/mg/ maths general: mochi edition

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/mg/ maths general: mochi edition Anonymous Mon Mar 4 00:32:52 2019 No.10436214 [Reply] [Original]

talk maths, formerly >>10417432

>Thm 1.10 - Probabilistic Version - part 06 - "Second Term"
https://www.youtube.com/watch?v=kzcmFYSA6hQ

>Thm 1.10 - Probabilistic Version - part 07 - "Ramification Term"
https://www.youtube.com/watch?v=S8q4-IOBWoM

>Thm 1.10 - Probabilistic Version - part 08 - The Appearance of 6+eps in Szpiro
https://www.youtube.com/watch?v=cNr_P48uGjI

>>	Anonymous Mon Mar 4 05:02:59 2019 No.10436617 File: 68 KB, 840x820, turkpepe.jpg [View same] [iqdb] [saucenao] [google] >>10436214 Math is a pseudo-science

>>	Anonymous Mon Mar 4 05:03:56 2019 No.10436619 >>10436617 Earth is flat

>>	Anonymous Mon Mar 4 05:10:05 2019 No.10436624 File: 358 KB, 473x784, sosaku.png [View same] [iqdb] [saucenao] [google] >>10436619 How amusing nerd. But even flat-earthers have more relevance than all you fags combined. Imagine having your entire field adjacent to hard sciences lmao

>>	Anonymous Mon Mar 4 05:28:19 2019 No.10436642 File: 4 KB, 462x86, thepowerofmath.png [View same] [iqdb] [saucenao] [google] >>10436617 Based and engineer-pilled

>>	Anonymous Mon Mar 4 05:37:36 2019 No.10436654 How would you prove that the real protective plane cannot be embedded in the third dimensional euclidian space using exclusively the tools of protective geometry?

>>	Anonymous Mon Mar 4 05:43:21 2019 No.10436664 File: 127 KB, 659x697, 1534122657134.jpg [View same] [iqdb] [saucenao] [google] I can handle abstract algebra proofs so far but analysis fucks me. This cherry-popping course just leaves me biting the pillow every week

>>	Anonymous Mon Mar 4 08:04:58 2019 No.10436799 >>10436624 >fags Why the homophobia?

>>	Anonymous Mon Mar 4 08:05:59 2019 No.10436803 >>10436654 >How would you prove that the real protective plane cannot be embedded in the third dimensional euclidian space using exclusively the tools of protective geometry? What have you tried?

>>	Anonymous Mon Mar 4 08:07:07 2019 No.10436807 File: 1.80 MB, 1202x910, physical maths.png [View same] [iqdb] [saucenao] [google] Threadly reminder to work with physicists.

>>	Anonymous Mon Mar 4 10:59:40 2019 No.10437131 >>10436664 You'll get through it, just be patient.

>>	Anonymous Mon Mar 4 11:12:46 2019 No.10437152 Does this problem make a sense at all? If we're given a graph with random edges and vertices, what should we do in order to find every complete subgraph in there?

>>	Anonymous Mon Mar 4 12:05:22 2019 No.10437256 Anybody cares to reply? https://math.stackexchange.com/questions/3133360/proper-actions-in-complex-geometry

>>	Anonymous Mon Mar 4 12:08:08 2019 No.10437265 >>10436617 [/math] \pi = 3 = e [math]

>>	Anonymous Mon Mar 4 12:34:51 2019 No.10437333 >>10436807 >not being both

>>	Anonymous Mon Mar 4 12:35:59 2019 No.10437336 >>10437256 No, but I upvoted your post.

>>	Anonymous Mon Mar 4 12:40:58 2019 No.10437345 >>10437336 Mh, I don't care about mse points, but thanks for considering it anyway. If nobody answers I will probably go to annoy a teacher.

>>	Anonymous Mon Mar 4 12:41:53 2019 No.10437348 >>10437345 I supposed it'll gather some attention.

Anonymous Mon Mar 4 13:57:32 2019 No.10437545
File: 34 KB, 657x657, e07b20ffd67e495e5f6325dd395d0ac7.png [View same] [iqdb] [saucenao] [google]

>working on my undergrad thesis with my assessor
>"anon you are getting good at writing , I didn't find errors this time"
>"anon I told to change this proof, why you didn't, also you have a lot of mistakes I already told you to check"
>she hits me on the head with a newspaper
why are doctors so mean

>>	Anonymous Mon Mar 4 14:40:15 2019 No.10437658 >>10437545 This is too cute to be real

>>	Anonymous Mon Mar 4 16:18:23 2019 No.10437964 Anyone else in /mg/ remember the daily Putnam stickies? Putnam/Olympiad problem of the day >>10437887

>>	Anonymous Mon Mar 4 21:37:37 2019 No.10438683 >>10437545 PLEASE PLEASE PLEASE have coitus with her and tell us the story

>>	Anonymous Mon Mar 4 21:53:26 2019 No.10438707 >>10436807 >1968 lol, assuming they wouldn't be out protesting and doing Marxist shit like every other academic

>>	Anonymous Mon Mar 4 22:11:57 2019 No.10438745 >>10437545 She likes you, you autist

Anonymous Mon Mar 4 22:12:13 2019 No.10438746

Hello math people. I'm at work right now, in a factory producing plastic film, from that statement alone I'm sure you'll gather I'm no genius. Anyway, the film is wound onto rolls before further processing and conversion. I currently have a job on that will make 2 rolls, there's 1500 metres of film per roll and each roll will have a diameter of 860mm. How would I calculate the diameter if I where to put all the film on 1roll?

>>	Anonymous Mon Mar 4 22:18:31 2019 No.10438756 GOD PDEs is so boring. I can't wait for this semester to be over. Jesus Christ. FUCK

>>	Anonymous Mon Mar 4 22:24:47 2019 No.10438774 >>10438756 it's so much fun what book are you using, are you doing it with functional analysis / distributions / heavy theory and qualitative analysis, or is it focused on solving them?

>>	Anonymous Mon Mar 4 22:29:16 2019 No.10438786 >>10438774 Just focusing on solving them so far.. I think there will be some functional analysis, not 100% sure. The book is : Applied Partial differential Equations with Fourier Series and Boundary Value Problems, Richard Haberman, Fifth Edition.

>>	Anonymous Mon Mar 4 22:44:47 2019 No.10438832 >>10438786 lmao that's dumb imagine taking a class in "applied" pdes that's not even a math class pdes are beautiful and nuanced field and your meme class bastardizes them maybe it will improve by the end

>>	Anonymous Mon Mar 4 22:57:24 2019 No.10438863 File: 8 KB, 209x241, 1550910976133.png [View same] [iqdb] [saucenao] [google] >>10438832 Haha...yeah. I could only imagine. Imagine talking about heating metal rods... haha, couldn't be me.

>>	Anonymous Mon Mar 4 23:29:38 2019 No.10438935 File: 28 KB, 400x355, 4e7838b188bd9e0ed5e48834d75dd10a_400x1000.jpg [View same] [iqdb] [saucenao] [google] >>10438832 this

>>	Anonymous Tue Mar 5 00:44:01 2019 No.10439108 Taking linear algebra right now. If I can't figure out proofs right now, will I eventually get better or it or does it mean I have the big gay (the low IQ)?

>>	Anonymous Tue Mar 5 01:06:50 2019 No.10439156 >>10439108 Maybe you didn't have a good intro into proofs? My into linear algebra class had us writing very informal proofs, it was geared toward CS and engineering kids mainly. Maybe try reading an Intro to Proofs book on the side. Pick any one,

>>	Anonymous Tue Mar 5 01:30:43 2019 No.10439189 >>10439156 >Maybe try reading an Intro to Proofs book on the side. proof books = meme books

>>	Anonymous Tue Mar 5 02:20:18 2019 No.10439268 >>10439108 you'll get better at it, but this is the time to improve. don't give up on problems.

>>	Anonymous Tue Mar 5 02:51:15 2019 No.10439313 >>10436654 Actually, I had never thought of the proof of this but I'm glad I looked it up. Thanks anon.

>>	Anonymous Tue Mar 5 02:52:17 2019 No.10439315 >>10436807 In my uni students of physics meme hate mathematicians and viva Versa. Why is that?

>>	Anonymous Tue Mar 5 03:00:32 2019 No.10439329 >>10437545 She's being playful you idiot. If she didn't like you, she wouldn't have done that. Just correct the fucking errors and move on?

>>	Anonymous Tue Mar 5 03:38:20 2019 No.10439398 Why isn't point set topology taught before analysis or any analysis? It seems like it's built me up for a foundation more than any other class I've taken

>>	Anonymous Tue Mar 5 04:02:48 2019 No.10439434 Are there any interesting equivalences for arctan(pi) in terms of alternate representations?

Anonymous Tue Mar 5 06:28:21 2019 No.10439581
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>>10438746
Do you know the thickness of the film? If so, you might want to check this out — I've used something similar when working with paper rolls (pic related): http://handymath.com/cgi-bin/roll4.cgi?submit=Entry

>>	Anonymous Tue Mar 5 06:59:02 2019 No.10439620 >>10437256 I now really hope someone answers on this. Keep going, anon, in your scientific studies.

>>	Anonymous Tue Mar 5 08:07:42 2019 No.10439705 >>10436214 >unironically paying to study math literally lmaoing @ you rn, enjoy making literally 0 cash out of your "Degree"

>>	Anonymous Tue Mar 5 08:13:56 2019 No.10439714 >>10439398 Because you can't teach topology to people who don't know any real analysis. There's no way to motivate that level of generality, no (non-autistic) examples available at their level, and nothing is going to make any sense to them.

>>	Anonymous Tue Mar 5 09:09:15 2019 No.10439854 >>10439398 I'm doing this right now. Don't. It's dumb.

Anonymous Tue Mar 5 09:23:01 2019 No.10439875

Pic related is me. Physics major here. So far I have been doing maths just fine, but I took tensor analysis course and fuckity fuck me.
I've come to understand that I don't get theoretical math at all. And first you can note that I am literally retarded because all math is theoretical. I mean I like examples and applications.
Limits? Don't get the explanation but I can solve everything after observing a few examples.
Derivatives? Easy peasy after I see formulas and a few examples.
Integrals? Give me an example not the definition and I can do them.

Now I have only theory from classes and searching google has even more on that. Fuck this shit.
Can someone help me out to put theory into practice or just give me a hint to solving this.

I'm givena functiong f(x,y,z) and I need to find write f(x',y',z'), when given x', y', z' relation to x,y,z.

English not being my first language is a bother too.

>>	Anonymous Tue Mar 5 09:24:20 2019 No.10439878 File: 111 KB, 600x592, brainlet.png [View same] [iqdb] [saucenao] [google] >>10439875 the fact I can't even upload a picture makes me even more of a brainlet.

