/sci/ - Science & Math

File: 405 KB, 900x858, 92F4072D-5451-471B-BC80-EB76285AE2B4.png [View same] [iqdb] [saucenao] [google]

/mg/ - math general Anonymous Sat Jul 27 14:07:12 2019 No.10841541 [Reply] [Original]

previously: >>10828810

>>	Anonymous Sat Jul 27 14:17:42 2019 No.10841550 im gay lol

>>	Anonymous Sat Jul 27 14:19:24 2019 No.10841554 >>10841550 lol

>>	Anonymous Sat Jul 27 14:24:37 2019 No.10841569 >>10841550 lol

>>	Anonymous Sat Jul 27 14:53:23 2019 No.10841625 Who was the best mathematician last century and why was it Cartan?

>>	Anonymous Sat Jul 27 15:02:03 2019 No.10841641 >>10841625 me

>>	Anonymous Sat Jul 27 15:08:08 2019 No.10841656 >>10841550 lol

>>	Anonymous Sat Jul 27 15:57:17 2019 No.10841768 Does abelian seriously just mean commutative? What the fuck is the problem with algebraists?

>>	Anonymous Sat Jul 27 16:06:18 2019 No.10841785 >>10841768 makes them feel only they can do what they do, when in reality, every one can do it.

Anonymous Sat Jul 27 16:08:11 2019 No.10841790

does anyone else here lie about their degree? i just tell friends and family I'm in school for """Computer Science"""", the reactions are a lot less weird and ultimately I'd rather just lie and have things go smoothly and quickly since nothing they will say matters.

>>	Anonymous Sat Jul 27 16:13:03 2019 No.10841803 File: 26 KB, 809x631, free abelian group 2-simplex.jpg [View same] [iqdb] [saucenao] [google] >>10841541 Name a more beautiful algebraic object than the bar construction. Protip: you literally can't

>>	Anonymous Sat Jul 27 16:17:24 2019 No.10841812 >>10841790 you’re a math undergrad and you’re embarrassed so you instead tell them that you’re a cs cuck? that sounds like an awful way to live

>>	Anonymous Sat Jul 27 16:29:49 2019 No.10841842 >>10841812 it only happens like once or twice a year now, I'd just rather not have to explain any extra and saying cs seems to do the trick.

>>	Anonymous Sat Jul 27 16:34:50 2019 No.10841853 >>10841842 do you not get along with your family?

>>	Anonymous Sat Jul 27 16:38:24 2019 No.10841863 >>10841768 They needed to honor Abel somehow

Anonymous Sat Jul 27 16:39:10 2019 No.10841867

>>10841853
no i do just fine, but they are modern day boomers and think college should be for getting a high paying """engineering""" job. Physics also seems to be an acceptable answer. but math just doesn't jive well and raises too many questions so i just say something else normally.

>>	Anonymous Sat Jul 27 21:01:27 2019 No.10842399 >>10841790 holy shit anon you are either a massive faggot or just a spineless coward. not standing by and, if necessary, defending your life choices is one of the most despicable things you can do imo.

>>	Anonymous Sat Jul 27 23:22:28 2019 No.10842654 >>10841867 you don't like arguing with them and insinuating that their lives are a waste if they didn't study what they loved? maybe that's good, but i still like arguing with them about it

>>	Anonymous Sat Jul 27 23:25:21 2019 No.10842658 >>10841867 Understandable, my parents are similar though they mostly just want me to start a family I think. >>10842399 be nice

>>	Anonymous Sat Jul 27 23:27:29 2019 No.10842661 hey can we not post one fucking schedule 20 times this thread? keep your moronic scheduling questions to the new sqt. thanks for that remiposter.

>>	Anonymous Sun Jul 28 02:28:59 2019 No.10842895 File: 121 KB, 303x420, 1550196201077.png [View same] [iqdb] [saucenao] [google] >>10841541 Hey hey hey anon-kun, may I ask what is that picture about? :3

>>	Anonymous Sun Jul 28 02:30:25 2019 No.10842896 >>10841768 But I like it. It make me feel smart.

>>	Anonymous Sun Jul 28 02:31:55 2019 No.10842899 >>10842895 scutoids https://en.wikipedia.org/wiki/Scutoid

Anonymous Sun Jul 28 02:32:55 2019 No.10842900
File: 1.56 MB, 356x214, melgibson.gif [View same] [iqdb] [saucenao] [google]

Can someone please tell me how to make this formula undefined at x>2? No piecewise functions and no domain restrictions. The problem on my placement test just had an absolute value graph reflected over the x-axis, the graph stopped after x>2. The formula I came up with was y= -2*|x|....there has to be a rational expression or something in the denominator that makes the graph undefined

y= -2*|x|

>>	Anonymous Sun Jul 28 02:40:24 2019 No.10842915 >>10842899 Thanks~

>>	Anonymous Sun Jul 28 02:53:04 2019 No.10842929 >>10842900 f(x) = 1/(min(2, x)-2)

>>	Anonymous Sun Jul 28 03:04:51 2019 No.10842953 File: 16 KB, 569x510, Untitled.png [View same] [iqdb] [saucenao] [google] >>10842929 noooo. it's supposed to look like this.

>>	Anonymous Sun Jul 28 04:10:29 2019 No.10843049 >>10842900 You can multiply it with (\|x\|-2) / (\|x\|-2)

Anonymous Sun Jul 28 04:43:30 2019 No.10843106

>>10842953
Multiply the damn thing by sqrt(2-x)/sqrt(2-x). So f(x) = -2|x|sqrt(2-x)/sqrt(2-x),>>10842953
which is equal to -2|x| for all x <= 2 but undefined for x>2. If you want it to also be undefined for x<-2 then use the function f(x) = -2|x|sqrt(4 - x^2)/sqrt(4 - x^2).

This question sounds autistic as fuck. Ok so you can’t restrict the domain explicitly but you can throw shit like above inside that “””restricts the domain””” anyway.

Anonymous Sun Jul 28 04:50:04 2019 No.10843115

>>10843106
Ah ok...so my turn to ask a question. If S, T are linear operators on a finite dimensional vector space V, I have to show ST and TS have the same eigenvalues. For an eigenvalue c of ST, some non-zero eigenvector v of V is such that STv = cv. Then TS(Tv) = T(STv) = cTv, so Tv is in V, so if Tv is non-zero, it is an eigenvector of TS.

However if Tv = 0, then STv = 0. So c = 0. So in the case that the eigenvalue c IS 0, how can I show that it is an eigenvalue of TS as well? Thanks anons

>>	Anonymous Sun Jul 28 04:53:16 2019 No.10843121 Hiw can I mantain a career in math with a crippling alcoholism?

>>	Anonymous Sun Jul 28 05:03:23 2019 No.10843142 >>10843121 I wish you all the best anon, hope you conquer it.

>>	Anonymous Sun Jul 28 05:16:44 2019 No.10843164 >>10843121 Become a muslim

>>	Anonymous Sun Jul 28 05:17:17 2019 No.10843165 >>10843121 u cant

>>	Anonymous Sun Jul 28 05:48:15 2019 No.10843217 >>10843115 fucking retard

>>	Anonymous Sun Jul 28 05:55:53 2019 No.10843236 >>10843121 why would alcohol ever stop anyone who was going to make it?

>>	Anonymous Sun Jul 28 06:00:37 2019 No.10843245 >>10843115 >how can I show that it is an eigenvalue of TS as well? A matrix has zero as an EV if it's kernel is not trivial. If Tv=0, for v not 0 both TS and ST have a non trivial kernel, there are multiple ways too see that.

>>	Anonymous Sun Jul 28 06:26:08 2019 No.10843289 >>10843245 Thanks anon, will try to see why that’s so. >>10843217 Shut your piehole faggot. Did you get your ass hand-held all the way through your undergrad? I’m an amateur, I’ve never taken a linear algebra course. Of course I don’t know everything.

>>	Anonymous Sun Jul 28 06:30:59 2019 No.10843301 >>10841550 lol

>>	Anonymous Sun Jul 28 06:36:08 2019 No.10843313 >>10843121 shouldn't be a problem as long as you do your work t. top of my all my classes in Math alcoholic

>>	Anonymous Sun Jul 28 09:53:12 2019 No.10843548 >>10843115 >>10842900 Take your shit to the /sqt/ and stop being a retard here

>>	Anonymous Sun Jul 28 11:26:33 2019 No.10843696 How do I symbolically calculate the convolution of two functions?

>>	Anonymous Sun Jul 28 11:30:47 2019 No.10843705 >>10843696 Just like you would calculate any integral symbolically.

>>	Anonymous Sun Jul 28 11:36:17 2019 No.10843713 >>10843705 So in other words, very painfully? There's no good trick for high-dimensional convolutions?

>>	Anonymous Sun Jul 28 11:40:04 2019 No.10843718 >>10843696 Just leave it to the reader as an exercise.

>>	Anonymous Sun Jul 28 11:40:51 2019 No.10843721 what's the latest Mochizuki news

>>	Anonymous Sun Jul 28 11:44:48 2019 No.10843725 >>10843713 >So in other words, very painfully? Yes, of course, just like integrals can be very painful. >There's no good trick for high-dimensional convolutions? All tricks that are available for integration.

>>	Anonymous Sun Jul 28 11:45:10 2019 No.10843726 >>10843721 >what's the latest Mochizuki news http://www.kurims.kyoto-u.ac.jp/~motizuki/news-english.html

>>	Anonymous Sun Jul 28 12:18:07 2019 No.10843789 >>10842399 i just don’t really care, lol. I don’t think it has anything to do with cowardice or faggotry necessarily. you guys don’t get annoying / weird responses when you reply with ‘math’?

>>	Anonymous Sun Jul 28 12:20:08 2019 No.10843795 >>10842661 no regrets desu I’m very happy with it and happy to have my shit planned out

Anonymous Sun Jul 28 14:48:23 2019 No.10844146

>>10843106
Yes, greater than or equal to 2.

The question was on a placement test using ALEKS and it deactivates everything except the format they want, so you can't type a domain restriction. It was one of the only problems I got wrong.

How did you solve it algebraically? Or what is the process called so I can read about it? Thanks

>>	Anonymous Sun Jul 28 14:53:13 2019 No.10844159 >>10844146 >Or what is the process called so I can read about it? "Multiplying by a function that isn't defined for numbers less than some x and equal to 1 everywhere else".

>>	Anonymous Sun Jul 28 15:00:01 2019 No.10844179 >>10843795 you’re a massive faggot

>>	Anonymous Sun Jul 28 15:02:23 2019 No.10844186 >>10844179 >faggot Why the homophobia?

>>	Anonymous Sun Jul 28 15:06:58 2019 No.10844211 >>10841541 I like how a board that's literally made for math needs a math general thread.

