615607Git gud scrub.
 >> Anonymous Fri Jan 22 17:29:29 2021 No.12615612 [/itex]
 >> Anonymous Fri Jan 22 17:33:00 2021 No.12615620 >>12615611Yeah. Come to think of it, if you affix a point like you did (the origin) you are already done. Cause then you already found infinitely many lines intersecting (p,q) by means of translation.
 >> Anonymous Fri Jan 22 17:34:32 2021 No.12615625 File: 56 KB, 300x647, solaire-of-astora.jpg [View same] [iqdb] [saucenao] [google] [report] >>12615611>Git gud scrubGot platinum trophy for the 3 souls and I'm pretty good at PvPing, dunno what else I can do anonAlso, I just want to get good at math
 >> Anonymous Fri Jan 22 17:37:41 2021 No.12615635 >>12605661Pre-calculus is generally gonna be trigonometry.Wouldn't skip unless you're very familiar. Large sections of calculus are based on unit circle manipulation and identities. I did know a guy who made it through calc 1 without it but he had to teach himself trig along the way and worked very hard at it.If you aren't a very self motivated person or you are taking other heavy science or math classes simultaneously I would not recommend but if your other classes are humanities or something you could likely do it without much issue if you found a decent tutor through your University.
 >> Anonymous Fri Jan 22 17:39:19 2021 No.12615644 File: 168 KB, 1920x1080, 8f7if8.jpg [View same] [iqdb] [saucenao] [google] [report] >>12615620Yeah because any (p, q) is (m+p', n+q') for some integers m, n and some rationals p', q' strictly between 0 and 1. No need to care about m and n.>>12615625I don't know. Self diagnose impostor syndrome and then you can pretend you are good but insecure. That's my style. Fake it till you make it.
 >> Anonymous Fri Jan 22 17:41:12 2021 No.12615649 >>12615414>The proof for this is trivial and left as an exercise for the reader.
 >> Anonymous Fri Jan 22 17:42:15 2021 No.12615653 >>12615446Based
 >> Anonymous Fri Jan 22 17:43:11 2021 No.12615654 >>12615644>impostor syndromei don't understand this one bit. how could anyone feel like an imposter unless they are one?
 >> Anonymous Fri Jan 22 17:43:22 2021 No.12615656 >>12615611you know you want to <3
 >> Anonymous Fri Jan 22 17:46:57 2021 No.12615662 File: 20 KB, 300x245, monadAlgebras.png [View same] [iqdb] [saucenao] [google] [report] What is the most high iq introduction to abstract algebra book you know? The more esoteric, the better.
 >> Anonymous Fri Jan 22 17:47:55 2021 No.12615666 >>12615662Mr P. Pseud's big book of abstract algebra pseuds
 >> Anonymous Fri Jan 22 17:50:57 2021 No.12615678 >>12615666Based pseud trips
 >> Anonymous Fri Jan 22 17:55:04 2021 No.12615693 >>12615653I think the canonical isomorphisms $\mathbb{C}\mapsto\mathbb{R}^{2(\times 2)}$ have a certain beauty to them.
 >> Anonymous Fri Jan 22 17:55:37 2021 No.12615697 >>12615654I don't know. I'm more of a Dunning-Kruger myself.>>12615656Please don't tempt me. I bought wine and it's getting me.
 >> Anonymous Fri Jan 22 17:59:32 2021 No.12615719 >>12615504Explain
 >> Anonymous Fri Jan 22 18:00:37 2021 No.12615723 >>12615484Which one
 >> Anonymous Fri Jan 22 18:07:12 2021 No.12615740 >>12615719Suppose the distance were x miles. Then the speed of the ship plus the speed of the stream equals x/2 miles per day, and the speed of the ship minus the speed of the stream equals x/3 miles per day. The first equation minus the second equation yields twice the speed of the stream equals x/6 miles per day, so the speed of the stream is x/12 miles per day. A raft travels at the speed of the stream, so to travel x miles at x/12 miles per day would take 12 days. Of course, anyone who's not a retard could figure that out.