Anonymous Tue Mar 5 11:40:50 2019 No.10440148
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>>10439398
literally every fucking thread some moron comes in here whining about how confusing they find topology
without fail, you can ask them "have you taken real analysis" and they will respond "no"
and then when you call them an idiot they start blubbering and going "IT WASNT REQUIRED!!!!"
universities need to require idiots like this to take analysis before topology to save them from themselves and their pathetic crutch of intuition

Anonymous Tue Mar 5 11:42:47 2019 No.10440152
File: 39 KB, 600x511, blini.jpg [View same] [iqdb] [saucenao] [google]

>>10439875
holy cow imagine being this dumb
isn't there a containment thread for your type up right now?
just fuck off back to stupid questions thread or whatever if not
this isn't your little personal advice column
oh my god it makes me laugh how hopeless physicists are

>>	Anonymous Tue Mar 5 11:44:37 2019 No.10440162 >>10436642 literally no mathematician claims this is true. Everyone agrees that the sum diverges.

>>	Anonymous Tue Mar 5 11:45:42 2019 No.10440167 >>10440148 I don't blubber, the question asks why am I taking topology before analysis and I give the answer. If you don't want an answer don't ask the question. I have never defended myself for being an idiot.

>>	Anonymous Tue Mar 5 11:54:57 2019 No.10440199 >>10440152 >imagine being this dumb rude

>>	Anonymous Tue Mar 5 12:39:05 2019 No.10440276 >>10440162 nice job admitting you aren't a mathematician it diverges, but thats because your baby fucking definition of infinite series is intuitionist garbage

Anonymous Tue Mar 5 12:43:34 2019 No.10440289

>>10439398
Essentially, Analysis is taught twice because the first time we assume you know Calc, and the second we assume you know Topology and Measure theory.
There isn't a point in doing Analysis just after topology, and there usually isn't enough time to do Measure and then Analysis.

Anonymous Tue Mar 5 12:55:27 2019 No.10440315
File: 28 KB, 360x499, 51zU2Qe+5cL._SX358_BO1,204,203,200_.jpg [View same] [iqdb] [saucenao] [google]

Hey, fellow mathematicians, I need some help figuring out my future:

I'm halfway through my Math degree, but I realized that I want to pursue an academical career in Theoretical Physics. Should I continue my degree and go for a PhD in TP or is it better to change right now to a Physics degree?

The stick says to post career advice on /adv/ but I doubt I would find any meaningful answer there regarding this subject. Thanks.

>>	Anonymous Tue Mar 5 12:59:06 2019 No.10440322 >>10440315 Undergrad physics is just a holding pattern until you know enough math for graduate physics.

Anonymous Tue Mar 5 13:04:45 2019 No.10440333

>>10440322
I see, I read it a lot around here, but is it common for physicists to get first a degree in Math and then go for a PhD in Theoretical Physics?

How much math is used in TP anyway? Are things like Topology, Complex Analysis, Abstract Algebra, Algebraic Geometry etc important for the modern physicist?

>>	Anonymous Tue Mar 5 13:06:34 2019 No.10440337 >>10440333 >Are things like Topology, Complex Analysis, Abstract Algebra, Algebraic Geometry etc important for the modern physicist? Is this bait?

>>	Anonymous Tue Mar 5 13:09:46 2019 No.10440344 >>10440337 No.

>>	Anonymous Tue Mar 5 13:22:15 2019 No.10440371 Can someone hit me up with the definition of Torsion Product? >>10440333 Yukariposter is my only source for physics, and apparently they use stuff like Arithmetic Geometry.

>>	Anonymous Tue Mar 5 13:37:18 2019 No.10440418 >>10440333 Topology and geometry are extremely important in physics as well as Lie algebra

Anonymous Tue Mar 5 13:45:44 2019 No.10440450

>>10440333
Mathematical disciplines like Lie theory, differential geometry and representation theory are entangled with modern theoretical physics.
There Are also unexpected connections between string theory, quantum gravity, number theory, and group theory

Anonymous Tue Mar 5 14:47:35 2019 No.10440651

>>10440148
Interesting I guess. Undergrad Topology (point set) seems more straight forward than analysis but that is also because I have a couple semesters of analysis already under my belt and it was the first real math class I've taken.
>>10440289
I never taken a second course in analysis but I have no idea about measure theory although I hear it's pretty cool from /mg/

Anonymous Tue Mar 5 16:21:04 2019 No.10440942

>>10438746
Given you know the diameter of the roll you can calculate the volume of the roll (or the area of a circular cutsection if you want) using formulas for the area of a circle. Doubling the amount of film on a roll doubles the volume/area, so you then use the same formula to find what diameter is required to give a roll of that volume.

>>	Anonymous Tue Mar 5 16:36:22 2019 No.10440990 File: 1.26 MB, 360x363, lissajous1p5.gif [View same] [iqdb] [saucenao] [google] Does anyone know where I can find a description of the embedding of Lissajous curves into R^3? It's clearly where they ought to live.

Anonymous Tue Mar 5 18:44:39 2019 No.10441304

>>10439714
i learnt topology before real ana...
actually, it felt to me that the questions topology asks are a lot more intuitive to think about, so the end goal is clearer.
real ana was pitched to me at the time as "let's prove that calculus works"

it just so happens that i learnt complex ana before properly learning real ana, so maybe it's just bc i'm a geometer :\

Anonymous Tue Mar 5 18:50:37 2019 No.10441319

>>10441304
>actually, it felt to me that the questions topology asks are a lot more intuitive to think about,
this is bullshit
what kind of questions can you even ask (that are answerable within a semester) in a topology course to students who don't know any analysis?

>>	Anonymous Tue Mar 5 18:52:54 2019 No.10441325 >>10441319 Not him, but plenty of examples and questions can be asked just from the topology from multivariable calc.

>>	Anonymous Tue Mar 5 18:57:06 2019 No.10441340 >>10441325 >plenty of examples and questions can be asked just from the topology from multivariable calc. Post a couple of them then.

Anonymous Tue Mar 5 19:08:15 2019 No.10441373

>>10441340
Do you thin euclidean space has no interesting topological structure? Are you retarded? Well firstly you can simply ask in constructing the topology what properties depend fundamentally that you are on some [math]\mathbb{R}^n[/math]. Many questions about the closure, interior boundary can be shown to need only the basic postulates. The idea of basis is not that new if you already know many definitions of continuity use open balls and how from them you can construct the topology. Also, while maybe you will not fully realize the power topology has in more abstract spaces, like banach spaces or in differential geometry, most books have plenty of examples in [math]\mathbb{R}^n[/math].

Anonymous Tue Mar 5 19:26:47 2019 No.10441425

>>10441373
>Many questions about the closure, interior boundary can be shown to need only the basic postulates. The idea of basis is not that new if you already know many definitions of continuity use open balls and how from them you can construct the topology.
Yes, but this is all the content of a basic real analysis course. No multivariable calculus course is going to spend several weeks doing a rigorous development of metric space topology regarding continuity conditions, open/closed/compact sets, interiors and closures, etc.
What you are saying is precisely my point, you need familiarity with the concept of continuity in Euclidean space in order to be able to move to the abstract setting.

>>	Anonymous Tue Mar 5 19:29:04 2019 No.10441431 >>10441425 I forgot burgers think real analysis means "rigorous calculus". Even shithole latin countries see that shit in their calculus courses.

>>	Anonymous Tue Mar 5 19:34:40 2019 No.10441450 >>10441431 You're welcome to post some proof that brmonkeys are doing chapters out of Rudin in their calculus courses. Until then you're still bullshitting.

>>	Anonymous Tue Mar 5 19:38:00 2019 No.10441460 >>10441450 Here is the standard calc 3 book from a spic uni http://lya.fciencias.unam.mx/paez/J_Paez_Calculo_III.pdf You don't need fucking rudin to understand what continuity is and know about the toplogy in R^n

>>	Anonymous Tue Mar 5 19:47:26 2019 No.10441488 File: 91 KB, 1098x755, Screenshot_2019-01-02_23-07-47_190305-074950.png [View same] [iqdb] [saucenao] [google] >>10441450 >brmonkeys pic related is as rigorous as Rudin (at the very least) and it's used in courses in Chile and Brazil.

>>	Anonymous Tue Mar 5 19:56:28 2019 No.10441505 >>10441488 Im sorry!

>>	Anonymous Tue Mar 5 20:00:36 2019 No.10441518 >>10441450 No, it's usually (translated) Spivak. >>10441488 That's for the two semester analysis course that happens later. Calc is Calc.

>>	Anonymous Tue Mar 5 20:27:01 2019 No.10441574 What is the most useful foreign language for grad school?

>>	Anonymous Tue Mar 5 20:28:58 2019 No.10441576 >>10441574 French.

>>	Anonymous Tue Mar 5 20:56:06 2019 No.10441632 >>10441576 Elaborate

>>	Anonymous Tue Mar 5 20:58:18 2019 No.10441637 >>10441632 Éléments de géométrie algébrique

>>	Anonymous Tue Mar 5 21:09:20 2019 No.10441660 >>10441488 Elon Lages' book is as rigorous as Rudin? Does it have exercises on the same level as well? I'm genuinely curious.

>>	Anonymous Tue Mar 5 21:18:31 2019 No.10441669 someone give me a QRD on the "kernel trick" also, what makes kernels so useful for assessing non-additive/non-linear relations among "high-dimensional" data

>>	Anonymous Tue Mar 5 21:36:56 2019 No.10441697 File: 26 KB, 628x116, an action of Ass.jpg [View same] [iqdb] [saucenao] [google] >>10436214 How do I inject into an Ass algebra?

>>	Anonymous Tue Mar 5 22:33:34 2019 No.10441806 >>10441669 >QRD ?

>>	Anonymous Tue Mar 5 22:35:19 2019 No.10441809 >>10441806 quick rundown

>>	Anonymous Tue Mar 5 22:43:45 2019 No.10441826 >>10441697 are all degenerate ass algebras prolapsed algebras?

>>	Anonymous Tue Mar 5 23:04:54 2019 No.10441861 File: 881 KB, 1890x1490, memelist.png [View same] [iqdb] [saucenao] [google] how's my memelist for myself (currently on apostol/rudin)

>>	Anonymous Tue Mar 5 23:05:39 2019 No.10441866 >>10441861 >(currently on apostol/rudin) Rudin is a meme.

>>	Anonymous Tue Mar 5 23:06:17 2019 No.10441869 File: 101 KB, 360x330, math-broken.png [View same] [iqdb] [saucenao] [google] Will you fight?

>>	Anonymous Tue Mar 5 23:10:01 2019 No.10441875 >>10441866 the problems are thought provoking but pedagogically I think the book is garabge, so I'm just doing it for the problems

>>	Anonymous Wed Mar 6 00:41:11 2019 No.10442027 What's an example of a finite non-commutative ring?

>>	Anonymous Wed Mar 6 00:52:55 2019 No.10442047 >>10442027 Exterior algebra over [math]\mathbb{F}_p^n[/math] for p prime.

Anonymous Wed Mar 6 01:17:19 2019 No.10442075
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>>10441875
I've been wondering if I should brush up on stuff I may have missed in undergrad real analysis since I didn't have the full analysis sequence. Does rudin mainly focus on metric spaces and riemann integration? Or does it also get into lebesgue integration and measure theory?