>>	Anonymous Sun Jul 28 16:00:44 2019 No.10844401 >>10844179 no u

>>	Anonymous Sun Jul 28 16:01:51 2019 No.10844403 >>10844211 It's essentially the same reason /g/ needs a programming general.

Anonymous Sun Jul 28 18:01:04 2019 No.10844690

Post your best memorisation tricks.
>Jacobi's identity
>fix a, b and c
>bracket [ab]c
>permute without moving the brackets, [ab]c+[ca]b+[bc]a=0
It's particularly nice how the choice of bracketing doesn't affect anything, you just need to stay consistent.

>>	Anonymous Sun Jul 28 23:34:52 2019 No.10845531 >>10843289 >did you get your ass hand held through linear algebra no but seems like you want to think for 3 seconds next time

>>	Anonymous Sun Jul 28 23:48:31 2019 No.10845552 >>10844690 >memorisation you mean you don't deduce everything from ZFC on the spot? pssh

>>	Anonymous Mon Jul 29 02:36:22 2019 No.10845774 >>10845552 >set theory Get a load of this boomer

Anonymous Mon Jul 29 05:01:15 2019 No.10845957

>>10844146
Hey fren sorry I’m late. But yea it’s what this guy says >>10844159

Just notice that sqrt(2-x) is not defined when 2-x is negative, that is, when x>2. Also, sqrt(2-x)/sqrt(2-x) = 1 for all x less than or equal to 2, but undefined for x>2. Multiply this to any function and its domain becomes implicitly restricted to (-inf,2]. Sound ok?

Anonymous Mon Jul 29 05:09:11 2019 No.10845968
File: 67 KB, 1200x1200, 6103256E-EA65-4603-8F43-2D24BE4C96FF.jpg [View same] [iqdb] [saucenao] [google]

>>10845957
You can also use other functions which have an implied domain restriction by the way. sqrt is the most obvious one, but even things like taking the 4th root, 6th root, even roots. What this does as above is to restrict the domain to (-inf,2]

Functions like log or ln will be much more useful if you want to restrict your domain to an open interval. If I wanted to restrict to (-inf,2) I could multiply by log(2-x)/log(2-x) because log is undefined for negative values and 0.

These 2 functions along with linear factors like (x-a)/(x-a) should be enough to restrict domains to subsets of R with as many undefined points as you like.

Anonymous Mon Jul 29 05:24:55 2019 No.10845990

>>10845968
So some small questions to see if you got me:

1) Find a function f such that f(x) = sinx for all real x with the exception that, if x = -3 or x >= 1, f is undefined.

2a) consider the function f(x) = [x], known as the floor function. For all real x, [x] is the largest integer that is less than or equal to x. For example, f(2) = 2, f(3.14) = 3, f(-2.3) = -3. Draw a sketch of f on the interval [-3, 3].

Let g(x) = x - [x]; draw the graph of g, and convince yourself that x - [x] = 0 if and only if x is an integer. What is the domain of the function (1/g) defined by (1/g)(x) = 1/(x - [x])?

2b) find a function h such that h(x) = sinx, except when x is an integer multiple of pi. i.e. h undefined at ..., -pi, 0, pi, 2pi,...

>>	Anonymous Mon Jul 29 10:18:29 2019 No.10846433 >>10844690 >fix abc >permute abc u see how stupid this sounds

>>	Anonymous Mon Jul 29 11:09:31 2019 No.10846542 >>10845990 >he makes a list of fucking exercises about this one autistic problem Sensei!

Anonymous Mon Jul 29 16:28:16 2019 No.10847230

>>10841541
geometry question

I've been practicing with differential forms, and I want to check that the following is true:

Consider a hypersurface parameterized by some subset R of R(n-1) in Rn using r:R(n-1)->Rn. I can associate vector fields F on Rn with (n-1) forms in a way such that dF=div F: use the basis (-1)^i dx(I\i), where dx(I\i) is the wedge of every dxj in order, except for i; then, associate the ith coordinate of F(p) with a coefficient in front of (-1)^idx(I\i).

Now, my question is about pulling F back along r. You get what looks a lot like a cross product of the (n-1) partial derivative vectors of r in each variable of R(n-1). Comparing this to the divergence theorem, it seems like this should be the field of vectors normal to the surface.

a) Is this true? (i.e. is r*(F1 dx2dx3...dxn-F2dx1dx3... +(-1)^n dx1...dx(n-1))=F*normal?)
b) Is there an easy way to show it without resorting to coordinate computations?

>>	Anonymous Mon Jul 29 16:29:43 2019 No.10847240 What're some good resources to learn about generating functions? I stumbled on them and I'm curious. t. highest math course was diffeq

>>	Anonymous Mon Jul 29 16:33:49 2019 No.10847256 >>10847240 generatingfunctionology by herbert s. wilf

>>	Anonymous Mon Jul 29 16:34:24 2019 No.10847259 >>10847256 Thank you sir

Anonymous Mon Jul 29 17:25:05 2019 No.10847397

>>10841768
might be imagined, but while synonymous, I see "Abelian" used more when referring to a group operation, but "commutative" when referring to multiplication in a ring. Having the adjective have its modificand built in helps disambiguate sometimes.

>>	Anonymous Mon Jul 29 18:21:17 2019 No.10847499 >>10845990 extraordinarily high quality post thank you for your contribution to /mg/, it is an inspiration to future posters

>>	Anonymous Mon Jul 29 19:12:01 2019 No.10847574 >>10847240 Just want to mention, great choice. Generating functions are magic.

>>	Anonymous Mon Jul 29 19:14:54 2019 No.10847579 >>10847574 I'm just super autistic about infinite series

Anonymous Mon Jul 29 19:24:38 2019 No.10847598

>>10847579
Check out some of the early sections in Polya and Szego's Problems and Theorems in Analysis if you can find it, probably don't buy it though. There are some sick ass generating functions problems which cover all sorts of incredible combinatorial and number theoretic results.

>>	Anonymous Mon Jul 29 19:40:54 2019 No.10847638 >>10847598 Added it to my list, thank you

>>	Anonymous Mon Jul 29 19:54:32 2019 No.10847671 >A proof of the existence theorem has been given by J. Tits (IHES Publ. Math. 31 (1966)) Wait, hold up. Did Cartan classify the Lie Algebras without showing that the elements in his classification existed?

Anonymous Mon Jul 29 20:38:49 2019 No.10847754
File: 57 KB, 600x434, 138778490083.png [View same] [iqdb] [saucenao] [google]

HELLO MATH

I ONCE SAW SOMEONE POST ARTISTIC PICS FROM A REALLY COOL MATH BOOK, I BELIEVE IT WAS SOME SORT OF HIGHER GROUP THEORY TEXTBOOK.

CAN THE ANON THAT POSTED THOSE OR KNOWS ABOUT THOSE LET ME KNOW ABOUT THE ARTISTS NAME AND WORK?

>>	Anonymous Mon Jul 29 20:44:35 2019 No.10847766 File: 35 KB, 373x499, 51EZKZJWB8L._SX371_BO1,204,203,200_.jpg [View same] [iqdb] [saucenao] [google] >>10847754

>>	Anonymous Mon Jul 29 20:45:54 2019 No.10847768 >>10847671 No Cartan showed existence. But it's a lot easier to classify positive definite integral quadratic forms than to construct E8.

>>	Anonymous Mon Jul 29 21:51:30 2019 No.10847953 After finishing calc 2 I realized that algebra is much more important in real life and don't need to go any further than integrals. Could you recommend 3 books on algebra so I can be more read on the subject than 95% of humans.

>>	Anonymous Mon Jul 29 21:53:44 2019 No.10847965 >>10841790 No but I lie and say I finished

>>	Anonymous Mon Jul 29 21:56:11 2019 No.10847978 >>10847768 Ah, thanks, lad. Any idea why Carter emphasizes that Tits proved it?

>>	Anonymous Mon Jul 29 21:59:29 2019 No.10847999 >>10847953 a first course in abstract algebra by john b fraleigh

>>	Anonymous Mon Jul 29 22:06:45 2019 No.10848016 >>10847953 Use this http://abstract.ups.edu/download/aata-20130816.pdf

>>	Anonymous Mon Jul 29 22:09:51 2019 No.10848024 >>10847754 It was probably me posting pictures from Fuchs-Fomenko's Homotopical Topology. You can find a pdf very quickly. Excellent book with excellent art.

>>	Anonymous Mon Jul 29 22:12:15 2019 No.10848033 >>10847953 "Algebra" by Serge Lang "Algebra: Chapter 0" by Aluffi "Algebraic Geometry" by Hartshorne

>>	Anonymous Mon Jul 29 22:12:44 2019 No.10848036 >>10847999 >>10848016 Thanks. How about a more basic algebra book to start with? I guess it would probably more advanced high school orientated.

>>	Anonymous Mon Jul 29 22:13:28 2019 No.10848037 >>10848036 >advanced high school

>>	Anonymous Mon Jul 29 22:30:19 2019 No.10848083 >>10848037 You didn't take advanced classes in HS? I want to start at the bottom not w graduate algebraic geometry.

Anonymous Mon Jul 29 22:31:33 2019 No.10848089

>>10848036
Algebra for calculus is last course algebra high school level, (college algebra is just repacked high school algebra for burgers).

Real math algebra is about abstract structures called groups,fields,rings.

This is the more easy book about Modern algebra / abstract algebra.

http://abstract.ups.edu/download/aata-20130816.pdf

Other books assume pure math linear algebra as prerequisite or one course proof based math.

>>	Anonymous Mon Jul 29 22:33:45 2019 No.10848097 >>10848036 >>10848083 okay, fine. gelfand algebra or lang basic mathematics.

>>	Anonymous Mon Jul 29 22:45:25 2019 No.10848128 >>10848097 >>10848089 Great I'll start with these. Any recs fit s concurrent proofs book?

>>	Anonymous Mon Jul 29 22:46:52 2019 No.10848129 >>10848128 http://www.people.vcu.edu/~rhammack/BookOfProof/Main.pdf

>>	Anonymous Tue Jul 30 01:10:32 2019 No.10848344 anyone knows if there is an errata for munkres' elements of algebraic topology?

>>	Anonymous Tue Jul 30 01:24:25 2019 No.10848366 >>10848344 actually, do math books usually have errata? I never seem to be able to find them for books that I like even after looking at the professors page.

>>	Anonymous Tue Jul 30 03:38:40 2019 No.10848632 File: 6 KB, 153x142, foob.png [View same] [iqdb] [saucenao] [google] >>10845990 what's the answer to 2b

Anonymous Tue Jul 30 03:59:21 2019 No.10848660

>>10848632
Recall that for a function f, by defining g by g(x) = f(x/a), the graph of g is that of the graph of f scaled by a factor of a along the x-axis. So if f is undefined at x’, g is undefined at ax’, since g(ax’) = f(ax’/a) = f(x’), if and only if f(x’) exists, and in this case f(x’) does not exist.

