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# /sci/ - Science & Math

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No.11446627 [Reply] [Original] [archived.moe]

talk maths, formerly >>11432923

https://arxiv.org/pdf/2003.01890.pdf
>One could think of anabelomorphy in the following picturesque way: One has two parallel universes (in the sense of physics) of geometry/arithmetic over $p$-adic fields $K$ and $L$ respectively. If $K$, $L$ are anabelomorphic (i.e.$K\leftrightsquigarrow L$) then there is a worm-hole or a conduit through which one can funnel arithmetic/geometric information in the $K$-universe to the $L$-universe through the choice of an isomorphism of Galois groups $G_K\cong G_L$, which serves as a wormhole. Information is transfered by means of amphoric quantities, properties and alg. structures. The $K$ and $L$ universes themselves follow different laws (of algebra) as addition has different meaning in the two anabelomorphic fields $K$, $L$ (in general). As one might expect, some information appears unscathed on the other side, while some is altered by its passage through the wormhole. Readers will find ample evidence of this information funneling throughout this paper (and also in [Moc12e, Moc13, Moc15] and [Moc12a, Moc12b, Moc12c, Moc12d] which lay the foundations to it).

 >> Anonymous Fri Mar 6 21:00:46 2020 No.11446728 >>11446627>Open Number Theory paper>see Robin's Theorem>Close Number Theory paper
 >> El Arcón Fri Mar 6 21:22:49 2020 No.11446769   File: 151 KB, 880x1050, TIMESAND___476ffaf4fzutyfh6ieutkdjcyftzzzwi463wqbetfwri90jg4uii3axtjs00wrgfjscvcsxzqzqwhw6qhr.png [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Fri Mar 6 21:30:52 2020 No.11446778 >>11446769whats a galois group
 >> Anonymous Fri Mar 6 22:01:28 2020 No.11446845 >>11446769Oh, its been so long
 >> Anonymous Fri Mar 6 22:02:47 2020 No.11446849 >>11446778The group of automorphisms of the field
 >> Anonymous Fri Mar 6 22:16:03 2020 No.11446869 >>11446849which field? whas an automorphism?
 >> El Arcón Fri Mar 6 22:17:53 2020 No.11446874   What is the Latin alphabet?
 >> Anonymous Fri Mar 6 22:20:34 2020 No.11446875 >>11446869A field is a mathematical generalization of a flat grassy piece of land. An automorphism is a theoretical framework for transforming one kind of car into another.
 >> Anonymous Fri Mar 6 22:23:24 2020 No.11446879 >>11446849No.
 >> Anonymous Fri Mar 6 23:04:47 2020 No.11446945 What text would be good for getting into complex analysis? I have an EE degree and did some work doing differential modeling of natural system dynamics in Mathlab for a mathematics minor, and would like to get back into it all.
 >> El Arcón Sat Mar 7 00:32:28 2020 No.11447309   File: 1.40 MB, 3376x3024, TIMESAND___Thievery.png [View same] [iqdb] [saucenao] [google] [report] I actually have a whole section in my free book about how other people besides Mochi-kunt had already stolen big parts of my research aside from the part that Mocki-kunt stole. Pic related.Original section:>The General Relevance of the Modified Cosmological ModelEventual Hamiltonian:>Time Arrow Spinors for the Modified Cosmological Model>>11446945When I need to remember something about CA, I go to Orloff's undergrad MIT notes.
 >> Anonymous Sat Mar 7 00:44:03 2020 No.11447337 What does Kashiwara mean by a “U set” is a set isomorphic to a set belonging to U. (U is a Grothendieck Universe). He doesn’t define isomorphisms before that. Is Isomorphism = Bijection in this context?
 >> Anonymous Sat Mar 7 00:47:45 2020 No.11447349 File: 26 KB, 640x533, 1582679131677.jpg [View same] [iqdb] [saucenao] [google] [report] EE undergrad hereif I don't want to annoy the math people on my upcoming senior project to death what should I not do?I already know being prideful about easy stuff like calculus or the beginner ODE's I was taught is bad along with dick waving in general, but is there anything else that's obviously bad?
 >> Anonymous Sat Mar 7 00:49:46 2020 No.11447353 File: 1.80 MB, 1202x910, physical maths.png [View same] [iqdb] [saucenao] [google] [report] Threadly reminder to work with physicists.
 >> Anonymous Sat Mar 7 01:13:19 2020 No.11447403 >>11446879y not?
 >> Anonymous Sat Mar 7 01:18:21 2020 No.11447410 >>11447349Don't be loose with your reasoning, try being as concrete and clear as possible, understand the common nomenclature, don't use words that have both a technical and colloquial meaning in any other circumstance except technical (you start saying things like "there a manifold reasons for blah" and it'll just get weird), try putting some diagrams and pictures in there people love that shit, don't spend too long on trivial details most mathematicians worth their salt can fill in the gaps just give the broad strokes and give details only where crucial.
 >> Anonymous Sat Mar 7 02:51:29 2020 No.11447580 Can I get an operator K theory book suggestion? I took a class on algebraic K theory and have some exposure to topological K theory, so it seems silly that I have no operator background.
 >> Anonymous Sat Mar 7 03:33:54 2020 No.11447647 >>11447337Likely
 >> Anonymous Sat Mar 7 03:39:12 2020 No.11447653 What is the best way to develop an intuition for tensor algebra (from a rigorous mathematical perspective)?
 >> Anonymous Sat Mar 7 04:21:07 2020 No.11447747 >>11447653Think of tensors as linear functionals defined on product spaces.
 >> Anonymous Sat Mar 7 05:06:47 2020 No.11447812 File: 61 KB, 1080x1080, 1548307257083.jpg [View same] [iqdb] [saucenao] [google] [report] >14F05>14F20>14F30>14H57>14K22>18GXX>19AXX>19E08>19E15>19E20
 >> Anonymous Sat Mar 7 05:22:16 2020 No.11447839 >>11447647Thank you
 >> Anonymous Sat Mar 7 10:40:58 2020 No.11448288 Presheaf? I barely even knew her!
 >> Anonymous Sat Mar 7 10:55:39 2020 No.11448310 just realised that "second quantification" [in Quantum Physics] comes from the fact that the Hilbert space is "second countable"funny that
 >> Anonymous Sat Mar 7 10:57:02 2020 No.11448314 >>11447337Yeah, isomorphism in the category of sets.
 >> Anonymous Sat Mar 7 10:58:34 2020 No.11448317 >>11447580Pretty sure your options are Blackaddar, Blackaddar and also Blackaddar.It's available on his website for free.https://wolfweb.unr.edu/homepage/bruceb/Book6.pdf
 >> Anonymous Sat Mar 7 11:14:24 2020 No.11448357 >>11446769Sauce?
 >> Anonymous Sat Mar 7 11:15:38 2020 No.11448360 >>11448310Mhm, I'd like to believe that but I'd guess the expression "second quantification" comes from early 20'th century physicists who where by and large not talking in those particular mathematical terms. Mind you, the formalization even of set theory and quantum field theory is barely 50 years apart.
 >> Anonymous Sat Mar 7 11:16:59 2020 No.11448365 >>11448310Pretty sure second quantization originally comes from quantizing a second time.Nowadays it just means something something Fock spaces.
 >> Anonymous Sat Mar 7 11:18:41 2020 No.11448369 >>11448365ye mum focks spaces
 >> Anonymous Sat Mar 7 11:21:18 2020 No.11448378 >>11448365Agreed, and even that is historically grown and rather inaccurate term. It's not like they didn't have field theories and cooking up Lagrangian formulations of field's differential equations before going from classical to quantum mechanics. Moreover, I don't think "second countable" has a German correspondence with "zweit" (i.e. 2nd) in it, which makes >>11448310 even more unlikely
 >> Anonymous Sat Mar 7 11:23:15 2020 No.11448381 >>11448365>>11448360>>11448378You're probably right, but the textbook I'm reading it from [i'm arguably not at a very advanced level] really makes it look like there's a parallel at least between the two thingsBefore introducing the actual photons and radiation quantas, it starts by quantifying a simple continuous model (the continous vibrating string), and it makes a good deal of showcasing how you go from a continous model to infinitely countable quantasIt's really, really funny how it makes me think of something completely abstract and unrelated (the isomorphism between l-2 spaces and the space of continuous square-integrable periodic functions)I guess this was just being over-excited about something I could string together
 >> Anonymous Sat Mar 7 11:40:07 2020 No.11448409 File: 151 KB, 1079x1500, 71jDdUuRi8L._AC_SL1500_.jpg [View same] [iqdb] [saucenao] [google] [report] >It's really, really funny how it makes me think of something completely abstract and unrelated (the isomorphism between l-2 spaces and the space of continuous square-integrable periodic functions)I think it's hard to find two things in math which are entirely unrelated. That whole function space spiel just as much relates to character theory, Pontryagin duality, Rigged Hilbert spaces and eventually trickle into the position-momentum conundrum you have in quantum mechanics. What you look at then more concretely is this similar transformhttps://en.wikipedia.org/wiki/Segal%E2%80%93Bargmann_space>it starts by quantifying a simple continuous model (the continous vibrating string), and it makes a good deal of showcasing how you go from a continous model to infinitely countable quantasYou mean quantifying or quantizing here? The modes of a compact system are already countable discrete in the classical setting and you might also speak of "quantizing" here, so the language get's a bit fuzzy. For telling things apart-sake, I'd speak of QM exactly at that point where it involves an algebra of observables (whatever the means of obtaining real measurement values is) that is a non-commutative algebra.>>11448381>but the textbook I'm readingWhich book?I've recently ranted a bit about a history book here (and there's a follow-up video more concretely about the life of B. L. van der Waerden')https://youtu.be/5zLr7hAnrZY
 >> Anonymous Sat Mar 7 11:44:24 2020 No.11448416 >>11448409English isn't my first language, sorry for the confusion, yeah I know the vibrating string already has a "quantification" with eigenmodes and dispersion relationIn a way, I guess this discussion helped me to understand that we are now quantizing "again" by imposing the energies to be "packets of $h \nu_k$, hence the name 2nd quantificationThanks!The book is "Quantum Mechanics" by Cohen, Diu, Laloë
 >> Anonymous Sat Mar 7 12:36:56 2020 No.11448517 >>11448416What's in a name? I wouldn't read too much into it, it's historical.
 >> Anonymous Sat Mar 7 13:40:42 2020 No.11448687 >>11447653Noncommutative polynomials in your basis vectors obviously
 >> Anonymous Sat Mar 7 13:55:00 2020 No.11448716 File: 1.81 MB, 1208x1084, balls.png [View same] [iqdb] [saucenao] [google] [report] The spatial transformations (for which time isn't relevant) are called Euclidean transformations.Now how come the homogenous Galilean transformations don't have their own name? (In parallel to how the homogenous Poincare transformations are called Lorentz transformations.)
 >> Anonymous Sat Mar 7 14:07:06 2020 No.11448757 >>11448314But wouldn’t the U-set and the set in consideration be in possibly different Set categories, since they might be living in different universes?
 >> El Arcón Sat Mar 7 14:12:44 2020 No.11448766   >>11448357The blurb is from OP paper. I put together that picture in this 2013 paper.>Geometric Cosmology
 >> Anonymous Sat Mar 7 14:19:30 2020 No.11448776 >>11448757The category of sets has all sets, anon.
 >> Anonymous Sat Mar 7 14:29:53 2020 No.11448794 >>11448776even itself?