 >> Anonymous Fri Jan 22 18:09:35 2021 No.12615752 File: 15 KB, 700x700, Image0.png [View same] [iqdb] [saucenao] [google] [report] >>12609665>>12613031Alright, here's my proof of why it's impossible:Lemma 0: The congruent parts cannot be a 2x4 rectangle.The proof of this is trivial.Lemma 1: The congruent parts cannot have a dimension of 5 (as in, a part either occupies both columns A and E or occupies both rows 0 and 4).The proof of this is as follows: suppose the congruent parts have a dimension of 5. Without loss of generality, suppose one of the congruent parts occupied both columns A and E. Then the other two congruent parts cannot occupy both rows 0 and 4, as they would have to cross the first part, so they too must occupy both columns A and E. When the grid is cut, it is clear that there is a top part, a middle part, and a bottom part. Without loss of generality, suppose the removed square is below the middle part. If any of the middle part occupied row 4, it would be impossible for the top part to be above the middle part, so row 4 must be completely occupied by the top part. Then, in order to be congruent, the middle part occupies a complete row by itself. Call this row X. The space between row 4 and row X must be occupied by the three squares of the top part not in row 4 and, in order to maintain congruence between the top and middle part, either zero or three squares of the middle part not in row X. So the space must be occupied by either three or six squares. However, the space between row 4 and row X must be a multiple of five. Then it is a contradiction, and the congruent parts cannot have a dimension of 5.
 >> Anonymous Fri Jan 22 18:11:10 2021 No.12615759 >>12615461I hope you think that's a bad thing
 >> Anonymous Fri Jan 22 18:15:31 2021 No.12615775 File: 15 KB, 700x700, Image1.png [View same] [iqdb] [saucenao] [google] [report] >>12615752Now for the actual proof:There are four corners of the 5x5 grid: A1, A4, E1, and E4. By Lemma 1, a part cannot occupy more than one corner. Then three corners must be occupied by three different parts, and the fourth corner must be the square removed. Without loss of generality, the squares may be coloured like the picture, with red, green, and blue representing the squares occupied by the different parts, and the black square denoting the square removed.
 >> Anonymous Fri Jan 22 18:17:22 2021 No.12615785 >>12615697pwetty pwease :3
 >> Anonymous Fri Jan 22 18:18:40 2021 No.12615788 File: 15 KB, 700x700, Image2.png [View same] [iqdb] [saucenao] [google] [report] >>12615775By Lemma 1, row 0 cannot be occupied by either red or blue, so it must be occupied solely by green. Similarly, column E must be occupied solely by blue.
 >> Anonymous Fri Jan 22 18:20:05 2021 No.12615790 >>12615697We'll just pretend you've never posted it. It's going to be ok.
 >> Anonymous Fri Jan 22 18:30:14 2021 No.12615823 File: 15 KB, 700x700, Image3.png [View same] [iqdb] [saucenao] [google] [report] >>12615788Because both green and blue contain a straight line of four squares, red must too contain a straight line of four squares. Without loss of generality, suppose this straight line of four squares is horizontal. This straight line must occupy columns A through D of one of the rows from 1 to 4. It cannot be row 1, as that would prevent green from occupying eight squares. It cannot be row 2, as green would then have to be a 2x4 rectangle, which by Lemma 0, is impossible. Suppose it were row 3. By Lemma 0, the three remaining red squares cannot be in row 4, so there must be a red square in row 2. Then there are red squares on both sides of the straight line of four red squares. For green to be congruent, there must be green squares on both sides of the straight line of four green squares. However, because the straight line of four green squares is on the bottom row, and it is impossible to make another straight line of four green squares (excluding the one that will make green a 2x4 rectangle), it is impossible for green squares to be on both sides of the straight line. So it cannot be row 3.
 >> Anonymous Fri Jan 22 18:34:39 2021 No.12615833 redpill me on spivak
 >> Anonymous Fri Jan 22 18:39:59 2021 No.12615852 File: 15 KB, 700x700, Image4.png [View same] [iqdb] [saucenao] [google] [report] >>12615823Suppose it were row 4. By Lemma 1, A1, A2, and A3 must be occupied by red or green. In order for red and green to be congruent, D1, D2, and D3 must be occupied by the opposite color of A3, A2, and A1 respectively. However, if D1, D2, and D3 are occupied by red and green, then blue cannot occupy the necessary eight squares. Then it cannot be row 4.Therefore, it is impossible to remove a square from a 5x5 grid and cut the remaining squares into three congruent parts. QED.