Define f by f(x) = (x/pi - [x/pi]). When is f(x) = 0? What does this tell us about the expression (x/pi - [x/pi])/(x/pi - [x/pi])?

>>	Anonymous Tue Jul 30 04:05:27 2019 No.10848667 >>10847953 Chrystal’s Elementary Algebra I & II will make you an algebra demon.

>>	Anonymous Tue Jul 30 04:32:08 2019 No.10848690 >>10843115 it's trivial if T is invertible, now notice that invertible matrices are open and dense in the space of all matrices and use some kind of continuity argument.

Anonymous Tue Jul 30 05:32:25 2019 No.10848758

>>10848690
Hey anon, I don't know how to use that argument but I think I got it. I only know some very small real analysis so metric space type arguments are not in my alley.

Here's my argument. If ST has eigenvalue 0, then it is not injective so it is non-invertible. So at least one of S and T is non-invertible as well, such that TS is non invertible, so non-injective. From which it can be gleaned that TS(x) = TS(y) for some x,y in V where x =/= y. Then TS(x - y) = 0, and x-y =/= 0, so 0 is an eigenvalue of TS.

Anonymous Tue Jul 30 05:49:25 2019 No.10848774

>>10847953
I'll never understand how people looking for HS-level books never ever consider buying actual HS textbooks and instead go for a 1971 outdated book by Lang. Pick it up right where you left it, just look up which textbooks are currently being used in high schools

>>	Anonymous Tue Jul 30 07:39:30 2019 No.10848918 >>10848667 OK I'll look into it. >>10848774 I have no problem with that if you know any top tier ones

>>	Anonymous Tue Jul 30 08:58:17 2019 No.10849034 >>10848690 Haha I love that. Good post. Algebraists BTFO!

Anonymous Tue Jul 30 09:02:52 2019 No.10849041

>>10848758
that's correct, but to clean up your argument recall that a matrix is injective if and only if its kernel/nullspace is 0. so once you get TS is non injective you immediately know there is a nonzero vector x such that TSx = 0. of course your proof merely contains the proof of one direction of the injective/nullspace result, so you're still totally right.

>>	Anonymous Tue Jul 30 09:15:55 2019 No.10849062 Is there any math branch that study specifically study piecewise function?

>>	Anonymous Tue Jul 30 09:16:52 2019 No.10849065 >>10849041 Thanks anon that’s neat.

>>	Anonymous Tue Jul 30 09:16:57 2019 No.10849066 >>10849062 *that specifically study

>>	Anonymous Tue Jul 30 10:47:42 2019 No.10849227 >>10848774 anon basic math was ready in the 18th century, it makes no sense to think a 1971 book can be outdated in this subject

Anonymous Tue Jul 30 10:56:40 2019 No.10849249

>>10841768
I say "Abelian" when I want to exploit some important theorem of the commutative groups on my objects when it's not immediately obvious that this follows from the objects being commutative.

In general it's a clusterfuck though. Having a consistent nomenclature across so many different fields is very difficult if not impossible.

Anonymous Tue Jul 30 11:46:15 2019 No.10849332

>>10848774
guess who high school textbooks are written for? high schoolers. why not use a book which is written for adults instead, on the same material? do you think anon needs to pay an upcharge for all those pictures of skateboard dudes making approximate parabolas? no.
and the notion that anything would be "outdated" from a 50 year old book on the most basic possible mathematics is absolutely laughable. if anything, it will be a hell of a lot better than a modern book, because it remains well known after so many years. same deal as classic art, literature and music: sure, there may be art today which is of the same caliber, but all the classics have been vetted so you know the proportion of great ones will be a lot higher than the proportion in a modern collection.

>>	Anonymous Tue Jul 30 11:53:06 2019 No.10849346 >>10849249 >across so many different fields fields are already commutative by definition, no need for an extra qualifier

>>	Anonymous Tue Jul 30 12:02:24 2019 No.10849363 File: 1.37 MB, 1140x4777, 1563323896840.png [View same] [iqdb] [saucenao] [google] Will I get memed with this?

>>	Anonymous Tue Jul 30 12:04:37 2019 No.10849369 >>10849363 Also what'a the name of last two books?

Anonymous Tue Jul 30 12:14:55 2019 No.10849385

>>10843713
You can take the transform (using whatever basal functions are most convenient) of each function then multiply the transformed functions and invert the product.

Quick and easy way computationally with FFT, but I dunno if that'll help you symbolically

>>	Anonymous Tue Jul 30 12:36:31 2019 No.10849467 I’m taking abstract lin alg in the fall. What should I expect? It’s my first “real” math class other than a class that was an intro to proofs last semester

>>	Anonymous Tue Jul 30 12:50:38 2019 No.10849510 >>10849363 this was obviously written by a differential geometer. so it depends if you want to differential geometery.

Anonymous Tue Jul 30 12:51:25 2019 No.10849512

>>10849363
Yeah. The analysis is extremely weak, the number theory/combinatorics/graphs theory is just about nonexistent, the algebra is mediocre, the pacing for algebraic geometry is surreally slow, and the subject choices are entirely defined by Verbitsky's autism boner for Kahler manifolds.
Just make sure you know everything before junior and then do whatever catches your interest.

>>	Anonymous Tue Jul 30 13:01:01 2019 No.10849537 >The palindromic prime number 1000000000000066600000000000001 is known as Belphegor's Prime, due to the significance of containing the number 666, on both sides enclosed by thirteen zeroes and a one.

>>	Anonymous Tue Jul 30 13:03:31 2019 No.10849544 >>10849537 The number of the beast.

Anonymous Tue Jul 30 13:06:53 2019 No.10849553
File: 1.49 MB, 1920x1020, sketch-1564506155892.png [View same] [iqdb] [saucenao] [google]

Why does the subspace have to be f(0)=0 (pass through origin) and cant it be like any random 0 outside of the origin? Last 2 lines of pic related, this is like first 10 pages and theres nothing explaining why f(0) has to be 0, and i only recall somethinh like that on linear applications which isnt the same as subspace

>>	Anonymous Tue Jul 30 13:18:14 2019 No.10849577 >>10849544 what's a simple way to prove it's a prime?

Anonymous Tue Jul 30 13:52:21 2019 No.10849621

>>10848918
Are you interested in a specific topic (i.e., Algebra I, Algebra II, etc.) or in a specific grade (grade 10/11/12 math textbook)?
>>10849332
I am sorry anon, but Euler's "Vollständige Anleitung zur Algebra" (1765) won't probably do it for most learners
>>10849227
It ain't outdated in that the math is wrong, but the treatment of the material is far from acceptable. Also he leaves off some important stuff and puts in some irrelevant shit.

Anonymous Tue Jul 30 14:02:43 2019 No.10849631

What's the best way to review freshman Calculus series? From single and multivariable to vector calculus. I used Stewart's text, should I just pop that bad boy open and try exercises at random? I don't want to get caught up in hairy details and spend 6 months reviewing, so I'm adverse to going chapter by chapter and would instead like to overview high level concepts and make sure I can solve basic problems from each section, and maybe a few harder exercises too. Sound good?

>>10848918
>I'll look into it
If you want more expositions on what is called 'elementary algebra' (aka high school / college algebra, not modern or abstract algebra), see "Elementary Algebra for Schools by Knight and Hall" or "Elements of Algebra by Euler". What is probably more up you're alley though are these, coupled with some of Gelfand's elementary books:
>https://www.youtube.com/playlist?list=PL5A714C94D40392AB
>https://www.youtube.com/playlist?list=PLIljB45xT85DpiADQOPth56AVC48SrPLc

>>	Anonymous Tue Jul 30 14:04:13 2019 No.10849633 >>10849363 take it one book at a tme faggot, any meme list is exactly that. you will know what you need to do after finishing the book and doing the thing. a better question is always "i just finished $book, what should I read next?"

Anonymous Tue Jul 30 14:20:41 2019 No.10849677

>>10849631
>Elements of Algebra by Euler
>actually recommending a book from the 18th century
>Elementary Algebra for Schools by Knight and Hall
>date: 1885

>What's the best way to review freshman Calculus series?
Have you considered going straight to the source, and reading Newton's "Method of Fluxions" (1736)?

Anonymous Tue Jul 30 14:23:11 2019 No.10849684

>>10849677
>Have you considered going straight to the source, and reading Newton's "Method of Fluxions" (1736)?
yeah, I enjoy reading source material. Anyway, Chrystal's Algebra is still the best elementary algebra text around imo. It's not liek algebra's changed, and in fact most elem alg books are watered down and too easy / boring

Anonymous Tue Jul 30 15:07:44 2019 No.10849797

>>10849553
Because fields don't admit zero divisors.
Ask in sqt and I'll give an answer you can understand.
>>10849631
>what's the best way to review
Answering questions in /sqt/.
Pick up a physics book like Griffith's Electrodynamics and read the appendix reviewing stuff.

>>	Anonymous Tue Jul 30 16:33:25 2019 No.10850044 >>10849577 divide it by every prime number between zero and sqrt(1000000000000066600000000000001)

>>	Anonymous Tue Jul 30 17:02:17 2019 No.10850137 >>10850044 fuck primes

>>	Anonymous Tue Jul 30 17:58:07 2019 No.10850272 >>10841550 lol

Anonymous Tue Jul 30 18:04:21 2019 No.10850287

>>10849621
>i am sorry...
i agree with you. you're taking my point to a logical extreme. there is a happy medium between the 2019 edition of pearson "algebra for zoomers" and a book by euler. gelfand is perfectly doable for anyone with motivation and a bit of time. nothing about it is "outdated."

>>	Anonymous Tue Jul 30 18:05:23 2019 No.10850289 >>10849631 You should be reviewing using a tougher book like Spivak or possibly Apostol, trying your hand at some of the tougher problems in these books.

>>	Anonymous Tue Jul 30 18:08:26 2019 No.10850298 >>10849677 alright you're the annoying mcgraw-hill shill but this post was pretty funny

Anonymous Tue Jul 30 20:15:11 2019 No.10850602

>>10849553
>Why does the subspace have to be f(0)=0
What does "The subspace is f(0)=0" even mean?
If you mean "Why does f being linear implies that f(0)=0", then that's because f(0)=f(0+0)=f(0)+f(0), and by cancelling from each side you get f(0)=0
If you mean "Why does a subspace have to contain 0", then that's pretty much straight from the definition of subspace.