 >> Anonymous Sat Mar 7 14:30:58 2020 No.11448796 >>11448776Kashiwara doesn’t allow the Category of all Sets. He takes the viewpoint of Grothendieck Universes. But I think I understand the idea now, one assumes that both universes U, V are contained in a bigger universe W, and then the V set and the U set are isomorphic in Set_W.
 >> Anonymous Sat Mar 7 14:36:04 2020 No.11448803 >>11448794Categories aren't set. (Just "function" shouldn't mentally be set equal to "set of pairs, and with the function property")
 >> Anonymous Sat Mar 7 16:20:25 2020 No.11448998 Are there any good books on constructivist / intuitionistic approaches to mathematics? You always see it mentioned in books which have axiomatic approaches to mathematics but I'm having trouble finding actual references for the material. In particular, I'm just having a hard time imagining proving properties about mathematical objects via some set of axioms without ever using proof by contradiction - it seems like some propositions can be made specifically so they can only be proved via a reductio ad absurdum argument with reference to "it contradicts the axioms so it must be false."
 >> Anonymous Sat Mar 7 16:48:56 2020 No.11449057
 >> Anonymous Sat Mar 7 16:57:12 2020 No.11449074
 >> Anonymous Sat Mar 7 17:03:27 2020 No.11449092 File: 368 KB, 339x533, taosnap.gif [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Sat Mar 7 17:07:44 2020 No.11449104
 >> Anonymous Sat Mar 7 17:08:03 2020 No.11449106 >>11448998The only places intuitionistic logic gets used seriously is HoTT and some abstract varieties (hehe) of alg geo and diff geo. And that ultimately boils down to the fact that the internal logic of a topos is inherently intuitionistic.
 >> Anonymous Sat Mar 7 17:09:17 2020 No.11449108 File: 8 KB, 231x218, 1583617872560.jpg [View same] [iqdb] [saucenao] [google] [report] How is your PhD studies going?
 >> Anonymous Sat Mar 7 17:11:22 2020 No.11449111 >>11449108rejected from all the places I applied to and am now in my mother's basement deciding what to do with this useless master's degree
 >> Anonymous Sat Mar 7 17:11:53 2020 No.11449115 >>11448998There are number of different approaches. Bishop's book "Foundations of Constructive Analysis" is probably most accessible.
 >> Anonymous Sat Mar 7 17:21:04 2020 No.11449133 >>11449111>rejected from all the places I applied toI can't imagine how this even happens unless you shot way too high and the worst school you applied to was Cornell or somethingI came from a trash no-name school, GPA wasn't perfect, no research experience except a single summer, and only 2 good letters and I still got into around half the programs I applied for, and I only applied to R1s.
 >> Anonymous Sat Mar 7 17:24:50 2020 No.11449145 >>11446769This is just like saying comparative philology is a complete science with 100% sure morphisms.
 >> Anonymous Sat Mar 7 17:25:14 2020 No.11449146 >>11449133I think the worst school I applied to was Colorado State University I got past the stage where I blamed factors outside my control for failing to get into a PHD program and accepted that I'm just shit and seriously should to consider suicide.
 >> Anonymous Sat Mar 7 17:30:40 2020 No.11449159 >>11449146Just get a job and apply again next year. Apply for PhD positions in shit holes in Europe.
 >> Anonymous Sat Mar 7 17:37:01 2020 No.11449184 >>11449146why would you do that? you're obviously much much smarter than almost everyone if you've made it this far
 >> Anonymous Sat Mar 7 17:38:59 2020 No.11449190 >>11449146because a professional tripfag on /mg/ and publish all your work under that pseudonym
 >> Anonymous Sat Mar 7 17:39:00 2020 No.11449191 >>11449159Dude's fucked bro. My adviser told me that programs fucking toss out applications with a master's degree due to the assumption that if the candidate got his Masters they should have finished their PHD, otherwise they're just going to waste what little spots they have for US residence
 >> Anonymous Sat Mar 7 18:24:46 2020 No.11449260 File: 85 KB, 949x733, 2chan's math board.jpg [View same] [iqdb] [saucenao] [google] [report] http://cgi.2chan.net/m/futaba.htmHas anyone ever been to the math board of 2chan - it's surrealpic related
 >> Anonymous Sat Mar 7 18:25:55 2020 No.11449261 >>11449260It's almost like they're (sub)humans, like us
 >> Anonymous Sat Mar 7 18:33:06 2020 No.11449286 >>11449159Too bad my mom lives in a job deadzone and unless you got a degree in nursing, enjoy working at walmart >>11449184Examining my undergrad/grad career, part of my success could be attributed professors just letting people pass so they didn't have to be bothered with them. Yeah the school is accredited but it was a tier 2 State school so they have incentive in ensuring a certain percentage pass their class otherwise administration will get on their ass. The other factor was less my ability to solve problems or anything IQ related and more my ability to tenaciously work hard until I passed out. That strat got me more Bs then As in grad school.That said, I'm at an age where if I haven't made it, I won't make it. >>11449190Ah yes, like that one guy who continues to post his proof of the Riemann Hypothesis despite the fact that other anons either ignore him or point out a glaring flaw with his logic. Regardless I don't really know how to do mathematics research because my adviser basically went AWOL and I had to use one of the alternative graduate conditions (doing a fucking report which is basically taking someone else's work and presenting it to 3 professors who don't want to be there) [which also means I don't have a C.V. FUCKING THANKS PROF]>>11449191Thanks for the honesty
 >> Anonymous Sat Mar 7 18:34:22 2020 No.11449289 File: 217 KB, 800x1118, __chen_touhou_drawn_by_poronegi__13b16d6e663e3c1d034d7e0729692a57.jpg [View same] [iqdb] [saucenao] [google] [report] We have the set $S$ of maps $\mathbb{Z} \rightarrow \mathbb{Z}_{10}$ which are bounded below, that is, for every map $f$ there is some $N$ such that $n0$ would be written $0.99999 \cdots$, $\pi$ would be $g(0)=3$, $g(1)=1$, etc for the n-th digit, and the lower bound on $f$ really just ensures the integer part is finite.Anyhow, I want to know if you lads know or can come up with any "no go" theorems for group structures on $S$, in particular showing that we can't define the real numbers as the lexicographically ordered elements of $S$ and expect reasonable properties.
 >> Anonymous Sat Mar 7 18:37:05 2020 No.11449292 >>11449111Jesus fuck. This is why state unis should be outlawed for STEM fields. They aren't qualified to teach jack diddly shit.
 >> Anonymous Sat Mar 7 18:37:43 2020 No.11449295 >>11449289>those are actually just the positive stringsFuck.Please pretend the formalism somehow works.
 >> Anonymous Sat Mar 7 18:52:03 2020 No.11449313 >>11446875I know what a field is. But which one? Auto.. morphism. What is an automorphism?
 >> Anonymous Sat Mar 7 18:57:08 2020 No.11449323 >>11449191I dont understand this at all, why does having a masters means that you should have finished a phd? Most phd positions require a masters
 >> Anonymous Sat Mar 7 18:59:01 2020 No.11449331 >>11449286>thanks for the honestythat's completely false in europe, stop believing everything you read on the internet just because it reinforces your current beliefs
 >> Anonymous Sat Mar 7 20:05:09 2020 No.11449504 File: 1.37 MB, 1140x4777, official mg curriculum.png [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Sat Mar 7 21:59:38 2020 No.11449751 >>11449323Maybe back in 1969, but this is CURRENT YEAR
 >> Anonymous Sat Mar 7 23:23:00 2020 No.11449900 >>11449260Good to know they're also full of undergrads falling for the same old bait threads.
 >> Anonymous Sat Mar 7 23:29:30 2020 No.11449910 File: 717 KB, 688x653, when you solve the riemann hypothesis.png [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Sat Mar 7 23:40:04 2020 No.11449931 What do you do when you have no one to talk to about what you love doing?No one even in my own offices/classes enjoys delving into topics more than they have to for their job or for their grade. To be honest it's starting to get to me how alone it feels to be at my job.
 >> Anonymous Sat Mar 7 23:50:07 2020 No.11449941 >>11449931I talk with people like me on /mg/.I also find different things like good TV shows or video games etc that people like to talk about.
 >> Anonymous Sun Mar 8 01:34:02 2020 No.11450102   File: 88 KB, 634x394, TIMESAND___590gh6754th45sdryq5757nnyyb0dgmth45sdryq5757nnyth45sdrth45sdryq5757nnyyq5757nnyb0dgmth45pn78.jpg [View same] [iqdb] [saucenao] [google] [report] >>11449910ftfy
 >> Anonymous Sun Mar 8 04:03:36 2020 No.11450270 >>11449289For one (I might say something dumb here), I'm not sure if the topology of those "formal strings" carries useful properties. Could you define, say, a distance on it ? Is your space complete with respect to that distance ?If limits are not possible, what about filters ?I don't think so, obviously a limit of elements of S converges outside of S
 >> Anonymous Sun Mar 8 05:18:40 2020 No.11450371 >>11449931>What do you do when you have no one to talk to about what you love doing?deal with it, it's part of being mathematician
 >> Anonymous Sun Mar 8 05:35:12 2020 No.11450388 >>11449931deal with it. talk about something else.
 >> Anonymous Sun Mar 8 07:28:59 2020 No.11450579 >>11448998Go to the respective Wikipedia articles and click the book reference links at the bottom there. You also find approaches in the computability field
 >> Anonymous Sun Mar 8 07:43:32 2020 No.11450614 Stats question:If a car tire machine has a 0.15 probability of making a defect tire, and the machine stops after 3 defects, what is the probability of making 5 tires before stopping?
 >> Anonymous Sun Mar 8 07:51:15 2020 No.11450638 >>11450614it's actually probability and that's fairly easy.5 times before stopping = 2 failures in the first 4 tries AND a failure at the 5thThis makes it$p = \left(C^2_4 * (0.85)^2 * (0.15)^2\right)*0.15$With $C^2_4 = \frac{4!}{(4-2)!2}$, as any combination of two failures in the first 4 tries is possible(explicitely)F F S SF S S FF S F SS S F FS F F SS F S F
 >> Anonymous Sun Mar 8 08:09:04 2020 No.11450673 >>11450638i meant the probability that it produces at least 5 or more tires before it gets stopped*
 >> Anonymous Sun Mar 8 08:20:29 2020 No.11450695 >>11450673I calculated the probability of it to stop at exactly 5 times.You should adapt it and find the probability to stop at 4 tires, 3 tires. (it can't stop at 2 or 1 ofc)Then it's 1 minus the sum of those probabilities.Come on dude, probabilities aren't that hard. Write down a tree, use your intuition, and formalise it.
 >> Anonymous Sun Mar 8 08:21:53 2020 No.11450698 >>11450614It's 1 minus the probability of not making 5 tires.Consider the probabilities of all strings of length 7 or less with exactly 3 defects.That should be enough, I'm not doing your homework for you.
 >> Anonymous Sun Mar 8 08:23:36 2020 No.11450701 >>11450695>>11450698Okay, thx. i was expecting a poisson random variable but it was easier than i thought, thanks. :)
 >> Anonymous Sun Mar 8 08:29:27 2020 No.11450715 >>11450701don't think of a theorem before looking at the problem, just look at the question, use your intuition, formalise it, do some test cases with low/easy numbers, draw potatoes and trees [knowing how to draw potatoes to visualise something is a very important mathematical skill], and then see which theorems, techniques, and tools might be usefulgood luckwhat's your degree?
