/sci/ - Science & Math

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/mg/ - Math general Anonymous Mon Mar 26 22:03:01 2018 No.9622175 [Reply] [Original]

What are you learning, /mg/?

>>	Anonymous Mon Mar 26 22:19:45 2018 No.9622210 What are some applications of vector spaces which do not have a basis?

>>	Anonymous Mon Mar 26 22:22:35 2018 No.9622223 >>9622175 everything i should have in the last 2 months since my exams are next week

Anonymous Mon Mar 26 22:23:46 2018 No.9622226
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>want to keep working on first semester modern algebra homework
>can't because too fucking worried about my operations research grade
>professor assigned our second exam online last week
>exam was open book, open notes. instructions were to print, complete, scan, submit in a 2hr 15min period.
>finished on saturday morning (two days ago).
>received grades this afternoon
>0/100
>my 98.8% average dropped to a 64.5%.
>have no fucking clue what went wrong.
>there is no way I missed every single question on the exam
>either I submitted the wrong pdf (I don't think I did that, I remember double-checking) or I am suspected of cheating (which I didn't do).
>worst case scenario, it was a bug in our open source online homework platform
>I have fought against such bugs before, it rarely ends in my favor
>swear to fucking god I'll withrdraw from enrollment and join the navy if this doesn't end well. I am tired of playing the online student game as a resident student.
I have no fucking idea what I should do, short of talking to the prof during his office hours tomorrow. Should I talk to my advisor? He's respected in the department. Would he be able to help if this goes south?

>>	Anonymous Mon Mar 26 22:24:51 2018 No.9622234 >>9622210 Every vector space has a basis. On the other hand, not every module has a basis (i.e. not every module is free).

>>	Anonymous Mon Mar 26 22:25:06 2018 No.9622235 >>9622226 >asking 4chan for irl advice

>>	Anonymous Mon Mar 26 22:25:42 2018 No.9622239 >>9622234 He's a subhuman shitposter. Don't reply to him.

>>	Anonymous Mon Mar 26 22:28:03 2018 No.9622248 >>9622239 People like you are why sci sucks.

>>	Anonymous Mon Mar 26 22:28:30 2018 No.9622249 >>9622235 /mg/ is not the same as /b/, my dude. I've received solid advice from 4chan before.

>>	Anonymous Mon Mar 26 22:28:55 2018 No.9622250 >>9622248 no u

>>	Anonymous Mon Mar 26 22:30:30 2018 No.9622255 >>9622248 Lurk or read the archive before posting, idiot.

>>	Anonymous Mon Mar 26 22:31:46 2018 No.9622257 Theorem: >>9622248 Proof. >>9622255 >>9622250 QED.

>>	Anonymous Mon Mar 26 22:33:22 2018 No.9622262 >>9622257 ∎

>>	Anonymous Mon Mar 26 22:33:55 2018 No.9622264 >>9622226 Email the professor ASAP.

>>	Anonymous Mon Mar 26 22:36:26 2018 No.9622273 >>9622248 Don't reply to the spammer.

>>	Anonymous Mon Mar 26 22:37:06 2018 No.9622277 >>9622210 congesting /mg/ with pointless arguments

>>	Anonymous Mon Mar 26 22:39:10 2018 No.9622281 What are you learning, /mg/? not >Crucify the shitposter and repliers, /mg/

>>	Anonymous Mon Mar 26 22:39:47 2018 No.9622284 >>9622264 this especially if you can remember your answers, if even one is right, it means you hit a buggu

>>	Anonymous Mon Mar 26 22:42:05 2018 No.9622294 >>9622245 Yes I just barely passed my calc 1 class and am barely passing calc 2

>>	Anonymous Mon Mar 26 22:48:41 2018 No.9622312 >>9622234 >Every vector space has a basis. ZFC + ¬AC begs to differ.

>>	Anonymous Mon Mar 26 22:49:42 2018 No.9622314 >>9622234 >>9622312 Fugg I meant ZF + ¬AC lol

>>	Anonymous Mon Mar 26 22:51:02 2018 No.9622316 >>9622314 to be fair, ZFC + ¬AC also proves that some vector spaces don't have bases (:

>>	Anonymous Mon Mar 26 22:54:47 2018 No.9622327 >>9622316 Even in ZFC most vectorspaces don't have bases unless you assume they do

Anonymous Mon Mar 26 22:59:09 2018 No.9622340

>>9622294
One of the biggest sources of difficulty in math is bad learning habits. People get used to not actually understanding what they're doing, and then they forget what actually understanding something is like in the context of math, and then their ability to learn math at all atrophies, because learning requires you to be able to actively engage in a process of fixing what you don't get.

Semirelated quote:
>Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?

Anonymous Mon Mar 26 23:00:12 2018 No.9622343

>>9622327
Working in the context of ZF, the axiom of choice is provably equivalent to the statement that every vector space has a basis. Therefore, it is true in ZFC that every vector space has a basis—the assumption you mention is precisely the C in ZFC.

>>	Anonymous Mon Mar 26 23:01:17 2018 No.9622345 >>9622343 >Therefore, it is true in ZFC that every vector space has a basis—the assumption you mention is precisely the C in ZFC. Right, like I said, they don't have a bases unless you assume they do

>>	Anonymous Mon Mar 26 23:03:37 2018 No.9622347 >>9622345 Yes, you are correct.

>>	Anonymous Mon Mar 26 23:03:52 2018 No.9622348 >>9622345 I think you meant ZF and not ZFC then buddy

>>	Anonymous Mon Mar 26 23:04:39 2018 No.9622350 >>9622348 Don't feed the trolls.

>>	Anonymous Mon Mar 26 23:06:20 2018 No.9622355 >>9622340 thank you anon, I'll think about that

>>	Anonymous Mon Mar 26 23:15:47 2018 No.9622366 >>9622348 >I think you meant ZF and not ZFC then buddy Choice and existence of bases are equivalent in the category of axioms (i.e. isomorphic objects), just labelled differently like [math] \frac{1}{2}=\frac{2}{4} [/math]

>>	Anonymous Tue Mar 27 00:06:18 2018 No.9622411 >>9622355 Good luck!

>>	Anonymous Tue Mar 27 00:18:05 2018 No.9622425 >>9622175 >ksi dropped

>>	Anonymous Tue Mar 27 00:19:45 2018 No.9622430 PDEs I'm glad this is the last pure math course I ever have to take ;_;

>>	Anonymous Tue Mar 27 00:20:55 2018 No.9622431 >>9622175 Category Theory https://github.com/hmemcpy/milewski-ctfp-pdf

>>	Anonymous Tue Mar 27 00:29:01 2018 No.9622438 >>9622430 I'm confused anon. What do you think happens in applied math?

>>	Anonymous Tue Mar 27 00:36:11 2018 No.9622449 File: 41 KB, 567x434, 8166b799fa254b2b9161bdf4f3a9febe__elementary_landscape_art_elementary_art.jpg [View same] [iqdb] [saucenao] [google] What's a good source to learn finite calcul us?

>>	Anonymous Tue Mar 27 00:36:29 2018 No.9622450 >>9622438 Numerical solutions, what else?

Anonymous Tue Mar 27 00:41:17 2018 No.9622453

>>9622450
Seperating math into "applied", "pure", "whatever", was a bad idea imo. Applied math is mostly considered to be anything that is concerned with PDEs and of course numerics. But numerics is not just using big calculators, the theoretical aspects of it are usually more complicated than a lot of "pure" stuff since you need a lot of different concepts from other fields like analysis, (metric) topology, combinatorics, graph theory...

Unless you don't study proper math, then yes, applied math is literally using calculators.

>>	Anonymous Tue Mar 27 00:42:15 2018 No.9622455 >>9622453 What is categorized as pure math Am I an applied math or pure mathematician

>>	Anonymous Tue Mar 27 00:42:54 2018 No.9622456 >>9622453 >Seperating math into "applied", "pure", "whatever", was a bad idea imo. You can't separate something which is not well-defined.

>>	Anonymous Tue Mar 27 00:43:24 2018 No.9622458 >>9622453 >Unless you don't study proper math I'm an engineer

Anonymous Tue Mar 27 00:45:23 2018 No.9622464

>>9622458
K, then you can probably relax a little in your applied math courses.
>>9622456
Really brings my neuronal schlongers into swinging motion. Also yes.
>>9622455
>What is categorized as pure math
Usually everything that is not PDEs, numerics, stochastics, statistics. It's stupid though.

>>	Anonymous Tue Mar 27 00:46:18 2018 No.9622466 >>9622464 My rule is that if the professor uses the word "theorem," it's pure math.

>>	Anonymous Tue Mar 27 00:49:05 2018 No.9622468 >>9622449 Please respond

>>	Anonymous Tue Mar 27 00:52:13 2018 No.9622471 >>9622453 >>9622455 >applied math No such thing.

>>	Anonymous Tue Mar 27 00:53:39 2018 No.9622473 >>9622471 >math No such thing.

Anonymous Tue Mar 27 01:54:01 2018 No.9622545
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>>9622175

This is a legal game of Connect Four. After some experimentation, I found a sequence of play (encoded as the natural number 2167127614743451375325622663157315723654) which ends with the second player (yellow) winning.

What's slightly interesting about this is that it illustrates how a /legal/ (although certainly not typical in "normal" play!) game may conclude with multiple "fours", obtained all at once, by the winning player. It also calls attention to the central importance of the game's center column, and especially the board's central two cells. Consider that in principle, either such cell may participate in one of thirteen game-winning four-in-a-rows; here, the winning move simultaneously generates eleven distinct fours in the same blow. The result is the more interesting in that upon inspection the board-state given happens to show the conclusion of a legal game (which may be reached by multiple distinct games, of course).

Anonymous Tue Mar 27 02:52:35 2018 No.9622614

I've stopped using khanacademy as a learning tool and I've found myself at a faster pace by using just a textbook, Paul's Online Math Notes, Professor Leonard and profrobob's youtube tutorials.

How long would it take for me to get to calculus? I am currently on Algebra II factoring.

>>	Anonymous Tue Mar 27 03:25:18 2018 No.9622651 File: 10 KB, 240x240, 0ep76f66.jpg [View same] [iqdb] [saucenao] [google] Does a functor mapping spectra to (to the equivalence classes of) their Postnikov towers serve any purpose?

>>	Anonymous Tue Mar 27 04:09:39 2018 No.9622696 >>9622651 Math simply, platonically, Is. Xie doesn't exist to entertain you.

>>	Anonymous Tue Mar 27 05:19:44 2018 No.9622757 >>9622466 That's retarded.

>>	Anonymous Tue Mar 27 05:35:18 2018 No.9622770 File: 149 KB, 600x600, sdo2ug2dbl0.png [View same] [iqdb] [saucenao] [google] >>9622192 >you guys are fucking lucky. must be why people here talk about killing themselves so often huh

>>	Anonymous Tue Mar 27 05:39:20 2018 No.9622775 >>9622770 >must be why people here talk about killing themselves so often huh That's just one of the female regulars

Anonymous Tue Mar 27 05:44:14 2018 No.9622779

>>9622455
Applied math is math being used for real-world applications. Pure math is math for its own sake. The latter often grows out of the former, for example geometry came about because of a practical need in construction and land measurement, but when Euclid wrote his elements the primary concern was the mathematical objects and structures themselves.

>>	Anonymous Tue Mar 27 06:02:28 2018 No.9622803 File: 40 KB, 400x400, 46ca3fa1.jpg [View same] [iqdb] [saucenao] [google] >>9622770 It's so tempting~

>>	Anonymous Tue Mar 27 06:25:13 2018 No.9622841 >>9622455 pure maths is for smart people applied maths is where brainlets are redirected by default when they have less than a 4.0

>>	Anonymous Tue Mar 27 06:44:42 2018 No.9622867 File: 134 KB, 317x475, 29771233.jpg [View same] [iqdb] [saucenao] [google] >>9622175 >What are you learning, /mg/?