Anonymous Tue Jul 30 20:27:36 2019 No.10850628

>>10850602
Yeap the problem was in your first explanation, guess its kinda worse reading this after already having taken some shitty linear algebra class before, i was thinking of the thing related to the null space, as in there can be a certain x where f(x) =0 so f(0+x)=0 and x may be different than 0, but again that wouldnt be linear(?) guess ill keep reading

>>	Anonymous Tue Jul 30 21:11:15 2019 No.10850741 >>10850289 >spivak I am - but Spivak doesn't have all those applied numerical problems. Spivak is more like analysis, innit? whereas stewart is applied calculus

>>	Anonymous Tue Jul 30 21:12:29 2019 No.10850746 Just started Hatcher's Point Set notes a few days ago. Point set is turning out to be pretty fun. I am kind of thinking of taking it with Real Analysis next semester. Would that be a nice synergetic pair of courses?

>>	Anonymous Tue Jul 30 22:07:43 2019 No.10850919 If a Hausdorff space is separable, it's subspaces are also separable. Did this also count for dense sets with other cardinalities? I've figured out a proof, but it fucks up once you can't exploit finite intersection.

>>	Anonymous Tue Jul 30 22:18:40 2019 No.10850936 >>10850741 What are you, a physicist? Take the Courant John-pill

>>	Anonymous Tue Jul 30 22:30:39 2019 No.10850965 >>10850919 Never mind about the proof, I fucked up. Tell me if it's true, tho.

>>	Anonymous Tue Jul 30 22:30:55 2019 No.10850968 File: 101 KB, 300x300, 2D3834D4-976F-45D8-A34C-AD94C46467AC.png [View same] [iqdb] [saucenao] [google] >>10849537 >tfw there are infinitely many prime numbers of this form

>>	Anonymous Tue Jul 30 22:42:16 2019 No.10850999 I want to win a Field's Medal. Which one of the Millennium Problem is the 'easiest' to solve?

>>	Anonymous Tue Jul 30 23:00:22 2019 No.10851053 >>10850999 Found some research in langrands program, global analysis or PDE, millenium problems are just insane.

>>	Anonymous Tue Jul 30 23:02:52 2019 No.10851059 >>10850999 P vs NP.

>>	Anonymous Tue Jul 30 23:04:51 2019 No.10851065 >>10851053 I don't even understand the problem...

>>	Anonymous Tue Jul 30 23:26:38 2019 No.10851137 >>10850999 Yang mills. Difficult af, but plenty of math faggs hate it because muh physics.

>>	Anonymous Tue Jul 30 23:42:48 2019 No.10851182 >>10850936 no, im just a regular guy

>>	Anonymous Tue Jul 30 23:45:13 2019 No.10851191 >>10850746 Yes, those pair very well together especially if you have some idea for how point set works going in. They complement each other perfectly.

>>	Anonymous Wed Jul 31 00:01:48 2019 No.10851232 >>10851137 that isn't easy, just has less competition. if we are reasoning on competition alone, then probably the collatz conjecture. though who the fuck would seriously want to solve that?

>>	Anonymous Wed Jul 31 00:10:41 2019 No.10851251 >>10851182 Well you seem to want the best of everything, applications and theory. If you have time and autism this is for you. I use Spivak and even his is difficult.

>>	Anonymous Wed Jul 31 01:28:36 2019 No.10851410 >>10841550 me too

>>	Anonymous Wed Jul 31 02:24:15 2019 No.10851502 >>10849797 >Pick up a physics book like Griffith's Electrodynamics and read the appendix reviewing stuff. This is really solid advice.

>>	Anonymous Wed Jul 31 03:28:27 2019 No.10851592 >>10849577 (%i1) ifactors(1000000000000066600000000000001); [[1000000000000066600000000000001,1]] It's pretty easy.

Anonymous Wed Jul 31 03:35:01 2019 No.10851599

>>10851232
You seem to ignore the post said
>Difficult af
And the collatz conjecture isn't a millenium problem. It's impossible to tell. But most of the mathphys community has gone towards methods in TQFT and Geometric Quantization in order to study quantum gravity I think. Mostly because physicists are pretty satisfied with their QFT already and people look at it like as just tedious formalization.

>>	Anonymous Wed Jul 31 03:50:26 2019 No.10851613 >>10851599 >quantum gravity Sounds like something straight out of >>>/x/.

>>	Anonymous Wed Jul 31 03:58:41 2019 No.10851617 >>10851251 Well, I don’t plan to spend that much time reviewing the applied stuff. It will just come in handy for some upcoming courses, so it seemed sensible. But yeah Spivak is hard, good luck and godspeed. And no, I’m not really an applied person.

>>	Anonymous Wed Jul 31 04:31:03 2019 No.10851644 >>10850919 That does not sound right. For open subspaces sure, but otherwise I dunno. Topology is weird

Anonymous Wed Jul 31 05:57:15 2019 No.10851730
File: 76 KB, 676x526, 2019-07-31 11_54_58-Grafräknare - GeoGebra.png [View same] [iqdb] [saucenao] [google]

Hey I need some help with a problem which I can't really wrap my head around... So the three bisectors of a triangle always go through the middle point of the inscribed circle. AA1 is the bisector of angle A. The middle point is O. Look at the picture for what I need to prove.

>>	Anonymous Wed Jul 31 09:05:27 2019 No.10851947 >>10851617 high school calculus isn't "hard"

>>	Anonymous Wed Jul 31 09:24:18 2019 No.10851982 >>10851730 think about areas of triangles AOC, BOC, AOB

>>	Anonymous Wed Jul 31 09:57:45 2019 No.10852047 IMC (biggest university math competition in europe) is currently underway check out the problems if you care https://imc-math.org.uk/imc2019/imc2019-day2-questions.pdf

>>	Anonymous Wed Jul 31 10:01:26 2019 No.10852053 Redpill me on finance. Can I make $300k starting from a PhD? Can I get out before they steal my soul?

>>	Anonymous Wed Jul 31 10:04:19 2019 No.10852057 >>10851982 sorry I don't get what you mean

Anonymous Wed Jul 31 10:10:02 2019 No.10852067

>>10852053
>Redpill me on finance.
Fancy word for office clerks.

>Can I make $300k starting from a PhD?
Not even quants make that much anymore and in any case since Deutsche Bank laid off 10k people worldwide you won't find work in the foreseeable future while competing against experienced and desperate job seekers.

>Can I get out before they steal my soul?
Why don't you look for work in software development instead? At least that way you'll have reasonable job security. Either way you're academic career/student life is over as soon as you start working full time. Whatever you had going for before you needed money it's over now.

Anonymous Wed Jul 31 10:25:09 2019 No.10852088

>>10852057
area of AOB = 1/2 * AB * r, same for other sides
from this you can obtain (AB + BC + AC)/BC = area(ABC) / area(BOC)
draw heights AG and OH in triangles ABC and BOC
area(ABC) / area(BOC) = AG / OH
from tales AG / OH = AA1 / OA1

thus we have (AB + BC + AC)/BC = AA1 / OA1, easy to turn into desired eq.
im typing with one hand so i don't write not much details, i hope you can get this

>>	Anonymous Wed Jul 31 10:51:14 2019 No.10852146 >>10847256 seconding this, freely available too

>>	Anonymous Wed Jul 31 11:03:21 2019 No.10852171 >>10852047 Looking tough my dude.

>>	Anonymous Wed Jul 31 11:22:52 2019 No.10852214 >>10852088 oh I'm following you all the way. I'm probably being retarded but I've tried but can't turn (AB+AC+BC)/BC=AA1/OA1. How do I get rid of AA1 and the BC. Am I missing what I need to substitute?

>>	Anonymous Wed Jul 31 11:24:03 2019 No.10852221 >>10852214 substract 1 from each side

>>	Anonymous Wed Jul 31 11:31:54 2019 No.10852237 >>10852221 omg thanks I think I got it!

Anonymous Wed Jul 31 11:32:22 2019 No.10852239

>>10852047
For problem 6, note that, since f is continuous, f - g’ is the derivative of a function (fundamental theorem of calculus), hence it satisfies the intermediate value theorem (Darboux’ theorem).
I guess the problem would be to reprove this theorem, which is not very hard (but not trivial)

Anonymous Wed Jul 31 11:50:46 2019 No.10852268

>>10852047
>https://imc-math.org.uk/imc2019/imc2019-day2-questions.pdf
This is literally just MVT, bionomial expansion convergence test, bilinear property exploitation and "follows trivially" (from taking the first affine hyperplane cut and arguing the furthest vertex point probability of each binary space partition).

Not saying it's easy, but I expect at least challenging problems to go with all European snobbishness about the supposed quality of their undergrad programmes.

>>	Anonymous Wed Jul 31 11:52:39 2019 No.10852272 >>10852268 >This is literally just MVT Nah, its by itself irrelevant. g' isn't continuous.

>>	Anonymous Wed Jul 31 11:53:59 2019 No.10852275 >>10852268 nice bluff amerilard

Anonymous Wed Jul 31 11:56:19 2019 No.10852280

>>10852272
>g' isn't continuous

It's not only continuous, it's differentiable, you might argue that it isn't smooth, but MVT only requires continuity (modern generalisations only require Lipschitz continuity).

I think you might be overthinking the problems a bit Anon. I could be underthinking it though.

>>	Anonymous Wed Jul 31 11:57:59 2019 No.10852285 >>10852272 >>10852275 >Let f, g : R − R be continuous functions such that g is differentiable >continuous functions >functions >s >[math]s[/math] I'm not sure I deserve to be attacked like this for reading the question correctly.

>>	Anonymous Wed Jul 31 11:58:01 2019 No.10852286 >>10852280 >it's differentiable, Stop embarrassing yourself Amerilard and read my post and alternatively the question CAREFULLY again.

>>	Anonymous Wed Jul 31 11:59:24 2019 No.10852288 >>10852285 g DASH >g' >g' >g'

>>	Anonymous Wed Jul 31 12:02:13 2019 No.10852291 >>10852239 that's correct >>10852268 congrats you failed the first problem also the problems are in ascending order of difficulty

Anonymous Wed Jul 31 12:10:17 2019 No.10852309

>>10852286
>>10852288
>>10852291

The question says:
A) g is continuous
B) g is differentiable

Therefore g' is at least continuous (not necessarily smooth if g is pathological)

And again g Does not have to be [math]C^1[/math] for modern MVT to apply.

>>	Anonymous Wed Jul 31 12:13:35 2019 No.10852314 >>10852309 >Therefore g' is at least continuous A-are you sure about that?

>>	Anonymous Wed Jul 31 12:16:47 2019 No.10852319 >>10852314 For all R it is either continuous or does not exist, there is no discontinuity. Non-existence is allowed in the proof outline I have in mind.

>>	Anonymous Wed Jul 31 12:19:40 2019 No.10852322 >>10852319 But that’s wrong though, it is the whole point these anons are getting at

Anonymous Wed Jul 31 12:25:18 2019 No.10852332

>>10852319
>or does not exist
Is 1/x continuous because "1/0 does not exist"?
Or what exactly are you getting at?