>>	Anonymous Wed Mar 6 01:21:07 2019 No.10442077 >>10441861 >lang lang is a meme

Anonymous Wed Mar 6 05:30:59 2019 No.10442381

>>10441669
Lots of things we want to compute depend only on the inner product between elements. Sometimes instead of applying a non-linear transformation then taking inner products it is more computationally efficient to do this in one step (as a kernel function).

>>	Anonymous Wed Mar 6 05:54:15 2019 No.10442401 File: 97 KB, 960x648, IMG_7259.jpg [View same] [iqdb] [saucenao] [google] Farewell, friends, it's been a great ride but I'm not gonna make it. Math physics is going to kill me, Sobolev spaces I can't get through. Goodbye.

Anonymous Wed Mar 6 07:37:30 2019 No.10442496

>>10441861
The section after Apostol/Rudin is pretty dumb. Dummit/Foote is 1000 pages long and Stein/Shakarchi is ~1200. Dummit and Foote, while an excellent textbook, is horrible for self-study because it's so large that reading the entire thing will take you forever and has so many hundreds of problems you shouldn't realistically do even most of them.

Find yourself an intro algebra textbook you can actually finish by the end of the year, and replace Stein/Shakarchi by something with a more reasonable page count (a decent graduate analysis book will cover everything you really need from the 3 non-complex volumes in one book).

Anonymous Wed Mar 6 07:41:02 2019 No.10442500

>>10442075
>Or does it also get into lebesgue integration and measure theory?
There are a pair of chapters at the end of Rudin that do an extremely brief coverage of integration of differential forms and Lebesgue theory (respectively) but even a lot of people who took courses from Rudin don't remember this, because they're so shitty that even profs who like the book don't like them and I've never heard of anyone actually teaching them. Most Rudin courses do chaps. 1-9 and stop.

>>	Anonymous Wed Mar 6 11:08:30 2019 No.10442785 >>10441866 It's a bad intro but a decent text to solidify your understanding, right? I haven't read it myself because I fell for the siren song of alg*bra.

Anonymous Wed Mar 6 11:52:02 2019 No.10442883
File: 309 KB, 838x849, Screenshot_2019-03-06_13-19-54.png [View same] [iqdb] [saucenao] [google]

>>10441518
Hm, it might depend on the institution. I did a math major in Chile, and Lima's work is recommended reading for first-year Calc in pretty much all universities that offer such a major. My own course was largely based on it.
>>10441660
Curso de Análise and Baby Rudin are very alike in topics covered and the level of mathematical rigor they're treated with. The main difference is that Lima doesn't cover the Lebesgue integral, as this is usually left for a later course in measure theory. It also doesn't explicitly define what a metric space is since this generalization is treated in Lima's Espaços Métricos (and the only metric space you'll work with at a first/second year level is [math]\mathbb{R}^n[/math] anyway). The exercises are good, each chapter has roughly fifty of them in escalating difficulty and most are very interesting.
>>10441574
>>10441632
A good deal of the past century's relevant mathematics: Bourbaki school, Dieudonné, Grothendieck etc. Depends largely on your area of study though.
>>10441869
got that shit on Watch Later since like a week ago and still haven't watched lol

Anonymous Wed Mar 6 12:04:21 2019 No.10442911

What kind of jokes could you put into your dissertation and get away with? I know about shit like citing the Unabomber, but I doubt I could shoehorn in his work.
A friend said that it's common to put a reference to a fictional paper of Moriarty from the Sherlock Holmes books but looking it up it doesn't even seem to be true. Besides I am not a fan and haven't even read any of them so it seems really stupid.
Would it be acceptable to cite one of Jon Tooker's papers?

>>	Anonymous Wed Mar 6 12:58:28 2019 No.10443034 >>10440162 Disprove the proof, then.

Anonymous Wed Mar 6 13:09:51 2019 No.10443082

>>10442911
I had to use the existence of a nonvanishing vector field on an odd dimensional sphere for some proof and I couldn't be bothered to find a reference to cite it so I showed its existence by using Adams's result on the number of nonvanishing vector fields on spheres which i had shown before. To those unaware, this would be analogous to showing cube root of 2 is irrational with Fermat's last theorem

Anonymous Wed Mar 6 13:13:40 2019 No.10443097

>>10442911
Tasteful references to classical literature.
>>10442883
Pretty sure just about every brazillian university does the standard Calc 1-4 (or 3, depends) and then one or two semesters of real anal.
>that exercise 19
Wew lad. Wondering how you prove it without going a fortiori now.

>>	Anonymous Wed Mar 6 13:23:22 2019 No.10443123 >>10442911 "The following proof was revealed to me in a dream" followed by the most cookie-cutter apply-the-definition type proof

>>	Anonymous Wed Mar 6 13:34:50 2019 No.10443152 >>10443097 If f(Q) is not a singleton, there are two points a and b with f(a) != f(b). By the mean value theorem f(R) contains the interval from f(a) to f(b), which has uncountable many irrationals. As Q is countable, this is a contradiction.

Anonymous Wed Mar 6 13:39:03 2019 No.10443162

>>10443152
My bad, I'd misread the question. I'd assumed it was something like "Show that there's no bijective continuous function which maps rationals to irrationals and vice versa" and was wondering how you'd prove it without proving for all functions.

>>	Anonymous Wed Mar 6 13:51:29 2019 No.10443195 >>10440276 >t. wildberger wannabe

>>	Anonymous Wed Mar 6 13:53:53 2019 No.10443201 >>10443195 >t knows literally nothing how in the name of god is someone who defends infinite series even remotely fucking close to wildberger

>>	Anonymous Wed Mar 6 14:17:21 2019 No.10443277 >>10437545 I’m came

>>	Anonymous Wed Mar 6 15:12:48 2019 No.10443391 >>10442047 What is an exterior algebra?

Anonymous Wed Mar 6 15:16:28 2019 No.10443400
File: 217 KB, 600x753, 1551025943599.jpg [View same] [iqdb] [saucenao] [google]

>>10438746
The diameter of the resultant roll after adding to one roll another 1500 m of tape is given by:

860mm +2an

where a is the thickness of the tape and n the number of windings.
Each successive winding will remove from the 1500 meters of tape the circumference of the winding. Hence, we have:

(1500/2pi)-C1-C2-...-Cn=0

C1=.860
C2=.860+a
C3=.860+2a
...

So we have:

1500/2pi=.860n+a(n-1)n/2.

n can easily be solved as a function of a via the quadratic formula. Thus:

n(a)=(1/a)(sqrt([.860-a/2^2]+750a^2\pi)-(.860-a/2).

Measure the thickness of the tape and input what you get into the function above. n may only assume integral values, so round down. Substitute what you get for n into the function for diameter.

Anonymous Wed Mar 6 16:30:52 2019 No.10443579

>>10443391
https://en.m.wikipedia.org/wiki/Exterior_algebra

Basically, you take the tensor algebra of tensors [math]v_1\otimes\cdots\otimes v_n[/math] where you kill the ideal of tensors where two of the [math]v_i[/math] are equal.

If you take n=2 you get the quotient of the free algebra on two generators x, y with relations [math]x^2=y^2=xy+yx=0[/math]

>>	Anonymous Wed Mar 6 16:52:54 2019 No.10443623 File: 1.91 MB, 2336x1835, IMG_20190306_215002.jpg [View same] [iqdb] [saucenao] [google] There are plenty of evenly proportioned, symmetric even, forms of this singularity, but hartshorne chose this. What did he mean by this?

>>	Anonymous Wed Mar 6 17:22:44 2019 No.10443685 >>10443623 This is a great answer to >>10442911

>>	Anonymous Wed Mar 6 17:45:51 2019 No.10443740 >>10443579 Is there no simpler finite non-commutative ring?

>>	Anonymous Wed Mar 6 17:50:53 2019 No.10443750 File: 329 KB, 600x800, __shiki_eiki_touhou_drawn_by_hammer_sunset_beach__8500924fb5b9a67214aa5b503f6a1ee9.jpg [View same] [iqdb] [saucenao] [google] >>10443740 Any matrix ring. Say, 2x2 over the integers.

Anonymous Wed Mar 6 17:54:32 2019 No.10443755
File: 329 KB, 600x800, __shiki_eiki_touhou_drawn_by_hammer_sunset_beach__8500924fb5b9a67214aa5b503f6a1ee9.jpg [View same] [iqdb] [saucenao] [google]

>>10443740
Any nxn matrix ring with n>1 and over a ring with non-trivial multiplication (ab=0 for any a and b).

>>	Anonymous Wed Mar 6 17:59:07 2019 No.10443765 >>10443750 >finite

>>	Anonymous Wed Mar 6 17:59:29 2019 No.10443766 >>10443765 Yah but that's obvious.

>>	Anonymous Wed Mar 6 18:00:42 2019 No.10443768 >>10443766 stupid animeposter

>>	Anonymous Wed Mar 6 18:51:18 2019 No.10443895 Is there a collection of nice, fairly self-contained papers / notes on interesting topics? I wanna broaden my familiarity with math beyond what you see in your standard uni courses

Anonymous Wed Mar 6 19:48:06 2019 No.10444039
File: 69 KB, 402x354, yukari_boyfriend.png [View same] [iqdb] [saucenao] [google]

>>10439315
>students
That's your answer. It's well known that all research mathematicians want a physicist bf.
>>10440315
In general it's never good to go back and fill in gaps in your knowledge when you're doing a PhD, regardless if it's math gaps or physics gaps. The best thing to do is to take extra physics courses so that you get familiar with the jargon/concepts while you're finishing up your math degree. You may also attend physics colloquia so that you understand what kind of problems physicists are interested in.
>>10443895
Check out the "What is...?" series. They should be on arXiv.

>>	Anonymous Wed Mar 6 19:54:27 2019 No.10444054 File: 104 KB, 645x768, ah my side.jpg [View same] [iqdb] [saucenao] [google] >>10441861

>>	Anonymous Wed Mar 6 20:14:36 2019 No.10444093 >>10444039 >Check out the "What is...?" series Thanks! I found a link the whole series here http://www.ams.org/publications/notices/whatis/noticesarchive

Anonymous Wed Mar 6 20:44:15 2019 No.10444146
File: 21 KB, 300x360, roberts-david.jpg [View same] [iqdb] [saucenao] [google]

https://inference-review.com/article/a-crisis-of-identification
>It is not often that major conjectures in number theory are proved—much less conjectures stated in elementary terms. Any time a well-respected mathematician claims to have done so, the mathematical world pauses until the experts have interrogated the argument. It is always possible that a subtle mistake may be hiding inside a long proof; there is no lasting shame in such a thing when it is handled with grace. All mathematicians have had the experience of convincing themselves that a result is true only to have it collapse or wobble under later inspection. That said, experts have highly trained intuitions, and can quickly recognize and separate novel ideas from routine procedures, and powerful techniques from symbol shuffling. When Andrew Wiles first revealed his first, and ultimately flawed, proof of Fermat’s Last Theorem, number theorists could still confidently say that his work was groundbreaking. Before Grigori Perelman’s proof of the Poincaré conjecture was vetted, it was clear his ideas were incredibly novel.