 >> Anonymous Sun Mar 8 08:32:27 2020 No.11450720 >>11450715I see, and thanks. well, math, first year
 >> Anonymous Sun Mar 8 08:49:10 2020 No.11450751 File: 2.80 MB, 3072x4096, IMG_20200308_134512959.jpg [View same] [iqdb] [saucenao] [google] [report] I just saw in the library that Arnold Neumaier who keeps lurking on the web of physics and numerical optimization, so you might have come across him online) finally wrote up his thermodynamics-related fundamental physics views, let's say, in a book. Anybody read him (online or otherwise)?
 >> Anonymous Sun Mar 8 08:50:26 2020 No.11450754 File: 12 KB, 200x200, bead9ff6ddc7c095d18968ec950edb4d.jpg [View same] [iqdb] [saucenao] [google] [report] >>11450751he usually uses this badly cropped ava
 >> Anonymous Sun Mar 8 09:26:24 2020 No.11450806 >>11450715Do you know how I calculate the expected value of how many tires it will produce before it gets stopped?
 >> Anonymous Sun Mar 8 09:29:53 2020 No.11450815 >>11450806Get a general expression for the probabilities of stopping after N tries. Calculate the sum of $N * P_N$.It will most likely be a geometrical series or the derivation terms-by-terms of a geometrical series
 >> Anonymous Sun Mar 8 10:14:40 2020 No.11450894 File: 2.54 MB, 1555x2200, montyhall.png [View same] [iqdb] [saucenao] [google] [report] Do you change the gumball?
 >> Anonymous Sun Mar 8 10:49:45 2020 No.11450962 >>11450815I found P(X=k) where k is the amount of tires produced, but the sum of k*P_k converges to a decimal number, like 0.0016875 which makes no sense...
 >> Anonymous Sun Mar 8 11:02:08 2020 No.11450987   ${ \mathcal E }(A^*\, A) = { \mathcal E }(A)^*\, { \mathcal E }(A) + \sigma_A^2$
 >> Anonymous Sun Mar 8 11:03:44 2020 No.11450992 ${ \mathbb E }(A^*\cdot A) = { \mathbb E }(A)^*\cdot { \mathbb E }(A) + \sigma_A^2$
 >> Anonymous Sun Mar 8 11:16:36 2020 No.11451025 >>11450894Yes. And also what is the manga's name.
 >> Anonymous Sun Mar 8 11:17:30 2020 No.11451027 >>11450962can probably be written as a fraction
 >> Anonymous Sun Mar 8 11:24:42 2020 No.11451052 >>11450894Makes no difference. But I just barely passed stochastics...
 >> Anonymous Sun Mar 8 11:26:20 2020 No.11451059 >>11450894monty hall is illuminati propaganda and not real probability theory
 >> Anonymous Sun Mar 8 12:06:46 2020 No.11451152 >>11451059I understand my reptilian overlord
 >> Anonymous Sun Mar 8 12:08:01 2020 No.11451154   File: 28 KB, 640x525, multiple homologous saddle connections; topological picture.jpg [View same] [iqdb] [saucenao] [google] [report] *shudders*
 >> Anonymous Sun Mar 8 12:23:28 2020 No.11451178 File: 28 KB, 640x525, multiple homologous saddle connections; topological picture.jpg [View same] [iqdb] [saucenao] [google] [report] 󠛡 󠛡fucking rad man
 >> Anonymous Sun Mar 8 13:50:56 2020 No.11451422 File: 32 KB, 230x210, 1574044235062.jpg [View same] [iqdb] [saucenao] [google] [report] >>11449941>>11450371>>11450388I absolutely refuse to believe this. The sciences can chat merrily about their subjects, hailed and represented by media. Yet here we are in the basement of Omelas; we are called saints because we do what's necessary, but kept more than an arm's length away.Do we even talk here? Most of the prattle that goes on are half-baked memes or dick-measuring contests, there is no fun revisits to simpler theorems or questions that aren't just copy-pasted from a book.I refuse to believe that there does not exist some individual out there who considers math their primary source of entertainment, who also wishes to be social about it.
 >> Anonymous Sun Mar 8 13:59:22 2020 No.11451477 >>11451422Okay. Firstly, why do you believe that anyone here is even qualified to talk about anything beyond Highschool mathematics (which is profoundly boring)?Secondly mathematics tends to be very specialized and hard to communicate to people with little knowledge in your field, or even mathematics in general.Thirdly, be the change you want to see in the world, try to talk about something interesting and if a miracle happens somebody who at least has a bachelors will give you a non-idiotic reply.
 >> Anonymous Sun Mar 8 14:05:45 2020 No.11451509 File: 14 KB, 366x298, seriously I had a student who would not shut up about this set despite not knowing what it really is also she failed my course.gif [View same] [iqdb] [saucenao] [google] [report] >>11451422Consider a few factors.First, some fields of mathematics are so far out there that one expert in mathematics can't talk to another due to how disparate their chosen fields are.Next, 99% of anyone outside of mathematics (especially if they're a lolmerican) can NOT discuss anything beyond arithmetic. There is no way to bridge the gap between 'you know clopen sets are a thing' and '52 is an even number, right?" in the time it takes to have an average conversation.Thirdly, Mathematics is hard work. I DON'T want to talk about it with my colleagues or peers because it invariably ends up as either gossip or dick measuring. All I want is to publish my shitty paper that is not going to advance our understanding of mathematics in the slightest, but I gotta to get tenure, and go watch a Monster Truck show. Fuck ultra autistic fields of math, fuck people who keep bringing up the mandlebot set WITHOUT FUCKING KNOWING WHAT IT IS, and Fuck my colleagues for making my job harder then it needs to be.
 >> Anonymous Sun Mar 8 14:10:18 2020 No.11451533 >>11451422i'll be honest with you, at my university i spend a lot of time with a group of at least 20 to 30 people all of whom absolutely adore mathematics and talking about it. they have other interests too but i never have felt the isolation you talk about.maybe you're just at a shit uni or something? or you need to find the right group? as far as i can tell outside of my group no one gives a shit about math.
 >> Anonymous Sun Mar 8 14:12:37 2020 No.11451544 >>11449931>>11451422I usually talk to my physicist friend who appreciates mathematics. He at least finds it interesting, or pretends to, so it's nice. Also, at conferences you end up meeting people who have similar interests as you, so try making friends and keeping in contact with them, maybe sending an email here and now about a particular topic you think is worth discussing or interesting. Also, the only time I think one can't talk with colleagues is if you work in a department with no one else in your specialization, which is atypical. Usually there is at least one person in your field there.
 >> Anonymous Sun Mar 8 15:06:03 2020 No.11451758 >>11451025yancha gal no anjyou-san, the girl on the page posted is only a side character though
 >> Anonymous Sun Mar 8 15:08:44 2020 No.11451772 >>11451509Oh I love the Mandelbrot set and I'm bad at math just like that student. One of the first things I ever coded in high school was a fractal renderer.
 >> Anonymous Sun Mar 8 15:15:50 2020 No.11451792 How much commutative algebra does one need to read FOAG?
 >> Anonymous Sun Mar 8 15:21:23 2020 No.11451805 >>11449313Dude? Is this bait?
 >> Anonymous Sun Mar 8 15:34:08 2020 No.11451847 >>11451792can you do a*b=b*a?If so you're good
 >> Anonymous Sun Mar 8 15:35:17 2020 No.11451852 >>11451792Sorry I'm ancient, FOAG?On an unrelated note:[eqn]\prod_{n=1}^{\infty}\frac{(2n)^{2}}{(2n-1)(2n+1)}=\frac{\pi}{2}[/eqn]I'm astounded I've never seen this before and I'm trying to play around with it without peeking at proofs, I find product convergences quite fascinating since we don't tend to play with them in any classroom setting.
 >> Anonymous Sun Mar 8 15:41:41 2020 No.11451870 File: 359 KB, 754x600, double torus.jpg [View same] [iqdb] [saucenao] [google] [report] >>11451178that looks delicious
 >> Anonymous Sun Mar 8 15:55:16 2020 No.11451903 >>11451852Probably Grothendieck's FGA, but anon translated the title for no reason.
 >> Anonymous Sun Mar 8 16:23:59 2020 No.11451987 >>11451852Product convergence is just illuminati series convergence, with $\ln$ involved.A few complex analysis textbooks go into it. Alfhors has a short but interesting segment on it.
 >> Anonymous Sun Mar 8 16:47:43 2020 No.11452068 >>11451903>FGADo you mean EGA?Or is it SGA? Please only use the french titles, this is less confusing.
 >> Anonymous Sun Mar 8 17:04:19 2020 No.11452108 >>11451987Is complex analysis really necessary for product-to-series considerations of purely positive numbers? Surely some decomposition exists without...
 >> Anonymous Sun Mar 8 17:14:45 2020 No.11452133 >>11452108it is possible, it's not very interesting.the key argument is that the power series and the infinite product both represent the same analytic function. the zeros in the product correspond to the zeros of the analytic function as well.it will be very hard for you to prove convergence, absolute convergence, and other dumb shit without analycity and a properly defined log. you'll also miss on some interesting applications (the gamma function, for starters).
 >> Anonymous Sun Mar 8 17:18:54 2020 No.11452143 >>11452068>Do you mean EGA?Or is it SGA?No.https://en.wikipedia.org/wiki/Fondements_de_la_G%C3%A9ometrie_Alg%C3%A9briqueFoundations of Algebraic Geometry, FOAG, translated literally.
 >> Anonymous Sun Mar 8 17:39:29 2020 No.11452205 File: 36 KB, 800x450, rawww.jpg [View same] [iqdb] [saucenao] [google] [report] >want to do math research>find out about cranks>afraid to do math research because I don't want to get labeled a crank by the greater math community
 >> Anonymous Sun Mar 8 17:46:43 2020 No.11452230 >>11451758Thank you very much.
 >> Anonymous Sun Mar 8 17:48:23 2020 No.11452236 >>11452205Why are you afraid to be labeled as a crank? Are you an obnoxious egotistical retard?
 >> Anonymous Sun Mar 8 17:49:54 2020 No.11452243 >>11452236>Are you an obnoxious egotistical retard?I post here... so by definition yes?
 >> Anonymous Sun Mar 8 17:53:34 2020 No.11452253 >>11451903Not the Anon, but FOAG is the pretty standard abbreviation for Ravi’s book.
 >> Anonymous Sun Mar 8 18:01:26 2020 No.11452283 File: 122 KB, 725x1024, prof_yukari.jpg [View same] [iqdb] [saucenao] [google] [report] >>11448310Nope. Second quantization is named so inorder to distinguish it from first quantization. Given a symplectic space $(\Omega,\omega)$, second quantization quantizes fields, namely promotes sections of vector bundles on the $\infty$-jet bundle $J^\infty \Omega$ to operators, while first quantization quantizes coordinates, namely promotes the smooth Poisson algebra $C^\infty(\Omega)$ to operators.>second countableDid you mean separable? Second countable means a countable base for the metric topology, which is weaker than having a countable basis for the linear structure of $\mathcal{H}$. Being separable is an assumption that allows us to leverage reflexibility and Riesz representation to study duals and preduals. This extremely useful in QM, since it in particular allows for a faithful infinite-matrix representation on $\mathcal{B}(\mathcal{H})$ and hence a resolution of unity.>>11448716Because it's just $SO(3)$.>>11449108It's looking up. Thanks for asking.
 >> Anonymous Sun Mar 8 18:08:01 2020 No.11452301 >>11452283>Because it's just SO(3).Na, it's also a 6-dim Lie group.Also, second is still a bad name, imho. The models aren't technically ina succession, or at least you'd not jump along models in such a progression. Should be avoided.