Are you pretending? Because what you are saying is stuff any person in the first semester learns that it is wrong, but maybe that is just Europe though.

I also suggest that you read:
https://math.stackexchange.com/questions/292275/discontinuous-derivative

>>	Anonymous Wed Jul 31 12:26:20 2019 No.10852334 >>10852309 >>10852319 idiot. let f(x) = x^2 sin(1/x) for x != 0, f(0) = 0. f is differentiable everywhere on R but the derivative is not continuous at 0. the most basic fucking introductory real analysis counterexample.

Anonymous Wed Jul 31 12:26:23 2019 No.10852335

>>10852322
What exactly is wrong? There can't be any jump disconuities correct? Then I read the question correctly. There are many ways the answer can be found and of course IVT can obviously be used, but being stuck on the first intuition is why you can't see how easy it is to find a quicker solution. I think maybe you are not accounting that the question says the inequality can be assumed?

>>10852275
>>10852286
>>10852291
Also this rude attitude is extremely uncalled for, especially disregarding the other answers and claims that because "the problems are in ascending order of difficulty" the first question should be considered difficult.

The last question literally just involves two hand computations to prove it.

>>	Anonymous Wed Jul 31 12:29:04 2019 No.10852342 >>10852335 you're new to this board, aren't you? go ramble about le jump discontinuity on >>>/r/eddit you fucking freshman tier moron.

Anonymous Wed Jul 31 12:31:52 2019 No.10852348

>>10852239
For problem 7, we always have [math]a_n \le \frac{n}{p}
[/math] where p is the smallest prime that divides p, unless n is the square of a prime.
If n is the square of a prime p, then we have [math]a_n = 2p[/math] and therefore [math]\frac{a_n}{n} = \frac{2}{p} < \frac{1}{2}[/math] unless n = 4.
Hence, for all n in C except 4, we have [math]\frac{a_n}{n} \le \frac{1}{2}[/math], hence the series converges.

>>	Anonymous Wed Jul 31 12:38:47 2019 No.10852372 >>10852335 Not having jump discontinuities is not the same as being continuous, as the extremely informative >>10852332 shows. So no, it is not "obvious" that IVT can be used. It is the whole crux of the problem

Anonymous Wed Jul 31 12:39:35 2019 No.10852376

>>10852335
>Also this rude attitude is extremely uncalled for
To quote:
>Not saying it's easy, but I expect at least challenging problems to go with all European snobbishness about the supposed quality of their undergrad programmes.
You read what you sow, Amerilad.
And if you do not know the basics of Analysis you better stop trashtalking other undergraduate programs.

Anonymous Wed Jul 31 13:42:06 2019 No.10852492

>>10852334
>>10852332
>Look at me guys! I can copy text from stackexchange!

MUHAMMAD FUCKING CHRIST LET ME JUST TYPE IT OUT FOR YOU STUPID MOUTH BREATHING WHORESONS

IT IS ASSUMED (BY THE QUESTION NOT BY ME) THAT
[math]\frac{f(0) - g'(0)}{g'(1) - f(1)} > 0[/math]

IF [math]g'(0)[/math] HAS A DISCONTINUITY THEN BECAUSE [math]g(0)[/math] IS DIFFERENTIABLE IT HAS TO BE A NON-EXISTENCE AND NOT A JUMP CONTINUITY, FOR EXAMPLE CONSIDER SINGULARITY DISCONTINUITIES AT 0 AND 1, IF [math]lim_{x \rightarrow 0}g'(x) = \infty[/math] THEN SINCE [math]f[/math] IS CONTINUOUS THE NOMINATOR WILL DOMINATE SO THE ONLY POSSIBILITY IS [math]lim_{x \rightarrow +0}g'(x) = - \infty[/math], SIMILARLY AT THE DENOMINATOR THE ONLY POSSIBILITY IS [math]lim_{x \rightarrow 1}g'(x) = \infty[/math]

HOWEVER, AND THIS IS THE IMPORTANT PART, YOU SEWERRAT RAPING HARPY SPAWN. SINCE THERE HAS TO BE A (AT LEAST CONTINUOUS IF NOT DIFFERENTIABLE) SUBDOMAIN IN THE DOMAIN [math]c \in (0, 1)[/math] WHERE [math]g'[/math] EXIST AND IS CONTINUOUS (AGAIN BECAUSE THERE ARE NO JUMP DISCONTINUITIES) WHEREIN THE THEOREM CAN BE APPLIED.

COOL.

THEREFORE WE ONLY CARE ABOUT THE PARTS WHERE THE FUNCTION [math]g'[/math] IS CONTINUOUS IN THE DOMAIN, IT DOES NOT HAVE TO BE CONTINUOUS ACROSS THE WHOLE DOMAIN of c, BUT ANY SUBDOMAIN WILL DO. IN FACT YOU SYPHILIS INFECTED, YELLOW TEETH, FETAL ALCOHOL SYNDROME CUNTS MADE ME DOUBT MYSELF ENOUGH TO CHECK, BUT EVEN THE FUCKING WIKIPEDIA PAGE (WHICH DOES NOT CONTAIN THE MOST GENERALISED THEOREM) CONFIRMS THIS, READ HERE THE LIMITS CAN EQUAL INFINITY OR MINUS INFINITY:
https://en.wikipedia.org/wiki/Mean_value_theorem#Formal_statement

FUCK.

YOU DON'T NEED TO SPELL ANY OF THIS OUT IN A PROOF BECAUSE IT IS A KNOWN FUCKING PROPERTY OF DIFFERENTIABLE FUNCTIONS. NOW YOU CAN HAVE SUPER ELEGANT AND BEAUTIFUL FUCKING PROOF USING THE THEOREMS BECAUSE THE COMPACT DOMAIN IS 1 SO THE FRACTIONS ARE EVEN EASIER TO WORK WITH. IT CAN LITERALLY BE DONE IN 3 LINES, JUST LIKE ALL THE OTHER QUESTIONS.

>>	Anonymous Wed Jul 31 13:49:36 2019 No.10852513 >>10852492 >

>>	Anonymous Wed Jul 31 13:55:14 2019 No.10852528 File: 239 KB, 1080x1143, fascist.jpg [View same] [iqdb] [saucenao] [google] http://www.cis.upenn.edu/~jean/math-basics.pdf Just saw this got an update, maybe you're interested

Anonymous Wed Jul 31 14:01:12 2019 No.10852544

>>10852492
Okay I don’t know if you’re trolling or retarded, but none of what you wrote is an argument. You cannot have "nonexistence" of g’ at a point since g is assumed differentiable everywhere, but g’ may not be continuous. As a consequence, you cannot have g’ diverge to infinity in the neighborhood of a point either (otherwise, we would get a jump discontinuity).
Of course, g’ cannot be non-continuous everywhere. That is not possible.
But you still cannot apply the IVT or MVT directly.
Not sure what the rest of your schizo rant was about but if you are unwilling to read anything in good faith, I think I’m going to give up and I advise others to do the same.

>>	Anonymous Wed Jul 31 14:12:09 2019 No.10852578 >>10852528 >2000 pages i doubt anyone is going to read that

>>	Anonymous Wed Jul 31 14:21:10 2019 No.10852603 >>10852348 correct >>10852528 she was lucky to not get the paint on her eyes why is your picture called FASCIST, iam too brainlet to get the joke

>>	Anonymous Wed Jul 31 14:25:38 2019 No.10852619 >>10852603 >she Why are you assuming they're a "she"?

>>	Anonymous Wed Jul 31 14:25:41 2019 No.10852620 File: 71 KB, 500x717, hodl_girl.jpg [View same] [iqdb] [saucenao] [google] >>10852603 you won't be able to deduct meaning from it, don't worry

>>	Anonymous Wed Jul 31 14:58:33 2019 No.10852680 >>10852619 are you trying to call her 'he' just because she has penis fuck right back to /pol/

>>	Anonymous Wed Jul 31 15:27:55 2019 No.10852747 >>10850919 >Did this also count for dense sets with other cardinalities? What do you mean by this?

>>	Anonymous Wed Jul 31 15:53:33 2019 No.10852805 >>10844690 Why would you spend time memorizing shit? If you need it look it up. Testing on that would be retarded

>>	Anonymous Wed Jul 31 16:42:25 2019 No.10852948 >>10852805 >why would you remember delta=b^2-4ac? you can look it up

>>	Anonymous Wed Jul 31 18:12:20 2019 No.10853225 File: 1.24 MB, 3264x2448, 79BD2AAB-7038-4EF1-AF9A-35769396ADC6.jpg [View same] [iqdb] [saucenao] [google] I get that this is clearly true but can someone explain rigorously without waving their hands.

>>	Anonymous Wed Jul 31 18:17:32 2019 No.10853232 >>10853225 \|-v\| = \|v\| by definition, what more do you need?

>>	Anonymous Wed Jul 31 18:18:20 2019 No.10853233 >>10853232 Damn I guess my brainletism is in full force today. Thanks

Anonymous Wed Jul 31 18:52:16 2019 No.10853316

Is there a rigorous proof of Helmholtz Theorem with that uses only calc + basic analysis? Maybe this amounts to a basic proof of the green's funcion for the laplacian in the sense of proving that, at least for [math]C1[/math] functions we have that:

[math]\int_{V}f(x')\left(-\frac{1}{4\pi}\nabla^2\frac{1}{|x-x'|}\right)dV=f(x)[/math]

For bounded domains. I don't how this is done though.

>>	Anonymous Wed Jul 31 19:08:41 2019 No.10853369 >>10853316 Did you try using the L^2 inner product to get an orthogonal decomposition?

>>	Anonymous Wed Jul 31 19:11:58 2019 No.10853380 >>10853316 something something pde is not math, le engineering, im an alggeo cuck, blah blah blah i fucking hate people on this board

>>	Anonymous Wed Jul 31 19:12:08 2019 No.10853381 >>10853369 By basic analysis I meant basic delta-epsilon arguments, limits whatever. I suppose I could rephrase it as >Is there a rigorous proof of Helmholtz Theorem that only uses non american college level calc

>>	Anonymous Wed Jul 31 23:59:20 2019 No.10853962 File: 5 KB, 240x250, 1491273903500.jpg [View same] [iqdb] [saucenao] [google] >>10852288 Wait, there are people who read g' out loud as "g dash?" Is this a Yuropoor thing?

>>	Anonymous Thu Aug 1 00:14:36 2019 No.10853985 >>10853381 okay did you try using the L^2 inner product to get an orthogonal decomposition?