>Shinichi Mochizuki’s purported proof of the abc conjecture is otherwise. The proof itself is embedded in a framework that Mochizuki calls inter-universal Teichmüller theory (IUT). There is disagreement about the proof between leading number theorists and some of Mochizuki’s few, but very confident, supporters. In December 2017, a rumor spread that Mochizuki’s papers were to appear in a journal of which he is the editor in chief. Much of his work had already been made accessible to mathematicians. Publication would have served to give his results the authority of peer review. Number theorists started expressing their concerns online. “Since shortly after the papers were out,” wrote a mathematician going by the initials PS, “I am pointing out that I am entirely unable to follow the logic after Figure 3.8 in the proof of Corollary 3.12.”

>>	Anonymous Wed Mar 6 22:15:17 2019 No.10444332 File: 197 KB, 220x220, 1551676975055.gif [View same] [iqdb] [saucenao] [google] How do I prep for a data science interview??

>>	Anonymous Wed Mar 6 22:27:53 2019 No.10444352 >>10444332 You practice grabbing hands sternly and staring them right at their dicks and demanding a job.

Anonymous Thu Mar 7 01:12:50 2019 No.10444678

>>10441431
This fucking favela monkey again.
Its obvious that your butthurt you didnt get into an american uni because you were to busy making fart porn videos(your national sport). But for all us non portuguese favela niggers we dont give two shits about your shitty college and shitty education. Keep seething. Cant wait until your power cuts out and you get gang raped by a pack of niggers

>>	Anonymous Thu Mar 7 01:39:07 2019 No.10444735 >>10444039 fuck off trash

>>	Anonymous Thu Mar 7 01:57:29 2019 No.10444762 File: 22 KB, 400x400, cpK2emxp_400x400.jpg [View same] [iqdb] [saucenao] [google] >>10438707 stay woke

>>	Anonymous Thu Mar 7 02:09:49 2019 No.10444779 File: 843 KB, 1024x883, 1538684884257.jpg [View same] [iqdb] [saucenao] [google] >>10444762

>>	Anonymous Thu Mar 7 02:49:39 2019 No.10444828 >>10442027 [math]M_2(\mathbb{F}_2)[/math]

Anonymous Thu Mar 7 07:54:19 2019 No.10445197
File: 42 KB, 1016x628, minkowskisum.png [View same] [iqdb] [saucenao] [google]

I hate sometimes when books print wrong thing in them because you will try to rationalize it's correct but it is wrong.

Can someone tell me the diagram of minkowski difference in these are right or wrong. I bet the top part of diagram on right cannot be flat.

>>	Anonymous Thu Mar 7 09:10:20 2019 No.10445283 >>10438707 Marxist professors are based

>>	Anonymous Thu Mar 7 10:16:05 2019 No.10445385 >>10445197 Munkres's topology is the best intro book to a new concept ever made. Convince me wrong.

>>	Anonymous Thu Mar 7 13:12:45 2019 No.10445724 File: 22 KB, 343x543, 1482082008631.jpg [View same] [iqdb] [saucenao] [google] I am literally shaking holy shit https://pdfs.semanticscholar.org/4e56/c6fea76922082400dfc6e13a3a169ae7b9a6.pdf

>>	Anonymous Thu Mar 7 13:25:39 2019 No.10445756 >>10436642 It's still equal to (∞(∞+1))/2

>>	Anonymous Thu Mar 7 14:08:13 2019 No.10445849 File: 3.01 MB, 2336x2590, IMG_20190307_190702.jpg [View same] [iqdb] [saucenao] [google] Just stole this from the library Post your hauls

>>	Anonymous Thu Mar 7 14:14:19 2019 No.10445871 >>10445849 Uni comes back day 11, will steal then.

Anonymous Thu Mar 7 15:01:01 2019 No.10445967

Hi guys im a pre algebra brainlet, mind answering an ezpz question for me?
Say you have a repeating pattern of 1,2,3,1,2,3 and so on. How can you make this into an algebraic formula to calculate what number N (term) will be at any point? How do we figure out for example, at term 117 whether it will be 1,2 or 3 using algebra?

>>	Anonymous Thu Mar 7 15:04:49 2019 No.10445975 >>10445967 a=n mod 3

>>	Anonymous Thu Mar 7 15:06:02 2019 No.10445979 >>10445975 what is mod? What does that mean?

>>	Anonymous Thu Mar 7 16:38:00 2019 No.10446231 If I talk about functions as a ring would the multiplication be the function product (f * g)(x) or the function composition fg(x)?

>>	Anonymous Thu Mar 7 16:41:15 2019 No.10446242 >>10446231 The first one. Usually, the second one will not make sense

>>	Anonymous Thu Mar 7 16:42:29 2019 No.10446250 >>10446231 Usually the first one, but there's no way to know without context. For instance, the ring of endomorphisms of a vector space uses the second one.

>>	Anonymous Thu Mar 7 16:43:16 2019 No.10446251 >>10446242 >>10446231 Composition is the canonical operation when talking about automorphism or endomorphism groups >>10445967 Modular arithmetic

>>	Anonymous Thu Mar 7 16:59:14 2019 No.10446311 >>10446242 Oh right, because composition doesn't distribute in general

>>	Anonymous Thu Mar 7 17:03:44 2019 No.10446323 >>10446311 Not even that, but in general two functions on a set will not even be composable

Anonymous Thu Mar 7 17:05:56 2019 No.10446335

>>10446311
No, usually the problem is that unless you're working with maps that go from the same space into itself, you can't speak about composition of functions since then they won't have the same domain and are not well defined.

Addition is usually defined pointwise for homomorphisms so composition is well defined

>>	Anonymous Thu Mar 7 17:12:47 2019 No.10446360 >>10446251 >endomorphism groups Nope, pointwise operations. Doesn't even form a group otherwise.

>>	Anonymous Thu Mar 7 18:57:01 2019 No.10446697 File: 128 KB, 1024x595, 1506865347970 - Kopie.jpg [View same] [iqdb] [saucenao] [google] AAAAAAAAAAAAAAAAAAAA

>>	Anonymous Thu Mar 7 19:47:55 2019 No.10446825 File: 956 KB, 1003x1024, 236830659023212.png [View same] [iqdb] [saucenao] [google] >>10445871 Vai não.

>>	Anonymous Thu Mar 7 20:25:25 2019 No.10446880 >>10445975 >>10446251 Thanks, seriously

Anonymous Thu Mar 7 22:31:34 2019 No.10447116
File: 112 KB, 900x900, 1471573406404.jpg [View same] [iqdb] [saucenao] [google]

Why does everything in statistics seems either boringly obvious or absolutely non sensical with no middle ground? Fuck, I just want to learn it quickly to work on Machine Learning.

Anonymous Thu Mar 7 23:34:55 2019 No.10447218
File: 29 KB, 741x568, download (55).png [View same] [iqdb] [saucenao] [google]

Are primes still NP or are they P? If I am understanding P=NP correctly if primes are P doesn't that mean something like goldbach's conjecture is something we should've been able to prove with generality a while back? How come primes are considered P but we still can't prove or disprove goldbach's conjecture?

>>	Anonymous Thu Mar 7 23:39:27 2019 No.10447224 File: 2 KB, 125x95, download (55).jpg [View same] [iqdb] [saucenao] [google] >>10447218 what

Anonymous Thu Mar 7 23:42:47 2019 No.10447231
File: 107 KB, 700x692, 656071_b.jpg [View same] [iqdb] [saucenao] [google]

>>10447224
Maybe I am misunderstanding what it means to be P or NP but if something is P wouldn't it mean that it would be easy to generalize what a prime number is the same way we can generalize even numbers as 2n and odd numbers as 2n+1

>>	Anonymous Fri Mar 8 01:15:11 2019 No.10447403 >>10447218 >>10447231 This is beyond a misunderstanding. It's literal word salad.

Anonymous Fri Mar 8 01:20:41 2019 No.10447414

>>10447116
>Why does everything in statistics seems either boringly obvious or absolutely non sensical with no middle ground?
Because it is. That's fundamentally what the field is.
All of statistics outside of the intuitive, naive methods is about trying to cope with the fact that your data is too shitty for naive methods to work well. The shittier your data is, the shittier your methods for coping with it end up being.

Anonymous Fri Mar 8 01:22:41 2019 No.10447416

>>10447403
From my understanding P means something is easy to solve and easy to verify NP means something is hard to solve but easy to verify. Things like evens are easy to solve for and verify which is why we can generalize evens as 2n samething with odds but they are 2n+1. Primes are claimed to be P however we do not have some generalization for prime numbers like we do with even and odd numbers. How come primes are P and not NP if its something we can't generalize to the point we can prove or disprove something like goldbach's conjecture if primes are actually indeed P. Maybe I am missing something here but shouldn't we have been able to generalize primes the same way we were able to generalize even and odd numbers a while back now.

>>	Anonymous Fri Mar 8 01:39:58 2019 No.10447440 >>10439875 If you can, look at Schutz's general relativity book. He explains tensors very well.

Anonymous Fri Mar 8 01:51:19 2019 No.10447457

>>10447416
First off, there are a couple things wrong here;
>P means something is easy to solve and easy to verify NP means something is hard to solve but easy to verify.
This is very false. First off, P vs. NP only refers to _decision_ problems; those with yes or no answers. It's not any problem you want to solve. I imagine whatever idea you have in mind by "generalizing primes" (this is extremely vague) is probably too strong a question to be in the P/NP discussion at all.
Second, it's important that NP does NOT mean "hard to solve but easy to verify". It is only the second part; if we know what the answer is, is it easy to plug it back into the problem and check? In particular, this means that every P problem is also automatically an NP problem, since we could be stupid and "check" it by just solving it. The meat of P v. NP is whether or not there exist problems that are easy to check (NP) but fundamentally very hard to solve (not P).

When somebody says "PRIMES are in P", they mean something very specific, namely
>given one number as input, deciding whether or not that number is prime is not too hard
Nothing more.

>>	Anonymous Fri Mar 8 01:53:30 2019 No.10447460 How do you guys study for your math tests? I tried putting an emphasis on theorems but got burnt really bad in going to apply these to the SIMPLEST examples.

Anonymous Fri Mar 8 02:03:05 2019 No.10447480

>>10440333
Yes everything you mentioned is extremely important for a modern physicist. I will now recommend a shit ton of books to look at. Both math and physics. Just to get a taste of what's involved.

Artin algebra. Hermann lie groups. Baez gauge fields. Bertlmann anomalies in qft. Isham diferential geometry. Bott Tu differential forms in alg topology. Hatcher alg topology. Cahn semisimple lie algebras. Schlichenmaier riemann surfaces. Griffiths Harris alg geometry. Guillemin Pollack differential topology. Geroch mathematical physics. Hori mirror symmetry. Zinn-Justin qft. Nair qft. Rubakov gauge theory. Scharf finite qed. Henneaux and Teitelboim quantization of gauge systems. Schottenloher conformal field theory. Di Francesco conformal field theory. Henkel conformal invariance. Warner differentiable manifolds. Milnor characteristic classes.