Anonymous Tue Mar 27 06:50:41 2018 No.9622871
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>>9622192
Not a single thing in mathematics implies intelligence. I wouldn't be surprised if the regulars here were mostly people who just memorize theorems and definitions for exams and then forget them, never understanding the stuff. This would explain why these threads are full of failures posting about categorical stuff and thinking they are cool, but really their posts are just barrages of buzzwords without any real content. An example of such a post would be >>9622696 as a reply to a legit question. These failures come together to these threads to post the same stuff every time, and some unlucky and innocent people fall for their traps every time, or are the other losers and start a shitpost fest by replying to them just for the sake of shitposting. Smartness isn't just having a high IQ, but also about being able to use it for something. These people may have almost 120 points as their scores, but for all mankind they have contributed nothing. This should itself prove you don't need to be smart to study math. On the other hand, your submissive attitude makes me think it is better for you to simply stop trying or even breathing, as you would only get trampled by people with stronger wills.

Anonymous Tue Mar 27 06:56:44 2018 No.9622876

>>9622871
>Not a single thing in mathematics implies intelligence. I wouldn't be surprised if the regulars here were mostly people who just memorize theorems and definitions for exams and then forget them, never understanding the stuff. This would explain why these threads are full of failures posting about categorical stuff and thinking they are cool, but really their posts are just barrages of buzzwords without any real content. An example of such a post would be >>9622696 as a reply to a legit question. These failures come together to these threads to post the same stuff every time, and some unlucky and innocent people fall for their traps every time, or are the other losers and start a shitpost fest by replying to them just for the sake of shitposting. Smartness isn't just having a high IQ, but also about being able to use it for something. These people may have almost 120 points as their scores, but for all mankind they have contributed nothing. This should itself prove you don't need to be smart to study math. On the other hand, your submissive attitude makes me think it is better for you to simply stop trying or even breathing, as you would only get trampled by people with stronger wills.
cringe

>>	Anonymous Tue Mar 27 07:06:01 2018 No.9622895 >>9622871 then why do math and physics graduates have higher average IQ than other fields?

>>	Anonymous Tue Mar 27 07:14:17 2018 No.9622910 >>9622867 lang basic math

Anonymous Tue Mar 27 07:17:33 2018 No.9622914

>>9622235
sometimes, it's better to ask anons on 4chan, then friends and family. Actually 4chan is a great place to ask irl questions, bc, literally there are thousands of people, who definitely know more than your family,who are much smarter, who work and study in many many different professions, who can unselfishly give you a good irl advice, and answer probably all of your questions.

>>	Anonymous Tue Mar 27 07:18:00 2018 No.9622915 File: 213 KB, 845x740, tirsk.jpg [View same] [iqdb] [saucenao] [google] >>9622895 Irrelevant. That is not needed to get a degree.

>>	Anonymous Tue Mar 27 07:18:57 2018 No.9622916 File: 1.03 MB, 1500x1900, __kizuna_ai_a_i_channel_drawn_by_jimmy__853fc434a488073683afeb7e0644c6af.jpg [View same] [iqdb] [saucenao] [google] >>9622871 Someone is jealous.

>>	Anonymous Tue Mar 27 07:26:12 2018 No.9622932 File: 79 KB, 847x944, 56b2fb51.jpg [View same] [iqdb] [saucenao] [google] >>9622916 Jealous for what?

>>	Anonymous Tue Mar 27 07:40:02 2018 No.9622947 >>9622910 >lang basic math Lang is a meme.

>>	Anonymous Tue Mar 27 07:41:24 2018 No.9622948 >>9622947 it's a good meme

>>	Anonymous Tue Mar 27 07:49:39 2018 No.9622954 File: 52 KB, 500x373, gorilla-leaf.jpg [View same] [iqdb] [saucenao] [google] What's the geometric intuition for projective transformations?

>>	Anonymous Tue Mar 27 08:00:05 2018 No.9622961 >>9622916 jealous of that hot 2D body

>>	Anonymous Tue Mar 27 08:18:31 2018 No.9622993 >>9622947 Your entire life is a meme, yet you are alive somehow. Why haven't you killed yourself anon?

>>	Anonymous Tue Mar 27 09:05:10 2018 No.9623040 >>9622841 >gpa >measure of intelligence

>>	Anonymous Tue Mar 27 13:18:06 2018 No.9623415 >>9622871 Die whore

Anonymous Tue Mar 27 14:20:50 2018 No.9623558

>>9622226
>>9622235
>>9622264
>>9622284
I talked to him today. He gave everyone a zero on the exam because he hadn't finished grading them(!). Apparently, I was the fifth person to ask him about it since he posted the grades yesterday morning. You thought he would have posted an announcement or something on the class website?

>>	Anonymous Tue Mar 27 15:17:35 2018 No.9623721 Can someone please tell me why would someone in it's right mind prefer to define the tangent space in terms if derivations? Just so you can justify abuse of notation? I thought mathematicians weren't like this.

>>	Anonymous Tue Mar 27 15:20:09 2018 No.9623733 >>9622954 I cannot think of a good explanation, but you might want to look into some "mathematics for open gl" book. This might be a good source of intuition.

>>	Anonymous Tue Mar 27 15:56:11 2018 No.9623832 >>9622175 Give me some simple but tricky problems.

>>	Anonymous Tue Mar 27 15:58:23 2018 No.9623839 >>9623558 U just got troled!

>>	Anonymous Tue Mar 27 16:06:01 2018 No.9623852 Currently I'm trying to understand the classification of semisimple Lie algebras and their representation theory. Humphreys presents this pretty well, in my opinion.

>>	Anonymous Tue Mar 27 16:07:08 2018 No.9623855 >>9623721 Because it works for any locally ringed space. i.e. Manifolds, Analytic Spaces, Varieties, Schemes

>>	Anonymous Tue Mar 27 16:10:58 2018 No.9623866 >>9622464 >PDEs Eh PDEs can definitely be pure math.

Anonymous Tue Mar 27 16:11:40 2018 No.9623867

>>9623832
Here's one that I came up with for myself. It's rather easy but you need a slight idea:
Let [math] n [/math] be and even, positive integer and let
[math] \pi: \mathbb{Z}/n\mathbb{Z} \to \mathbb{Z}/n\mathbb{Z} [/math] be bijective.
Show that there are [math]x,y \in \mathbb{Z}/n\mathbb{Z} [/math] with [math] x \neq y [/math] and
[math] x - y = \pi(x) - \pi(y) [/math].

>>	Anonymous Tue Mar 27 16:13:11 2018 No.9623872 >>9623855 Then why it's also used in more practical textbooks designed for physicists? Lie brackets make no sense with that formalism.or maybe I'm just a brainlet idk.

>>	Anonymous Tue Mar 27 16:23:57 2018 No.9623888 >>9623558 your professor is a moron

>>	Anonymous Tue Mar 27 16:36:28 2018 No.9623910 >>9623872 Lie brackets in that formalism are essentially just the commutator. Nothing really confusing there. The derivation definition is also often more convenient for actually computing tangent spaces.

Anonymous Tue Mar 27 16:44:29 2018 No.9623933

How does one go about actually computing concrete tensor products in practice?
I mostly understand how they're defined and what they do but I struggle to figure out on my own even very simple examples of them because there doesn't seem to be any obvious way of "solving" for it

>>	Anonymous Tue Mar 27 16:45:31 2018 No.9623935 >>9623558 how irresponsible of him, hopefully you end up doing well on the exam in that case

>>	Anonymous Tue Mar 27 16:49:55 2018 No.9623941 >>9623933 Put them in a basis and distribute the sum, but besides quantum entanglement and information, it's really not something done in practice I believe

Anonymous Tue Mar 27 16:51:44 2018 No.9623947

>>9622867
Mathematical Statistics and Real Analysis. I've finished chapters 1-7 of baby rudin, and gonna start doing chapters 9 and 11 next. I've heard it's shit though. What's a good book to learn about the Lebesgue integeral/measure theory?

Also no one here knows any good stats books, huh

Anonymous Tue Mar 27 16:53:49 2018 No.9623951

>>9622614
Not long. I would finish your algebra 2 stuff and then just dive right in with calculus. I did pre-calculus before calculus and I honestly dont know if it was necessary at all. Just make sure you learn some trigonometry as you do algebra 2.

Don't be scared of calculus, the operations are actually pretty easy. You'll be fine if you do well on the algebra 2 material.

>>	Anonymous Tue Mar 27 16:58:12 2018 No.9623962 >>9623933 tensor products of what

Anonymous Tue Mar 27 17:13:15 2018 No.9623988

>>9623947
There are no good stats books. Statistics is a dung heap of a subject kept alive by it's practicality.

As for measure theory, there's a book by Robert Ash called Probability and Measure Theory that I really like.
I think it's a really good idea to teach measure and probability simultaneously, it's the easiest way to see that rigorous integration isn't just pointless autism but is actually good for something. Most other places where it's worthwhile to ditch Riemann are difficult to show to undergrads.

>>	Anonymous Tue Mar 27 17:20:35 2018 No.9624000 File: 5 KB, 250x223, PTSD.jpg [View same] [iqdb] [saucenao] [google] Crammed through 200 pages of linear algebra textbook without sleep I just want to die

>>	Anonymous Tue Mar 27 17:24:05 2018 No.9624008 >>9624000 and tomorrow you will remember 15% of it

>>	Anonymous Tue Mar 27 17:26:06 2018 No.9624012 File: 254 KB, 1252x843, 1519998931241.jpg [View same] [iqdb] [saucenao] [google] >>9624008 studying only because I have a test on it tomorrow

>>	Anonymous Tue Mar 27 17:30:24 2018 No.9624017 >>9623988 >Statistics is a dung heap of a subject kept alive by it's practicality. lmao, yeah its a weird subject. Somehow nothing is rigorous even in "mathematical" statistics. Thanks for the book rec, will check it out.

Anonymous Tue Mar 27 17:33:02 2018 No.9624025

>>9623933
Tensor product of vectors could be made in the next way. You have a vector $a = (a_1, a_2) \in A$ and $b = (b_1,b_2,b_3) \in B$ . Vector $c \in C = A \otimes B$ will be $c = (a_1 b_1, a_1 b_2, a_1 b_3, a_2 b_1, a_2 b_2, a_2 b_3)$. I dunno what are you afraid of.

Anonymous Tue Mar 27 17:35:43 2018 No.9624031

Tensor product of vectors could be made in the next way. You have a vector [math] $a = (a_1, a_2) \in A$ [/math] and [math] $b = (b_1,b_2,b_3) \in B$ [/math]. Vector [math] $c \in C = A \otimes B$ [/math] will be [math] $c = (a_1 b_1, a_1 b_2, a_1 b_3, a_2 b_1, a_2 b_2, a_2 b_3)$ [/math]. I dunno what are you afraid of.

Anonymous Tue Mar 27 17:39:40 2018 No.9624036

>>9623839
I did. I felt fucking destroyed yesterday.
>>9623888
He's sharp when it comes to statistics and operations research related things. I get the feeling that he isn't so sharp with other things, mostly technology. He does most of his lecturing with this digital whiteboard and he fucks up the most basic shit (screenshots and copying-pasting images in Windows 10). I'm sure giving us all zeros was a quick-fix to a "bug" he ran into while grading. Who the hell knows.
>>9623935
Anything is better than a 0/100 after this shit, and it was only worth 20% of our final grade. Can't wait for this class to end desu. Operations research without spreadsheets is just fucking tedious.