 >> Anonymous Fri Jan 22 18:44:54 2021 No.12615870
 >> Anonymous Fri Jan 22 18:52:53 2021 No.12615897 >>12615740>equals x/2 miles per dayMiles are never mentioned in the original question, only how long it takes to get there each way. You're assuming things that aren't in the original question too.Opinion discarded.
 >> Anonymous Fri Jan 22 18:54:53 2021 No.12615903 >>12615897The original question implies a distance, and any distance can be converted to miles. Kill yourself you retarded nigger.
 >> Anonymous Fri Jan 22 18:55:45 2021 No.12615905 >>12615903Yes, and you said it is two miles per day.It only mentions that it takes two days.Miles do not equal days bro, you got the wrong conversion tables
 >> Anonymous Fri Jan 22 18:59:12 2021 No.12615910 >>12615662Lang
 >> Anonymous Fri Jan 22 18:59:54 2021 No.12615911 >>12615662Jacobson Basic Algebra I&II
 >> Anonymous Fri Jan 22 19:07:33 2021 No.12615926 >>12615905You retarded mother fucker. I said x/2 miles per day. X over fucking 2. You mother fucking retard. Please do everyone a favor and kill yourself.
 >> Anonymous Fri Jan 22 19:09:05 2021 No.12615932 >>12615926Guess what brother, x divided by 2 just equals x/2Congratulations on pulling 12 out of your ass
 >> Anonymous Fri Jan 22 19:11:34 2021 No.12615936 If you are given a shape, like triangle vertices for instance, is it possible if given work = 3 to find a vector field that would make that statement true?
 >> Anonymous Fri Jan 22 19:17:40 2021 No.12615958 >>12615932Kill yourself
 >> Anonymous Fri Jan 22 19:19:53 2021 No.12615967 >>12615833Like, the calculus book?
 >> Anonymous Fri Jan 22 19:21:00 2021 No.12615973 >>12615958X/2 Minus X/3 is equal 1/6xNot 12lmao you can't even do basic algebra
 >> Anonymous Fri Jan 22 19:49:52 2021 No.12616051 >>12615936What?
 >> Anonymous Fri Jan 22 19:53:04 2021 No.12616065 >>12613251No x x x x x = x^5
 >> Anonymous Fri Jan 22 19:57:57 2021 No.12616088 >contact techer>he never repliesbruh
 >> Anonymous Fri Jan 22 19:58:12 2021 No.12616090 >>12616051It's a Gilbert Strang calculus problem where he asks you to find the field around a unit square in which work is equal to 4
 >> Anonymous Fri Jan 22 19:59:40 2021 No.12616096   File: 206 KB, 913x753, IMG_20210123_002644.jpg [View same] [iqdb] [saucenao] [google] [report] >>12615785>>12615790I'm gonna regrte´et this in the morning. But here you go. All you will get.
 >> Anonymous Fri Jan 22 20:08:54 2021 No.12616123 >>12615752lemma1 assumes the 3 congruent pieces must be connected
 >> Anonymous Fri Jan 22 20:16:05 2021 No.12616133 Pretty.
 >> Anonymous Fri Jan 22 20:24:41 2021 No.12616150   >>12615580 I'd like to see her feet first
 >> Anonymous Fri Jan 22 20:29:28 2021 No.12616163 >>12616096Cute hand
 >> Anonymous Fri Jan 22 20:56:07 2021 No.12616228   >>12616133>>12616163I missed? Please send
 >> Anonymous Fri Jan 22 21:01:59 2021 No.12616252 >>12616123Is that not implied from the question?
 >> Anonymous Fri Jan 22 21:04:56 2021 No.12616264 >>12616228If she deleted it I'm not comfortable sharing without permission. Sorry
 >> Anonymous Fri Jan 22 21:09:47 2021 No.12616277   File: 206 KB, 913x753, anitranny.jpg [View same] [iqdb] [saucenao] [google] [report] >>12616228No time stamp but he posted this.