 >> Anonymous Sun Mar 8 18:08:04 2020 No.11452303 >>11452283you're late af and your jargon isn't interestingthe other anons explained why I was wrong much betterand I did mean second countable before for me, you were constructing a basis of eigenstates out of something that felt "countinous"I was wrong as fuck and I realised that after other anons explained it to me and I know what 2nd quantification means now thanks to themdumb animelord
 >> Anonymous Sun Mar 8 18:10:02 2020 No.11452306 >>11452303give the weeb a break, I think nLab stuff should be shilled where it's accessible. I'm not sure jet budles will ever make it into the applied realm, sadly.
 >> Anonymous Sun Mar 8 18:12:25 2020 No.11452308 >>11452306the way he types makes me want to punch him in the face through the computer screenit's probably because I'm a brainlet whose still learning QM and intermediate level maths while he's a big smart guy, but by the lord his jargon is the opposite of what pedagogy should be
 >> Anonymous Sun Mar 8 18:17:17 2020 No.11452314 >>11452283>it's just SO(3)What about speeding up time tho?>>11452308You shouldn't get angry at him, you should get angry at yourself, and use that anger to study harder.
 >> Anonymous Sun Mar 8 18:17:28 2020 No.11452316 >>11452308my only issue is that he uses the same anime images over and over again as a psudoform of identification
 >> Anonymous Sun Mar 8 18:21:25 2020 No.11452319 File: 94 KB, 650x800, __yakumo_yukari_touhou_drawn_by_marimo_tarou__bfe6e6b3ee76fb79e00af996776ef9d6.jpg [View same] [iqdb] [saucenao] [google] [report] >>11452301The Lie algebra of the entire Euclidean group is 6D, yes. Without time we don't know what "boosts" are so your question depends on what you mean by "homogeneous". We have ${\bf E}(3) \cong \mathbb{R}^3\rtimes O(3)$ anyway and if by "homogeneous" you mean orientation preserving then it's $SO(3)$; if by homogeneous you mean that $\mathbb{R}^3$ is a homogeneous space under it then it's the entire group.>>11452306>I'm not sure jet budles will ever make it into the applied realmPutting a contact structure on $J^\infty\Omega$ lets you define the Lagrangian density as $\Omega^n(J^\infty\Omega)$, which lets you do quantum/classical field theory as if you're doing quantum/classical mechanics. I don't know what you mean by "applied" but it's the backbone of theoretical physics. Sardanashvily has a few nice articles on this.>>11452314>What about speeding up time tho?In the non-relativistic case "time" is just the parameter on a physical trajectory, and time evolution is just an automorphism $\alpha_t$ on $C^\infty$ generated by the Poisson bracket $\{H,\cdot\}$ with the Hamiltonian. Again, "boosts" don't exist here and speeding up time just scales this parameter. It's not actually part of the isometries of space.
 >> Anonymous Sun Mar 8 18:22:18 2020 No.11452321 File: 607 KB, 789x565, based_and_wife_pilled.png [View same] [iqdb] [saucenao] [google] [report] >>11452314>What about speeding up time tho?I was talking about the Galileian group (10 dim) without the translations (in 4d). There's no speeding up time, it's quite a plain thing.>>11452308We're all faggots, but anybody taking the effort of writing more than 5 sentences in response should stay imho>>11452316I do that too, it helps the conversation tbqh and also helps you find your own posts. If I add a random pic to the post, I can easily read up what I missed tomorrow from where I left it.
 >> Anonymous Sun Mar 8 18:22:27 2020 No.11452322 >>11452319>Lagrangian density asas an $n$-form in*
 >> Anonymous Sun Mar 8 18:25:44 2020 No.11452324 >>11452319Yeah, you skipped the part where I wrote Galilean, but whatever.I guess by applied I mean that more than 50% of Profs who teach QM know what it is. That's certainly not the case with J^\inftyfoo
 >> Anonymous Sun Mar 8 18:26:00 2020 No.11452326 File: 59 KB, 602x339, BWAAAA.jpg [View same] [iqdb] [saucenao] [google] [report] >>11452321>it helps the conversation tbqh and also helps you find your own posts>helps you find your own posts>find your own postsWhat
 >> Anonymous Sun Mar 8 18:27:30 2020 No.11452328 >>11452314I do something like 3-4 hours a day + my internship slavery. Being an engineer trying to get a PhD in interesting physics is painful, but I think I already did something worthwhile if I read (and understood) half of Rudin. Now, just gotta do the other half.>>11452321I just don't think vomiting jargon at someone is very polite or encouraging.
 >> Anonymous Sun Mar 8 18:27:37 2020 No.11452329 >>11451792Eisenbud or Atiyah-Macdonald should cover enough.>>11452308>tfw anon wasn't here for ribbon category autismGood times.
 >> Anonymous Sun Mar 8 18:28:47 2020 No.11452332 >>11452321just use 4chanx
 >> Anonymous Sun Mar 8 18:29:52 2020 No.11452333 File: 231 KB, 752x1200, ENTdrb3UwAIpyVc.jpg [View same] [iqdb] [saucenao] [google] [report] >>11452328>I just don't think vomiting jargon at someone is very polite or encouraging.We're all just fishing for people who want to talk about the stuff we find interesting>>11452332Might do.>>11452326If I come here in 18 hours tomorrow and scroll down, I know that I left for bed around the post that has the Justin Murphy pic. I don't need to read to find my last post. Good bye.
 >> Anonymous Sun Mar 8 18:30:16 2020 No.11452335 File: 144 KB, 796x700, __remilia_scarlet_touhou_drawn_by_noai_nioshi__4fed8eea28cb8f0a977bb63e65ca339b.jpg [View same] [iqdb] [saucenao] [google] [report] >>11452321>If I add a random pic to the post, I can easily read up what I missed tomorrow from where I left it.High IQ.
 >> Anonymous Sun Mar 8 18:30:32 2020 No.11452336 >>11452321>I do that too, it helps the conversation tbqhit's called avatarfaggotry, and it's against the rules for a reasonalthough that said there's no point in reporting it because jannies don't give a shit about this board
 >> Anonymous Sun Mar 8 18:32:54 2020 No.11452341 File: 143 KB, 1300x951, the-last-supper-year-1996-director-stacy-title-cameron-diaz-A1B7JR.jpg [View same] [iqdb] [saucenao] [google] [report] >>11452336Yes, I do understand the dilemma of the situation
 >> Anonymous Sun Mar 8 18:34:59 2020 No.11452344 File: 405 KB, 1474x1328, __yakumo_yukari_touhou_drawn_by_nameo_judgemasterkou__d361e7aa66a282581994c23b9906b59b.jpg [View same] [iqdb] [saucenao] [google] [report] >>11452324Maybe you have something else in mind when you meant "Galilean", but I took that to mean the Euclidean group, i.e. the group of isometries of Euclidean space.If you're thinking about 4D then it's $O(4)$ or $SO(4)$, depending on if "homogeneous" means "orientation-preserving" to you. Again, for any $n$ in general we have ${\bf E}(n) \cong \mathbb{R}^n \rtimes O(n)$. On a lattice this is called Bieberbach's theorem, not sure if there's a name for it in the continuum but you can just pass to it from Bieberbach's by the embedding homomorphism of the point group $\rho: P_n \hookrightarrow O(n)$.
 >> Anonymous Sun Mar 8 18:43:28 2020 No.11452378   >>11452344You may or may not have noticed me saying >>11452301 "Na"and >>11452321 "but whatever"and I've talked down on myself by calling me faggot in your defense etc.Why don't you let it be? The Galelaen group is 10 dimensional by all accountshttps://en.wikipedia.org/wiki/Galilean_transformation#Galilean_grouphttps://en.wikipedia.org/wiki/Representation_theory_of_the_Galilean_grouplet's change topic>if "homogeneous" means "orientation-preserving" to youYou are indeed, I have to agree with the other guy, a bit annoying
 >> Anonymous Sun Mar 8 18:49:31 2020 No.11452402 >>11452344>not sure if there's a name for it in the continuumThe classification of Euclidean isometries?>you can just pass to it from Bieberbach's by the embedding homomorphism of the point group ρ:PnO(n).IIRC the classic proof went something like this:>dude>subtract the image of the 0>the translation part is now gone>notice how any point is completely determined by it's distance from n+1 points>consider an orthonormal basis plus zero>take the image>still orthonormal plus zero>induces an orthogonal map>coincides on n+1 points with the original, coincides everywhere, and we're done
 >> Anonymous Sun Mar 8 18:55:14 2020 No.11452419 >>11452402>notice how any point is completely determined by it's distance from n+1 pointsActually, I think it was n+1 points that didn't fit into a single hyperplane.
 >> Anonymous Sun Mar 8 18:59:45 2020 No.11452431 File: 445 KB, 746x676, yukari_smile.png [View same] [iqdb] [saucenao] [google] [report] >>11452402>>11452419Yep, it's pretty standard so it probably just doesn't have a name.>the classic proof went something like thisThat looks like the right idea, which is to identify the classifying space $BO(n)$ as the real flag Grassmannian $\operatorname{Gr}_n(\mathbb{R})$. Each collection of $n+1$ non-planar points defines an $n$-plane up to a frame, hence an element in $\operatorname{Gr}_n(\mathbb{R})$.Also any non-symmorphicity (preventing the splitting into a semi-direct product) of the lattice is killed off in the continuum.
 >> Anonymous Sun Mar 8 19:12:16 2020 No.11452462 >>11452402>>11452431Maybe a name for it pops up in a book on the study of well behaved Riemannian manifolds. I know there's names for theorems I can't recall or find right now
 >> Anonymous Sun Mar 8 19:22:30 2020 No.11452481 File: 262 KB, 450x690, 1581748238345.png [View same] [iqdb] [saucenao] [google] [report] >>11452462>Maybe a name for it pops up in a book on the study of well behaved Riemannian manifolds.I looked it up in a book about affine geometry.It's really just "Classification of Euclidean motions".Not a particularly good book, tho.
 >> Anonymous Sun Mar 8 19:26:43 2020 No.11452487 File: 1.25 MB, 857x2352, hags_theorem.png [View same] [iqdb] [saucenao] [google] [report] >>11452481Alright. Thanks for looking.
 >> Anonymous Sun Mar 8 19:31:53 2020 No.11452496
 >> Anonymous Sun Mar 8 20:29:08 2020 No.11452634 >>11446875In this context though, automorphism stands for the sworn enemies of the deceptimorphisms.
 >> Anonymous Sun Mar 8 20:58:30 2020 No.11452732 >>11446845since I last have seen my son
 >> Anonymous Sun Mar 8 21:08:16 2020 No.11452756 >>11452634when an automorphism takes in a deceptimorphisms or vice versa, does it produce the identity element?
 >> Anonymous Sun Mar 8 21:26:17 2020 No.11452795 >>11452431You are incredibly fucking infuriating, and make everything way more complicated than it should be.
 >> Anonymous Sun Mar 8 21:37:47 2020 No.11452829 >>11452795Are you implying that an elementary fact about manifolds is "way more complicated than it should be?"Wow.
 >> Anonymous Sun Mar 8 21:51:52 2020 No.11452859 >>11452829I'm saying he's talking way more obtusely than necessary. Mentioning that $BO(n)$ is a classifying space or that $\text{Gr}_{\text{n}}(\mathbb{R})$ is a flag manifold is completely useless, it just makes it all seem complicated when it's not warranted. Also, please tell me what the fuck "Also any non-symmorphicity (preventing the splitting into a semi-direct product) of the lattice is killed off in the continuum." means, because to me, he's not really saying anything. Probably one of those empty statements mathematicians love which only mean anything to the people who already know what it's being talked about, and sometimes not even then. But please do proceed to interpret it however you please and chastise me for not being able to understand an obtuse statement.