Anonymous Tue Mar 27 17:43:14 2018 No.9624041 [DELETED]

File: 333 KB, 1698x1131, Kratom-Powder.jpg [View same] [iqdb] [saucenao] [google]

Im currently majoring in Mathematics and I feel like im not hitting the potential that I could with amphetamines. My smartest friends use adderall, vyvanese etc. but I used to use meth as a young teen so I feel that I could relapse if I do this. Anyone here use Kratom as a performance-enhancer for mathematics?

>>	Anonymous Tue Mar 27 17:44:34 2018 No.9624045 File: 339 KB, 843x1034, 1484101154064.jpg [View same] [iqdb] [saucenao] [google] >>9624041 GTFO degenerate junkie.

>>	Anonymous Tue Mar 27 17:45:41 2018 No.9624049 >>9623040 0.5 correlation is non-negligible

>>	Anonymous Tue Mar 27 17:46:44 2018 No.9624052 File: 81 KB, 182x249, 1488193431445.gif [View same] [iqdb] [saucenao] [google] >>9624041 >My smartest friends use adderall, vyvanese etc I have a feeling that they are not very smart

Anonymous Tue Mar 27 17:57:55 2018 No.9624095

I need some form of strictly noncommutative algebra (i.e. a*b != b*a for all distinct (a,b)) for an proof attempt at representing combinatorical objects algebratically

The only noncommutative algebra I know of that can be calculated easily are matrices but they don't suit my needs. Are there any other such algebratic structures?

>>	Anonymous Tue Mar 27 18:04:32 2018 No.9624116 >>9624095 differential operators [math] \sum_k f_k(x) \dfrac{d^k}{dx^k} [/math]

>>	Anonymous Tue Mar 27 18:08:51 2018 No.9624133 >>9624041 How do amphetamines compare to nootropics?

>>	Anonymous Tue Mar 27 18:14:45 2018 No.9624142 >>9624133 Amphetamines are nootropics

>>	Anonymous Tue Mar 27 18:17:11 2018 No.9624150 >>9624142 As in nootropics like racetams, ampakines, etc

>>	Anonymous Tue Mar 27 18:19:36 2018 No.9624158 >>9622175 jacobian, hessian matrices, that kind of stuff. I'm a 2nd year math undergraduate in Paris-VI and I've an exam tomorrow

>>	Anonymous Tue Mar 27 18:45:31 2018 No.9624214 >>9624158 i thought the french liked abstract nonsense

>>	Anonymous Tue Mar 27 19:18:01 2018 No.9624292 >>9623867 is pi a group or ring homo? or is it a set function?

>>	Anonymous Tue Mar 27 19:20:33 2018 No.9624301 >>9624095 any group modulo the center

>>	Anonymous Tue Mar 27 19:26:11 2018 No.9624316 >>9623933 >How does one go about actually computing concrete tensor products in practice? That's more of an engineering question.

>>	Anonymous Tue Mar 27 19:30:37 2018 No.9624326 >>9622871 >This would explain why these threads are full of failures posting about categorical stuff and thinking they are cool, but really their posts are just barrages of buzzwords without any real content. What are you referring to?

>>	Anonymous Tue Mar 27 19:56:37 2018 No.9624378 >>9624041 Use them! They help a lot! Also there are no sideffects at all.

>>	Anonymous Tue Mar 27 20:25:30 2018 No.9624422 Is is common to think of the phase space for a system with 2n degrees of freedom as a complex vector space of degree n?

>>	Anonymous Tue Mar 27 20:27:45 2018 No.9624427 >>9624422 Refer to >>>/sci/eg/.

Anonymous Tue Mar 27 20:31:08 2018 No.9624433

>>9624422
Many things wrong. Phase space is in general a manifold and it doesn't have to be a vector space. Also, complex manifolds have many strong properties you really don't ask for a physical system. You can embedded a manifold in some R^2n and then identify it as C^(n) but it's not needed.

>>	Anonymous Tue Mar 27 20:31:58 2018 No.9624434 >>9624433 >physical system Refer to boards such as >>>/toy/ and the engineering thread at >>>/sci/en/.

>>	Anonymous Tue Mar 27 21:31:58 2018 No.9624553 >>9624434 >>9624427 Hamiltonian mechanics is math, you fool.

>>	Anonymous Tue Mar 27 21:32:30 2018 No.9624555 >>9624553 Don't reply to the spammer;

>>	Anonymous Tue Mar 27 22:07:15 2018 No.9624637 >>9624553 Not really. Maybe you should post in threads which actually discuss the things you are interested in? I suggest >>>/toy/physics/ and >>>/sci/en/.

>>	Anonymous Tue Mar 27 22:22:19 2018 No.9624673 >>9622175 What's a good Android calculator app?

>>	Anonymous Tue Mar 27 22:49:47 2018 No.9624730 Right now I'm delving deep into the murky depths of econometrics, specifically classical panel data model tests and the linear algebra related to their proofs Fucking hausman, I want his brain to tell me it's secrets

>>	Anonymous Tue Mar 27 22:51:14 2018 No.9624734 >>9624673 >>>/sci/sqt/ >>9624730 Why did you decide to share this here? There is a special thread for people with your interests. Use >>>/sci/en/.

>>	Anonymous Wed Mar 28 00:29:52 2018 No.9624962 I feel triggered after I got 77% on my combinatorics test today It's a weird feeling knowing that I'm neither a complete brainlet nor a genius How do I deal with this feel

Anonymous Wed Mar 28 02:11:13 2018 No.9625145
File: 83 KB, 700x845, amd-haataja-jpg-e1463668930381-700x845.jpg [View same] [iqdb] [saucenao] [google]

>>9622175

Something for /math/ to know about: a decade ago, a newly minted Ph.D. died a gruesome and rather romantic death in rural Nebraska, which has become the subject of a memoir and a documentary film.

Steven Paul Haataja (pronounced Ha-deee-JAH), algebraist and longtime teacher, had spent his life in Minnesota, South Dakota, and finally Nebraska, where he earned his Ph.D at Lincoln, a place where he'd also taught in the past. Shortly after completing his doctorate in 2006, Haataja accepted a post in very rural Chadron, Nebraska and struck up relations with the locals - and a few months later, went missing. Still a few more months later, his body was found burnt to a crisp, and tied to a tree, off in a back country behind the local college. Since nothing ever happens in Chadron, the death became a frame story for local author and eccentric Poe Ballantine, and has become a sort of small town mystery. Ballantine's book (and later doco) of the same name, "Love and Terror on the howling plains of nowhere", chronicle all of this. Technically, the case remains open, and although the circumstances suggest foul play on its face, Haataja had also attempted suicide in the recent past, and is supposed to have gotten some coal and liquor on the night of his disappearance.

I have managed to discover two publications of Haataja's (an early one seems to have regrettably misspelled his name as Stephen), and his third, the dissertation. the two relevant algebrai items, C* algebras and all that:

http://u.math.biu.ac.il/~margolis/papers/HMM%20Amalgams.pdf
https://arxiv.org/pdf/1007.1192.pdf

t. a family friend retired to Chadron in recent years which is how I came to be aware of this story

>>	Anonymous Wed Mar 28 02:17:04 2018 No.9625154 >>9624095 You could just make multiplication work like a free group. It's somewhat unsatisfactory, but it should work.

>>	Anonymous Wed Mar 28 03:14:46 2018 No.9625222 >>9624158 >la fac

>>	Anonymous Wed Mar 28 03:33:03 2018 No.9625255 File: 113 KB, 1280x720, oui_baguette.jpg [View same] [iqdb] [saucenao] [google] >>9624158 Why are there so many frogs here?

Anonymous Wed Mar 28 03:45:44 2018 No.9625267

Help me with an easy proof, /math/?
For G a transitive group on (1,2,...n) let Ki be the subgroup that leaves elements 1 to i fixed. Prove G = Sn if and only if Ki != Kj for all pairs i,j such that i != j and i < n-1.
the only if is easy but the only way I figured out how to prove the if is through construction generating first (n-1, n) and then going down the ladder. It was really involved compared to the other proofs in this book, which is at a pretty low level, so I think I'm missing something obvious. The section deals with normal cosets, lagrange's theorem on groups, and the subgroup generated by an arbitrary subset of a group. the previous problem was a proof that for Hi the stabilizer of i in a transitive subgroup of Sn, |G| = n * |Hi|

Anonymous Wed Mar 28 06:26:18 2018 No.9625460
File: 992 KB, 704x954, 1509861662117.png [View same] [iqdb] [saucenao] [google]

>>9625145
It's pronounced HAA-ta-ya, where Haa is pronounced like Haar but without the r, ta is like in tapir, and ya is like in ya'll niggas don't even smoke crack. This is how amerimutts twist even the names of their ancestors. Really makes me want to puke.

Anonymous Wed Mar 28 06:30:56 2018 No.9625473
File: 178 KB, 1180x664, langland.jpg [View same] [iqdb] [saucenao] [google]

http://www.cbc.ca/news/canada/british-columbia/b-c-born-professor-awarded-nobel-prize-of-mathematics-1.4587328

>B.C.-born professor awarded 'Nobel Prize' of mathematics
>A Canadian mathematician has been awarded the Abel Prize — often referred to as the Nobel prize of mathematics, for a theory 50 years in the making.
>Robert Langlands, 81, who was born in New Westminster, B.C., was awarded the prize for developing what the Abel Prize citation describes as a "grand unified theory of mathematics."

Isn't the Fields medal often referred to as the Nobel prize of mathematics?

>>	Anonymous Wed Mar 28 06:34:48 2018 No.9625475 How do i prove the collatz conjecture?

>>	Anonymous Wed Mar 28 06:37:07 2018 No.9625479 File: 2.38 MB, 720x480, iut.webm [View same] [iqdb] [saucenao] [google]

>>	Anonymous Wed Mar 28 06:56:25 2018 No.9625512 >>9625475 By inspection.

>>	Anonymous Wed Mar 28 07:04:22 2018 No.9625519 >>9625475 its trivial so trivial nobody can be bothered to write it down

>>	Anonymous Wed Mar 28 07:37:49 2018 No.9625572 >>9625475 exhaustion

>>	Anonymous Wed Mar 28 08:35:05 2018 No.9625627 File: 42 KB, 400x567, bfbpte.jpg [View same] [iqdb] [saucenao] [google] >>9625255 big frog brains

>>	Anonymous Wed Mar 28 08:43:33 2018 No.9625637 File: 2.15 MB, 200x150, 1496021464390.gif [View same] [iqdb] [saucenao] [google] >>9622545 Hey anon this is neat!

>>	Anonymous Wed Mar 28 09:27:04 2018 No.9625690 discrete math is literally shit

>>	Anonymous Wed Mar 28 09:29:44 2018 No.9625693 >>9625690 Engineering has a tendency to be literal shit.

>>	Anonymous Wed Mar 28 09:41:45 2018 No.9625708 >>9625693 true that. especially if studying on such a shitty uni, like i (unfortunately) do

>>	Anonymous Wed Mar 28 11:23:32 2018 No.9625855 >>9622545 Is there a legal game where more than eleven different wins are achieved? 13 seems a bit of a stretch, but maybe you can get 12, can you not?

>>	Anonymous Wed Mar 28 11:55:22 2018 No.9625902 >>9622175 Got some good introductions to set theory and some question sets?

>>	Anonymous Wed Mar 28 12:14:33 2018 No.9625947 File: 219 KB, 577x576, 98959919bd9c4b8aac6c8f5581c15d512cf9f945d57033ddd20dd84578f8e8bc.png [View same] [iqdb] [saucenao] [google] >>9625902 Are question sets related to Freyd's solution sets?