 >> Anonymous Fri Jan 22 21:11:20 2021 No.12616284 >>12616277>heWatch it buddy
 >> Anonymous Fri Jan 22 21:11:21 2021 No.12616285 >>12616277>ifyouonlyknewhowbadthingsreallyare.jpg
 >> Anonymous Fri Jan 22 21:13:41 2021 No.12616292
 >> Anonymous Fri Jan 22 21:16:49 2021 No.12616305   >>12616264>>12616277Thanks, I'll delete my comments now then. Don't leave pic for too long, it is the least we do in return
 >> Anonymous Fri Jan 22 21:31:59 2021 No.12616335 what are some good ODE books for us mathchads
 >> Anonymous Fri Jan 22 21:35:46 2021 No.12616346 >>12616335I thin Arnold's book is usually considered a good one.
 >> Anonymous Fri Jan 22 21:36:46 2021 No.12616348 Can you reach any $\mathbb{Q}$ by adding/subtracting an arbitrarily large but finite amount of elements from the set {1 and $\sqrt{2}$}? If not, is there any finite set that would let you do so?
 >> Anonymous Fri Jan 22 21:40:42 2021 No.12616359 >>12616348You can't reach any rational number besides the integers that way.
 >> Anonymous Fri Jan 22 21:43:39 2021 No.12616364 >>12616348No finite set of rationals will give you that.Rationals form a moduel over integers with no finite free-basis.
 >> Anonymous Fri Jan 22 22:00:37 2021 No.12616414 File: 34 KB, 480x630, a3elg.jpg [View same] [iqdb] [saucenao] [google] [report] >>12616348You need to habe 1/p for every prime and then require it to be closed under multiplication and addtuon.
 >> Anonymous Fri Jan 22 22:00:44 2021 No.12616415 >>12615723Calculus Early Transcendentals 4th Ed. Rogawksi
 >> Anonymous Fri Jan 22 22:48:21 2021 No.12616545 File: 67 KB, 500x474, 1610393918668.jpg [View same] [iqdb] [saucenao] [google] [report] I'll be honest here, all this blogposting that has been happening in the last few threads is extremely annoying. I don't really care about your personal life and what stuff you're into. I'm just here to talk about mathematics like everyone else. So please, have some self-awareness and restrain the subject of your posts to be strictly about math. No offence, but no one other than a few underages or trolls seeking attention care if you're trans or if you're new to college or whatever excuse you people have to start blogposting. Problem is that those underages and trolls have a loud voice and it gets even louder when someone gives them a reason to shitpost and that's exactly what you're doing.
 >> Anonymous Fri Jan 22 22:50:09 2021 No.12616552 What's the intuition behind studying exact sequences in abstract algebra? I am rather unfamiliar with algebra so I can understand the definition and apply it to prove some toy statements but I don't have a good understanding of why they're useful objects to study.
 >> Anonymous Fri Jan 22 22:57:32 2021 No.12616575 >>12616545>personal lifeThe vast majority of what has been posted was either math or stuff about the mathematical life. We also discuss aspects of being a math student or researcher in /mg/, it has never been strictly pure mathematics. If you really thought like that, you wouldn't even post unrelated picutres like the anime pic you sent, you're just annoyed because it rubs you the wrong way. Just ignore and scroll.
 >> Anonymous Fri Jan 22 23:08:21 2021 No.12616600 File: 29 KB, 540x540, 1610035682330.jpg [View same] [iqdb] [saucenao] [google] [report] >>12616575Not really no, most of those posts are a mix of math with blogposting. I could post dozens of them here from the last two threads and in this one they've gone as far as to post a picture of themselves to get attention. >We also discuss aspects of being a math student or researcher in /mg/, it has never been strictly pure mathematics.That's welcome, what's not welcome is when your post is 70% blogposting and 30% actual mathematics/math life/research life.>If you really thought like that, you wouldn't even post unrelated picutres like the anime pic you sentLol>you're just annoyed because it rubs you the wrong way.Oh, and how so? I literally didn't get what you tried to imply here.>Just ignore and scroll.Great way to excuse criticism. I guess all off topic posts should be allowed now, after all one just needs to ignore and scroll, am I right?
 >> Anonymous Fri Jan 22 23:26:59 2021 No.12616640 >>12616600So by "blogposting" you mean the pictures and sexual-related stuff? Come on anon, wasn't much and some were even funny. A tiny bit of slightly off-topic here and there is ok imo, it's not a problem if doesn't become spam.>LolIt's not a joke, some people have argued just like you're doing but regarding anime. Sometimes it's not even just pictures. Why should they tolerate it? Strictly speaking, it has nothing to do with math.>Oh, and how so? I literally didn't get what you tried to imply here.It's a non-constructive existence claim, you being annoyed is enough proof. >Great way to excuse criticism. I guess...I addressed eveything you said, and you're snowballing. When newbies post bs they could answer by thinking for 3 minutes or googling I also get annoyed, but it's part of the ride, I just ignore and scroll.