 >> Anonymous Sun Mar 8 22:06:00 2020 No.11452890 >>11452795>>11452829are you two gonna get a divorce?
 >> Anonymous Sun Mar 8 22:14:00 2020 No.11452911 >>11452890Did we remind you of some dark times anon?
 >> Anonymous Sun Mar 8 22:23:09 2020 No.11452939 >>11452911I'm just waiting for the part where one of you complains about child support to your 8 year old son you know, the child your child support goes to
 >> Anonymous Sun Mar 8 22:28:17 2020 No.11452954 >>11452939It's times like this where I wish I were a roastie, so that I could give you a hug and make you feel better. But alas, I'm just some random retard on the internet.
 >> Anonymous Sun Mar 8 22:33:35 2020 No.11452967 Here's tonight's little proof for those who want a small brain dessert.Prove or Disprove:[eqn]4|(3^{k}+2+(-1)^{k})[/eqn]
 >> Anonymous Sun Mar 8 22:39:38 2020 No.11452982 >>11452967high school homework goes in /sqt/
 >> Anonymous Sun Mar 8 22:41:17 2020 No.11452987 >>11452967I'm retarded, forgot to mention $k\in\mathbb{W}$, (that's $\mathbb{N}\cup\{0\}$ proper for you lazy ones who forgot the difference between whole numbers and natural numbers.)>>11452982>divisibility proofs are high school homework durr hurrYeah I wish, good meme.
 >> Anonymous Sun Mar 8 22:43:07 2020 No.11452994 >>11452987yes, modular arithmetic is taught to high schoolersif you went to a crappy high school maybe this is your freshman uni homework, either way, /sqt/
 >> Anonymous Sun Mar 8 22:44:15 2020 No.11452998 >>11452987The natural numbers already include zero, what are you talking about?
 >> Anonymous Sun Mar 8 22:45:27 2020 No.11453000 File: 81 KB, 500x686, mods-are-asleep-post-confused-looking-anime-girls-with-question-2668527.png [View same] [iqdb] [saucenao] [google] [report] >>11452998>The natural numbers already include zero
 >> Anonymous Sun Mar 8 22:45:30 2020 No.11453001 >>11452987Suppose $4 \nmid \left( 3^k+2+(-1)^k\right)$. Then $4 \nmid \left( 3^k+2+(-1)^k\right)$. $Q.E.D.$
 >> Anonymous Sun Mar 8 23:04:52 2020 No.11453036 >>11452994>even and odd, sometimes divisibility-by-three and eleven tricks are played with pre-uni, therefore modular arithmetic is coveredGenius. Shitters like you are why there's no fun in this thread when someone likes writing problems/quizzes.>>11452998For computer science babies perhaps, whole and natural should never be considered the same. There is no need to have two names for the exact same thing in mathematics.>>11453001You're right, but this proves the wrong thing :-(
 >> Anonymous Sun Mar 8 23:40:06 2020 No.11453089   >>11453036Fine. Suppose $4 \textbar \left(3^k+2+(-1)^k\right)$. Then $4 \textbar \left(3^k+2+(-1)^k\right)$. $Q.E.D.$
 >> Anonymous Sun Mar 8 23:41:52 2020 No.11453092 >>11453036Fine. Suppose $4 | \left(3^k+2+(-1)^k\right)$. Then $4 | \left(3^k+2+(-1)^k\right)$. $Q.E.D.$
 >> Anonymous Sun Mar 8 23:50:08 2020 No.11453110 >>11453089\bottomtext
 >> Anonymous Sun Mar 8 23:51:58 2020 No.11453111 >>11452939Actually, it's his wife's son. I'm the dad. The wife is Yukari.
 >> Anonymous Sun Mar 8 23:55:22 2020 No.11453116 >>11452967I mean this is just obvious. What is 3^k mod 4? The sequence goes 1, 3, 9 = 1, then 3 again, so it's 1 when k is even and 3 when k is odd. But 2 + (-1)^k is 3 when k is even and 1 when k is odd. So the sum is always 4 = 0 mod 4, and the number is always divisible by 4.
 >> Problemancer !FJmII4R11c Mon Mar 9 00:13:08 2020 No.11453142 >>11453116Thank you for humoring me. Your reward is another, perhaps less obvious challenge.Prove for all whole numbers n, where D is a natural number that satisfies $D*6^{5^{n}}\equiv D(mod 10^{n})$ and $D=\sum_{k=0}^{n-1}10^{k}d_{k}$ and for any index i $d_{i}\in\{0,1,2,3,4,5,6,7,8,9\}$[eqn]2^{n}|\sum_{k=0}^{n-1}2^{k}d_{k}[/eqn]
 >> Anonymous Mon Mar 9 04:17:14 2020 No.11453591 >>11452487I don't get the issue, what's wrong with Haag?
 >> Anonymous Mon Mar 9 04:30:56 2020 No.11453621 File: 40 KB, 845x123, AllahWillingThisWillBeAnswered.png [View same] [iqdb] [saucenao] [google] [report] Would a kind gentleman be able to provide an answer to this question? Cheers.
 >> Anonymous Mon Mar 9 08:54:13 2020 No.11454033 File: 65 KB, 223x310, 1576531122601.jpg [View same] [iqdb] [saucenao] [google] [report] >>11453092This is the contrapositive of what you said before>>11453142Excuse me, but what the fuck
 >> Anonymous Mon Mar 9 10:26:53 2020 No.11454194 >>11452795>>11452859very much this
 >> Anonymous Mon Mar 9 10:37:54 2020 No.11454206 >>11452634can someone PLEASe tell me what an automorphism is? and can i get a number 9 large extra fries with that? and a math gf?
 >> Anonymous Mon Mar 9 13:10:35 2020 No.11454536 >>11452859>>11452795yeah it's just jargon for the sake of jargon at this pointwhat he says is not completely unworthy of attention and devoid of mathematical value, it's just not interesting and useful for a conversationhe's like a Rick and Morty character except that he posts anime and actually know the jargon.>>11454206an automorphism is a map from one set unto itself that is also an isomorphism.more precisely, it must be bijective (to each element x there is precisely one and only one f(x) ) and preserves some structure.
 >> Anonymous Mon Mar 9 13:56:33 2020 No.11454615 File: 267 KB, 796x699, 1582634867015.png [View same] [iqdb] [saucenao] [google] [report] This entire fiasco is so depressing to look at I actually took five minutes to make a frog meme about it.
 >> Anonymous Mon Mar 9 14:26:24 2020 No.11454688 imagine being so btfo that you had to frogpost
 >> Anonymous Mon Mar 9 16:00:20 2020 No.11454912 >>11454615pathetic.
 >> Anonymous Mon Mar 9 16:14:41 2020 No.11454954 >>11454688>>11454912t. big boys
 >> Anonymous Mon Mar 9 16:21:38 2020 No.11454973 >>11454954t. rick & morty watcher
 >> Anonymous Mon Mar 9 16:36:38 2020 No.11455034 Question for y’all, I’m utilizing the law of cosines for a proof and I think I’ve discovered that the law of cosines seems to hold not just for triangles but to any 3 points in the plane, even collinear points, where the angle at the middle point is pi and the angles at the other two are 0.If that’s true that makes my proof significantly simpler to write out, so I’m wondering if anybody else has seen that before, or if I’m wrong and my proof has a mistake?Also I tried cases where we don’t have 3 unique points, and it seems to hold there too, but with the caveat that the angle between a point and the same point is undefined, however in such a scenario that angle will always be multiplied by 0 in the formula.
 >> Anonymous Mon Mar 9 16:45:41 2020 No.11455052 File: 878 KB, 2000x1500, Julia_set_for_the_rational_function.png [View same] [iqdb] [saucenao] [google] [report] Isn't it kinda ironic that founder of classical mechanics also found a method of generating fractals?
 >> Anonymous Mon Mar 9 17:02:32 2020 No.11455101 >>11455034yes, you are correctthe formula just states the obvious when the triangle is degenerate
 >> Anonymous Mon Mar 9 17:04:37 2020 No.11455106 >>11455101Right okay thank you
 >> Anonymous Mon Mar 9 19:27:42 2020 No.11455399
 >> Anonymous Mon Mar 9 20:27:21 2020 No.11455561 >>11455052>ironicI see no irony in that at all
 >> Anonymous Mon Mar 9 21:04:49 2020 No.11455638 Any complex analysis anons on here?I looked at this website: http://tetration.org/Tetration/index.htmlI'm interested in doing what he did for a function, only the function is meromorphic with a residue at its (Attractive)fixed point. The function also has poles past the 1st derivative, also at its fixed point, unfortunately. Any resources for finding a formula, a way I could solve schroeder's equation?
 >> Anonymous Mon Mar 9 22:59:44 2020 No.11455854 File: 985 KB, 1034x1989, babaa_scattering.png [View same] [iqdb] [saucenao] [google] [report] >>11453591Haag theorem states that interacting QFT is not unitarily equivalent to (products of) single-particle QFT. This means that most of scattering calculations done by physicists is wrong and there's no such thing as "the interacting picture".Given sufficient regularity of the interacting potential, however, Goldstone's theorem in fact proves the asymptotic free-ness of interacting states in the $|t|\rightarrow\infty$ limit. So the best we can do is to add the axiom of asymptotic completeness to the Sterater-Wightman axioms of QFT and compute $S$-matrix elements with far future/past single-particle scattering states. We can't probe intermediate scattering events unless someone develops an interacting/many-body QFT ab initio.
 >> Anonymous Mon Mar 9 23:55:30 2020 No.11455950 >>11454615great image, accurate, well donet. left frog
 >> Anonymous Tue Mar 10 00:03:41 2020 No.11455960 File: 92 KB, 1200x1807, imaginary-mathematics-for-computer-science.jpg [View same] [iqdb] [saucenao] [google] [report] Do you guys think studying math as an accelerator to understanding all other difficult science-y/tech stuff is a meme? Of course doing a lot of math beats nothing/jerking off/watching anime but you're probably better off learning CS/coding/engineering/etc. directly instead of hoping that advanced math study will pay off somehow (in my estimation)Thoughts?
 >> Anonymous Tue Mar 10 00:28:40 2020 No.11456009 I would like to get a copy of Neukirch ANT, and Geometric Modular Forms and Elliptic Curves. But each of the books cost >100 dllrs. ANT is for some reason not available for MyCopy. Does anyone know if there are cheap international editions for either of those books? For World Scientific books in general? Otherwise I think I’ll end up printing them. I learn faster from actual textbooks because it’s easier to flip pages, before frugal Anons start giving me shit.
 >> Anonymous Tue Mar 10 01:16:27 2020 No.11456103 havent heard back about my grad school application, how fucked am i?
 >> Anonymous Tue Mar 10 01:32:06 2020 No.11456128 >>11456103Did you only apply to one place?
 >> Anonymous Tue Mar 10 01:57:22 2020 No.11456158 >>11456128Yes... I didnt have time or money to apply to others. Considering suicide currently.
 >> Anonymous Tue Mar 10 03:10:54 2020 No.11456251 >>11456158What tier uni did you apply to? Roughly speaking, what was your GPA and all that stuff? You can always try next year, with better fit Unis.