>>	Anonymous Wed Mar 28 12:16:27 2018 No.9625950 >>9625947 Probably not...

Anonymous Wed Mar 28 13:34:47 2018 No.9626118

>>9625855
Nah, don't think you can have more than 11 wins on a legal game, at least I think that is the case. The horizontal and vertical lines are already full and the stones fall so yozu can't have mroe than one win vertically.

What may be interesting is the total number of wins possible on an n/n+1 board of 4 connect.
Or the total number of wins possible on an n/n+1 board of m-connect. (n,m are natural numbers of course)

Anonymous Wed Mar 28 14:02:47 2018 No.9626195
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>>9625855

The first person who replied is not the one who made the initial post FWIW, I am.

The game's available material (in this instance, of course) is itself a limiting factor. In order to actually have an arrangement with thirteen simultaneous four (in-a-rows), (leaving aside game legality!), the winning player would need to have laid down 22 checkers (imagine the pic being filled up in the last two spots with yellow checkers). But each player only has 21 checkers, and plays in turn either until a win or until the board is filled up with no win, producing a draw.

A paper on the solution of connect four. It's fairly autistic and more CS-y than math-y, but of interest.

http://www.informatik.uni-trier.de/~fernau/DSL0607/Masterthesis-Viergewinnt.pdf

Pic related is a heatmap of the board I whipped up quick. Each number represents the possible fours in which a given cell may participate. As you can see, center spots are at a premium.

Anonymous Wed Mar 28 14:47:59 2018 No.9626290
File: 21 KB, 480x480, yes.jpg [View same] [iqdb] [saucenao] [google]

>>9624422
No. In general given a coordinate space [math]M[/math] the phase space is [math]M\times T^M[math], where your momenta are treated as vector fields on [math]M[/math]. Hence the smooth structure as well as the differential structure is already fixed. You can only do it if you in addition also have a complex structure on M.

>>	Anonymous Wed Mar 28 14:51:25 2018 No.9626297 >>9625267 halp with this? It's for self study so I'm never going to get told how to do it properly

>>	Anonymous Wed Mar 28 15:05:19 2018 No.9626315 >>9626290 nice TeX brainlet

>>	Anonymous Wed Mar 28 15:28:15 2018 No.9626359 >>9624422 on all levels but physical, you want to be a Calabi-Yau manifold.

>>	Anonymous Wed Mar 28 16:46:22 2018 No.9626497 File: 41 KB, 500x703, pehmo.jpg [View same] [iqdb] [saucenao] [google] Have you done any math today? I didn't know enough to actually understand a paper on arxiv, but it introduced quandles to me. I learned something new.

>>	Anonymous Wed Mar 28 19:03:18 2018 No.9626718 File: 341 KB, 500x356, 1477623997492.gif [View same] [iqdb] [saucenao] [google] >>9626497 But coalgebras and Hopf algebras seem pretty dank.

>>	Anonymous Wed Mar 28 19:23:04 2018 No.9626752 >>9626497 >>9626718 You're cute :3

>>	Anonymous Wed Mar 28 19:30:10 2018 No.9626781 >>9624292 It works whenever [math] \pi [/math] is a bijection of sets. You don't need it to be a group homomorphism.

>>	Anonymous Wed Mar 28 19:49:10 2018 No.9626810 >>9626297 what do you know about group actions? My first instinct would be to try using the following theorem: A transitive left action on a set A is G-equivariant to a left action on G/H where H = stab(a) for any a in A

>>	Anonymous Wed Mar 28 20:07:38 2018 No.9626841 >>9623867 i havent cracked it but after a couple computations i think its actually stronger: for any x, there exists a y such that x-y=pi(x)-pi(y)

>>	Anonymous Wed Mar 28 20:18:02 2018 No.9626868 >>9626841 This doesn't seem to be right: on [math] \mathbb{Z}/4\mathbb{Z} [/math] take the cycle (2 3 4). Then for x = 0 there is no other y that fulfils the condition.

>>	Anonymous Wed Mar 28 20:19:03 2018 No.9626871 >>9626868 (1 2 3), I meant.

>>	Anonymous Wed Mar 28 20:27:28 2018 No.9626893 trying to learn some basic homotopy theory out of hatcher will i ever stop forgetting that my maps have to be maps of pairs/triples? always makes me feel like a brainlet when it hits me

>>	Anonymous Wed Mar 28 20:41:29 2018 No.9626929 >>9626359 Or just Kahler

>>	Anonymous Wed Mar 28 20:45:56 2018 No.9626936 >>9626893 Yes, once you do enough of the proofs.

Anonymous Wed Mar 28 20:59:19 2018 No.9626973
File: 1.10 MB, 1920x1040, 1508375082373.png [View same] [iqdb] [saucenao] [google]

>>9625145
I grew up in Chadron. I was around when Haataja went missing. I know most of the people Ballantine interviewed in his book/documentary. I even studied math at Chadron State College, so I know the people and the program pretty well. If you have any burning questions, please ask. I may be able to answer them.
>>9625460
Ballantine probably wrote that pronunciation key. I don't know what the fuck he was getting at, no one in Chadron pronounces it Ha-deee-JAH.

Anonymous Wed Mar 28 21:59:01 2018 No.9627111

>>9622871
>I wouldn't be surprised if the regulars here were mostly people who just memorize theorems and definitions for exams and then forget them, never understanding the stuff. This would explain why these threads are full of failures posting about categorical stuff and thinking they are cool, but really their posts are just barrages of buzzwords without any real content.
I agree agree with this part. But please don't post pictures of my girlfriend without her consent.

>>	Anonymous Wed Mar 28 22:00:43 2018 No.9627116 >>9625473 >journalists

>>	Anonymous Wed Mar 28 22:02:00 2018 No.9627118 >>9627111 Why do you agree with it?

>>	Anonymous Wed Mar 28 22:03:10 2018 No.9627119 >>9627118 I haven't seen many insightful posts here. It's mostly circle jerking.

>>	Anonymous Wed Mar 28 22:12:10 2018 No.9627128 >>9627119 The last few months have been pretty shit, but I've seen plenty of "insightful" or at least helpful posts in the past which were made precisely by those 1-2 "regulars" who that post seems to disparage.

>>	Anonymous Wed Mar 28 23:00:24 2018 No.9627182 >>9627128 >regulars

Anonymous Thu Mar 29 00:17:05 2018 No.9627263

>>9626810
absolutely nothing, it's from an introductory text. I don't know what equivariant means, but I'll look it up I guess. My approach was this horrible proof by induction where I demonstrated that you can transform each element in Kn not in K(n-1) to the transposition (a,n) for each a in [1,n], to give you an idea of the level it's at. I just had this nagging feeling that there should be something about e order of the group being (n-1)! that I don't see

>>	Anonymous Thu Mar 29 00:40:32 2018 No.9627290 >>9627119 circle-up-to-homeomorphism jerking or circle-up-to-homotopy-equivalence jerking?

>>	Anonymous Thu Mar 29 00:41:09 2018 No.9627293 Holy fucking shit I finally finished my linear algebra test Went through 300 pages of material in 2 days

>>	Anonymous Thu Mar 29 00:42:10 2018 No.9627295 >>9627293 >linear algebra test What are you, some kind of first-year brainlet?

>>	Anonymous Thu Mar 29 00:43:32 2018 No.9627297 >>9627295 3rd year course I regret taking this everyday

>>	Anonymous Thu Mar 29 00:46:09 2018 No.9627301 File: 85 KB, 790x641, ss (2018-03-29 at 05.45.17).png [View same] [iqdb] [saucenao] [google] >>9627295 >>9627297 pic related it's so incredibly boring I literally fell asleep in the only few lectures I attended

>>	Anonymous Thu Mar 29 00:48:55 2018 No.9627304 >>9627301 It's your own fault for taking engineering courses.

Anonymous Thu Mar 29 01:09:14 2018 No.9627344

>>9626973

1) Are you aware of any other mathematical works whatsoever having Haataja as an author, apart from the two I linked, and the dissertation? If so, please give a pointer.

2) Attached is a map giving approximate locations. In red at top is 200 1/2 Bordeaux (or thereabouts), in orange in the middle is the rough area where Math/Sci is located, and the big black dot is the approximate location where the body was found. All info taken from the film. Please let me know if any of this is factually wrong, or misrepresents locations.

3) What is your personal view on the circumstances of Dr. Haataja's death?

4) Did you happen to take any classes with Haataja?

5)

>no one in Chadron pronounces it Ha-deee-JAH

If that is true, then why is it that in the film, community members Kathy Bahr (12:46), Poe Ballantine of course (31:35, 4:00 among others), DA Vance Haug (4:45), local paper publisher George Ledbetter (41:58) and grad student Steve Welch (1:00:32) ALL USE THE EXACT SAME HAA-DEE-JAH pronounciation which is clearly audible at 0:50 of the link?

https://www.youtube.com/watch?v=P2H4yr9lD3E

>>	Anonymous Thu Mar 29 01:10:52 2018 No.9627346 File: 193 KB, 1212x880, jej.png [View same] [iqdb] [saucenao] [google] >>9627344 map.

>>	Anonymous Thu Mar 29 02:19:12 2018 No.9627439 File: 1.98 MB, 620x717, 12358.gif [View same] [iqdb] [saucenao] [google] >>9626973 Ah, I see. Then I have no problem with it. >>9627344 5) here makes me worry, though.

Anonymous Thu Mar 29 02:49:08 2018 No.9627473

>>9627344
5. My apologies, I misinterpreted your pronunciation key. I thought the "JAH" in your key sounded like "jaw" instead of "yah."
1. I think you've found them all. I searched for his pubs in the UNL digital commons and found a partial copy of his PhD thesis (https://search.proquest.com/docview/305273734).). He might have a master's thesis floating around too? He did finish an MS at UNL before tackling the PhD.
2. Your dots for 200 1/2 Bordeaux and the Math and Science Bldg. are definitely accurate. I am less confident in the placement of the black dot because I haven't actually visited the site of Haataja's death. The bearing looks accurate (southeast of Math and Science), but I am less confident in the distance. It's been a while since I watched the documentary, how did Ballantine describe the location of Haataja's death? Didn't he show a map?
3. When Haataja's body was first discovered, my mom was convinced it was a hate crime. She (and many others) thought Haataja was a nutty gay professor that a bunch of hicks decided drag out and kill. Once I learned that Haataja was not bound with barbed-wire at the time of his death (a rumor that was floating around Chadron at the time), I accepted the idea that he committed suicide.
4. I did not take any classes with Haataja, but I have taken classes with Cary and Vogl. I worked with Wentworth, but never took any of her classes.

Anonymous Thu Mar 29 03:22:39 2018 No.9627522

>>9627473

Thanks for your replies. Since several posts have been spilt on the pronounciation issue already, with at least one admitted misinterpretation, I felt it was essential to get some audio in the conversation.

As to your question about the body site, a map in the film clearly shows the approx. location in relation to Chadron (a short piece SE of the college on the ranch land). It is (was?) a very small copse of trees on the land, it seems. And yes, the film shows a map and even shows Haataja's death certificate, Social Security Number and all (despite face blurrings on old photos), which is where I got the 200 1/2 Bordeaux address. To clarify with the above, this is what I assume to have been Haataja's final residence. That he was (?) apparently in the habit of walking to and from work and home for his brief time in Chadron would further validate the notion of him being able to take his final walk under his own power, his recent accident notwithstanding, if that's what happened.

Your mother's view also resonates with the initial thoughts depicted in the film. However, the film's "third act" basically gives up the charcol and liquor purchases, plus prior attempt, which is where things actually click for me. Upon viewing the film, I also came away with the impression that it is in fact a suicide, albeit a very strange one, and so I'm gratified that a local close to the story has the same impression. Haataja's depression and prior attempt, and moving out to rural Nebraska ffs (no offense) also validate this view.