As for degrees. It's probably best to just finish up your math degree if it's easier to finish it. As others have said, most of undergrad math and physics is irrelevant to modern math and physics so it won't matter too much. At the very least I would recommend getting a good quantum mechanics and quantum field theory course done. The sooner you see this stuff the better if you plan on doing physics. Things really open up once you know it.

Anonymous Fri Mar 8 02:04:49 2019 No.10447483

>>10447460
Math tests (in my experience) generally consist of maybe 20% definitions/theorem statements and 80% problems/computations. Your study plan should have roughly the same shape, maybe slanted a little more towards problems if your memory is decent.
In my experience profs don't like to put difficult proofs from the textbook in the tests, because it's not fair to ask anyone to make them up on the spot in 10 minutes and if they warn you it's going to be on the test they're just asking you to memorize a page of the book, which is stupid.

>>	Anonymous Fri Mar 8 02:06:29 2019 No.10447488 >>10442785 It's too basic in scope. Once you're at that level, you might as well just read deeper books like Rudin's real and complex analysis or Lieb and Loss instead. Rudin does have good problems though.

Anonymous Fri Mar 8 02:20:35 2019 No.10447506

>>10441861
If you want to save your time, you could read Artin's algebra and Lieb and Loss's analysis instead of ALL 4 VOLUMES of Stein and Shakarchi. You should study differential geometry, Lee's smooth manifolds is fine. Bott and Tu's differential forms in algebraic topology worth reading as well, although you'll need some familiarity with differential forms, most mathematicians read Spivak's calculus on manifolds for this but I hate it. Lang's algebra is useless. Just read actual books on representation theory, commutative algebra, etc instead. Etingof's representation theory is good. Fulton and Harris is a very concrete book as well. Atiyah and MacDonald's commutative algebra is amazing, work all the problems and you will learn so much. Folland's book isn't perfect, you should probably read Rudin's real and complex analysis alongside. For algebraic geometry, An Invitation to Algebraic Geometry is a very nice intro to classical varieties. For schemes I found Eisenbud's geometry of schemes helpful.

Anonymous Fri Mar 8 02:20:55 2019 No.10447507

>>10447483
Yeah I now realize I have to change my study routine, and do more problems. I guess it was like a spaced repetition type of studying. There was a problem of a chapter I didn't really glance over at all so was lost. To make matters worse I spilled spaghetti and completely forgot that the cofinite topology was is another name for the finite complement topology (lol), and fucked up another easy problem that had me wanting to kill myself when I walked out of the room. It sucks because I felt I was finally experiencing some growth in understanding most of it but was brought back down to earth when trying to utilize everything I learned to the point it all came out as a scattered mess. It's like some of the stuff I wrote down was something I'd never write down while studying and that's due to the fact I have my hand held by the book when studying. I've been beating myself up over it for the last day and a half, and it's not really the grade I'm worried about even though it will be horrible but the fact that I didn't put myself in a position to actually do anything.

Anonymous Fri Mar 8 02:24:59 2019 No.10447512

>>10442075
>>10442500
Yeah Rudin technically gets into measure and differential forms near the end. But the treatment is truly awful. I can't even comprehend what Rudin was thinking when he wrote them. I get the forms section, he's not a geometer. But why is the Lebesgue theory section so bad when his Real and Complex analysis treats it so well.

>>	Anonymous Fri Mar 8 02:26:48 2019 No.10447514 >>10445197 >lacking visual imagination It's right.

>>	Anonymous Fri Mar 8 04:41:52 2019 No.10447656 >>10447460 Well my math tests consist of 90% theory and like 10% problems. I divide theory on: theorems, deffinitions and proofs and just study them. Each day getting roughly the sam amount of stuff from each part.

Anonymous Fri Mar 8 11:30:02 2019 No.10448301

>>10436214
Don't know if this question fits here.

"
In a 3-person group, the number of possible relationships is 6.
In a 4-person group, the number of possible relationships is 25
In a 6-person group, the number of possible relationships is 301
"

How did he the 301? I have looked at combinatorics, factorial, permutational and just cannot find out which formular he used.

t. stupid social science student

Sincerely thanks to the person that can answer, I has been bugging the whole day, after I read it.

>>	Anonymous Fri Mar 8 12:08:47 2019 No.10448354 >>10448301 i dont know what definition of relationship you're using

>>	Anonymous Fri Mar 8 12:11:42 2019 No.10448362 >>10448354 A person talking to another person

>>	Anonymous Fri Mar 8 12:18:50 2019 No.10448375 >>10448362 Does it matter who is doing the talking? I mean, does that mean that person A talking to person B is a different relationship than person B talking to person A?

>>	Anonymous Fri Mar 8 12:21:35 2019 No.10448383 >>10448301 >>>/sci/sqt

>>	Anonymous Fri Mar 8 12:31:56 2019 No.10448405 >>10448301 I'm not really sure what's going on here but those are Stirling numbers. Look up a table of them and work from there

>>	Anonymous Fri Mar 8 12:35:26 2019 No.10448408 >>10448375 I was only given what is written within the quotation marks except that relationship is defined as a person talking to another person. However! I assume that it works both ways, since a 3 person group is 6.

Anonymous Fri Mar 8 12:42:34 2019 No.10448420

>>10448405
Hey,

https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind#Explicit_formula

I can see here on the chart at "Table of Values" that, 6,25 and 301 is on it.

However, I am too much a brainlet to find out how to get there logically. Like what are all the steps.

But thanks for the input, definitely you're right about them being Stirling numbers, greatly appreciate the help.

>>	Anonymous Fri Mar 8 12:44:28 2019 No.10448425 >>10448408 The information given doesn't make sense. Those are type 2 Stirling numbers that represent the number of ways to partition sets into non-empty subsets, but it seems all wrong, like the lecturer copied the wrong column off a table.

>>	Anonymous Fri Mar 8 13:00:14 2019 No.10448452 >>10448301 Your buddy is either retarded or has some _very_ weird definition of relationship. You should ask him which is the case.

>>	Anonymous Fri Mar 8 14:20:25 2019 No.10448648 >>10448452 kek

>>	Anonymous Fri Mar 8 16:41:54 2019 No.10448955 I'm looking for a textbook to review my linear algebra. Hoffman and Kunze or Axler?

>>	Anonymous Fri Mar 8 20:01:14 2019 No.10449448 >>10448955 Axler and another source for determinants

>>	Anonymous Fri Mar 8 21:39:20 2019 No.10449710 >>10448955 Shilov

>>	Anonymous Fri Mar 8 21:58:02 2019 No.10449741 >>10448955 Lay

>>	Anonymous Sat Mar 9 02:48:51 2019 No.10450309 https://www.youtube.com/watch?v=pTAnUBbunlY

>>	Anonymous Sat Mar 9 02:52:21 2019 No.10450316 >>10448955 ma boi gil straaaaaaang dr strangloov innit bruv

>>	Anonymous Sat Mar 9 02:55:41 2019 No.10450322 >>10450316 https://www.youtube.com/watch?v=FHftdD7I4f8 HIT IT UN BASS MAKER RIDDIM SELECTA MASTA SELECTA timin decomposition your basis components innit aiiiiight

>>	Anonymous Sat Mar 9 02:59:38 2019 No.10450334 >>10450322 >>10448955 Axin axler Not doin problems? Wrong bitch please let it go https://www.youtube.com/watch?v=vkOJ9uNj9EY

>>	Anonymous Sat Mar 9 03:00:42 2019 No.10450336 WHERE MY PROBLEMS AT

>>	Anonymous Sat Mar 9 03:03:22 2019 No.10450347 VI Arnold crew Bourbaki motherfucker

Anonymous Sat Mar 9 03:08:24 2019 No.10450360

“Problems for children from 5 to 15” by V.I. Arnold

>The booklet consists of 77 problems for development of thinking culture, either selected or composed by the author. Most of them do not require any special knowledge beyond the general education. However, solving some of them may turn out challenging even for professors. The book is addressed to school and university students, teachers, parents – to everybody who considers the thinking culture an essential part of the personality development.

Arnold’s words:

>“I put these problems onto paper in Paris in spring 2004 when Russian Parisians asked me to help their young children gain the thinking culture traditional for Russia. I am deeply convinced that this culture is most of all cultivated by early independent reflection on simple, but not easy questions similar to those below (problems 1, 3, 13 are the most recommended)…”

https://imaginary.org/news/problems-for-children-from-5-to-15-by-v-i-arnold-now-available-in-english-and-russian

Enjoy realizing how shit you are

>>	Anonymous Sat Mar 9 03:09:46 2019 No.10450365 https://www.youtube.com/watch?v=znttboYNrbY >Bourbaki BTFO

>>	Anonymous Sat Mar 9 03:26:25 2019 No.10450391 >>10436214 I have exactly 3 months to go from illiterate in math to have a high school senior level . Anons how fucked am i ?

>>	Anonymous Sat Mar 9 03:28:24 2019 No.10450392 >>10450391 not at fucked at all

Anonymous Sat Mar 9 03:58:01 2019 No.10450445

>>10450391
luckily math has no hand-waving magic. It's as easy as the time you put in.

So be honest with yourself, review bottom-tier grinding stuff if you have to. But remain satisfied with the understanding that everything builds on previous things, and soon enough you'll be reading arxiv and able to work along.

I mean that's not exactly truthful. The reality is that mathematics blows up as a complete graph on infinite nodes. But that will be a joy for you.

what the fuck am I talking about I'm drunk sorry. I think it's all mostly right. I'm shit at math but have a degree in it. Ask me anything.

Anonymous Sat Mar 9 05:52:54 2019 No.10450612
File: 138 KB, 413x549, ap,550x550,12x16,1,transparent,t.u3.png [View same] [iqdb] [saucenao] [google]

>>10450445
It's very kind of you do you have an irc channel or something where i can contact you ?
By the way to explain my current situation i'm an 19 years old who already graduated from the French high school exam "bac" but in the social sciences major . I chose it in the beginning because i was always very decent in economy , languages and history without even trying .
Now i'm retaking the same exam but this by
all by myself as an independent candidate as a math/science major .
I'm doing this because i know that if i want to be competitive enough to be recruited by a foreign corporation in a more stable
country i need to follow a "stem" program and become an engineer so i can hope of leaving this shit hole .
PS : My reasons for wanting to leave are not "economical " in the sense that i want to have a higher salary , it's just that in my country without any environmental problems there is already an 8%+ inflation rate and 40% employment rate for graduates so i can't even imagine the situation in situation with desertification that will ruin soil and water scarcity .
PS ' : I was supposed to continue studying business in either Canada or France but since i'm a very lucky person our currency it's worth anything anymore so i don't have the financial resources to do it anymore .
PS " : LOL at this monologue

>>	Anonymous Sat Mar 9 06:14:53 2019 No.10450650 >>10450612 Can't you just move to your neighboor germany?

>>	Anonymous Sat Mar 9 06:26:26 2019 No.10450667 >>10450650 I'm not in France , i'm in north africa . I just have a french degree .