 >> Anonymous Tue Mar 10 04:20:03 2020 No.11456354 File: 35 KB, 541x511, 3c8964bf.jpg [View same] [iqdb] [saucenao] [google] [report] >>11449108Quite nicely. Producing new shit every week. My supervisor told me to slow down, but I must X C L R 8
 >> Anonymous Tue Mar 10 04:23:12 2020 No.11456356 >>11456251He's as fucked as that Master's kid above if he keeps playing the try again next year game. Graduate programs hunt for hot young blood, not 2 year old rotten sausages
 >> Anonymous Tue Mar 10 04:25:57 2020 No.11456360 >>11452998There is no void, no vacuum, no nothing in nature, and hence no 0 in the natural numbers.
 >> Anonymous Tue Mar 10 04:32:08 2020 No.11456367 >>11455854I thought the issue is with the word "Haag"
 >> Anonymous Tue Mar 10 04:46:20 2020 No.11456380 >>11454536So basically, the Galois group of a field is all the possible ways it could be mapped onto itself?
 >> Anonymous Tue Mar 10 05:17:56 2020 No.11456413 >>11456380No, you oversimplified it too much. What the other anon said is the bare minimum (and I still think it should have more stuff) of the definition of an automorphism.
 >> Anonymous Tue Mar 10 05:33:39 2020 No.11456423 >>11456380Basically, you have a field k. Then you extend it to K and consider the automorphisms of K that fix k.
 >> Anonymous Tue Mar 10 08:12:34 2020 No.11456568 What's the real difference between $\mathbb{C}$ and $\mathbb{R}^{2}$?.They are isomorphic as vector spaces over $\mathbb{R}$ and also as metric (topological) spaces with their usual metrics. I assume the difference is in their algebraic structures, but how does that translate into analysis on $\mathbb{C}$ being different than analysis on $\mathbb{R}^{2}$?I hope this is not a stupid question.
 >> Anonymous Tue Mar 10 09:07:47 2020 No.11456647 >>11456568R^2 is not a field.
 >> Anonymous Tue Mar 10 09:08:08 2020 No.11456648 >>11456568C is algebraically closed whereas R^2 has no algebraic properties.C with the multiplication and addition has the structure of a field.If you go into more analytic details, you will find that this field structure lets you derive useful properties. Theory of complex integration and analytic fonctions shows examples of that.
 >> Anonymous Tue Mar 10 09:10:32 2020 No.11456652 >>11456568The difference is that $\mathbb C$ has a multiplication and that the definition of $\mathbb C$-derivative takes into account that extra structure. Simply put, analysis on $\mathbb C$ is a very special case of analysis on $\mathbb R^2$. Holomorphic functions are differentiable functions on $\mathbb R^2$ in the usual sense but whose differential is a similitude at every point (this translates to the Cauchy-Riemann equations).In the language of complex numbers, it corresponds to saying that it is a differentiable function whose derivative is the multiplication by a complex number.
 >> Anonymous Tue Mar 10 10:43:24 2020 No.11456781 Is there a book/website that list all the commonly known convergent series and sequence?
 >> Anonymous Tue Mar 10 10:48:38 2020 No.11456792
 >> Anonymous Tue Mar 10 10:50:03 2020 No.11456795 >>11456781Wikipedia lmaoFor real though, I doubt that can really be done since some are just generalisations of others so it would be arbitrary which special cases to include
 >> Anonymous Tue Mar 10 11:00:05 2020 No.11456813 >>11456413So I looked up some examples on Wikipedia and basically, the Galois Group of a Field extension is all the ways the extension could be changed without changing its effects. For example instead extending the rationals by square root of 2, we could also use negative square root of 2 without a difference. Therefore we have two automorphisms, this one and the identity one.Yes?
 >> Anonymous Tue Mar 10 11:05:32 2020 No.11456823 >>11446627What are some good books for babbies first topology on metric spaces class?
 >> Anonymous Tue Mar 10 11:10:55 2020 No.11456832 >>11456823maybe the one by Thomson and Bruckner - Elementary Real Analysis it's analysis but it covers basic topology of the real line and metric spaces I think it's by far the most gentle introduction to the subject out there
 >> Anonymous Tue Mar 10 11:16:54 2020 No.11456848 >>11456813>without changing its effects.Can you elaborate on this? > Therefore we have two automorphismsWe can also extend it with 3 times squareroot of 2, and that doesn’t mean we have three distinct automorphisms. Read the first few pages of Chapter 15 in dummit and foote. It’s very readable without much background.
 >> Anonymous Tue Mar 10 11:20:47 2020 No.11456860 >>11456832Thanks, will check it out!
 >> Anonymous Tue Mar 10 13:14:00 2020 No.11457096 I'm looking for the paper in which Jean Leray first introduced the notion of a sheaf. Can someone help me out?
 >> Anonymous Tue Mar 10 13:22:48 2020 No.11457120 >>11457096nevermind. I've found it. It is L’anneau d’homologie d’une représentation. But does anyone know where I can get it? It's not on libgen
 >> Anonymous Tue Mar 10 14:08:31 2020 No.11457254 >>11456367It's just a joke lad
 >> Anonymous Tue Mar 10 14:14:16 2020 No.11457268 starting to lack motivation to read more "theoretical" stuff on the side/on the week-end now I started the job.
 >> Anonymous Tue Mar 10 14:15:24 2020 No.11457271 File: 291 KB, 640x550, yukari_smile3.png [View same] [iqdb] [saucenao] [google] [report] >>11456158Some European/Asian universities have no application fee for their PhD programs. Try them again next year hun.>>11456568Having a complex structure gets you a Hodge decomposition $\Omega^n_\text{dR} = \bigoplus_{n = p+q}\Omega^{p,q}_\text{Dol}$ of the forms. You can't do this in $\mathbb{R}^2$ because you can have harmonic maps that don't satisfy Cauchy-Riemann.
 >> Anonymous Tue Mar 10 14:21:29 2020 No.11457286 >>11456158Are you seriously considering doing a non-funded PhD?Because I wouldn't recommend it at all. It's insane that unis should require you to pay for them for helping them with their work. PhDs students are already overexploited even when paid.>>11457271>Having a complex structure gets you a Hodge decomposition [...] of the forms. You can't do this in R2 because you can have harmonic maps that don't satisfy Cauchy-Riemann.That's not what he asked at all, and mention of harmonic maps that don't satisfy Cauchy-Rieman is completely gratuitous and I'm not sure if that's very useful even if we consider the big abstract picture. If we are really doing autistic shit, the Quaternion field also allows analytic functions that aren't harmonic.
 >> Anonymous Tue Mar 10 14:23:57 2020 No.11457291 >>11457271>Some European/Asian universities have no application fee for their PhD programs. Try them again next year hun.>hunWhat a kind way to tell someone to neck themselves.
 >> Anonymous Tue Mar 10 14:25:07 2020 No.11457300 >>11457291are you that surprised Yukarifag has the tism
 >> Anonymous Tue Mar 10 14:25:22 2020 No.11457302 >>11457286The quaternions aren't a two-dimensional real vector space, tho.
 >> Anonymous Tue Mar 10 14:28:50 2020 No.11457316 >>11457254What's the payoff, why is it funny
 >> Anonymous Tue Mar 10 14:28:59 2020 No.11457317 >>11456158>>11457271There are decent American unis that don't have application fees either. Carnegie Mellon has no fee at all, and Ohio State charges $5. I'm sure there are others but those were the only two I remember from when I applied.Realistically though, "I didn't have money" is not an excuse. Fees are like$80-90 a pop for most schools including mailing the GRE scores. It raises serious questions about whether or not you were actually even serious about getting a PhD if in all the months leading up to your applications you couldn't be bothered to find $200 or$300 somewhere so you're not risking an entire year of your academic life on a coinflip.
 >> Anonymous Tue Mar 10 14:30:28 2020 No.11457323 >>11457302That answer is already more connected to the OG question and helps him with what actually matters, R2 is a 2-d vector space, so is C, but the complex also form a field. It so appears that this property leads to making Hodge decompositions or something very smart ; that's very interesting, but not really what the dude asked and it's not presented in a way that makes it look interesting, it's just a math word salad.Yukarifag didn't have enough professors yelling at him that his shit is off-topic at best and completely hides the point at worst. Knowing how to present your results should be the basic skill taught to PhD students.>>11457317who the fuck does PhDs for freedo you enjoy being exploited, or are you just afraid of having to provide results?
 >> Anonymous Tue Mar 10 14:30:40 2020 No.11457324 File: 16 KB, 102x155, yukari_(not cameron_diaz).png [View same] [iqdb] [saucenao] [google] [report] >>11457286>That's not what he asked at all,That's exactly what he asked, hun. To quote, "... how does that translate into analysis on $\mathbb{C}$ being different than analysis on $\mathbb{R}^2$?">big abstract pictureNow THIS is not what he ask for at all.>>11457316There's no payoff.
 >> Anonymous Tue Mar 10 14:34:39 2020 No.11457337 >>11457323>who the fuck does PhDs for freewhy do you keep interjecting this into a discussion about application fees?please go google what the word FEE means
 >> Anonymous Tue Mar 10 14:37:51 2020 No.11457346 >>11457337Any funding that provides a monthly stipend for living/expenses usually also covers the application/tuition fees.
 >> Anonymous Tue Mar 10 14:42:02 2020 No.11457356 >>11457346Not really, tuition yes but usually not the application fees. Granted, application fees are much lower than tuition fees, but they can add up.
 >> Anonymous Tue Mar 10 14:42:44 2020 No.11457360 >>11457346>Any funding that provides a monthly stipend for living/expenses usually also covers the application/tuition fees.Yeah. How do you get from that to "anyone paying a fee is not doing a funded PhD"?You still have to pay the fucking fee upfront you retard. Yes, the one school you accept an offer from will give you a fee rebate as part of your package, but all the schools you turn down will not, and all the ones that reject you won't either.
 >> Anonymous Tue Mar 10 14:43:30 2020 No.11457364 >>11457120pwease guys. does no one know?
 >> Anonymous Tue Mar 10 14:44:31 2020 No.11457368 >>11457360I don't understand why you would pay for even seeing phDs proposals at all. Go on sites like findaphd.com and directly email the professors without setting up an account on the goddamn uni website.
 >> Anonymous Tue Mar 10 14:46:33 2020 No.11457374 >>11457356what does it cost to send an email to the teacher with the proposed subject
 >> Anonymous Tue Mar 10 14:48:40 2020 No.11457384 >>11457368>>11457374you're making an awful lot of noise for somebody with literally no idea how PhD applications work
 >> Anonymous Tue Mar 10 14:51:28 2020 No.11457390 >>11457384>see PhD proposal on university website, industrial webpage, or whatever>send email to person responsible with attached CV and cover letter>wait for them to respond and start exchanging from thereit's like finding a job or an internship. I'm going to pay them for giving me work.
 >> Anonymous Tue Mar 10 14:52:32 2020 No.11457394 >>11457390i'm not*
 >> Anonymous Tue Mar 10 14:55:07 2020 No.11457397 >>11457390>>11457394You're free to not pay them, but you won't get any work either. The fact that you think you can get into a program without filing an application makes it blatantly obvious you've never applied anywhere, which is why I'm simply suggesting you shut the fuck up about PhD applications.
 >> Anonymous Tue Mar 10 14:58:14 2020 No.11457407 >>11457384maybe I'm just being bamboozled by your statement and not understanding. Are you talking about GRE and other annex stuff?>>11457397i was always told to send emails directly, or even better, use the networking you've done through internships to hook you up with a proposal. have you never done internships? The one I'm doing right now has basically a thesis at the end if I want and things go well.
