/mg/ maths general: Manin edition

[Anonymous No.9837232]

talk maths, formerly >>9825089

https://arxiv.org/pdf/1806.10801.pdf
>Homotopy types and geometries below Spec Z
>Yuri I. Manin, Matilde Marcolli
>(Submitted on 28 Jun 2018)
>After the first heuristic ideas about `the field of one element' F_1 and `geometry in characteristics 1' >(J.~Tits, C.~Deninger, M.~Kapranov, A.~Smirnov et al.), there were developed several general approaches to the construction of `geometries below Spec Z'. Homotopy theory and the `the brave new algebra' were taking more and more important places in these developments, systematically explored by B.~To\"en and M.~Vaqui\'e, among others.
>This article contains a brief survey and some new results on counting problems in this context, including various approaches to zeta--functions and generalised scissors congruences.

[Anonymous No.9837437]

>>9832700

Why? Can someone explain why those books might be a better choice for learning linear algebra?

[Anonymous No.9838021]

Great general

[Anonymous No.9838085]

math aint a /sci/ence

[Anonymous No.9838094]

[eqn]\sf\color{red}{Gook}\; \color{orange{moot}\; \color{yellow}{\bb STILL}\; \color{green}{hasn't}\; \color{cyan}{fixed}\; \color{blue}{the}\; \color{indigo}\TeX\; \color{violet}{tags}[/eqn]

[Anonymous No.9838103]

>>9838085
Nobody cares. The board is for science AND math, so kys you're shelf.

[Anonymous No.9838123]

>>9838103
Did you kiss your mother with that mouth?

[Anonymous No.9838125]

>>9838123
I've never kissed any of my relatives. Only my boyfriends.

[Anonymous No.9838336]

Can you guys help me? I'm losing love for math, undergraduate books are tiresome(I'm tired of reading the same shit in 1000 different books, yes I know what a set is) and I'm not mathematically mature enough for most graduate level books.

Is there a middle of the road? Can you guys recommend me math books(pure) that can help me make this bridge from undergraduate do graduate stuff?

[Anonymous No.9838351]

>>9838336
>I'm tired of reading the same shit in 1000 different books, yes I know what a set is
Did you read chapter 2?

[Anonymous No.9838360]

>>9838351
Didn't bother, here's why:
If the first chapter is the same in every undergrad book, then how the hell can chapters 2 differ, if they are supposed to follow logically from chapters 1?

[Anonymous No.9838362]

>>9838351

kek, yes I did. What I was trying to convey is that I've been reading a lot of books that stay in a very limited number of topics that generally overlap to much. I'm asking for books that go a little further than the basics of Analysis/Algebra/Topology

[Anonymous No.9838366]

>>9838362
What do you mean basics? Once you finish an undergrad book, read a grad book. There's nothing inbetween. Although for reading advanced books it usually helps to have familiarity with multiple subfields.

[Anonymous No.9838367]

>>9836908
>>9836909
I don't think that they require DELF (though you should probably check it out, I don't know) and in the case of Paris VI, where I did my M2, you don't need to be fluent in French.
The professors will switch to English whenever there is a non-francophone student in the class.

[Anonymous No.9838372]

>>9838366

ok, can you recommend graduate level books for someone that is starting a graduate course? Beginning graduate level stuff is what I'm looking for.

[Anonymous No.9838375]

>>9838367
That being the case, I would still advise to learn at least some French because in most other aspects of practical life, you will have to deal with people who don't speak English, and some may be kind of dicks about it ("customer is always right" is not really the way we do things here).

[Anonymous No.9838378]

>>9838372
Follow your uni's recommended books. Or if you feel they are too easy/basic, check out the books in the /sci/ wiki

[Anonymous No.9838385]

>>9838336
Read the AMS Student Mathematical Library series. They are designed to provide introductions to various advanced topics in a way that is intelligible to motivated undergrads. Of course, they are no substitutes for actually learning the subject in depth, but they can motivate you to learn things, and see some tools that you have learned about in action.

[Anonymous No.9838408]

>>9838385

thanks for the recomendation, will read em

[Anonymous No.9838423]

>>9838336
I really liked Aluffi's algebra chapter 0. It kind of implicitly assumes some familiarity with undergraduate abstract algebra, but it goes from the beginning starting with set theory (which is not ideal in your case) but it quickly turns to categories and describes algebra in a very modern way, which makes it quite compatible as a bridging book.