>>	Anonymous Thu Aug 1 00:16:19 2019 No.10853986 >>10841641 this guy

>>	Anonymous Thu Aug 1 01:14:03 2019 No.10854072 >>10853225 from an intuitive perspective: the distance from a to b is, of course, the same the diistance from b to a, so in other words \|a-b\|=\|b-a\|, and, by that logic, if \|a-b\| <= c, then \|b-a\| <= c

>>	Anonymous Thu Aug 1 01:17:39 2019 No.10854076 File: 18 KB, 420x420, 9E3C0C6D-FE98-4ED6-B0F5-35821C7FAECB.png [View same] [iqdb] [saucenao] [google] >>10852492 ANON FIRED UP TODAY

>>	Anonymous Thu Aug 1 01:18:06 2019 No.10854077 >>10851947 i agree. but I know you're trying to imply that spivak's calculus is high school level, and I assure you, it's not. if you think that, I admire this mysterious country you went to high school in.

>>	Anonymous Thu Aug 1 01:40:34 2019 No.10854103 what’s /mg/‘s official programming language? >inb4 latex

>>	Anonymous Thu Aug 1 03:53:01 2019 No.10854243 >>10854103 Lean

Anonymous Thu Aug 1 04:01:45 2019 No.10854254

>>10841541
When dealing with matricies how to tell the order of matrix multiplication when putting a matrix on the other side of the equation?

Suppose I have 3 matricies A,S,L:
A*S=S*L
How do I know it will be:
S^(-1)*A*S=L

instead of
A*S^(-1)*S=L or A*S*S^(-1)=L

Anonymous Thu Aug 1 04:16:48 2019 No.10854270

>>10854254
Whatever you do to one side you have to do to the other. If you left multiply by [math] S^{-1} [/math] on the right side of your equation you also need to left multiply by it on the left side. So [math] S^{-1}AS=L[/math] is the correct answer.

Be careful though since not all matrices are invertible so [math]S^1[/math] may not exist.

>>	Anonymous Thu Aug 1 04:21:05 2019 No.10854275 >>10854270 Thank you.

>>	Anonymous Thu Aug 1 04:32:55 2019 No.10854290 >>10854103 >implying mg does programming

>>	Anonymous Thu Aug 1 04:34:24 2019 No.10854292 >>10854254 Matrix multiplication is not commutative right? So whenever you have a product of matrices, when you multiply a new matrix then it will always be either left multiplication or right multiplication on both sides of the equation.

>>	Anonymous Thu Aug 1 04:39:02 2019 No.10854296 >>10852492 Irrelevant. It's my response to you saying: >The question says: >A) g is continuous >B) g is differentiable >Therefore g' is at least continuous Which betrays a fundamental lack of understanding of undergrad analysis on your part.

>>	Anonymous Thu Aug 1 04:55:59 2019 No.10854311 >>10854077 it is tho just not for poors

>>	Anonymous Thu Aug 1 04:58:53 2019 No.10854316 How the FUCK do I prove [math]\lim_{n\rightarrow \infty} \left ( 1 + \frac{1}{n} \right )^n = e[/math]?

>>	Anonymous Thu Aug 1 04:59:51 2019 No.10854318 Can someone explain what "arithmetic" means when used as in "Arithmetic Geometry" or "Arithmetic Curves"

>>	Anonymous Thu Aug 1 05:02:20 2019 No.10854322 File: 520 KB, 888x894, 9AC2A31C-D982-4D77-A76C-D43C20AB713C.png [View same] [iqdb] [saucenao] [google] >>10854316 Proof: By definition, this is so. QED

Anonymous Thu Aug 1 05:11:07 2019 No.10854340

>>10854316
Depends on your definition of e. If you set it to be the sum of the 1/k! for example, then you might try to use binomial expansion on the LHS and see what happens

>>10854318
It means that instead of considering systems of polynomial equations over algebraically closed fields (as you would in a classical setting), you consider systems of equations over rings of arithmetic interest, typically global fields (so finite extensions of Q or Fq((t)) ) or their rings of integers.

Anonymous Thu Aug 1 06:52:12 2019 No.10854452
File: 104 KB, 832x1024, Omega-exp-omega-labeled.svg.png [View same] [iqdb] [saucenao] [google]

'sup /sci/, quick question.

In my set theory class we've defined the following concepts, for a given linear order X:
(#) A subset Y ⊆ X is said to be cofinal, if for every x ∈ X there exists some y ∈ Y such that x ≤ y.
(#) The cofinality of X is defined to be the least cardinal k such that there exists a cofinal subset of X whose cardinality is k.

It is then stated in my book (without explanation) that cof(ℵ) is uncountable, where ℵ denotes the cardinality of the continuum.

But why is that? Seems to me that the natural numbers form a subset of the reals that is cofinal. Why, then, is it not the case that cof(ℵ) = ω? What have I missed?

>>	Anonymous Thu Aug 1 07:44:05 2019 No.10854531 >>10854452 > Set theory class A...anon I'm so sorry...

>>	Anonymous Thu Aug 1 08:00:21 2019 No.10854548 >>10854452 you are right that the real numbers with the obvious order have cofinality omega. are you sure that's exactly what's in your book? A similar statement is true: 'the first uncountable ordinal has uncountable cofinality'

>>	Anonymous Thu Aug 1 08:17:51 2019 No.10854572 >>10845990 lmao

>>	Anonymous Thu Aug 1 08:22:47 2019 No.10854582 >>10848632 [math] \frac{\sin(x)^2}{\sin x} [/math]

>>	Anonymous Thu Aug 1 08:29:33 2019 No.10854593 >>10849467 easy, but worth taking the time to learn at a deep level >>10849633 This is good advice in general >>10849034 based

>>	Anonymous Thu Aug 1 08:40:03 2019 No.10854607 >>10854452 Depends on the order you put on the cardinality of the continuum, yes? Do you mean the corresponding ordinal?

>>	Anonymous Thu Aug 1 08:51:59 2019 No.10854625 >>10854452 This >>10854607. You need to put a well order on R

Anonymous Thu Aug 1 09:57:11 2019 No.10854718
File: 12 KB, 200x310, 517272a-i1.jpg [View same] [iqdb] [saucenao] [google]

stupid question. not sure if this even makes sense, more so a piss in the dark. what goes into formalization? how did the nigger in pic go about rediscovering elementary measure theory?

(more generally i am trying to investigate the functions that relate fluid cognition to the dialectic of mathematical reformulation, but i don't expect an answer to such a specific question here, or fucking anywhere. really i am fucked)

>>10848690
what texts deal with analytical arguments for algebraic questions?

>>	Anonymous Thu Aug 1 10:24:19 2019 No.10854770 >>10854718 >how did the nigger in pic go about rediscovering elementary measure theory? He got brain cancer on purpose and it really boosted his brain power for a while.

Anonymous Thu Aug 1 12:06:15 2019 No.10854979

>>10854718
please don't use racial slurs here, this isn't /tv/. i can't stop you, but people on /mg/ tend to be a little more frugal with our language.
elementary measure theory is one of the most obvious possible things you can think of. the instant you see the cantor set for the first time, as an analyst, your first thought should be "well how long is it?" and once you see within 4 seconds that it should have length 0, your second thought should be "can i make one with nonzero length?"
from there, all you need to get basic measure theory and the lebesgue integral is autism and dedication. there are absolutely no creative ideas, except when you get to showing L^p duals and perhaps picking the "right" generality for a measure to capture the dual of the continuous functions on a compact hausdorff space.

Anonymous Thu Aug 1 12:11:24 2019 No.10854993

>>10854718
>>10854979
just to be clear, grothendieck deserves tons of credit for the crazy creative shit he invented to revolutionize algebraic geometry and all fields of math within even the slightest vicinity of it. it's just kind of pathetic that people give him so much credit for the measure theory thing whent there are so many things that are actually insanely impressive.

>>	Anonymous Thu Aug 1 12:12:27 2019 No.10854995 >>10854993 >invented i mean discovered. whoops.

Anonymous Thu Aug 1 12:24:04 2019 No.10855009

>>10854607
Do you mean that whenever we assume the usual order on R, then R has cofinality ω, but whenever we well-order R so that it is isomorphic to some unique ordinal, then the said ordinal has uncountable cofinality?

(And if so, how do we prove the last statement - if I understood your intention?)

Thanks for replying

>>	Anonymous Thu Aug 1 12:30:07 2019 No.10855018 File: 237 KB, 727x868, 1553114966702.jpg [View same] [iqdb] [saucenao] [google] > WEIGHT DISTRIBUTION OF CODEWORDS IN COSETS OF REED MULLER CODES

>>	Anonymous Thu Aug 1 12:34:50 2019 No.10855024 >>10854979 >please don't use racial slurs here Why is /mg/ full of faggots?

Anonymous Thu Aug 1 12:35:15 2019 No.10855025
File: 772 KB, 1280x1280, cover.jpg [View same] [iqdb] [saucenao] [google]

Is there an interesting connection between the homology of a finite group and that of its p-Sylow subgroup? Or is there an interesting application of Shapiro's lemma to such a subgroup scenario?

>>	Anonymous Thu Aug 1 12:37:00 2019 No.10855029 >>10854243 Based leanbro. What projects are you working on?

Anonymous Thu Aug 1 14:19:34 2019 No.10855207

>>10852747
A separable space admits a countable dense subset.
For a cardinality a, an "a-separable" space admits a dense set with cardinality a. This name is made up, and I'm pretty sure there's a better name for it, but it still feels simple enough to get what it is by the name.

I had this autistic proof in my head where you took the countable set, ordered it, and took a series f_n of maps that send the point x to an open set that contains x and doesn't contain all other points up to n. The union of all the images is countable, and simply selecting a point in each open set "should" have given a nice restriction, but I completely fucked up since that union isn't necessarily a base (for intuitive purposes, picture all the rationals except 0, and we just take increasingly smaller sets around them, except the entire thing still doesn't contain zero).
Anyhow, wikipedia confirmed it false, so it wasn't just the proof.
Sorry for bothering.

>>	Anonymous Thu Aug 1 18:15:23 2019 No.10855723 Are there any Monasteries where monks study nature instead some religious texts? I just want to flee from society to do math all day and some manual labour to clear the mind

>>	Anonymous Thu Aug 1 18:17:52 2019 No.10855731 >>10855723 Become a professor and do yardwork when you're at home.

>>	Anonymous Thu Aug 1 18:21:20 2019 No.10855740 >>10855723 Try a Gnostic religion. There's a lot to choose from.

Anonymous Thu Aug 1 18:25:15 2019 No.10855750

>>10855024
Perhaps I might answer your question with a question.
Why the homophobia?
And, along the same lines, why would you make the assumption that a place for smart people contains people who make stupid decisions, merely due to the surroundings of that place (a surrounding, I will admit, in which a number of stupid people make very stupid decisions)?

>>	Anonymous Thu Aug 1 18:26:40 2019 No.10855753 >>10855025 >is there an interesting group theory babble no, purely by the nature of the field

>>	Anonymous Thu Aug 1 18:29:50 2019 No.10855762 >>10855723 Anon, I'll miss you if you leave.