 >> Anonymous Tue Mar 10 15:03:06 2020 No.11457424 >>11457407>i was always told to send emails directly,you do. But this does not somehow replace having to file an application. The very best-case outcome you will get from an email is>I think you'd be a good student. Apply and I'll mention to the committee that I'm interested in youEven if the prof offers to support you out of their own funding (like often happens in e.g. Canada) and your acceptance is guaranteed, you STILL have to go through a formal application. You simply will not get in anywhere without one.
 >> Anonymous Tue Mar 10 15:05:20 2020 No.11457428 >>11457424I once did the automatic admission thing and got an automated email saying that weren't looking for student at this time. The next day, I got another email from the prof supervising the thing I was trying to get info about correcting the automated system.
 >> Anonymous Tue Mar 10 15:06:32 2020 No.11457434   >>11457364This isn't incredibly helpful but it's included in volume 1 of his selected papers published by Springer. Unfortunately that's not on libgen either but it might be easier to find through your library system than the standalone original paper, and if worst comes to worst and you really need it you can buy a copy without having to sell a kidney.
 >> Anonymous Tue Mar 10 15:27:35 2020 No.11457495
 >> Anonymous Tue Mar 10 15:36:17 2020 No.11457528 >>11457271>>11457286>>11457317It's for MSc. My gpa is only 2.7, so an American or Euro uni is out of the question. Plus I wouldnt be able to afford moving there as I am in Canada. The only hope I have is my 4 years research experience, TA experience, and community outreach volunteer experience (involving math). How did I get this you may ask? The prof I volunteered with got me the RA and TA jobs without ever asking for a transcript. The profs I met from all that never suspected I had a low GPA as I excelled at research and teaching. They were bamboozled when I asked for reference letters and finally asked for my transcript. I got A's in classes and C's in others, depending on how interested I was. Also had tough home life and worked to pay for my semesters before those jobs. I'll commit suicide if I can't keep doing math.
 >> Anonymous Tue Mar 10 15:38:25 2020 No.11457534 >>11457528You should use this teaching experience to create a network. This is how most people get PhDs anyways.
 >> Anonymous Tue Mar 10 15:43:32 2020 No.11457561 >>11457528>Plus I wouldnt be able to afford moving there as I am in Canada.This is actually not a bad thing for you. The Canadian system is less formal than the US one; if you talk to a professor and make a good impression (which you seem pretty capable of doing) then they have a lot more ability to pull strings to get you in compared to an American school, most of which are extremely bureaucratic. Your profs that like you may be able to put in a word for you with their friends as well.Although I don't see how you "wouldn't be able to afford" immigrating to the US from Canada. That costs basically nothing. Besides, if you end up having a year off, you might as well work so you're not a broke-ass nigga next application season.
 >> Anonymous Tue Mar 10 15:44:51 2020 No.11457566 >>11447403That's only true if you're dealing with a Galois extension.
 >> Anonymous Tue Mar 10 16:00:55 2020 No.11457607 >>11457534>You should use this teaching experience to create a networkCan you please elaborate?
 >> Anonymous Tue Mar 10 16:02:16 2020 No.11457612 >>11457607Whomever you were working with/for could write you a letter of recommendation.
 >> Anonymous Tue Mar 10 16:08:03 2020 No.11457622 >>11457528Anyways, if you think so fee is shitty, think of the non-English-natives students who have to coof up £250 for IELTS or equivalent despite being entirely proficient.
 >> Anonymous Tue Mar 10 16:10:41 2020 No.11457626 >>11457622>think of the non-English-natives students who have to coof up £250 for IELTS or equivalent despite being entirely proficient.What about the non-English-natives students who coof up the £250 for IELTS but who's speaking skills are so shit that it was obvious that they cheated?
 >> Anonymous Tue Mar 10 16:12:27 2020 No.11457631 >>11457612Why do you insist on talking when you have no idea how anything works and can't even read?Letters of recommendation are mandatory. If he applied, it's a certainty he already has letters, and the post you responded to explicitly said so.
 >> Anonymous Tue Mar 10 16:13:19 2020 No.11457637 >>11457631>Letters of recommendation are mandatoryNot in my country at all.
 >> Anonymous Tue Mar 10 16:16:07 2020 No.11457648 >>11457637Then you're in some third world shithole with no standards, which explains why you have no clue how Western PhD programs work, but please don't act like your shithole experiences apply to the first world.
 >> Anonymous Tue Mar 10 17:16:09 2020 No.11457802 >>11457648>please don't act like your shithole experiences apply to the first world.Expect for China and IndiaGraduate Programs welcome the Massive influx of students from China and India who are going to a western university for the status symbol!
 >> Anonymous Tue Mar 10 17:29:12 2020 No.11457837 >>11457495thanks, anon!
 >> Anonymous Tue Mar 10 17:38:15 2020 No.11457862 File: 86 KB, 998x747, 2020-03-10-223300_998x747_scrot.png [View same] [iqdb] [saucenao] [google] [report] Can someone tell me what this shorthand notation means, the highlighted square brackets with h inside?h := x -a and T(x,a) is the Taylor Polynomial. So somehow the square brackets [h, ... ,h] transform into the coefficients of the sum of partial derivatives?!
 >> Anonymous Tue Mar 10 17:43:47 2020 No.11457885 >>11457862It's tensor contraction. $f^{(n)} = \partial_{i_1}\dots\partial_{i_n}f$ is a rank-$n$ tensor and it is contracted with $[h,\dots,h] = h_{i_1}\dots h_{i_n}$
 >> Anonymous Tue Mar 10 17:45:48 2020 No.11457894 What is tropical geometry and what are some cool open problems in the field?
 >> Anonymous Tue Mar 10 17:48:45 2020 No.11457903 File: 1.86 MB, 985x819, davidd2.png [View same] [iqdb] [saucenao] [google] [report] >>11457862so wie du mit nem Vector das inner Produkt mit h nehmen kannst, und mit einer Matrix hinten und vorne h drauf klatschen kannst um nen Skalar zu bekommen, so machst du es in beliebige Ordnung weiter.Siehehttps://en.wikipedia.org/wiki/Taylor_series#Taylor_series_in_several_variables
 >> Anonymous Tue Mar 10 17:48:54 2020 No.11457904 >>11457885oh right, I have not been exposed to tensors yet but I understand the concept somewhat, thanks
 >> Anonymous Tue Mar 10 21:07:53 2020 No.11458391 File: 18 KB, 524x585, 839A6B7F-20A8-4CEA-BDEA-5F5A710F8FCD.jpg [View same] [iqdb] [saucenao] [google] [report] >Real Analysis>Differential Equations
 >> Anonymous Wed Mar 11 02:14:19 2020 No.11459057 Is noncommutative probability theory fun to learn?
 >> Anonymous Wed Mar 11 02:23:11 2020 No.11459070 Bros, why do i still struggle with undergrad physics when i pick a book even though i have a math degree and have studied grad level math
 >> Anonymous Wed Mar 11 02:42:02 2020 No.11459091 >>11459070Which book?
 >> Anonymous Wed Mar 11 03:29:45 2020 No.11459150 >>11459070because physics is not only math
 >> Anonymous Wed Mar 11 04:28:16 2020 No.11459234 File: 999 KB, 500x360, STOP YELLING AT ME.gif [View same] [iqdb] [saucenao] [google] [report] >>11459070>>*Gets finished proving the Riesz–Fischer theorem* >Hi, I need you to calculate this series of measure conversion in Ch 1 of this textbook>>No Problem bro, that's trivial wor->Also I need an approximate result that used scientific notation that is only 5 decimals long>>What rules of approximation are we using? In fact, can I get a section 0 of the textbook that has a lot of questions just on approximation and scientific notation so that I can get a feel fo->I'M NOT GOING TO TELL YOU THAT ASSHOLE YOU'RE THE STUDENT>>*Proceeds to start working on Chapter 1 of an Undergraduate Physics Textbook*>>*keeps getting the answer wrong, either due to a the solution manual arbitrary deciding to drop scientific notations for answers of a specific length, a sudden unexplained change of length of the approximation, or an approximation error but never told what an acceptable radius of error is or (and this is a good one) the solution manual failing to use it's own rules of approximation*>WHATS WRONG MATHEMATICIAN?>I THOUGHT MATHEMATICIANS WERE SUPPOSED TO BE SMART STOP ITI'VE ONLY EVER HAD TO GIVE EXACT ANSWERS!!!!
 >> Anonymous Wed Mar 11 05:13:38 2020 No.11459302 File: 34 KB, 186x146, what_did_i_mean_by_this.png [View same] [iqdb] [saucenao] [google] [report] >>11459070Because it wants you to develop intuition. At the research level it's what allowed e.g. Bethe/Laughlin/Feynman to guess the ground states and correlations of non-exactly solvable many-body quantum theories without knowing what a Yangian/Virasoro/Hodge algebra is, let along their representation theory. This is also what gives my previous advisor the gall to shit on mathematicians constantly.https://arxiv.org/abs/hep-th/9310158v1Sure, proving that a certain ansatz is valid is nice, but knowing where to look in the first place takes a whole different training.
 >> Anonymous Wed Mar 11 08:13:44 2020 No.11459525   File: 143 KB, 1063x808, Screenshot_2020_0311_174154.png [View same] [iqdb] [saucenao] [google] [report] Is it true? Also how much do you use your mobile? Is there any effect of it on you?
 >> Anonymous Wed Mar 11 08:47:50 2020 No.11459564 stats question:How do i interpret: "How big must a random sample from a normal distribution be so that the sample's expectation X with the probability > 90% is less than a standard distribution away from the distribution's expectation mean?"
 >> Anonymous Wed Mar 11 08:58:47 2020 No.11459579 >>11459564in other words:There is a normal distribution (it has some expected value E and some standard deviation sigma)you have n independent random variables x1,...xn, each has this normal distributionhow big n should be, in order to have the inequality$P(|\frac{x_1+...+x_n}{n} - E| < \sigma) > 0.9$?
 >> Anonymous Wed Mar 11 09:18:55 2020 No.11459590 >>11459579I'm completely lost and I feel stupid.
 >> Anonymous Wed Mar 11 09:25:59 2020 No.11459597 folks I have a test in 4 hours and I'm just solving the practice exam and I'm stuck in a problem, save my dumbass pleaseLet $I$ be an ideal in $S = K[x_1,...,x_n]$ and $f \in S$ any polynomial.I want to show that $(I:f^\infty) = (I:f^m)$ iff $(I:f^m) = (I:f^{m+1})$. One implication is trivial, but how do I get that $(I:f^m) = (I:f^{m+1}) \Rightarrow (I:f^\infty) = (I:f^m)$?. I've tried a direct proof and a proof by contradiction but I haven't gotten any progress so far. Here $(I:f^m) = \{g \in S : gf^m \in I \}$
 >> Anonymous Wed Mar 11 09:56:41 2020 No.11459645 >>11459579would it work to answer:0.68*0.9 = 0.612 = 61,2 % of the normal distribution must the random sample be? (0.68 from one standard deviation away)
 >> Anonymous Wed Mar 11 11:20:44 2020 No.11459778 >>11459597What’s the definition of f^infty
 >> Anonymous Wed Mar 11 11:55:16 2020 No.11459834 >>11459778$(I:f^\infty) = \{g \in S : gf^N, N \in \mathbb{N} \in I \}$
 >> Anonymous Wed Mar 11 12:53:30 2020 No.11459944 >>11459302how to get a phD in string theory memery like you seem to doas an engineer the most theoretical I can do is to develop ab initio models for transport phenomenons using DFT or other StatMech techniques and all the math I can do in my spare time isn't going to change my resuméI hate this tb'h
 >> Anonymous Wed Mar 11 13:08:11 2020 No.11459987 >>11459597>>>/sci/sqtHint hint: $(I : f^{ \infty} ) = \bigcap _{n \in \mathbb{N} } (I : f^n )$
 >> Anonymous Wed Mar 11 13:51:19 2020 No.11460117 >>11459987Isn’t it /cup?