 >> Anonymous Sat Jan 23 01:26:37 2021 No.12616895 File: 226 KB, 827x1024, Carter-827x1024.jpg [View same] [iqdb] [saucenao] [google] [report] how long did it take you to feel like you were "good" at math? i'm a university graduate and an amateur mathematician but i have never felt very good at math, even though i'm likely better then the average person.
 >> Anonymous Sat Jan 23 01:47:59 2021 No.12616942 What's a good masters program with a math/cs undergrad?
 >> Anonymous Sat Jan 23 01:56:37 2021 No.12616971 >>12616942Why in God's good name would you get a master's degree?
 >> Anonymous Sat Jan 23 02:08:52 2021 No.12617016 >>12616971I wanna work as a code monkey for a couple years and then do a career change to something else via a masters.
 >> Anonymous Sat Jan 23 02:17:16 2021 No.12617034 File: 33 KB, 720x541, FB_IMG_1611151914716.jpg [View same] [iqdb] [saucenao] [google] [report] Take the linear algebra pill
 >> Anonymous Sat Jan 23 02:51:17 2021 No.12617134 >>12612035wrong about what? You just defined two functions, and G doesn't even need to be a function on x.
 >> Anonymous Sat Jan 23 02:53:44 2021 No.12617142 >>12611640keked hard at this, based and alternate-pilled
 >> Anonymous Sat Jan 23 03:07:55 2021 No.12617181 >>12612146>>12612035shit negro what are you doing
 >> Anonymous Sat Jan 23 03:17:25 2021 No.12617206 >>12616895Define "good at math". Do you mean writing proofs or just rote monkey calculations? I felt good at writing proofs after doing about 1000 of them.
 >> Anonymous Sat Jan 23 03:40:11 2021 No.12617256 >>12605562do post, if you find them!
 >> Anonymous Sat Jan 23 04:23:49 2021 No.12617337 File: 85 KB, 715x715, 1 (156).jpg [View same] [iqdb] [saucenao] [google] [report] going back to math, i really want to fuck a tranny guys
 >> Anonymous Sat Jan 23 04:55:21 2021 No.12617407 >>12614137There are two types of tranniesi) faggotsii) faggotsYou are a faggot
 >> Anonymous Sat Jan 23 05:03:03 2021 No.12617428 File: 124 KB, 750x900, awhxi.jpg [View same] [iqdb] [saucenao] [google] [report] >>12616552OK, so I can give you an example that will not be a toy example. It's known as the Universal Coefficient Theorem. I don't know how much you know about homology, so I'll give you the basics first. If it sparks your interest, I recommend Rotman's book on algebraic topology.First of all, a chain complex of $R$-modules would be a sequence of modules and their homomorphisms $C_* = \cdots \to C_{n+1} \xrightarrow{\partial_{n+1}} C_n \xrightarrow{\partial_n} C_{n-1} \to \cdots$, one for each integer, such that $\partial_n \circ \partial_{n+1} = 0$ for all indices. This is the same thing as $\text{im} (\partial_{n+1}) \le \ker(\partial_n)$, so we may loo at the homology of this complex, and it is given by $H_n(C_*) = \ker(\partial_n)/ \text{im}(\partial_{n+1})$, for any integer n. Notice that vanishing homology for some n means exactness at $C_n$ in the complex. Let's then assume we are interested in the homology of some space $X$, and that $C_* = C_*(X; \mathbb{Z})$ is for example the singular chain complex (and now the ring is the integers). The groups in the complex vanish for negative indices, and for non-negatives we obtain $H_n(X; \mathbb{Z}) = H_n(C_*)$, the nth (integral) singular homology group of $X$. So far so good, no need for exact sequences.