>>	Anonymous Sat Mar 9 06:27:42 2019 No.10450669 >>10441637 Um hi there the stacks project works well enough for me thank you alot

>>	Anonymous Sat Mar 9 06:30:59 2019 No.10450670 >>10442077 Serge Lang is the best mathematics writer there ever was and ever will be. I read from Lang first before cracking another book.

>>	Anonymous Sat Mar 9 06:36:11 2019 No.10450676 >>10443082 Careful with those things, they may be circular, particularly for Fermat's last theorem since preliminary results are often used to build up the theorem.

>>	Anonymous Sat Mar 9 07:54:04 2019 No.10450779 >>10448425 It's supposed to be Grp of 4 [4,3] 6 Grp of 5 [5,3] 25 Grp of 7 [7,3] 301 Right?

Anonymous Sat Mar 9 15:19:33 2019 No.10451832
File: 97 KB, 504x470, 1361193965393.jpg [View same] [iqdb] [saucenao] [google]

Why did I suddenly start caring about maths now at 23?
Last 3 weeks all I do solve problems all day. When I try to take break and play video games etc. all I can think is how much I want to solve problems.

Could have used this shit 10 years ago.

>>	Anonymous Sat Mar 9 15:20:45 2019 No.10451836 >>10451832 You're entering manhood, that's why. Difference in priorities.

>>	Anonymous Sat Mar 9 18:38:56 2019 No.10452378 >>10451832 Just keep doing it. Enroll in a math program while you are at it.

>>	Anonymous Sat Mar 9 19:54:49 2019 No.10452526 >>10450360 >51 I really cannot imagine any 10 year old figuring out how to solve the Basel problem. Even 10 year olds in Russian enrichment programs.

>>	Anonymous Sat Mar 9 20:00:03 2019 No.10452533 Looking to buy a poster for my room. Any math related or inspired recs? UK based if possible. Also do you guys know if I can get something on a poster if I don't have copyright but just a file?

Anonymous Sat Mar 9 20:02:34 2019 No.10452536
File: 349 KB, 632x850, 1834682878272872.jpg [View same] [iqdb] [saucenao] [google]

>>10452533
>Any math related or inspired recs?
I don't know if you can buy posters of them anywhere (or find high enough resolutions to print one) but many of Anatoly Fomenko's drawings would make damn neat posters

>>	Anonymous Sat Mar 9 20:03:48 2019 No.10452539 >>10452533 On second thought, obviously I can print something online, but I was specifically thinking of taking something from Fomenkos art. No copyright issues or something? Also, if anyone can find high res Fomenko art please link me

>>	Anonymous Sat Mar 9 20:04:53 2019 No.10452544 >>10452536 >>10452539 Damn you took the words out of my post

>>	Anonymous Sat Mar 9 21:25:17 2019 No.10452726 anyone wanna help me with my implicit differentiation homework lol...

>>	Anonymous Sat Mar 9 23:25:04 2019 No.10452941 >>10452726 no it's trivial

>>	Anonymous Sun Mar 10 04:38:40 2019 No.10453459 can i complete upper division classes without a pencil/pen/writingutensil? can i get by on only a keyboard? i’ve tried to solve problems using keys before but it just doesn’t work the same as leaving a handrawn graphite/ink map of my efforts

>>	Anonymous Sun Mar 10 05:32:42 2019 No.10453528 File: 460 KB, 360x560, 18278.gif [View same] [iqdb] [saucenao] [google] >>10452726 no!

>>	Anonymous Sun Mar 10 05:40:58 2019 No.10453542 >>10453459 I've taken a ton of math classes without doing a lick of LaTex or tex because I dont like typing

>>	Anonymous Sun Mar 10 06:43:37 2019 No.10453587 >>10440162 Riemann is rolling in his grave.

Anonymous Sun Mar 10 07:03:11 2019 No.10453607

I don't really get proofs. Are they actually supposed to help you understand something or do they just show that is true?

Like, there are a ton of proofs of Pythagora's theorem but none of them really tell me anything about the relationship is the way it is from what I can tell. Not that I worry about Pythagoras really I just got used to it and don't think about it anymore.

>>	Anonymous Sun Mar 10 07:04:14 2019 No.10453609 >>10453607 why the relationship is the way it is*

Anonymous Sun Mar 10 09:36:30 2019 No.10453791
File: 8 KB, 253x78, Capture.jpg [View same] [iqdb] [saucenao] [google]

http://www.kurims.kyoto-u.ac.jp/~motizuki/2019-03-10-iu-teich-revisions.txt
>Inter-universal Teichmuller Theory III
>・Corrected a misprint ("n" ---> "j") in the notation immediately following the phrase "the collection of subsets" in the discussion immediately following the second display of the proof of Corollary 3.12

>Inter-universal Teichmuller Theory IV
>・Deleted the notation "+\eta_{prm}" (2 instances), together with the explanation of this notation, in the second paragraph of the proof of Corollary 2.2, (ii)
>・In the proof of Corollary 2.2, (ii), added the text "(P2)," to the proof of (P4)

Anonymous Sun Mar 10 09:46:45 2019 No.10453808

>>10453607
>Are they actually supposed to help you understand something or do they just show that is true?
Both, depending on the particular proof.
Ideally a proof will give you insight into why the result is true, although this is the best case and often (especially in newer, research-level results) people have to settle for a technical, unenlightening proof until somebody figures out the real reason.

That said, Pythagoras' theorem is very simple and very old, and all the common proofs should make it clear to you why the result is true. If they don't, you don't really understand what they're doing.

Anonymous Sun Mar 10 09:49:56 2019 No.10453811
File: 28 KB, 225x273, 2018-03-31-mochizuki-shinichi-shuuseiban.jpg [View same] [iqdb] [saucenao] [google]

>Log Volume Computations - part 0.1 - Idempotents In Tensor Products of Fields
https://www.youtube.com/watch?v=sSADSxNnycQ

>Log Volume Computations - part 0.2 - Total Rings Of Fractions
https://www.youtube.com/watch?v=1Q9-izNHnL0

>Log Volume Computations - part 0.3 (optional) - Integral Closures
https://www.youtube.com/watch?v=JbBgDCoD6To

Anonymous Sun Mar 10 12:26:48 2019 No.10454056 [DELETED]

Hey fellow mathematicians, so I'm going to learn Abstract Algebra this semester and the professor said he's going to use Jacobson's book for his classes, but then I read the wiki about this book and it said it's a graduate's book. So, is my professor crazy or something?

Anonymous Sun Mar 10 12:28:57 2019 No.10454061
File: 21 KB, 334x499, 41E77TmoK6L._SX332_BO1,204,203,200_.jpg [View same] [iqdb] [saucenao] [google]

Hey fellow mathematicians, so I'm going to learn Abstract Algebra this semester and the professor said he's going to use Jacobson's book for his classes, but then I read the wiki about this book and it said it's a graduate's book. So, is my professor crazy or something?

Anonymous Sun Mar 10 13:44:22 2019 No.10454261

>>10454061
Jacobson is probably not the best book for a first course, but it doesn't assume anything so it can still be used. I'd say the graduate part is more referring to his second book, since the first part is standard UG. It's pretty fast paced and covers a lot so you'd have to specify what sections you're going through. Most generic alegbra courses cover only the first two chapters and maybe a bit of field or module theory, so you can always consult other sources. Personally I've never needed to complement the course with a book since I went to class and paid attention, so if you go to class I wouldn't worry much. Maybe the skeleton of the course is Jacobson but he fills the gaps or has extra material from other books. It's always best to ask your lecturer anyways. If you're a bit scared just get something like Pinter's algebra book (cheap since Dover, or free online) and read it beforehand.

Anonymous Sun Mar 10 14:02:56 2019 No.10454316

>>10454261
I see, thanks, yeah he said he would cover the first two chapters only. I'm indeed scared, but it's mostly because I don't have a solid foundation of High School Algebra and this professor in particular has the fame of making really hard tests. What should I know beforehand? The professor said Euclid's Algorithm and Equivalence Relations would be important, anything else?

>>	Anonymous Sun Mar 10 14:08:46 2019 No.10454330 >>10454316 UG abstract algebra is pretty self-contained desu. All you need to know is what you learned in intro to proof and maybe a little bit of number theory.

>>	Anonymous Sun Mar 10 14:21:41 2019 No.10454356 >>10454316 What's highschool algebra to you? I can't remember it being more than rearranging equations and factoring. If that's a problem for you then my my... Gonna get rough

Anonymous Sun Mar 10 14:37:15 2019 No.10454395

>>10453542
I am asking if the inverse is feasible - never writing, only typing. I know it's possible, but I want to hear from some anons who can solve math problems through only a keyboard.

I just having tons of paper littered everywhere and always trying to organize it, maybe I'll start using paper as scratch and write a clean final solution on the laptop.

>>	Anonymous Sun Mar 10 14:39:51 2019 No.10454400 >>10454395 This is the epitome of stupid, personified

>>	Anonymous Sun Mar 10 14:43:34 2019 No.10454411 >>10454395 I work problems out on scratch paper and then TeX up the final answers. I've done this for every upper division math class. Typing out the proofs forces me to think about every detail and make sure I can justify it, before I type it up.

>>	Anonymous Sun Mar 10 14:44:11 2019 No.10454416 >>10454061 Which wiki? I would say Jacobson is in between graduate and undergraduate book like MacLane/Birkhoff.

Anonymous Sun Mar 10 14:44:14 2019 No.10454418

>>10454395
>I am asking if the inverse is feasible - never writing, only typing.
Probably not. Exams are pretty common even in grad courses and no prof is going to let you LaTeX your exams unless you have some kind of bizarre disability where you can't use a pencil.

Anonymous Sun Mar 10 15:56:04 2019 No.10454607

>>10454356I refer to things like Diophantine Equations, Congruence, Fermat's Theorem, Euler's Theorem, Wilson's Theorem, Modular Arithmetic, Equivalence Relations, etc

It's not that I don't know those, I just forgot most of them, I still remember some about Modular Arithmetic's though, but I don't know how useful that will be in Abstract Algebra.

>>	Anonymous Sun Mar 10 15:57:06 2019 No.10454613 >>10454416 /sci/'s wiki.

Anonymous Sun Mar 10 16:11:51 2019 No.10454659
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I really doubt you're expected to know Fermat and Euler, and you will most definitely prove both of them in class or hw. It's the quintessential application of Lagrange's theorem. Modular arithmetic you just have to know the basics like that they form a ring. Equivalence relations you can learn in 10 minutes, with modular arithmetic being a trivial example of one, although you'll need to understand that they partition stuff to understand cosets (again, 10 minutes). Wilson's is probably a tough hw problem, you won't need it. Diophantine eqns perhaps will be dealt with but in class.

The only thing I'd say you should revise is polynomial division, extended Euclidean algorithm, bezout identity and equivalence relations. In total should take you less than an hour

>>	Anonymous Sun Mar 10 16:12:55 2019 No.10454662 >>10454607 >>10454659

Anonymous Sun Mar 10 16:17:20 2019 No.10454674
File: 2.01 MB, 4032x3024, image_123923953.jpg [View same] [iqdb] [saucenao] [google]

>>10452536
>>10452539
>>10452544
I got you bros
http://monsterbrains.blogspot.com/2011/06/anatoly-fomenko.html
http://chronologia.org/art/
I actually love this book, be sure to buy a physical copy if you can.