As I say, I have slight connections. Dad's ex-bandmate moved in and has apparently played chess with Poe's autistic kid. The ex-bandmate gave dad the DVD, and now I have it which is how I got hip to all this. Also after me learning of all this, one time at the local grocery store a woman had a Chadron sweater and I mentioned that I knew it, without going into gory detail. She was impressed that anyone knew Chadron.

>>	Anonymous Thu Mar 29 04:08:52 2018 No.9627560 >>9622468 There's a small section on it in Concrete Math in case you haven't already read that

>>	Anonymous Thu Mar 29 05:11:35 2018 No.9627616 File: 88 KB, 1280x720, 1522272562860.jpg [View same] [iqdb] [saucenao] [google] >>9627560 >Concrete "Math" Please don't litter. Put that garbage in a trash can.

>>	Anonymous Thu Mar 29 05:30:48 2018 No.9627634 I hate this general.

Anonymous Thu Mar 29 06:09:46 2018 No.9627661

>>9627263
anon, I can't discern what level the book is at if you don't tell me exactly what you've learned about group actions, especially, because the theorem i posted is literally the second thing they prove in the book i looked up for reference. At least tell me what book you're using

Anonymous Thu Mar 29 09:59:34 2018 No.9627978
File: 97 KB, 766x1024, 1520783829595.jpg [View same] [iqdb] [saucenao] [google]

>What are you learning, /mg/?
I'm learning about the elliptic curves and primitive elements of prime 13 GFs. I also had the option of learning about prime 11 and 17 GFs, but they weren't my cup of tea.

>>	Anonymous Thu Mar 29 10:34:38 2018 No.9628028 File: 669 KB, 1280x720, keksi.png [View same] [iqdb] [saucenao] [google] >>9626752 A beautiful day to you too!

>>	Anonymous Thu Mar 29 11:11:45 2018 No.9628094 >>9625475 Pigeon hole principle

>>	Anonymous Thu Mar 29 11:37:29 2018 No.9628164 >>9624326 Himself obviously

>>	Anonymous Thu Mar 29 11:45:28 2018 No.9628178 File: 3.95 MB, 5312x2988, 20180329_184409.jpg [View same] [iqdb] [saucenao] [google] Happy Easter to my fellow mathemämmicians <3

>>	Anonymous Thu Mar 29 11:50:37 2018 No.9628190 >>9628164 >Him

>>	Anonymous Thu Mar 29 12:04:09 2018 No.9628207 >>9627616 The concrete in the title doesn't refer to what you think it does

>>	Anonymous Thu Mar 29 12:19:04 2018 No.9628232 File: 1.86 MB, 493x438, 1516962939136.gif [View same] [iqdb] [saucenao] [google] >>9628178 Cute (=･ω･=)

Anonymous Thu Mar 29 12:26:51 2018 No.9628245
File: 60 KB, 1280x720, 1481384892114.jpg [View same] [iqdb] [saucenao] [google]

>>9628232
No u. Have you done any interesting stuff lately? I was thinking about finding some quick rundown on Hopf algebras, so I could understand how Steenrod's algebras work. Rudyak gave some references.

Anonymous Thu Mar 29 12:32:07 2018 No.9628251

>>9628245
If you want a quick introduction to Hopf algebras, either search for some lecture notes on the internet or read the respective chapter in Kassel's "Quantum groups" (the book essentially continues with a discussion of concrete classes of Hopf algebras).

>>	Anonymous Thu Mar 29 12:32:10 2018 No.9628252 >>9622871 This. I literally just memorize theorems and proofs and I get by nicely in my classes.

>>	Anonymous Thu Mar 29 12:36:45 2018 No.9628259 File: 231 KB, 596x489, 1512852747132.png [View same] [iqdb] [saucenao] [google] >>9628251 >quantum T-that doesn't require any understanding of QM, does it? The name is unironically frightening.

>>	Anonymous Thu Mar 29 12:39:19 2018 No.9628263 >>9622175 Multivaried probability theory, pretty cool stuff

>>	Anonymous Thu Mar 29 12:40:35 2018 No.9628265 File: 928 KB, 971x1405, 1522291965205.png [View same] [iqdb] [saucenao] [google] >>9628178 What's that black goo on the right?

>>	Anonymous Thu Mar 29 12:41:47 2018 No.9628271 File: 14 KB, 309x333, b3f63c39.jpg [View same] [iqdb] [saucenao] [google] >>9628265 >not recognizing mämmi Third worlders pls leave.

>>	Anonymous Thu Mar 29 12:42:54 2018 No.9628273 >>9628265 mammi you pleb

>>	Anonymous Thu Mar 29 12:46:04 2018 No.9628284 >>9627560 Yeah I have that just wondering if there's more to the subject

Anonymous Thu Mar 29 12:46:50 2018 No.9628285

>>9628259
Actually, it is rather trendy to put the buzzword "quantum" before quantized structures...
Some ideas are indeed borrowed from physics but if you like knots, representation theory or Lie theory, you'll find another start.
I personally like the approach of seeing Hopf algebras as "even more non-commutative" algebraic groups (i.e. the coordinate rings become noncommutative, too - so they're behaving like function algebras over groups).
Quantization is mostly about "deforming" classical structures by seeing them as cases with specialized parameters...

Anonymous Thu Mar 29 12:47:13 2018 No.9628286

>>9625267
First I want to note that you need the assumption that the group action is faithful, which is equivalent to G being a subgroup of Sn. Otherwise it's very easy to come up with a counterexample.

The transitivity assumption is not actually needed, it follows by induction: assume K2 acts transitively on (2,...,n) then since K1 is not equal to K2, there must be some g in G such that g(1) is in the set (2,...,n).

The above observation implies, using your last statement, that |G|=n*K1=n*(n-1)*K2=...=n!.

>>	Anonymous Thu Mar 29 12:49:10 2018 No.9628289 File: 30 KB, 500x378, 1482239734394.jpg [View same] [iqdb] [saucenao] [google] >>9628285 I've been avoiding all that stuff for nothing... All this time...Thanks. You gave me something to think about.

>>	Anonymous Thu Mar 29 12:53:51 2018 No.9628300 >>9628286 Sorry the second isn't entirely correct, the transitivy assumption isn't needed if you let G be K0. Then K0 != K1 gives that there is a g in K0 such that g(1) is contained in the set (2,...,n), and induction gives transitivity of all the Ki.

>>	Anonymous Thu Mar 29 12:56:02 2018 No.9628311 >>9628289 You're welcome! You seem to be interested in topology, so knot invariants (from the Yang-Baxter equation) might be a nice application for you, too..

Anonymous Thu Mar 29 12:57:26 2018 No.9628316
File: 128 KB, 304x369, 1464736290167.png [View same] [iqdb] [saucenao] [google]

>>9628245
>Have you done any interesting stuff lately?
I'm learning about Grothendieck topologies and related stuff mainly from http://homepage.sns.it/vistoli/descent.pdf and other notes. Will probably pick up "Sheaves in Geometry and Logic" as well.

>>	Anonymous Thu Mar 29 12:57:39 2018 No.9628317 >>9628271 >is from fucking memeland >calls others third worlders perkele

>>	Anonymous Thu Mar 29 12:58:58 2018 No.9628320 >>9628259 It requires some physical intuition for black holes and algebraic TQFTs, but they are such empirical objects that the innate physical intuitions of a child will suffice.

>>	Anonymous Thu Mar 29 13:01:44 2018 No.9628330 >>9628320 And of course it requires some experience with sarcasm.

>>	Anonymous Thu Mar 29 13:03:06 2018 No.9628333 Will /mg/ ever get better again? I'm fine with not good, just better.

>>	Anonymous Thu Mar 29 13:03:10 2018 No.9628335 >>9628271 fuck off amerifat

Anonymous Thu Mar 29 13:05:02 2018 No.9628337
File: 393 KB, 696x717, 1494809136518.png [View same] [iqdb] [saucenao] [google]

>>9628311
I used to do algebraic topology, but then some stuff happened and I had to concentrate on other things, but now I'm recapping my stuff. What would be a good book on knots? I have will and time once again.

>>9628316
That's a nice book. Better than the one by Jonhstone, I'd say. I didn't finish it, though.

>>9628317
That really mämmified my sauna.

>>9628320
Ah, those are trivial hs level thingies.

>>9628335
If I was an amerifat, why would I want my people to leave?

>>	Anonymous Thu Mar 29 13:13:43 2018 No.9628347 Calculus I. is Apostol gud?

>>	Anonymous Thu Mar 29 13:17:48 2018 No.9628356 Lads which class is easier, Numerical Analysis, or Combinatorics?

Anonymous Thu Mar 29 13:22:44 2018 No.9628370

>>9627661
"elements of modern algebra" by gilbert
It's intended for those intro to proofs classes they give undergrads. basically at this point I know lagrange's theorem, cayley's theorem, and some definitions. the chapter that problem came from deals with normal subgroups. it introduces the product of a subset, then introduces cosets, demonstrates that the cosets of a subgroup partition a group, introduces the concept of an index, proves lagrange's theorem, introduces normal subgroups, gives theorems that hH = Hh and H^2 = H for any subgroup H and element in that subgroup, proves H is a normal subgroup iff xhx^-1 for all x in a group G, then introduces the set generated by a subgroup of G, and proves this is a subgroup. It's very concrete, and it's been helpful in getting back into math through self-study.
>>9628286
Yes, the group G is defined to be a subgroup of Sn in the question, sorry
yeah they very carefully did not define K0, so transitivity was necessary
Is there some mechanism by which we can assume Kn is transitive without using induction? The definition I'm given is for each i,j in [1,n] there exists g in G such that g(i) = j. All I could get out of this was there's some g in Kn-3 for example where g(n-2) = n-1 or n, then I had to use the permutations I constructed to show this could be made transitive. But that provides a much cleaner proof at least, I think that's probably what I was looking for. Thanks!

>>	Anonymous Thu Mar 29 13:23:01 2018 No.9628371 >>9628356 Combinatorics

>>	Anonymous Thu Mar 29 13:27:09 2018 No.9628383 File: 1.45 MB, 500x538, 1514510197743.gif [View same] [iqdb] [saucenao] [google] >>9628347 Probably, it's usually that or Spivak for rigorous calculus. If you want easier/brainlet/engineer then go for Stewart instead which is very easy

>>	Anonymous Thu Mar 29 13:33:46 2018 No.9628402 >>9628347 It's decent if it's your first time taking a Calc course (likely) and if you're not yet expected to be rigorous with limits and continuity (in that case you'd be better off with a book on analysis).

>>	Anonymous Thu Mar 29 13:34:15 2018 No.9628403 I'm trying to get into combinatorics, but every time I try to study from a source of info, it appeals WAY too much on intuition, and throwing formulas sometimes without explanation. So, what's a good book on combinatorics? Help.

>>	Anonymous Thu Mar 29 13:36:24 2018 No.9628409 >>9628347 >Calculus >gud No such thing.

>>	Anonymous Thu Mar 29 13:37:17 2018 No.9628411 >>9628347 I recommend >Spivak, Calculus on Manifolds >Rudin, Real and Complex Analysis >Munkres, Analysis on Manifolds or >Alain Robert, A Course in p-adic Analysis All good first-year textbooks.

>>	Anonymous Thu Mar 29 13:38:56 2018 No.9628418 >>9628383 >>9628402 I'm EE, but I could use some rigor. I'll check both spivak and apostol and see which one I like the most, thanks. I saw Stewart book but it was too colourful for me.