 >> Anonymous Sat Jan 23 05:04:05 2021 No.12617430 File: 46 KB, 800x600, wasted.jpg [View same] [iqdb] [saucenao] [google] [report] >>12617428Next, we ask what happens if we tensor the complex with some abelian group $A$ (over the integers). We obtain the complex $C_*(X; A) = \cdots \to C_{n+1}\otimes A \xrightarrow{\partial_{n+1} \otimes 1_A} C_n\otimes A \xrightarrow{\partial_n \otimes 1_A} C_{n-1}\otimes A \to \cdots$, the homology of which gives us $H_*(X; A)$, the singular homology of $X$ with coefficients in $A$. This is where many who see this the first time would assume "oh but $H_n(X; A) \cong H_n(X; \mathbb{Z}) \otimes A$", which is not true in general. Instead, there is an exact sequence $0 \to H_n(X; \mathbb{Z})\otimes A \to H(X; A) \to \text{Tor}(H_{n-1}(X; \mathbb{Z}), A) \to 0$ for every $n\ge 0$ ($H_{-1}(X; \mathbb{Z}) = 0$). Even better, yet not completely perfect: this sequence is split exact: $H_n(X; A) \cong H_n(X; \mathbb{Z})\otimes A \oplus \text{Tor}(H_{n-1}(X; \mathbb{Z}), A)$, but not naturally (for example Dylan Wilson's answer in https://math.stackexchange.com/questions/33685/what-does-splitting-naturally-mean-in-the-universal-coefficients-theorem).Some immediate things that follow from the UCT:(1) If the group $A$ is torsion-free, then $Tor(-, A)=0$, and so $H_n(X; A) \cong H(X; \mathbb{Z}) \otimes A$.(2) If $H_n(X; \mathbb{Z}) \otimes A = 0$, then $H_n(X; A) \cong \text{Tor}(H_{n-1}(X; \mathbb{Z}, A)$.(3) $H_0(X; A) \cong H_0(X; \mathbb{Z}) \otimes A$.If now $H_n(X; \mathbb{Z})$ is all torsion, or even a finite group, then it vanishes when tensored with $\mathbb{Q}$, and (2) applies. Furthermore, the rationals are torsion-free, so (1) applies and we get $H_n(X; \mathbb{Q}) = 0$. Many such cases!Reminder to get WASTED!
 >> Anonymous Sat Jan 23 05:06:42 2021 No.12617435 >>12617407yes i am a faggot tranny UwU can you fuck my slutty bussy now?
 >> Anonymous Sat Jan 23 05:19:48 2021 No.12617460 File: 206 KB, 842x589, BEFT.jpg [View same] [iqdb] [saucenao] [google] [report] >>12616895"Good" compared to the average person was when I got medals in math olympiads (very, very far from IMO level, but it was something) during early high school, and by that time I noticed that I could do it because I had a combination of a good math teacher in my last elementary school year who'd give lots of exercises every class, and new performance demands at home.But good at real mathematics... I did fairly better than the average math undergrad, but that just means having a minimum of math maturity. At PhD courses I'm being very close to average (probably below), and I have no idea how I'd do on research, probably bad at first.>>12617016Why would you do that?>>12604515>He's a big guy, I wouldn't compare myself to him.I wouldn't either, not in that sense.
 >> Anonymous Sat Jan 23 05:26:39 2021 No.12617467 >>12617134Just went through the section where you factor out functions into 2 separate equations, thought that’s what OP was referring to.>>12617181Up until this school year started, I hadn’t done math in a long time, and while I got decent grades & good test scores, I didn’t really try to learn the material back then so it didn’t stick with me.
 >> Anonymous Sat Jan 23 05:32:33 2021 No.12617474 File: 75 KB, 1170x461, ad0sn.jpg [View same] [iqdb] [saucenao] [google] [report] >>12617460I really liked the video of Knuth. If you are interested, there's this new channel https://www.youtube.com/channel/UCYRR0SgbYH59htIHkwTbqMw. I haven't watched the video yet, so I can't comment on that, but it could be your cup of tea.
 >> Anonymous Sat Jan 23 06:21:25 2021 No.12617523 If I have an algebraic projective curve $C$ over a field $k$, $\tilde{C}$ one of its affine parts/components (if that's how it's callled), $f, g\in k[\tilde{C}]$, then is it true that $\text{div}(f^*/g^*) \ge 0 \, \iff \, f/g \in k[\tilde{C}]$ ?Actually I've only seen divisors being defined for elements of $k(C)$ and $f^*/g^*$ wouldn't be one (unless it's an element of $k$), but that can be understood in terms of orders of zeros and poles.