>>	Anonymous Thu Aug 1 18:31:52 2019 No.10855771 >>10855207 >>10855762 I won't miss him.

>>	Anonymous Thu Aug 1 18:32:59 2019 No.10855772 >>10855771 Whoops, I forgot that I was going to respond to this: >>10855207 You're making me fucking angry. Stop invading topology with your disgusting higher cardinality bullshit. Any space that isn't separable isn't worth bothering with.

>>	Anonymous Thu Aug 1 18:40:35 2019 No.10855807 >>10855772 wew lad

>>	Anonymous Thu Aug 1 18:57:07 2019 No.10855853 >>10855750 >/mg/ is for smart people >/sci/ is for smart people >Using certain words affects this in any sense You are a massive faggot.

Anonymous Thu Aug 1 18:58:27 2019 No.10855859

>>10854979
Like you would have come up with the Cantor set independently lmao.
No the Lebesgue integral is not a trivial matter, especially on R. Yes, the theory (of abstract Lebesgue integration) is easy but it is easy because it has been distilled over a half a century. Moreover, the existence of the Lebesgue measure on R is absolutely nontrivial and the construction and proof are clever.
The idea of the inner and outer measures is smart (although, yes, intuitive enough that one could come up with it on their own), and proving that they do define a measure is tricky.
Everything is easy in hindsight when you are merely checking that everything works. Coming up with it on your own, finding the right definitions and the right statements to get what you want is what research is all about

>>	Anonymous Thu Aug 1 19:01:41 2019 No.10855867 >>10855859 Measure theory is unironically trivial if you're a seventeenth century lad working on probability. If anything it's weird that it didn't come from there.

>>	Anonymous Thu Aug 1 19:03:46 2019 No.10855868 >>10854979 please kys

>>	Anonymous Thu Aug 1 19:22:22 2019 No.10855895 File: 201 KB, 422x395, transedence.png [View same] [iqdb] [saucenao] [google] >>10841541 who online has the best coarse on tensors? (also is studied geometric algebra should I study algrabraic geometry next)

Anonymous Thu Aug 1 19:58:54 2019 No.10855990
File: 919 KB, 480x270, livkiss.gif [View same] [iqdb] [saucenao] [google]

>>10855853
>>/mg/ is for smart people
I would argue as much, yes.
>>/sci/ is for smart people
No, I would disagree. This is what I meant by "surroundings" if you had read my post.
>>Using certain words affects this in any sense
Yes, of course it does. If all you did was babble incoherently about mayonnaise, I would have good reason to imagine that you are not intelligent. In a similar sense, one who constantly spews derogatory language when given the opportunity most likely has little self awareness and control. This leads me to believe that they lack a propensity for concentrated study and self-improvement.
>You are a massive faggot.
I'm aware; I am indeed not a heterosexual. But is it really necessary to use such vile language?

Anonymous Thu Aug 1 20:05:37 2019 No.10856012

>>10855990
Not only a massive faggot but you are also fucking autistic. People post here because anonymity lets them not worry about self control/awareness. This place is not a model of usual human interaction. Making a general doesn't change that. Fuck of to discord if you want to pretend to have normal internet """"friends"""".

Anonymous Thu Aug 1 20:06:28 2019 No.10856018
File: 20 KB, 315x499, hartshorne.jpg [View same] [iqdb] [saucenao] [google]

>>10855859
i never said you had to discover the fucking cantor set, lol. i said the first natural question to ask when someone introduces it to you is "how long is it", and in answering this question any freshman will have already created the outer measure. of course they will not go through the painstaking formalism to show it works, but it is anything but a creative idea. coming up with the right definitions is nothing but the result of playing with what you're using for a little bit and seeing what works. sure, you might not capture dirac measures and such the first time, or notions of sigma-finiteness, etcetera. but the general gist of measure theory is extremely intuitive.
i mean come the fuck on dude, measure theory is the obvious foundation for one of the most intuitively accessible types of mathematics, probability. if you go "wow, i know how to compute the probability of an event from a finite set of events... wonder how to do it from an infinite set" you're going to come up with something extremely close to measure theory every time.
stop acting like this is some kind of amazing feat. like i said, there is just so so much more to give grothendieck credit for and the people who give him credit for le epic measure theory meme are people who know very little measure theory.
it's pathetic, stop.
>>10855868
yeah, i'm okay pal. doing just fine.

Anonymous Thu Aug 1 20:12:39 2019 No.10856033
File: 2.32 MB, 500x281, livlook.gif [View same] [iqdb] [saucenao] [google]

>>10856012
>people post here because anonymity lets them not worry about self control/awareness
>references discord
Perhaps you're more acquainted to a board such as /v/, /vg/ or /vp/? Or maybe /tv/? In any case, what you've claimed does indeed often apply to other boards, but I have yet to see it be someone's intent for posting here on /mg/. I doubt you speak for more than a small minority there. I don't claim that anyone here is my "friend." I claim that many of them are capable of upholding fine discussions without resorting to these animal impulses you reference. It's just kind of embarrassing that you carry this banner of "I'm being stupid ON PURPOSE" like it's some kind of badge.
And let's just be honest, if you have to WORRY about self control and self awareness and they don't come naturally, then maybe you aren't the most apt at critical thought.
I really do beg of you, please watch your language should you choose to respond.

Anonymous Thu Aug 1 20:36:06 2019 No.10856077

>>10856033
You and some other autist (who does it for the fucking memes) are the only ones who actually spam
>Why the homophobia XD
All the time. Yes, not every single post has to be a horrible shitpost, but just using certain words are not going to necessarily change the coherence of a post and it's part of this site's culture, like it or not. And so, just using "nigger" or "faggot" or "shit eating, mouth breathing, asspie" will not change much of the meaning. Though obviously you are free to fuck off and not respond to poorly worded and/or offensive posts.

Just because you regularly post here, and we have plenty of discord autists who use this as their only source of interaction, doesn't mean you represent any sort of average. Most serious posts hera are people who got ignored in /sqt/.

Though the reason I call you a faggot and autist is that it's possible that you actually believe your own words and you are judging anonymous posts and the discourse here. It takes a special kind of insecure faggot to care about how other people express themselves, and a special kind of autist to care about it in this type of site.

>>	Anonymous Thu Aug 1 20:43:57 2019 No.10856099 >>10856077 i figured we were both aware we were both screwing with each other, but now you're bringing that up so the facade has vanished guess it's time to talk about math again then

Anonymous Thu Aug 1 20:57:05 2019 No.10856115

>>10856099
K then
>>10856018
Measure theory is extremely intuitive, but it's foundations aren't. In the sense that the axiomatic construction of measures doesn't really illustrate how you can get certain results. I guess like in topology most can be constructed from studying measurable functions, as their properties are what permit you to really define the key objects of the theory, and random variables are just this. But well, the historical development was much more different, as Lebesgue motivation was really just looking for ways to generalize integration to arbitrary subsets.

>>	Anonymous Thu Aug 1 23:11:22 2019 No.10856382 what time of day are you best at maths?

>>	Anonymous Thu Aug 1 23:12:27 2019 No.10856384 >>10856382 at around 8:30-10am i have the best ideas. i'm most productive from 10-12.

>>	Anonymous Thu Aug 1 23:22:43 2019 No.10856402 >>10856384 what time do you get up? do you drink coffee or do anything else that might contribute to that, positively or negatively?

>>	Anonymous Thu Aug 1 23:32:36 2019 No.10856415 >>10856402 lol

Anonymous Thu Aug 1 23:53:44 2019 No.10856444
File: 761 KB, 1200x1486, yukari_lure.png [View same] [iqdb] [saucenao] [google]

>>10851599
>methods in TQFT and Geometric Quantization in order to study quantum gravity I think
The invariants developed with TQFT is not strong enough to detect the geometric details required for quantum gravity. Geometric quantization works well for systems with finite-dimensional gauge groups [math]G[/math] as long as
1. the symplectic manifold is Kahler or hyper-Kahler so you have a holomorphic structure compatible with the symplectic structure and you can do holomorphic quantization, and
2. you can find a moment map [math]M\rightarrow \operatorname{Lie}G[/math] that generates local operators under Kostant central extension.
Both of these fail for gravity outside of dimension 2.
>Mostly because physicists are pretty satisfied with their QFT already
Not when the failure of Borel summability of renormalization series is instantiated in an actual real system like fractional spin-Hall with defect impurities.
>>10853316
Treat the integral as an evaluation of a distribution [math]p \in\mathcal{S}'[/math] on test functions [math]f \in\mathcal{S}[/math]. Use a sequence of [math]C^\infty[/math] functions to approximate [math]p[/math] then prove that [math]p \rightharpoonup \delta[/math] weakly to the Dirac delta.
Alternatively you can use the heat kernel.

Anonymous Thu Aug 1 23:57:01 2019 No.10856448

>>10856402
i typically get up between 8 and 9, and i don't drink coffee. once in a while i have some tea or a smoothie. the main thing is that i go to sleep at around midnight every night, if not 11. i try to stay fairly consistent with that schedule, and i usually find that i'm tired enough to fall asleep by midnight especially when i put work in during the day and then spend the evening doing whatever i like and thinking about problems which i hadn't solved during the day.
it's not hard to keep such a schedule once you get yourself into the pattern, like anything. the thing that's tough is that people like to put off work, and then it's risky to go to sleep and have to finish it in the morning when you might have less time than you'd like. this is solved by just starting on things way earlier than you think you'll need to. such applies to any sort of mathematics (courses, now research, and i would imagine to a degree teaching as well)

>>	Anonymous Thu Aug 1 23:58:17 2019 No.10856452 >>10856444 he already said that some of the most basic shit (orthonormal basis for L^2) was too complicated for him don't bother with weak convergence and distributions.

Anonymous Fri Aug 2 00:02:03 2019 No.10856455

>>10856444
>>10856452
The question specifically said if it was possible to do with more basic tools. Not that I want any fucking proof of Helmholtz theorem. Mainly to see if it can be added into a rigorous calc 3 class without needing distribution theory, functional analysis or pde theory. How can you be this dense?

Anonymous Fri Aug 2 00:09:45 2019 No.10856463

>>10856448
ok, i tend to think best within my first couple hours of waking too, with productivity being at it's highest soon after. interesting. I drink coffee towards the latter portion of my morning / early afternoon (anywhere from 2-4 hours of being awake) and I'm beginning to suspect it detracts from my math ability, but it's a comfy habit nonetheless and helps with other things, maybe.

like you, i also have a second pm session, but it's a little more chill than my morning grind. anyway, ime, there's something especially creative about an early morning brain and late evening brain.

and yeah, regular sleeping schedule is very important. thanks for the detailed reply, I'm just trying to find what helps other /mg/ anons do their best work. of course, basics like diet and exercise help a ton too so I aim for roughly bidaily workouts as well (light am cardio, pm lifting or calinesthetics)

>>	Anonymous Fri Aug 2 00:34:33 2019 No.10856494 File: 121 KB, 960x960, brettlmao.jpg [View same] [iqdb] [saucenao] [google] >>10856455 >uhhh it's for my s-students!!