>>	Anonymous Thu Mar 29 13:48:10 2018 No.9628434 >>9628403 This isn't really a question for a math thread. Try asking at >>>/sci/en/ or >>>/sci/sqt/.

Anonymous Thu Mar 29 13:49:48 2018 No.9628441

>>9628370
Well of course for a given n induction isn't really needed, you can just apply the same argument (the one that gets you from i to i+1, or i+1 to i in this case) enough times until you reach n (or 0 in this case). If you want to understand the argument better, here it is in more detail.

Say we already know Ki acts transitively on [i+1,n]. So by definition for each pair k,j in [i+1,n] there is a g in Ki such that g(k)=j. We want to show the same holds for Ki-1 and [i,n]. Since Ki is contained in Ki-1 it is enough to show that for each j in [i,n] there is a g such that g(i)=j (note that then g^{-1}(j)=i). For j=i this is clear, namely take g to be the identity. If j != i then we showed that there is an h such that h(i) is in [i+1,n], and by assumption there is then a g' such that g'(h(i))=j, so we take g=g'h.

For the other guy's suggestion you should look up the orbit stabilizer theorem, and perhaps try to prove it yourself. It states that if G acts transitively on some set X, and if you let H be the stabilizer of some x in X then the map that sends gH to gx is a bijection G/H to X.

>>	Anonymous Thu Mar 29 14:07:37 2018 No.9628490 >>9622175 Cat woman on left has large ass.

Anonymous Thu Mar 29 14:11:01 2018 No.9628494
File: 136 KB, 1148x1080, Il y a un temps pour tout, un temps pour naître, et un temps pour mourir.jpg [View same] [iqdb] [saucenao] [google]

To the anon who needed money to go to the doctor, if he is still around and still needs help: post proof that it's you (maybe one of the pictures of your legs that you didn't post before, if you took more at the same time) and a way to contact you. I had something of an epiphany earlier today after deciding to read this bible and landing on the 3rd chapter of Ecclésiaste. I want to give you all the money I have left. I don't know anyone else that would really need it and this place is the closest I've ever gotten to having friends in the last couple of years.

I am going to wait until tomorrow morning for your reply. Please trust me, I'm not trying to prank you. Also, it's best if we use some crypto currency for the transfer, so I hope you have a bitcoin wallet or some other equivalent. I don't want to cause you legal problems by wiring you the money through some service that would track back to me and implicate you in my suicide.

Take care.

>>	Anonymous Thu Mar 29 14:15:59 2018 No.9628505 >>9628441 Wow that clears up a lot, thanks for taking the time to help me! I will check out that theorem!

Anonymous Thu Mar 29 14:28:13 2018 No.9628540
File: 11 KB, 184x234, L.jpg [View same] [iqdb] [saucenao] [google]

>You can ask: How did we guess the formulas expressing x and y in terms
of t in the first place? Answer: These formulas have been known for a long
time. As far as I know, history does not tell us who discovered them first,
but he was a good mathematician. What distinguishes someone with talent
for mathematics from someone without talent is that the first person will be
able to discover such beautiful formulas and the second person will not.
/mg/ on suicide watch

>>	Anonymous Thu Mar 29 14:37:42 2018 No.9628559 File: 11 KB, 236x236, aa4c8ffcf0c1d461d257c089b96cc87e--sushi-food.jpg [View same] [iqdb] [saucenao] [google] >>9628494 Send me moneys so I can afford Mendelson it's cheap ))

>>	Anonymous Thu Mar 29 15:11:54 2018 No.9628634 >>9622210 Grant money

>>	Anonymous Thu Mar 29 15:21:43 2018 No.9628655 >>9628540 >formulas The engineering threads are over at >>>/sci/en/.

Anonymous Thu Mar 29 15:42:38 2018 No.9628691
File: 54 KB, 540x443, 1515643652091.jpg [View same] [iqdb] [saucenao] [google]

Slowly chugging along as I work on AB calculus. I took it already, but that was 4 years ago.
Though is it strange that I'm having some sort of fun? I don't remember much, but when I do it's a nice feeling. I wish I wasn't a brainlet.

>>	Anonymous Thu Mar 29 15:42:54 2018 No.9628692 >>9628655 >I think I'm smarter than everyone else, therefore I am okay mssr. descartes

Anonymous Thu Mar 29 15:50:03 2018 No.9628701

>>9628403
Serious answer - most introductory books on combinatorics rather give you an overview of the big topics. "A course in combinatorics" (van Lint, Wilson) is an example of such a book.
The techniques vary extremely from subfield to subfield, so there might not be a unifying approach to all of them. But you should know a few techniques that are common knowledge in mathematics - e.g. the pigeon hole principle or the inclusion exclusion principle. Even power series are nice to know.

Anonymous Thu Mar 29 15:54:40 2018 No.9628705

>>9628337
>I used to do algebraic topology, but then some stuff happened and I had to concentrate on other things, but now I'm recapping my stuff. What would be a good book on knots? I have will and time once again.

Alas, I've never gone deeper into knot theory. I just know that there are are some nice knot invariants that can be constructed from solutions of the Yang-Baxter equation - and many of those come from noncommutative-noncocommutative (no typo!) Hopf algebras.

>>	Anonymous Thu Mar 29 16:04:58 2018 No.9628719 >>9628190 I'm not buying your tranny logic, my dude.

Anonymous Thu Mar 29 16:17:13 2018 No.9628738
File: 71 KB, 540x443, 1515643652091.jpg [View same] [iqdb] [saucenao] [google]

Slowly chugging along as I work on preschool arithmetic. I took it already, but that was 4 years ago.
Though is it strange that I'm having some sort of fun? I don't remember much, but when I do it's a nice feeling. I wish I wasn't a brainlet.

>>	Anonymous Thu Mar 29 16:46:46 2018 No.9628801 >>9628738 Keep on it, you'll get there.

>>	Anonymous Thu Mar 29 16:55:00 2018 No.9628816 File: 43 KB, 595x720, 845162.jpg [View same] [iqdb] [saucenao] [google] >>9628705 I see. What makes a Hopf algebra noncommutative-noncommutative?

>>	Anonymous Thu Mar 29 16:57:39 2018 No.9628824 >>9622234 MUH AC

Anonymous Thu Mar 29 17:08:56 2018 No.9628855
File: 84 KB, 535x439, 1515643652091.jpg .jpg [View same] [iqdb] [saucenao] [google]

Slowly chugging along as I work on counting to 10 for toddlers. I took it already, but that was 4 years ago.
Though is it strange that I'm having some sort of fun? I don't remember much, but when I do it's a nice feeling. I wish I wasn't a brainlet.

Anonymous Thu Mar 29 17:14:21 2018 No.9628873

>>9628816
You know the basic definitions of Hopf algebras?
A Hopf algebra doesn't only have a classical multiplication, i.e. a linear map [math] H \otimes_k H \to H [/math] fulfilling an associativity constraint but also a comultiplication [math] H \to H \otimes_k H [/math] fulfilling some kind of co-associativity. (there are also some structure maps from and to k and an antipode which essentially makes it analogous to a group). Also, the multiplication and comultiplication are again maps of coalgebras resp. of algebras, i.e. they're compatible with each other (so not just any pair of multiplication and comultiplication does it).
If you can interchange the factors of [math] H \otimes_k H [/math] without altering multiplication and comultiplication you have a commutative algebra resp. a cocommutative coalgebra. If neither of these holds... well, then things start to become a little more interesting.
Sorry, I was a little bit too lazy to write down the complete sets of axioms. Most of this stuff you also find in Wikipedia or some good book.
Most important is the insight that you can see the multiplication of an algebra as a linear map [math] H \otimes_k H \to H [/math] which fulfils a nice commutative diagram (associativity) and that the arrows could as well be turned around to get a commutative diagram fulfilled by objects with properties almost (!) dual to the properties of algebras.

Anonymous Thu Mar 29 17:17:52 2018 No.9628888

>>9628705
Knots can be identified with braids in a natural way, so every knot gives you an element of the braid group on a certain number of strands.
If you have a representation of the braid group, e.g. a map which assigns an invertible matrix to every crossing of neighbouring strands, then the braid relations in the group will give you the Yang-Baxter equation (if I'm not mistaken).
In particular, the image of the braid associated to your knot is a solution of the YB equation.
(This is of the top of my head, I might be misrepresenting some stuff)

Anonymous Thu Mar 29 17:25:04 2018 No.9628903

>>9628888
First of all, quads checked!
Yeah, that's what I still remembered from a lecture on knot theory. But I never went deeper into knot-theory.
The nice thing about a YBE-solution is that is gives you representations for braid groups on any (!) number of strands.
And you're right, the YBE must respect the braid relation in the same way as three neighboring strands do.

Anonymous Thu Mar 29 19:17:37 2018 No.9629204
File: 959 KB, 640x360, 1490842369371.gif [View same] [iqdb] [saucenao] [google]

>>9628873
The definition I have is that it is, for some commutative ring [math]R[/math], a Hopf algebra over [math]R[/math] is a quintuple [math](A, \mu, \eta, \Delta, \varepsilon)[/math] such that:
(1) [math](A, \mu, \eta, \varepsilon)[/math] is an augmented [math]R[/math]-algebra,
(2) [math](A, \Delta, \varepsilon)[/math] is an [math]R[/math]-coalgebra,
(3) [math]\Delta\colon A\to A\otimes A[/math] and [math]\varepsilon\colon A\to R[/math] are homomorphisms of [math]R[/math]-algebras,
(4) [math]\eta\colon R\to A[/math] is a homomorphism of [math]R[/math]-coalgebras.
Associativity and such stuff follow immediately from the use of multiplications and comultiplications. The definition of commutativity is based on the use of the isomorphism interchanging the objects in the tensor product, and you just require that the isomorphism followed by multiplication is the same as the multiplication alone, dualize that to get cocommutatitivity. I know this stuff, but hardly any more than this. It's pretty simple to characterize if you draw the diagrams. I'll try to read some source in order to get a firmer grasp of these things.

Now I just hope the latexing doesn't blow up when I press the post button...

>>	Anonymous Thu Mar 29 20:40:29 2018 No.9629394 Is algebra the chess of math?

>>	Anonymous Thu Mar 29 20:53:19 2018 No.9629419 >>9629394 Yes, and analysis is the Go of math.

>>	Anonymous Thu Mar 29 20:54:50 2018 No.9629421 >>9629394 Checkers would be more apt

>>	Anonymous Thu Mar 29 21:04:05 2018 No.9629439 Could vector spaces which do not have a basis be used in cryptography?

>>	Anonymous Thu Mar 29 21:06:01 2018 No.9629442 >>9629439 Anything can be used in cryptography

>>	Anonymous Thu Mar 29 21:11:58 2018 No.9629468 >>9629439 >vector spaces which do not have a basis No such thing.

>>	Anonymous Thu Mar 29 21:59:40 2018 No.9629605 What are some applications of ideals which are not contained in a maximal ideal? >H-how did I do guys?

>>	Anonymous Thu Mar 29 22:48:43 2018 No.9629706 I'm learning Taylor Series now. Shit's starting to get pretty interesting, desu senpai

>>	Anonymous Thu Mar 29 22:53:14 2018 No.9629720 >>9629706 >learning Taylor Series now >desu senpai wordfilters You have to be18 to post on this site, but that isn't so bad, once you're of age you probably leave that twitter babble behind you

>>	Anonymous Thu Mar 29 22:54:30 2018 No.9629722 >>9629720 you sound like a stan, my good senpai.

>>	Anonymous Thu Mar 29 23:04:29 2018 No.9629734 >>9629605 >What are some applications of ideals which are not contained in a maximal ideal? There are probably some cryptographic applications

>>	Anonymous Thu Mar 29 23:19:59 2018 No.9629785 >>9629706 Yeah, they're pretty cool and fucking everywhere.