 >> Anonymous Sat Jan 23 07:16:14 2021 No.12617638 Has anyone that old meme with the 1,i,0 right triangle?I thought it was just a meme but then a read about circles in projective space intersecting at +-i:1:0Also I'm trying to visualize what could that possibly mean geometrically, apart from satisfying the equations
 >> Anonymous Sat Jan 23 07:31:09 2021 No.12617681 >>12615662Bourbaki Algebra Ch 1-3 for groups, rings and modules. However you can look at the Stacks project chapter 9 for a good overview of fields, it's actually quite good.
 >> Anonymous Sat Jan 23 09:12:50 2021 No.12617907 >>12617428>>12617430Thanks for the useless face pic
 >> Anonymous Sat Jan 23 09:42:04 2021 No.12618006 File: 481 KB, 895x671, iq.png [View same] [iqdb] [saucenao] [google] [report] >>12617907>make a time stamp but forget to use it>use a pen to keep your hair under control>mess up the lighting an make everything look flat and eerie>look like a troll because you haven't washed your hair for two days>wake up to find out what you have doneAt least I covered my face and deleted the post.
 >> Anonymous Sat Jan 23 11:32:23 2021 No.12618380 >>12606654>I'm not sure why it isn't more widely used in undergrad.Probably just exercise count. The first exercise is >1.1. Locate a discussion of Russell’s paradox, and understand itand is one of 6 problems in its subchapterWhich in usual undergrad books comes near the end of a list of 20-30 exercises.The problem being that each subchapter performs the function that a chapter in something like beachy would. The difficulty in algebra comes from understanding the concepts, theorems and proofs and being able to supply proofs and the calculation is usually straightforward. For example in one experement most math phds spent hours trying to solve a given geometry problem taken from a middleschool textbook. Remember at one point most problems were research problems and the less the author gives the student to work with the harder the problem becomes. all in all taking a semester of algebra from an easy book and having more to background knowledge to read aluffi is easier than filling in everything that aluffi leaves out.Also, its still a bit ahead of it's time for teaching category theory to non-graduates
 >> Anonymous Sat Jan 23 11:50:37 2021 No.12618465 File: 72 KB, 878x878, 1 (182).jpg [View same] [iqdb] [saucenao] [google] [report] >>12606654>first text on abstract algebra>teaches category theoryhmmm i think i found the flaw
 >> Anonymous Sat Jan 23 12:03:43 2021 No.12618514 >Let $A$ be a nonempty set of real numbers which is bounded below. Let $-A$ be the set of all numbers $-x$ where $x \in A$. I need to show $\inf A = -\sup A$. I know there is an easier way to do this, but I want to see if my logic is correct:Let $\alpha = -sup A$. Then $-\alpha \geq -x \forall x \in A \implies \alpha \leq x \forall x \in A$. So $\alpha$ is a lower bound of $A$. Now I need to show this is the greatest lower bound. Let $\beta \in \mathbb{R}, \beta > \alpha$. Then $\beta > x, x \in A$. Hence $\beta$ is not a lower bound of $A$. Thus $\alpha = inf A \qed$
 >> Anonymous Sat Jan 23 12:05:18 2021 No.12618520 >>12618514I fucked up this post a bit, please tolerate my autism
 >> Anonymous Sat Jan 23 12:18:30 2021 No.12618576 File: 36 KB, 646x350, abnng.jpg [View same] [iqdb] [saucenao] [google] [report] >>12618514Your logic is correct but you need to work a bit on presentation. You have>Then $\beta > x, x\in A$and I know you mean some x in A, but I would interpret that as "for all x in A" if I had to grade your solution. Nothin' personnel, kid, but if you are to use quantifiers on x like that, you shouldn't leave x unquantified later. Add "for some" or use "$\exists x\in A: x < \beta$" instead!>>12618465Unironically this. First concepts from different areas, not only algebra, and then categories. Without examples, CT is total gibberish.
 >> Anonymous Sat Jan 23 12:20:53 2021 No.12618590 Haven't done math in a year after doing nothing but math for three years. Should I get back where I left or should I redo the basics?