 >> Anonymous Wed Mar 11 13:55:46 2020 No.11460132 >>11460117it is
 >> Anonymous Wed Mar 11 13:56:30 2020 No.11460135 File: 18 KB, 446x265, 1581752657259.jpg [View same] [iqdb] [saucenao] [google] [report] >>11460117If we're judging by the way anon wrote it, yes.But $a \in (I:f^n) \rightarrow a = gf^n \rightarrow a = (gf)f^{n-1} \rightarrow a \in (I : f^{n-1} )$, so it trivializes to $(I: f)$, and I'm thus assuming he forgot a for all in the definition.Also because I distantly recall seeing this stuff before.
 >> Anonymous Wed Mar 11 13:59:54 2020 No.11460148 >>11460135Never mind, I think I just mixed it up.
 >> Anonymous Wed Mar 11 14:09:51 2020 No.11460175 >>11460117i c u p
 >> Anonymous Wed Mar 11 14:18:42 2020 No.11460195 >>11459597Ok anon, basically you have ti prove two containments as usual. One of them is trivial, the other one follows by an argument similar to>>11460135To show that (I:f^m)=(I:f^(m+n)) for n>=1
 >> Anonymous Wed Mar 11 16:33:14 2020 No.11460541 Hey, I need some advice y'all. I study math in my free time as a way of challenging myself and I'm having trouble getting past proofs. I've gotten through Hammack's Book of Proofs and How to Prove It, but every time I try to learn linear algebra and a basic questions asks me to prove something, I draw a complete blank. I seem unable to apply what I've learned to more advanced subjects. Am I skipping a step? Are there any techniques that will enable me to retain and use the simpler mathematical concepts I've absorbed more effectively?
 >> Anonymous Wed Mar 11 16:40:07 2020 No.11460560 >>11460541practice, practice, and more practice.in basic Algebra though, it's usually about finding out correctly what exactly you know, what's asked of you, and the connection between the two.
 >> Anonymous Wed Mar 11 17:34:06 2020 No.11460756 File: 14 KB, 350x387, conway.jpg [View same] [iqdb] [saucenao] [google] [report] Bitch i found my path, still in school but im not good with math.
 >> Anonymous Wed Mar 11 17:37:22 2020 No.11460763 Did you espy the Seshat in the library? The fuck's up with that?
 >> Anonymous Wed Mar 11 18:22:01 2020 No.11460907 >>11459070grad math talks about doing math.undergrad physics does math.it's the difference between a music theorist and a musician. that's why astrophysics majors score higher on quant GRE than math majors, and within math majors operations research (applied math) score higher than "pure" (lmfao) math majors.none of this would be confusing if we didn't live in a society where we had to be polite to insecure people, but alas, we must.
 >> Anonymous Wed Mar 11 22:21:23 2020 No.11461460 >>11460907That's the dumbest thing I've ever heard
 >> Anonymous Thu Mar 12 04:06:06 2020 No.11462302 File: 85 KB, 184x571, 1566453761180.png [View same] [iqdb] [saucenao] [google] [report] >>11462240>If a 21:9 image is being displayed on a 16:9 1920x1080 Display, what would be the resolution of the empty spaces above and under the image?>~411 pixels>Op here, I think that's 5:18 for each empty space, then 5/18 multiplied by 1920 equals 533 pixels per empty space. I think the answer is 1920 x 533?>photoshop says 1920 x ~138.5 per each empty spaceCan /mg/ solve this?
 >> Anonymous Thu Mar 12 04:20:06 2020 No.11462330 >>11462302Based lost 4chins newfag
 >> Anonymous Thu Mar 12 06:46:21 2020 No.11462588 >>11446627i didnt understand a single thing, yet im a math major. is this bad?
 >> Anonymous Thu Mar 12 06:52:26 2020 No.11462601 >>11462588Are you capable of correctly deducing consequences of a given axiomatic system?
 >> Anonymous Thu Mar 12 06:53:32 2020 No.11462603 >>11462601huh?
 >> Anonymous Thu Mar 12 06:59:08 2020 No.11462609 >>11462603Have you ever noticed a correct theorem? Has a proof ever made sense to you? Have you ever verified a math statement on your own just to make sure it was correct?
 >> Anonymous Thu Mar 12 07:04:13 2020 No.11462618 >>11462609huh?
 >> Anonymous Thu Mar 12 07:06:31 2020 No.11462624 >>11462618huh? huh? huh?
 >> Anonymous Thu Mar 12 09:14:08 2020 No.11462825 >>11462609>Have you ever noticed a correct theorem?All theorems are correct.
 >> Anonymous Thu Mar 12 09:39:53 2020 No.11462865 File: 729 KB, 1260x518, Gifted Movie Clip First College Visit 4.png [View same] [iqdb] [saucenao] [google] [report] https://www.imdb.com/title/tt4481414/I kinda loved this film. Have any of you seen this?
 >> Anonymous Thu Mar 12 10:08:03 2020 No.11462901 >>11462825except that one inequality from a few years ago that was found to have been egregiously wrong despite the mathematics using it for over 40 yearswe don't talk about that one
 >> Anonymous Thu Mar 12 10:11:52 2020 No.11462906 >>11462901>except that one inequality from a few years ago that was found to have been egregiously wrong despite the mathematics using it for over 40 yearsThat wasn't a theorem.
 >> Anonymous Thu Mar 12 10:22:15 2020 No.11462931 >>11462906it is.
 >> Anonymous Thu Mar 12 10:22:17 2020 No.11462932 >>11462906Which theorem was that? Cohen did his thing more than 50 years ago.
 >> Anonymous Thu Mar 12 10:50:50 2020 No.11463023 File: 54 KB, 600x593, grafics.jpg [View same] [iqdb] [saucenao] [google] [report] >>11462932Jacobian conjecture is one. Supposed proved in 1939 by Keller and bestowed theorem status, it was assumed to be a proper theorem for years until the 1960's when Vitushkin took a giant shit on it and showed that over 90% of Mathematicians were fucking hacks because they couldn't be arsed to properly READ Keller's incorrect proof. But hey that's fine, just let them keep their PHDs while they sit in ivory towers casting judgment on Undergraduates for making the very same mistakes they did.
 >> Anonymous Thu Mar 12 11:42:31 2020 No.11463144 Who moving to online classes hereJust fuck my shit up
 >> Anonymous Thu Mar 12 12:37:54 2020 No.11463295 >>11463144mefuck this country
 >> Anonymous Thu Mar 12 15:07:09 2020 No.11463696 File: 66 KB, 640x480, jhbkjl.jpg [View same] [iqdb] [saucenao] [google] [report] >mfw BMC got cancelled
 >> Anonymous Thu Mar 12 16:25:13 2020 No.11463882 >tfw uni doesn't do online classesI can manage to keep up with the supposed curriculum, but the others? I don't think so...hopefully they get their sit together starting next week
 >> Problemancer !FJmII4R11c Thu Mar 12 17:09:45 2020 No.11464009 I see, perhaps this one was a bit too much.Unslain Beasts>>11453142Here's a new one that perhaps is easier:$(a_{n})$ is a real sequence with the following property true for all natural numbers $n$:[eqn]a_{n+1}^{2}+a_{n+1}=a_{n+2}^{2}+a_{n}[/eqn]Prove that a sequence such as this converges, and if so to what.
 >> Anonymous Thu Mar 12 17:16:03 2020 No.11464024 >>11463023Where can I find the wrong proof? Google doesn't turn up anything. Which journal did Keller publish it in?
 >> Anonymous Thu Mar 12 17:16:42 2020 No.11464025 >>11464009I don't follow.Let $a_n$ equal $1$ if $n$ is even, and $-2$ otherwise.Then $1+1^2=2=-2 + (-2)^2$.
 >> Problemancer !FJmII4R11c Thu Mar 12 17:40:15 2020 No.11464068 >>11464025>>11464009Ah you're right, apologies I didn't catch myself in drafting this, $a_{n}$ is a recursive, real sequence. Very quick work on the disproof though.
 >> Anonymous Thu Mar 12 17:48:08 2020 No.11464086 File: 38 KB, 433x433, 1580798674493.jpg [View same] [iqdb] [saucenao] [google] [report] >>11464068I misread the property as $a_{n+1}^2 + a_{n+1} = a_{n+2}^2 + a_{n+2}$ and just looked for a counterexample to $f(x)=x^2 +x$ being injective.
 >> Anonymous Thu Mar 12 19:32:41 2020 No.11464326 >>11453142Let n=4 and D=2016. Then the modulo checks out https://www.wolframalpha.com/input/?i=2016*6%5E625+%3D2016+modulo+10%5E4but 16 doesnt divide 6+1*2+8*2 = 24, right?
 >> Anonymous Thu Mar 12 19:38:18 2020 No.11464341 >>11464086Don't downplay yourself, your answer still works without mancer's correction
 >> Anonymous Thu Mar 12 19:47:43 2020 No.11464362 >>11464068how is this any correction to the problemthis sequence >>11464025 is still a counterexample
 >> Anonymous Thu Mar 12 19:52:36 2020 No.11464379 >>11464362Make it recursive then faggot
 >> Anonymous Thu Mar 12 19:56:20 2020 No.11464397 >>11464379what do you think "recursive" means faggotyou can't compute a_n+2 from the previous terms, because it could be a positive or negative square root
 >> Problemancer !FJmII4R11c Thu Mar 12 19:57:06 2020 No.11464401 >>11464326Perfection, well done.
 >> Anonymous Thu Mar 12 20:03:00 2020 No.11464424 >>11464397[eqn]a_{n+2}^{2}-a_{n+1}=a_{n+1}^{2}-a_{n}=C[/eqn][eqn]a_{n+1}=\pm\sqrt{C+a_{n}}[/eqn]Yeah suppose it could be negative you twat, what happens then? Someone has to retake Real Analysis.
 >> Anonymous Thu Mar 12 20:08:11 2020 No.11464448 >>11464424congratulations, now look here >>11464025 and realise that this still fits your formulas you dumb fuck, because we can choose the plusminus arbitrarily
 >> Anonymous Thu Mar 12 20:22:49 2020 No.11464488 >>11464448?[eqn]a_{1}=1;a_{2}=-2=-\sqrt{C+1}\Rightarrow3=C[/eqn][eqn]a_3=-\sqrt{3+(-2)}=-1[/eqn]Oops!
 >> Anonymous Thu Mar 12 20:31:10 2020 No.11464503 >>11464488$a_3 = \sqrt{3 + -2} = 1$it does not follow from the original equations in any way that you have to select ALWAYS PLUS or ALWAYS MINUSit's only a plusminus which may be sometimes plus and sometimes minus depending on n
 >> Anonymous Thu Mar 12 20:55:48 2020 No.11464578 >>11464503Plus/minus doesn't give you a pass to pick one, both must satisfy the circumstance.
 >> Anonymous Thu Mar 12 23:21:36 2020 No.11465005
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