>>	Anonymous Fri Mar 30 00:45:32 2018 No.9629970 >>9627522 My pleasure. I never thought I would see Chadron, let alone Haataja, in /mg/--I'm glad we had this little transaction.

>>	Anonymous Fri Mar 30 02:05:44 2018 No.9630065 File: 186 KB, 1105x960, 1515368431410.jpg [View same] [iqdb] [saucenao] [google] >>9629419 >analysis is the [blank] of math. But wouldn't it have to be a part of math for that to make sense?

>>	Anonymous Fri Mar 30 02:09:06 2018 No.9630068 File: 62 KB, 640x480, Great+khan+spurdo+fingolian.jpg [View same] [iqdb] [saucenao] [google] >>9628265 >>9628271 >>9628337 >>9628335 These Fingol Spurdos

>>	Anonymous Fri Mar 30 05:41:19 2018 No.9630288 File: 84 KB, 800x800, 1520738376471.png [View same] [iqdb] [saucenao] [google] What's a minimum non-brainlet score for tests? Got around 80% on combinatorics a few days ago and I'm not sure how to feel

>>	Anonymous Fri Mar 30 05:43:21 2018 No.9630292 >>9630288 believing that a cutoff exists is a sure sign you're a brainlet, sorry my dude

>>	Anonymous Fri Mar 30 06:45:34 2018 No.9630386 How can I build a cryptographic system based on the fact that some sets of non-empty sets do not admit a choice function?

>>	Anonymous Fri Mar 30 06:54:53 2018 No.9630398 >>9622355 feynmann wrote down everything he didn't understand in a notebook. it'll probably help if you try it out

>>	Anonymous Fri Mar 30 06:58:46 2018 No.9630400 File: 207 KB, 567x800, r.jpg [View same] [iqdb] [saucenao] [google] Why is Algebra so hard lol?

>>	Anonymous Fri Mar 30 06:59:01 2018 No.9630401 File: 119 KB, 313x399, 1485055696674.png [View same] [iqdb] [saucenao] [google] >>9629605 Google this: >applications for rings

>>	Anonymous Fri Mar 30 07:00:52 2018 No.9630406 https://en.wikipedia.org/wiki/Rng_(algebra)

>>	Anonymous Fri Mar 30 07:41:27 2018 No.9630470 >>9630386 >non-empty sets No such thing.

>>	Anonymous Fri Mar 30 07:43:39 2018 No.9630476 >>9630470 >No such thing. The burden of proof is on you.

>>	Anonymous Fri Mar 30 07:45:53 2018 No.9630483 >>9630398 >feynmann You might want to discuss that in the physical threads over at >>>/toy/.

>>	Anonymous Fri Mar 30 07:48:06 2018 No.9630487 What is the dimension of the [math] \mathbb{F}_2 [/math]-vector space of all axioms?

Anonymous Fri Mar 30 08:38:21 2018 No.9630552

>>9629204
The category of modules over a Hopf algebra has some interesting properties - if you have, for example, [math] H [/math]-modules [math] V,W [/math], the tensor product [math] V \otimes_k W[/math] also is an [math] H [/math]-module with the multiplication [math] h(v \otimes w) := \Delta(h) (v \otimes w) [/math].
Tensor products of group or Lie algebra representations can be seen as coming from Hopf structures on the group algebra resp. universal enveloping algebra - which are both cocommutative. This immediately leads to nice isomorphisms between [math] V \otimes W [/math] and [math] W \otimes V [/math]. If your Hopf structure is not cocommutative, there is no guarantee that these modules are related. But there are interesting cases where you still have a commutativity constraint (i.e. the respective tensor categories are braided) despite [math] H [/math] not being cocommutative.
By the way, I wouldn't see non-cocommutativity as something "special" because I like to think that "generic" bialgebras are very likely to be noncommutative/noncocommutative.

Anonymous Fri Mar 30 09:12:30 2018 No.9630584
File: 91 KB, 504x561, ooh.jpg [View same] [iqdb] [saucenao] [google]

>>9630552
Ah, I just realized I misread your post back then. You said non-COcommutative and not just non-commutative twice. Now I understand what you meant. I looked at the book on quantum groups by Kassel, and I'll probably borrow it from the library after the Easter break is over.

Since one can have modules over Hopf algebras, I came up with a little question. Suppose [math]A, A', R[/math] are rings such that [math]A[/math] is also a Hopf algebra over [math]R[/math] and [math]A, A'[/math] are Morita equivalent. Will [math]A'[/math] be a Hopf algebra over [math]R[/math] automatically, or will it be if we assume it is already an algebra over [math]R[/math]?

>>	Anonymous Fri Mar 30 15:02:49 2018 No.9631220 >>9630288 a true brain bull can rationalize any score on a test no matter how low

>>	Anonymous Fri Mar 30 19:24:39 2018 No.9631704 >>9627978 you should've gone for qt 3.14 GFs

>>	Anonymous Fri Mar 30 19:33:03 2018 No.9631715 >>9630487 >implying double negation elimination is valid also, countably infinite, since the space itself is countable and any finite-dimensional space over a finite field is finite

>>	Anonymous Fri Mar 30 21:22:41 2018 No.9631962 brainlet here how come the epsilon-delta definition of a limit says that collapsing on the y axis to some point must imply collapse on the x axis to some point? as opposed to collapse on the x axis implies collapse on the y axis?

>>	Anonymous Fri Mar 30 21:28:58 2018 No.9631981 >>9631962 What do you mean by "collapse"?

>>	Anonymous Fri Mar 30 21:30:39 2018 No.9631989 File: 78 KB, 640x360, 1522430357397.jpg [View same] [iqdb] [saucenao] [google] >tfw bad at algebra

>>	Anonymous Fri Mar 30 21:34:57 2018 No.9631997 >>9631962 besides your brainlet notation, you're reading your definition wrong. It's definitely the latter. For all points close enough to the limit c, then the values of f(x) will be close to f(c)

>>	Anonymous Fri Mar 30 22:16:38 2018 No.9632056 >>9631997 o wow my brainlet prof taught it backward

>>	Anonymous Fri Mar 30 23:27:58 2018 No.9632197 >>9630406 >tfw when wikipedia's definition of a ring is the wrong one >tfw some idiot is going to reply to this looking to start some shit

>>	Anonymous Fri Mar 30 23:34:08 2018 No.9632206 >>9622175 I'm relearning arithmetic because apparently I can do calculus but I can't do basic multiplication or division past a hundred in my head.

>>	Anonymous Sat Mar 31 00:32:50 2018 No.9632314 >>9632197 >>tfw when wikipedia's definition of a ring is the wrong one How so?

>>	Anonymous Sat Mar 31 00:37:33 2018 No.9632324 File: 112 KB, 500x400, cute_bunny_002.jpg [View same] [iqdb] [saucenao] [google] >>9628494 Why is it that you want to die anon?

>>	Anonymous Sat Mar 31 01:10:22 2018 No.9632371 >>9632206 This kind of. I say kind of because I'm learning arithmetic through 'Arithmetica' by Diophantus, and it's more or less teaching me about the rigorous methods of solving certain arithmetical problems.

Anonymous Sat Mar 31 01:26:47 2018 No.9632397

>>9632314

The two conventions hinge on the (incorrect) requirement of a multiplicative identity, a "1", while the "alternative" (correct) definition does not require such. the wiki itself is however careful to stress that there are in fact two prevailing conventions, it simply errs in choosing the wrong one.

>>	Anonymous Sat Mar 31 01:27:50 2018 No.9632399 >>9632371 How is that going? I think you were the anon who posted a "what am I in for" a week or so ago. t. have a very serious interest in history of math

>>	Anonymous Sat Mar 31 01:28:12 2018 No.9632400 File: 872 KB, 1000x600, BrainletBreaksReality.gif [View same] [iqdb] [saucenao] [google] >>9622175 Inter-Universal Teichmuller Theorem.

Anonymous Sat Mar 31 02:11:49 2018 No.9632468

>>9632399
It's going okay. Just started tonight. I'll be reading more of it tomorrow...

I mean, it's pretty simple, basic algebra. I had read Introduction to Arithmetic by Nicomachus before beginning this, so the change of pace is... interesting. Whereas Nicomachus used Elements V, VII, the extant books of Arithmetica use book IX, lol. A big upgrade. I, of course, read Elements as well, so it's always interesting to see propositions referenced that I had completely forgotten about.

I'm also reading the highly analytical 'Manual of Political Economy' by Vilfredo Pareto, and that is just fascinating, but 1000x harder than this simple mathematics.

Anonymous Sat Mar 31 02:12:01 2018 No.9632469
File: 83 KB, 500x561, complex-analysis-second-edition-principles-of-mathematical-analvsis-lars-v-30267491.png [View same] [iqdb] [saucenao] [google]

>studied a lot of math before getting into uni, specially calculus/introductory analysis, finished some books, was really fond of polynomials
>first evaluation, I quickly ace the algebra and the geometry tests in ~10 minutes, were no challenge for me
>introduction to calculus test comes in
>thisismytimetoshine.jpg
>only one question
>find the values of [math]\alpha[/math] [math]\beta[/math] in terms of a and b, if a and b (distinct from one another) are roots of the equation [math]x^2 + \alpha x + \beta = 0[/math].
>"holy shit this is too easy", I think to myself
>can only think of Viete's formulas
>mind goes blank
>completely forget everything about calculus
>can only think of polynomials and the fundamental theorem of algebra at this point
>blackguysweating.gif

why did you make me an autist, Lord?

got a 100% on the second and third test, and keeping a 100% average on algebra/geometry but fuck I felt like a brainlet

Anonymous Sat Mar 31 02:58:59 2018 No.9632520
File: 37 KB, 500x375, 9F2F45C4-3358-4D72-95C4-B947780ACFD1.jpg [View same] [iqdb] [saucenao] [google]

Hey /sci/, /ic/fag here. I fucked up college the first time around because of incompetence.

Thinking about going back because I feel like my current Job isn’t challenging enough. Before I do though, I wanna go over the basic stuff I fucked up in. What sources do you guys recommend for someone who left off on the high school level?

>>	Anonymous Sat Mar 31 03:00:08 2018 No.9632521 >>9632397 >The two conventions hinge on the (incorrect) requirement of a multiplicative identity How is it an "incorrect" requirement?

>>	Anonymous Sat Mar 31 03:01:00 2018 No.9632523 >>9632520 we have a really good wiki in the sticky that you can use to find book recommendations checkout libgen if you haven't too.

>>	Anonymous Sat Mar 31 03:08:28 2018 No.9632529 >>9632469 >calculus/introductory analysis >math Do you have any kind of brain damage?

Anonymous Sat Mar 31 03:14:56 2018 No.9632534
File: 110 KB, 1629x884, weapons_grade_autism_minimal_insight.png [View same] [iqdb] [saucenao] [google]

>>9632468

Please tell me more about the Nicomachus context. Is this the same of the "Nicomachean Ethics"?

For my part, I've fully analyzed the Rhind Papyrus third-hand via Chace to my own satisfaction, and at some point I'll take Cardano back up (a long stall-out here, I got bogged down in life and a counting argument to explain how Cardano feels it necessary to explain his "cases" as he did at the time, pic related) I've just finished a help-book on Gödel's proof (Nagel/Newman) which gives some insights on the business. Stupidly, a few years ago I actually tried to read Gödel straight-up and I got the impression from the prose that the Gödel numberings should map 1-1 onto all naturals, which is apparently not the case. Related to Cardano, I discovered some very abstruse Italian text of Ruffini's in the local top uni's math library. I wonder exactly what one it is (IIRC I'm not sure that it's his early, hideously long version of the impossibility proof).