Anonymous Sun Mar 10 16:17:48 2019 No.10454678

>>10454400
why?

>>10454411
I do this in classes too, but when just recreationally learning I don't bother, and I always regret it. Because of this I wish I could just think through my keyboard, but I seem completely unable to solve problems and explore theorems, proofs, etc without writing. Not sure if it's worth the time and discomfort of trying to break this dependence, so if any anon has some first hand experience that'd be nice.

>>10454418
I mean only while studying and learning. I don't mean never touching a pen/pencil for any of my classes.

>>	Anonymous Sun Mar 10 16:18:50 2019 No.10454681 >>10452533 look into escher's stuff

>>	Anonymous Sun Mar 10 16:20:00 2019 No.10454684 >>10454659 Thanks bro, I really want to get good grades on this subject, will try to study it every day.

>>	Anonymous Sun Mar 10 16:25:14 2019 No.10454697 >>10454674 As an added bonus, check out this russian animation using some of Fomenko's work. Weird as all hell but kind of entertaining. https://www.youtube.com/watch?v=J8aItG4HYjM

Anonymous Sun Mar 10 17:32:02 2019 No.10454869

>>10454061
I loved the book, as a second reading. The notation (and the book) is indeed old. You can probably find it in your local library, and nobody is reading it.
I would say, go for 'Aluffi Algebra: Chapter 0' or 'Bosch Algebra, from the viewpoint of Galois theory' (2018)

>>	medfag Sun Mar 10 21:25:04 2019 No.10455526 I have to learn Probability and Statistics for Bioinformatics. Any recommendations/suggestions? Or should I just stick to Udemy?

>>	medfag Sun Mar 10 21:31:40 2019 No.10455536 >>10439875 it's cool bro, that shit doesn't matter later on in physics when you're writing machine learning algorithms to find exoplanets or something. t. physics and biochem major

>>	Anonymous Sun Mar 10 22:04:32 2019 No.10455606 >>10441488 >>10442883 >Lima being posted on /sci/ Today is a great day. Btw donde hiciste la licenciatura ql?

>>	Anonymous Mon Mar 11 02:00:03 2019 No.10456066 >>10454613 >https://4chan-science.fandom.com/wiki/Mathematics#Second_Year_Algebra_.28Graduate.29 >Basic Algebra I & II (Dover Books) by Jacobson (Vol I is closer to 1st year books in terms of level)

>>	Anonymous Mon Mar 11 10:24:26 2019 No.10456616 Does anyone know of an Abstract Algebra text written for physicists? I mean beyond baby-tier Group Theory, of course.

>>	Anonymous Mon Mar 11 14:11:41 2019 No.10457217 >>10456616 No.

>>	Anonymous Mon Mar 11 14:15:08 2019 No.10457225 >>10456616 zee, georgi, those are nice

>>	Anonymous Mon Mar 11 14:43:03 2019 No.10457268 File: 17 KB, 495x362, 1526531485611.jpg [View same] [iqdb] [saucenao] [google] >>10438756 This class is so god damn boring, why do I put myself through this?

>>	Anonymous Mon Mar 11 15:06:18 2019 No.10457321 >>10457268 >he fell for the analysis meme I don't get how they do desu, differential equations in particular make me want to off myself.

>>	Anonymous Mon Mar 11 15:10:37 2019 No.10457333 >>10457321 I was thinking of getting memed next year with PDEs, they say it is useful in geometry, for Hodge theory and such, is it not worth it?

>>	Anonymous Mon Mar 11 15:35:05 2019 No.10457404 >>10444039 >In general it's never good to go back and fill in gaps in your knowledge when you're doing a PhD How the fuck does this make sense?

>>	Anonymous Mon Mar 11 16:04:11 2019 No.10457493 File: 2.08 MB, 3264x1836, 20190311_170512.jpg [View same] [iqdb] [saucenao] [google] >>10446825 Pssh.

>>	Anonymous Mon Mar 11 17:01:58 2019 No.10457669 >>10457493 t-tem outro lá?

>>	Anonymous Mon Mar 11 17:05:22 2019 No.10457677 >>10457669 Não. Por favor não faz os rolos pra eu ter que devolver.

>>	Anonymous Mon Mar 11 17:14:24 2019 No.10457703 >>10457677 Relaxa, anão.

>>	Anonymous Mon Mar 11 18:17:46 2019 No.10457851 I'm applying for grad school - what's the difference between a 'research statement' and a 'statement of intent'?

Anonymous Mon Mar 11 18:19:29 2019 No.10457858

OK, my mind is being messed with right now.
We have that for a (commutative with 1) ring [math]A[/math] and a module [math]M[/math] over it, then (trivially) [math]A\otimes_A M\cong M[/math]. But now my book is saying [math]A^n\otimes_A M\cong M^n[/math]. It seems like it should be a canonical isomorphism, but it's not obvious to me that the A^n-orbit of an element will cover all of M^n.

>>	Anonymous Mon Mar 11 18:39:38 2019 No.10457909 >>10457858 tensor products have the distributive property: (A +B) x C = AxC + AxB. Think about it like this, given (m1, ..., m_n) in M^n, it's covered by (1,0,..,0)x(m1) + (0,1,0,..,0)x(m2) + ... + (0,0,...,1)x(m_n)

Anonymous Mon Mar 11 18:45:38 2019 No.10457921

>>10457851
Usually A research statement is a more quantitative description of things related to math; your experience with doing research, what you want to study (doesn't need to be laser-specific, but you should know at the bare minimum whether you want to be in the algebraic geometry group or the probability group or the combinatorics group etc.), and anything else to argue the point that you and this department are particularly well-suited for each other.
A statement of intent is a fluffier essay discussing your motivations for going to grad school, your career goals, probably at least one stupid anecdote somewhere in there, other personal bullshit like that.

Most schools only require one essay, and in that case what you should be submitting is a blend of both of those. However I do know at least one school (Michigan) requires both of those statements, so probably a few others do too.

>>	Anonymous Mon Mar 11 18:56:18 2019 No.10457949 >>10457909 Damn I'm stupid, forgot finite products were sums.. thanks

>>	Anonymous Mon Mar 11 20:32:09 2019 No.10458236 Should I throw away my friends and families for the sake of mathematics?

>>	Anonymous Mon Mar 11 20:35:44 2019 No.10458245 File: 677 KB, 850x637, 37B79B9A-5BEA-4A2B-8EF9-DF2C62A45803.png [View same] [iqdb] [saucenao] [google] >>10454061 I highly recommend Dummit Foote Abstract Algebra

>>	Anonymous Mon Mar 11 20:45:42 2019 No.10458270 >>10457921 Thanks anon, this helps a lot. My school does require both, with the research statement being limited to 4000 words but no limit to the statement of intent.

Anonymous Mon Mar 11 21:02:06 2019 No.10458313
File: 57 KB, 512x512, 1.png [View same] [iqdb] [saucenao] [google]

Knot theory is pretty great, I got a good aftertaste of it. Made a report on Seifert surface today and it was quite entertaining. Also found a site that sells different types of knots in form of jewlery.

>>	Anonymous Mon Mar 11 21:10:14 2019 No.10458329 >>10438756 >>10457268 God, so relatable, I freaking hate math physics.

>>	Anonymous Mon Mar 11 21:28:44 2019 No.10458371 File: 10 KB, 684x172, probability.png [View same] [iqdb] [saucenao] [google] P[A] is given as 0.25, so why does it suddenly become 3/4 here? X is 1 if A happens and 0 if A doesn't occur. Am I a big dummy or is the book just wrong?

Anonymous Mon Mar 11 22:11:40 2019 No.10458462

Why is Axler's linear algebra book so shilled on /sci/? Is it actually good?
I already checked it and it seems to take a pretty different approach than most courses. It focuses on linear maps instead of matrices. It covers interesting topics, but it seemed rather dry. Not to sound like an engineer, but it left me wondering as I skimmed it "Why are we doing this?". It didn't provide any motivation whatsoever as far as I saw.
Am I not mathematically mature enough for it or is it actually not that good?

>>	Anonymous Mon Mar 11 22:20:36 2019 No.10458486 >>10458462 >Why is Axler's linear algebra book so shilled on /sci/? Because Axler is a meme and brainlets on /sci/ are afraid of determinants.

Anonymous Mon Mar 11 22:33:44 2019 No.10458523

>>10458462
It's very good at providing intuition into why results and definitions are as they are. Linear algebra will always be kinda dry unless it's applied to another field. Same as abstract algebra, but with LA at least you have some intuition on what's happening and picture it, and if you have good imagination you can actually try posing problems for yourself. Projective geometry is probably the most hands-on application of LA and it's very interesting on its own right. You can prove things like pappus or desargues theorem only using things like linear independence, and much more.

Axler is great in that it doesn't just make you compute matrices or eigenvalues, doesn't use the unintuitive determinant, and actually gives a more detailed treatment of what's going on.

Anonymous Mon Mar 11 22:37:19 2019 No.10458531

Lads, I had a meeting with my adviser the other day. I asked him to explain some concept from his paper and fuck, I almost cried. It was so beautiful. He explained the concept of monodromy and its connection to Galois theory, its effects on singularities of a variety, etc. I was unironically trying not to shed a tear.

Is this what not being depressed feels like? I want this to never stop happening

>>	Anonymous Mon Mar 11 22:51:59 2019 No.10458561 >>10436214 hey dudes, engineer here. i need to create a 2D finite difference method where some, but not all, of the nodes are already known and will give me a nice gradient between the known and unknown nodes. 'Preciate cha.

>>	Anonymous Mon Mar 11 23:02:35 2019 No.10458595 >>10458462 >It didn't provide any motivation whatsoever as far as I saw. If this matters to you and you still want Axler's level of rigor (and without his autistic avoidance of determinants), check out Hefferon's Linear Algebra.

>>	Anonymous Tue Mar 12 02:03:11 2019 No.10459014 >>10436214 How to I certify my autodidact mathematics education?

>>	Anonymous Tue Mar 12 02:16:52 2019 No.10459034 >>10458531 That's nice, when I ask my adviser questions he snaps at me angrily.

>>	Anonymous Tue Mar 12 03:30:11 2019 No.10459137 >>10457268 >>10457321 >>10457333 imagine being so dumb you don't like pde fuck off idiots & algebraists

>>	Anonymous Tue Mar 12 03:31:51 2019 No.10459140 >>10458462 >why are we doing this? motivation is a meme. go back to your engineering general

>>	Anonymous Tue Mar 12 04:27:49 2019 No.10459235 >>10458531 Yeah monodromy is cool. Did you know that if you take a small resolution of your singular variety you get a true group action on the exceptional fibre? Toric geometers will never know such joys.

>>	Anonymous Tue Mar 12 06:25:03 2019 No.10459308 File: 350 KB, 1438x1080, 056A6A7A-8747-4A41-B513-2353581E096A.png [View same] [iqdb] [saucenao] [google] Correct me if I’m wrong but Algebraic Geometry is just Linear Algebra but with system of nonlinear equations, right?