>>	Anonymous Fri Aug 2 00:36:05 2019 No.10856496 >>10856463 i would imagine that you're even more productive than i am, then, because i don't exercise much. but i do go out and walk quite often.

>>	Anonymous Fri Aug 2 00:36:29 2019 No.10856497 >>10856494 So you don't know?

Anonymous Fri Aug 2 00:44:38 2019 No.10856510

>>10856497
no, i don't, because i don't concern myself with "more basic tools"
when someone says "can you solve this with basic calculus/analysis" of course i immediately think of the most elementary functional analysis concepts. i can't conceive of a person who would need anything simpler than that, if they endeavored to understand the helmholtz theorem to begin with.

Anonymous Fri Aug 2 00:48:48 2019 No.10856516

>>10856510
Then I fucking clarified you autistic retard. I don't give a shit what you concern with, the point is that plenty of physicists start abusing dirac deltas in order to prove this shit and maybe there is a longer but rigorous way using only basic calc (at the level of spivak in terms of rigor and development). I don't understand why you are dickwaving in an underwater weaving forum.

>>	Anonymous Fri Aug 2 02:05:26 2019 No.10856629 >>10856496 well i’m a turbo brainlet trying my best to get off autopilot, so i doubt it, but hopefully i’ll catch up in a couple more years

>>	Anonymous Fri Aug 2 06:22:58 2019 No.10856992 >>10856452 >orthonormal basis The idea wasn't quite that, you just need to show that if <f, grad g>=0 for all g, then f=curl h, or the other one around. I mean, just defining the inner product and showing it's an inner product takes about 5 minutes.

>>	Anonymous Fri Aug 2 08:34:34 2019 No.10857149 >>10856516 saying i understand elementary undergraduate mathematics which both of us understand is not "dickwaving." it's standard.

>>	Anonymous Fri Aug 2 08:40:47 2019 No.10857165 >>10856992 yeah you're right, but i'm sure inner products are too complex for that other guy to understand.

>>	Anonymous Fri Aug 2 10:18:02 2019 No.10857362 >>10857149 >>10857165 This is some serious autism.

Anonymous Fri Aug 2 14:44:50 2019 No.10858165
File: 50 KB, 613x925, Screenshot_20190802_134312.png [View same] [iqdb] [saucenao] [google]

I always felt that a big motivation for functional analysis was calculus of variations, but even modern graduate books seem to not use of it's results fully. I was surprised when reading pic related, that in the brief part that mentions clasical actions and all that stuff, that it actually makes an analysis of the problem using Sobolev spaces, Lp spaces in general and abstract measure theory which was kinda a huge relief. It even mentions the frechet derivative which I always wanted to use and I could prove E-L in it's functional form with the direct definition and basic measure theory. Is there a book that takes this approach to calculus of variations?

Anonymous Fri Aug 2 14:48:37 2019 No.10858176

>>10858165
Maybe I want to mention that the book makes a huge assumption on the type of lagrangian, because it has a particular endgoal. I suppose I'm interested in a theory of infinite dimensional calculus and see what works and what doesn't, or precisely how restrictive or general are the classical C.o.V problems.

>>	Anonymous Fri Aug 2 17:33:36 2019 No.10858620 >>10857362 >everyone who is making fun of me has autism!!!! aaaahahahahahahahahahahaa!!!!

>>	Anonymous Fri Aug 2 17:35:03 2019 No.10858625 >>10858165 >>10858176 i... i don't understand how anyone would develop any calculus of variations without all of those tools... what kind of physishit garbage have you been reading?!

Anonymous Fri Aug 2 17:53:01 2019 No.10858661
File: 17 KB, 300x302, image823.png [View same] [iqdb] [saucenao] [google]

[math] (\mathbb{Z},+,\cdot) [/math] is initial in <b>Rng</b> and [math] (\{e\},\circ) [/math] is initial in <b>Grp</b>. And there is a forgetful functor
[math] F:\textbf{Rng} \to \textbf{Grp} [/math] which sends [math] (\mathbb{Z},+,\cdot) [/math] to [math] (\mathbb{Z},+) [/math]. But shouldn't a functor send intial objects to initial objects?

Anonymous Fri Aug 2 18:16:37 2019 No.10858707
File: 40 KB, 1070x1236, my three dollar mouse.png [View same] [iqdb] [saucenao] [google]

>>10858661
Consider the inclusion of [math]\mathcal{A}[/math] into [math]\mathcal{B}[/math].
You can check the entire thing manually in five minutes if you feel the need to.

>>	Anonymous Fri Aug 2 18:25:06 2019 No.10858725 >>10858707 Ah, stupid me, thx.

>>	Anonymous Fri Aug 2 18:32:10 2019 No.10858750 >>10858725 >le stoopid me :3 hehe im so weak and helpless >th-thanks senpai >if i announce that im an idiot it relieves me of the burden of being an idiot please stop doing this thanks

>>	Anonymous Fri Aug 2 19:18:12 2019 No.10858874 >>10858750 Fuck off, I like it when stupid anons thank me.

>>	Anonymous Fri Aug 2 19:20:38 2019 No.10858881 >>10858874 You are part of the problem

>>	Anonymous Fri Aug 2 19:54:03 2019 No.10858994 >>10858661 >But shouldn't a functor send intial objects to initial objects? Why would you just assume this about a functor?

>>	Anonymous Fri Aug 2 20:08:40 2019 No.10859025 Can anyone refer me to the naisu results about the sizes of the images of single variable polynomials on finite fields with n elements? Should I just read up on elliptic curves and arithmetic geometry?

Anonymous Sat Aug 3 00:28:33 2019 No.10859535
File: 402 KB, 1080x1920, Screenshot_20190803-132616.png [View same] [iqdb] [saucenao] [google]

Guys, any tip on getting started toward a vague understanding of Riemannian manifolds?
I did OK in linear algebra back in undergrad but this stuff here is new to me.

>>	Anonymous Sat Aug 3 00:36:10 2019 No.10859551 >>10859535 have iq

>>	Anonymous Sat Aug 3 00:39:59 2019 No.10859559 >>10859551 Ok, now what?

>>	Anonymous Sat Aug 3 03:51:53 2019 No.10859865 >>10859535 Read John Lee’s book Riemannian Manifolds: An Introduction to Curvature

>>	Anonymous Sat Aug 3 06:00:49 2019 No.10860037 >>10841625 Von Neumann, no question.

>>	Anonymous Sat Aug 3 11:44:19 2019 No.10860744 File: 1.83 MB, 1600x900, sin_city_3.png [View same] [iqdb] [saucenao] [google] >>10852528

>>	Anonymous Sat Aug 3 20:25:53 2019 No.10861837 Any good video series for Elementary Analysis?

Anonymous Sat Aug 3 20:34:30 2019 No.10861845

>>10841541

Does an unique analytical solution to a set a of differential equations imply that the system is an actual natural phenomena, eg. the prey predator model is an oversimplification, or is it the other way around where only those systems which cannot be analytically solved are actual physical phenomena?

>>	Anonymous Sat Aug 3 20:41:10 2019 No.10861853 David Gregory Ebin.

>>	Anonymous Sat Aug 3 21:12:35 2019 No.10861903 >>10852528 >cis wow that's pretty exclusionary

>>	Anonymous Sat Aug 3 21:50:05 2019 No.10861956 >>10858625 You can develop plenty of C.O.V with just regular calculus and thd fundamental lemma.

>>	Anonymous Sat Aug 3 22:08:01 2019 No.10861984 File: 291 KB, 640x550, yukari_smile3.png [View same] [iqdb] [saucenao] [google] >>10858165 Brezis.

>>	Anonymous Sat Aug 3 22:58:20 2019 No.10862044 How do I solve this problem? [math] S_{n+1}={S_n-1\over{x^{2n-3}}}\\S_1=\lim_{n->\infty}S_n [/math]

>>	Anonymous Sat Aug 3 23:05:41 2019 No.10862055 >>10862044 I was trying to solve [math]\sum^\infty_{n=0}x^{n^2}[/math] And that recursion came out as a way to represent S_1 in terms of itself

>>	Anonymous Sun Aug 4 00:12:16 2019 No.10862161 >>10861984 fuck off avatarfag might as well put a tripcode and announce your faggotry to the chans

>>	Anonymous Sun Aug 4 05:05:08 2019 No.10862554 File: 49 KB, 572x646, INTERVIEW.png [View same] [iqdb] [saucenao] [google] can /sci/ pass this interview?

>>	Anonymous Sun Aug 4 08:02:55 2019 No.10862857 >>10862554 Probably. I'm not sure I'd be able to solve the third degree polynomial to get the eigenvalue since I haven't memorised Cardano's and will hardly derivate it on the spot.

>>	Anonymous Sun Aug 4 09:01:03 2019 No.10862925 >>10862554 I'm not sure how to solve the second differential equation in the second last paragraph.

>>	Anonymous Sun Aug 4 09:35:38 2019 No.10862964 >>10862554 What company? The questions don't have a whole lot of depth and a guy with a Bachelor's in Math should be able to answer all of those provided he actually did well in his courses.

>>	Anonymous Sun Aug 4 12:07:25 2019 No.10863190 >>10862964 probably tech

>>	Anonymous Sun Aug 4 18:14:09 2019 No.10863852 None of you could solve this AAAA=16 BBBB=16 CCCC=1 DDDD= -2 ABBA = 20 BAAB = 14 AAAB = 14 BBBA = 32 ADDD = 3 ADDA = 0 ACCC = 5 CCDC = 0 DDCD = -1 ABCD = 6 DDDBBBAAACCC = ?

Advanced search
Text to find
Subject [?]Search by post subject. Leave empty for any.
Username [?]Search for user name. Leave empty for any user name.
Tripcode [?]Search for tripcode. Leave empty for any.
Email [?]Search by email. Leave empty for any.
Filename [?]Search by image filename. Leave empty for any.
From Date [?]Enter what date to start searching from. Format is YYYY-MM-DD
To Date [?]Enter what date to start searching until. Format is YYYY-MM-DD
Image hash
Search in	All Posts OPs Only
Deleted posts	Show all posts Show only deleted posts Only show non-deleted posts
Internal posts	Show all posts Show only internal posts Show only archived posts
Order	New posts first Old posts first
Capcode	All Posts Only by Users Only by Mods Only by Admins Only by Developers
Results	Posts Threads
Action	[ Simple ]