A diophantine problem of personal interest: the existence or non-existence of a perfect cuboid (a stronger version of an euler brick). This (the proving of such and such a lemma about same) is something else that I've had in storage for a while so I'll immediately reproduce it next.

>>	Anonymous Sat Mar 31 03:21:15 2018 No.9632541 >>9632534 Haha. Nicomachean Ethics is a treatise by Aristotle in reference to his son, Nicomachus. No relation between the two though.

>>	Anonymous Sat Mar 31 03:26:50 2018 No.9632549 >>9622175 Thats one smart friend.

Anonymous Sat Mar 31 03:33:00 2018 No.9632556

>>9632534

on the perfect cuboid/euler brick business I've just raised, here: it can be shown of an euler brick that by its definition, its side lengths must necessarily all be unequal. For if any two were equal, then their accompanying side diagonal would involve a √2 term and so not itself be an integer. So from shortest to longest, these side lengths can be designated a, b, c. Immediately, the corresponding ab (d) ac (e) bc (f) face diagonals are all likewise unequal, and can be designated d, e, f. And then the spatial diagonal g is even greater.

These considerations lead to a table of comparision, in which the seven quantities and their squares (per the original defining equations) may be compared with a view to strict inequality among them, in an effort to learn more about the problem. The place where I got stuck was the middle white area of this table, with the other stuff being an autistic logical chain of reasoning given the above. A very important few counterexamples entail that the longest edge length c may be shorter than the shortest face diagonal d and vice verse. Any civil thoughts on improving the table are welcome.

>>	Anonymous Sat Mar 31 03:34:06 2018 No.9632557 File: 79 KB, 1581x721, minecraft_I_like_trains.png [View same] [iqdb] [saucenao] [google] >>9632556 This is the relevant picture for this post.

>>	Anonymous Sat Mar 31 06:19:01 2018 No.9632708 >>9632056 no he probably wrote it as \|f(x)-f(c)\|< epsilon whenever \|x-c\|< delta

>>	Anonymous Sat Mar 31 06:54:57 2018 No.9632771 >>9632520 >>>/sqt/ is a better place to ask

>>	Anonymous Sat Mar 31 07:28:04 2018 No.9632818 >>9632708 is that well defined for all values of epsilon though?

>>	Anonymous Sat Mar 31 07:59:59 2018 No.9632902 File: 28 KB, 667x359, 4165614.jpg [View same] [iqdb] [saucenao] [google] >>9632818 Yes. It is nothing but two inequalities and a claim that if one holds, then the other holds. If the claim holds, then the function is continuous.

>>	Anonymous Sat Mar 31 08:14:17 2018 No.9632934 . or , for decimals?

>>	Anonymous Sat Mar 31 08:14:35 2018 No.9632936 How does multidimensional matrix operations work? The product of two three-dimensional matrices for example. Is the entries in the result matrix sort of combination of dot products of the vectors from relevant "planes"?

>>	Anonymous Sat Mar 31 08:14:55 2018 No.9632939 >>9632934 >decimals In what way is this relevant to math?

>>	Anonymous Sat Mar 31 08:16:20 2018 No.9632946 >>9632902 but isn't there a jump in the function for certain values of epsilon? that would probably mean that R^1 isn't a continuous manifold.

>>	Anonymous Sat Mar 31 08:16:36 2018 No.9632947 >>9632934 >. or , for decimals? .

>>	Anonymous Sat Mar 31 08:18:10 2018 No.9632950 >>9632939 there are numbers in math isn't there

>>	Anonymous Sat Mar 31 08:22:07 2018 No.9632961 >>9632950 There are certain objects which have "numbers" as their global elements but the "numbers" themselves aren't involved in mathematics, especially not "decimals".

>>	Anonymous Sat Mar 31 08:25:22 2018 No.9632974 >>9632961 i'm astounded Anyway, would you be so kind to tell me which symbol do you use?

Anonymous Sat Mar 31 08:28:08 2018 No.9632985
File: 81 KB, 1366x768, 7215193.jpg [View same] [iqdb] [saucenao] [google]

>>9632946
I'm not sure if I understand your post. Suppose there was a jump of r>0 at some real number x, but the claim was true nevertheless. For any [math]\varepsilon>0[/math], there is a [math]\delta>0[/math] such that [math]|x-y|<\delta \Rightarrow |f(x)-f(y)|<\varepsilon[/math]. Now, choose [math]\varepsilon = \frac{r}{2}[/math] to get, for a sufficiently small [math]\delta[/math], the contradiction [math]\frac{r}{2} < |f(x+\delta) - f(x)| < \frac{r}{2}[/math], so you can't have jumps if the claim holds. Latex bb, pls don't explode when I press the post button <3

>>	Anonymous Sat Mar 31 08:30:37 2018 No.9632994 >>9632961 >mathematics This is not well-defined.

>>	Anonymous Sat Mar 31 08:30:58 2018 No.9632995 >>9632974 Why would I use symbols for things I never use? I don't work in engineering or related fields. You might have better luck asking the engineers themselves, try doing that in >>>/sci/en/ or >>>/sci/sqt/.

>>	Anonymous Sat Mar 31 08:32:06 2018 No.9633000 >>9632995 What is your field?

>>	Anonymous Sat Mar 31 08:35:51 2018 No.9633012 >>9633000 Don't reply to the spammer.

>>	Anonymous Sat Mar 31 08:36:18 2018 No.9633015 >>9633000 Try guessing by reading the subject of the thread.

Anonymous Sat Mar 31 08:40:49 2018 No.9633028

>>9632985
isn't a continuous manifold required to satisfy the extra law [math]\displaystyle \sum_{x=0}^{\infty} ~ | f(x) - y | + \delta = \lim_{f' \to \infty} \frac{f'}{|f(\epsilon) - f(\epsilon^2)|} [/math] as f' approaches infinity?
jumps in the function wouldn't make sense physically on a continuous manifold like R^1 or C^1 or even C^2. i don't know how to rigorously prove this though.

Anonymous Sat Mar 31 08:47:37 2018 No.9633044
File: 35 KB, 600x541, en jaksa.jpg [View same] [iqdb] [saucenao] [google]

>>9633028
No idea. Why are you making babby's first continuity definition overcomplicated by summoning [math]C^k[/math] stuff from the depths of the abyss? Physical intuition isn't an argument either. You made my head hurt, please apologize.

Anonymous Sat Mar 31 09:28:28 2018 No.9633124
File: 44 KB, 1920x949, Drawing.jpg [View same] [iqdb] [saucenao] [google]

>>9633044
it's not physical intuition, it's physical knowledge. i can look at the ambient space around me and conclude empirically that no manifold can possibly have such jumps.
consider for example the continuous manifold in the attached drawing. denote it by [math]\mathcal{M}[/math]. then if any jump whatsoever exists in [math]\mathcal{M}[/math], then
[math]\displaystyle \prod_{p ~ \text{prime}} f(x) + \epsilon^p - f'(x) = \infty[/math] for every non-infinitesimal [math]x \in Ext^1_{\underline{\mathbb{Z}}}(\mathcal{M}^{\mathbb{Q}}, \underline{\mathbb{Z}})[/math] assuming f' exists as f' approaches zero which is an obvious contradiction physically speaking.

>>	Anonymous Sat Mar 31 09:37:25 2018 No.9633142 >>9632985 you know you can press the latex button at the top of the reply box to check if the latex is alright, no?

>>	Anonymous Sat Mar 31 09:37:44 2018 No.9633143 >>9633142 that doesn't always help.

>>	Anonymous Sat Mar 31 09:38:28 2018 No.9633146 >>9632936 look up tensors

Anonymous Sat Mar 31 09:40:55 2018 No.9633154
File: 27 KB, 800x473, yuuka.png [View same] [iqdb] [saucenao] [google]

>>9633124
>it's not physical intuition, it's physical knowledge. i can look at the ambient space around me and conclude empirically that no manifold can possibly have such jumps.
You can also look around yourself and conclude empirically that you see only a finite amount of things, so physical knowledge excludes infinite sets like [math]\mathbb{R}[/math]. Go to bed, you are drunk.

>>9633142
Yes I do, but >>9633143

>>	Anonymous Sat Mar 31 09:41:12 2018 No.9633155 >>9633146 they're physically meaningless most of the time. better look up prime vectors which give the correct picture.

Anonymous Sat Mar 31 10:03:42 2018 No.9633197
File: 116 KB, 1920x949, Universe.jpg [View same] [iqdb] [saucenao] [google]

>>9633154
let [math]\mathcal{U}[/math] denote our universe, let [math]\mathfrak{X} = \mathcal{U} \setminus \mathcal{DM}[/math] be our universe with all dark matter removed. we show that there are jumps in [math]\mathfrak{X}[/math]. this will obviously imply that no jumps exist in [math]\mathcal{U}[/math], thus showing that [math]\mathcal{U}[/math] is infinite.
assume there are no jumps in [math]\mathfrak{X}[/math], then it can be shown that for every [math]f \in \bigcup_{X} C^\infty(X) [/math] where [math]X[/math] is any continous metric space we have [math]\mathfrak{X}^{fin} \cup_f f'(\mathcal{S^1}) \cong \mathfrak{X}^{inf}[/math] where [math]\mathfrak{X}^{fin}[/math] and [math]\mathfrak{X}^{inf}[/math] are the "universal finitization" and "universal infinitization" of [math]\mathfrak{X}[/math] respectively and [math]\mathcal{S^1}[/math] is the finite circle. this is an obvious physical contradiction since you can't glue a finite amount of non-dark matter to get an infinite amount of dark matter.
see the attached drawing for intuition.

>>	Anonymous Sat Mar 31 11:58:22 2018 No.9633419 >>9633197 Every post you've made so far reads like utter nonsense. This is why we shouldn't allow physicists in the math general.

>>	Anonymous Sat Mar 31 12:05:27 2018 No.9633437 >>9633197 >our universe Is that well defined?

>>	Anonymous Sat Mar 31 16:49:04 2018 No.9634237 >>9633419 That's not even mathematical physics but just a naive physical worldview formulated mathematically.

Anonymous Sat Mar 31 16:52:57 2018 No.9634251

>>9630584
Sorry for the late answer. I don't know - I first thought that putting a tensor structure on [math]Mod-A[/math] directly leads to a Hopf structure but that might be wrong. Either way, a positive answer to your question would imply the existence of Hopf structures on arbitrary Matrix rings over arbitrary fields (which would be really nice).

Anonymous Sat Mar 31 17:03:46 2018 No.9634276

>>9633419
what about my posts is nonsense? it makes perfect sense. and i'm not a physicist, i'm a mathematical physicist which is obviously a big difference as we use rigor.
>>9633437
yeah. i don't see why it isn't. we live in it so it must be well defined.

Anonymous Sat Mar 31 17:19:42 2018 No.9634310
File: 178 KB, 1412x1175, 109.jpg [View same] [iqdb] [saucenao] [google]

>>9634251
It would be, yes. An isomorphism should preserve the structure, but that may be the limit for structural preservation. Unless there is some way to characterize them via their modules.

Anonymous Sat Mar 31 17:39:07 2018 No.9634352
File: 37 KB, 416x521, 1258052084820.jpg [View same] [iqdb] [saucenao] [google]

>>9632994
fuckface (what is the word the teacher says at the end of 'it's my turn' snake lemma clip?)

>>9634276
Very interesting indeed, write it down in word and submit it to arxiv on mathematical physics, we big friends will welcome you with 1 million gold minimum and have you join our special elitarian society and together archieve greatness.

>>	Anonymous Sat Mar 31 18:43:58 2018 No.9634519 >>9632961 Are you stupid or something ? There's an entire branch of mathematics about studying the properties of numbers.

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