 >> Anonymous Sat Jan 23 12:24:00 2021 No.12618607 >>12618590I'm exactly as you are. I finished my bachelor's in math and then stopped because my graduate degree is in a meme applied science field. I'm personally going over the basics (analysis, abstract algebra) to get my proof skills back and then plan on getting back to where I was.
 >> Anonymous Sat Jan 23 13:12:13 2021 No.12618854 Why are all videos explaining the euler maclaurin summation formula so dumb?It's like a bunch of midwits just read the wikipedia article and don't really understand what is going on.
 >> Anonymous Sat Jan 23 13:13:15 2021 No.12618863   File: 30 KB, 1145x137, maxmin_lagrange.jpg [View same] [iqdb] [saucenao] [google] [report] I dont see a stupid questions general but i need help on a calculus problem. you dont have to give me the answer but if someone could help me get started. its a max/min problem with lagrange multipliers. I can visualize the problem, its a square on the curve but what would that make the constraint equation? its some kind of multi-parabola looking thing.
 >> Anonymous Sat Jan 23 13:14:29 2021 No.12618870   >>12618863its a square on the curve of the surface of that equation which looks like an upward bowl, to clarify.
 >> Anonymous Sat Jan 23 13:15:03 2021 No.12618873 >>12618854>videosY I K E Sread a book brainlet
 >> Anonymous Sat Jan 23 13:22:38 2021 No.12618909 >>12618873Most books are pretty bad too desu.I have a better proof than anywhere I've seen that also allows for generalization.You can derive the bernoulli polynomials/numbers and the summation formula with remainder in less than a page using very basic principles/motivations.It only requires simple integration by parts, with the motivation of telescoping series.The bernoulli polynomials/numbers fall out effortlessly.
 >> Anonymous Sat Jan 23 13:25:54 2021 No.12618927   >>12618863OP here, maybe I can use x^1000 + y^1000 = 2 as the equation.
 >> Anonymous Sat Jan 23 14:40:31 2021 No.12619144 >>12618909I'll share it. I think people will appreciate the simplicity and hopefully make use of the idea.First natural thing to do: keep repeating integration by parts on the integral of 1*f.$\int\limits_{0}^{1}1*f(x)dx = \int\limits_{0}^{1}p_{0}(x)*f(x)dx \\ = \sum\limits_{m=0}^{M-1}(-1)^{m+1}[p_{m+1}(x)*f^{(m)}(x)]_{0}^{1}+ (-1)^M\int\limits_{0}^{1}p_{M}(x)*f^{(M)}(x)dx \\ where\ \ p'_{m+1}=p_{m}.$Ignoring the error and letting M = infinity gives you infinitely many constants of integration (one for each p_m, m>0) to freely choose.What would be a "convenient" choice for all of them?Wouldn't it be awesome if they were chosen so that if the formula was applied to [0,1] and added to the formula applied to [1,2] then there would be maximal cancellation for all derivatives of f at 1? (Telescoping)$Let\ P(x,t)= \sum\limits_{m=0}^{\infty}t^mp_m(x).\\P(x,0)=1\ and\ P_x=tP\ so\ P(x,t)=k(t)e^{xt}\ where\ k(0)=1.\\Telescoping\ at\ all\ derivatives\ of\ f\ would\ mean\ P(1,t)-P(0,t)=0.\\This\ can't\ happen\ since\ p_1(1)-p_1(0)=1\ no\ matter\ which\ constant\ of\ integration\ is\ chosen.\\The\ best\ that\ can\ be\ done\ is\ P(1,t)-P(0,t)=t.\\So\ k(t)*(e^t-1)=t,\ resulting\ in\ k(t)={t \over e^t-1}\ and\ P={te^{xt} \over e^t-1}.$The euler maclaurin summation formula and the generating function for bernoulli polynomials/numbers are obvious from here.I'll let you derive the "midpoint" method which has a much better error term.The trick for the midpoint method is to break [0,1] in half and use two alternating methods for the interval [0,1/2].P1 = k1(t)e^(xt) and P2 = k2(t)e^(xt).P1(1/2,t)-P2(0,t) = t and P2(1/2,t) - P1(0,t) = 0.
 >> Anonymous Sat Jan 23 14:43:58 2021 No.12619169 >>12619163>>12619163Please... Its cold...
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