Anonymous Tue Mar 12 08:44:43 2019 No.10459487

I'm about 6 weeks out from my first uni math test. My plan is to just randomly pick problems out of the chapters we've already covered in class, and if I get anything wrong that isn't a simple mistake, I re-read the theory for that chapter. I plan on doing this daily for the next few weeks, obviously ramping up as the test gets closer. Is this a good strategy? Is there anything else I can add or modify?

>>	Anonymous Tue Mar 12 09:16:32 2019 No.10459541 >>10459308 very wrong, algebraic geometry is nothing like linear algebra.

>>	Anonymous Tue Mar 12 09:40:32 2019 No.10459588 >>10443162 That is what it says though

Anonymous Tue Mar 12 10:05:23 2019 No.10459634

>>10459487
You're basically doing it right. The method of practicing and then immediately correcting problems you do wrong is the best way to improve.
The only thing I would suggest is not selecting problems randomly. If you look at a problem and it's immediately obvious that you can solve it in 3 minutes, doing it anyway is a waste. If you take the time to specifically look for the problems you're weakest on rather than trying to do a scatter of everything you'll improve faster.

Anonymous Tue Mar 12 10:35:15 2019 No.10459685

>>10459308
Partly. Over the complex numbers that is completely solved in an algorithmic way (gröbner bases). However, much more can happen. For example, studying singularities of varieties, intersections, over nonclosed fields it's a very different story. One of the biggest aims is the classification of varieties up to projective equivalence (literally up to linear change of variables, very strong condition), up to isomorphism (weaker), and up to birational equivalence (isomorphic "almost everywhere").

A very big theorem by hironaka showed that over a field of characteristic 0, every variety is birationally equivalent to a smooth variety. This is still open for positive characteristic.

Another problem is characterising ample bundles, which sort of classify the maps from a variety into projective space, and knowing all the maps from a variety is like knowing the variety itself

Anonymous Tue Mar 12 12:48:31 2019 No.10459946

>>10459541
>>10459685
Ok, thanks friends. Guess there’s no math branch that dedicated solely on the study of system of nonlinear equations. I’ve always been interested in the nonlinear world and I think Algebraic Geometry is the closest math branch to that area of study.

Anonymous Tue Mar 12 14:34:45 2019 No.10460179

>>10457333
Well holomorphic functions *are* solutions of a PDE. Many theorems in complex analysis (eg. existence of meromorphic functions, Serre duality for compact Riemann surfaces) are actually theorems about PDE so obviously you can expect higher dimensional complex geometry to rely on some serious analysis (PDE and functional analysis)

>>	Anonymous Tue Mar 12 14:36:58 2019 No.10460184 Redpill me on Lie algebras. Why are they useful in physics? Do you need to understand lie groups to make sense of them? t. slogged through the classification of simple lie algebras and feels nothing resembling enlightenment

>>	Anonymous Tue Mar 12 14:41:13 2019 No.10460191 >>10460184 >algebra >useful

Anonymous Tue Mar 12 14:41:23 2019 No.10460193

>>10458462
I stayed away from it thinking it was a meme for awhile (with a name like LADR, it sure sounds like one), but I ended up enjoying it much more than any other intro LA text.

I agree with the other anon that Axler excelled at developing proper intuitions. Compared to popular alternatives like Hoffman and Kunze, I liked the problems in LADR much more (straight to proofs).

My only gripe is that the typesetting on the 3rd edition make it look like a James Stewart public school text that I read in high school, so I stick with the 2nd edition.

>>	Anonymous Tue Mar 12 14:43:31 2019 No.10460197 >>10460184 the characterizing property of lie groups is literally being a differentiable manifold

Anonymous Tue Mar 12 14:45:40 2019 No.10460200
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I picked up Spivak's Calculus but got filtered around chapter 5, when epsilon-delta proofs are introduced.

Relatively speaking, I know it's a hard chapter, but I'm not sure what the more efficient route is here. Should I big dick energy my way through it, or take the virgin detour in pic related?

>>	Anonymous Tue Mar 12 14:46:45 2019 No.10460207 >>10458462 I think it's good, but it's boring as fuck. Maybe I'm missing something but it's the only math book I ever read where I actually was bored reading it.

>>	Anonymous Tue Mar 12 14:48:35 2019 No.10460215 >>10460191 What is cryptography? What is coding theory? What is chemistry?

>>	Anonymous Tue Mar 12 14:54:02 2019 No.10460228 >>10460200 Just do it, once you get used to it you'll wonder why you ever thought limit proofs were difficult

Anonymous Tue Mar 12 14:59:24 2019 No.10460247
File: 341 KB, 2518x1024, (You) on the left.png [View same] [iqdb] [saucenao] [google]

>>10460215
I know: Group theory gets used in quantum mechanics and elsewhere in physics, but the group theory used is trivial. E.g., never hear of Sylow's theorem, the Jordan-Holder theorem, the Feit and Thompson work on simple groups, etc. For group representations,you need to know very little about group theory to do group representations (I wrote my undergrad honors paper in it). Heck, I wrote a paper on multidimensional, distribution-free hypothesis tests based on groups of measure-preserving transformations, and the group theory needed was trivial. Similarly for the use of group theory in ergodic theory, ODE, and integer linear programming. Groups are nice, but really need to know only about 10 pages of the basics and can pick it up in an hour whenever need it. Or, you want group theory to attack Rubik's cube?

Yes, Hamming used some finite field theory in error correcting codes: Now that work and a dime won't cover a 10 cent cup of coffee. Instead, coding theory has moved on. Yes, yes, I know, from A. Wiles we finally have a proof of Fermat's last theorem; other than Wiles, who made any money with that?

Algebraic geometry is building expensive houses on-spec that stand empty too long. There's just no significant promise of return on investment there, or elsewhere in abstract algebra. E.g., the US NSA pushed hard on finite field theory for years before RSA showed that they had been wasting their time.

US mathematics' long, disastrous, self-destructive love affair with algebra, algebraic geometry, algebraic topology, algebraic number theory has been a major contributor to shrinking Federal research grants to mathematics, shrinking departments, mathematicians who'd swap their Ph.D. for an electrician's license, and the technology world putting mathematics on the back burner if not in the trash. Can cover nearly all abstract algebra in 1 word: Useless.

>>	Anonymous Tue Mar 12 15:03:44 2019 No.10460258 >>10460179 Thanks. I enjoy analysis but I didn't have time to follow functional analysis & pde this year, since I have to do a lot of geometry (and basic analysis and algebra). Hopefully next year I will have time to dedicate to them.

>>	Anonymous Tue Mar 12 15:03:57 2019 No.10460259 >>10460247 good post but you forgot that algebra is actually fun and interesting while analysis is boring and lame

>>	Anonymous Tue Mar 12 15:13:54 2019 No.10460285 For commutative modules, say, does M/N =0 imply M=N? I feel like this is obviously true but there are plenty of examples where M/N=M/P with P and N nonisomorphic

Anonymous Tue Mar 12 15:33:31 2019 No.10460337

>>10460228
I find myself often bouncing back to earlier chapters (Spivak structures the exercises like this, where you'll do a simple proof in an earlier chapter for something like Cauchy-Schwarz and in each chapter build on it) with much difficulty, like I'll completely forget how to solve the Cauchy Schwarz inequality from Chapter 2 or something, and I'll spend like 4 hours on it, when I'm really trying to solve a problem in chapter 5. is this healthy or advisable?

>>	Anonymous Tue Mar 12 15:44:36 2019 No.10460363 >>10460285 Follow from the definition. Take m in M, then the class of M is zero, meaning that m is in N. The other inclusion is left as exercise.

>>	Anonymous Tue Mar 12 15:46:54 2019 No.10460370 >>10460363 >the class of m >as an exerise fixed

>>	Anonymous Tue Mar 12 15:48:01 2019 No.10460377 >>10460370 fail.

>>	Anonymous Tue Mar 12 16:02:43 2019 No.10460410 >>10459946 >>>/trash/

Anonymous Tue Mar 12 17:07:23 2019 No.10460556

>>10460184
You can think of a Lie algebra as a linear approximation of a connected Lie group or algebraic group (at least that is the reason why they were first introduced).
It turns out that it contains a lot of information about the group which, in the linear algebraic complex case (ie. matrix groups over C, for example SL(n), O(n), etc.), is almost everything you need to know (basically, the group is almost determined by its Lie algebra).
In particular, if you have suffered through the classification theory of semisimple Lie algebras, then the study of reductive Lie/algebraic groups over C should not be very surprising. The methods are much more geometric and everything takes more effort (because everything is nonlinear), but the structure theory is very similar.

Anonymous Tue Mar 12 17:09:10 2019 No.10460562

>>10459541
?? Youre studying the splutions of systems of equations and characterizing the algebraic varieties of certain equations (generally polynomials), i.e. youre studying the nullspaces of linear operators by means of their characteristic equations.

Of course the techniques and methodology of algebraic geometry are somewhat different from those of linear algebra - namely in that the former employs the techniques of commutative algebra whereas the latter relies on matrix algebra - but the goals are generally comparable.

>>	Anonymous Tue Mar 12 17:14:51 2019 No.10460576 >>10459634 This makes sense, thanks

Anonymous Tue Mar 12 17:22:28 2019 No.10460595

I'm trying to choose my classes for next semester and I'm having trouble deciding between topology and mathematical logic. Did anyone here take one/both of these classes and wants to share their opinion? Which would you recommend and why? (I'll probably take both at some point in my degree, so it's not a matter of what's more essential)

>>	Anonymous Tue Mar 12 17:25:00 2019 No.10460601 >>10460595 Depends on the syllabus, both are huge areas of study. In terms of general mathematical usefulness, I'd say take topology but mathematical logic is also interesting.

>>	Anonymous Tue Mar 12 17:32:08 2019 No.10460620 >>10460595 Topology you absolute faggot. Mathematical logic is essentially "memorize these symbols lmao".

Anonymous Tue Mar 12 17:35:20 2019 No.10460630

>>10460562
By that logic C*-algebras and algebraic geometry are also the same.
There are definitely connections between the fields, but the actual techniques you use are very different.

For example, you can't in general localise in a non-commutative ring (such as a matrix algebra), you suddenly have to distinguish between left an right ideals, etc.

Anonymous Tue Mar 12 17:52:41 2019 No.10460668

>>10460620
Mathematical logic you absolute faggot. Topology is basically memorizing definitions and writing hand-wavy proofs that are comparable in length to your average English paper.

But srs, dont take topology unless youve already had both real analysis and a good two or three "upper level"/proofs based classes (e.g. abstract algebra, discrete maths, combinatorics/number theory/whatever similar math elective your university offers). Topology is certainly learnable without real analysis, but it looses most of its intuitive grounding and motivation.

>>	Anonymous Tue Mar 12 19:45:53 2019 No.10461020 >>10460620 >t. "I've never heard of model theory" then again that's why anon's decision depends on the syllabus and their level of mathematical maturity/passed courses.

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/sci/ - Science & Math