[Anonymous No.9838437]

>>9838360
>If the first chapter is the same in every undergrad book, then how the hell can chapters 2 differ, if they are supposed to follow logically from chapters 1?

[Anonymous No.9838444]

What is the standard Numerical Analysis Textbook? UCLA's list has some old-ass books so not sure when the last time they updated that list was.

[Anonymous No.9838459]

How do we save the EU for mathematics?

[Anonymous No.9838463]

>>9838367
So the University of Paris does NOT require French if you just pick the right number? Tres bon if true!

[Anonymous No.9838501]

Just got this, am I about to get memed?

[Anonymous No.9838514]

>>9838501
you've already been memed

[Anonymous No.9838515]

>>9838501
You already did if you bought a free book.

[Anonymous No.9838517]

>>9838501
>Just got this, am I about to get memed?
Why don't you read it and find out?

[Anonymous No.9838521]

>>9838514
Is HTT specifically a meme or is foundations in general a meme?

>>9838515
I didn't buy it, I mentioned I was interested in it to a professor and he lent me his copy.

[Anonymous No.9838522]

>>9838521
>is foundations in general a meme
This.

[Anonymous No.9838543]

>>9838521
>I didn't buy it, I mentioned I was interested in it to a professor and he lent me his copy.
Keep it for a few weeks and then return it to him. It will make him seem less of an idiot when even dropouts and other shit folk on /sci/ know that book is just pure autism.

[Anonymous No.9838941]

>>9838521
Ignore these fags. Brainlets can't appreciate the beauty of foundational mathematics.

[Anonymous No.9839003]

>>9838501
Any HoTT theorists here who can give me the rundown on type theory from Russel to today? Seems interesting and I'd like to learn some more theoretical computer science.

[Anonymous No.9839034]

>>9839003
What's your background?
Do you know formal logic, set theory, lambda calculus, Curry-Howard?

Here's an excellent text

https://www.cs.kent.ac.uk/people/staff/sjt/TTFP/ttfp.pdf

The guy who bought the HoTT book out of the blue should certainly also start here.

[Anonymous No.9839056]

>>9838463
Not that I know of

[Anonymous No.9839413]

>>9837437
bump

[Anonymous No.9839706]

IUT is a joke, just like Anon's future.

[Anonymous No.9839778]

>>9837232
HONONONONONONONONONONONONOHAHAHAHAHAHAHAHAHAHAHAHAHAHAHHAHAHAHAHAHAHHA_WILDERBERGER.JPG

[Anonymous No.9839834]

>>9839778
What does this have to do with Wildberger.

[Anonymous No.9840171]

I'm a cs and physics double major and since my school doesn't allow triple majors, I'm trying to self study pure math as hobby. I finished book of proofs and my prof recommended this book to me. R8 this book.please.

[Anonymous No.9840645]

How do I write proofs?

[Anonymous No.9840683]

>>9840645
1. Start with premise
2. Infer
3. ???
4. Profit

[Anonymous No.9840704]

>>9840645
With a pen on a paper. Using the alphabet you are familiar with.

[Anonymous No.9840705]

>>9840645
>How do I write proofs?
https://en.wikipedia.org/wiki/Coq

[Anonymous No.9840788]

>>9840171

your school doesn't allow triple majors? at my school, as long as your gpa meets a certain requirement, you can pile on as many majors as you want

[Anonymous No.9840957]

any cool topics of research related to healthcare?

[Anonymous No.9841145]

>>9840171
https://www.ocf.berkeley.edu/~abhishek/chicmath.htm
http://4chan-science.wikia.com/wiki/Mathematics
https://pastebin.com/raw/SF6JbbAK
This might help you, friend.

[Anonymous No.9841155]

WHAT'S THE FASTEST WAY TO LEARN TRIG WHAT THE FUCK HOW AM I SUPPOSED TO DO THOSE CRAZY INTEGRALS GUYS HELP ME I'VE BUILT A HOUSE ON A SHAKY FOUNDATION AAAAAAAAAAAAAAAAAAAAAA

[The Lord No.9841161]

Derivation of the Limits of Sine and Cosine at Infinity
http://www.vixra.org/abs/1806.0082

[Anonymous No.9841198]

>>9841155
Fast route is to memorize a trig identity sheet but it's just gonna bite you in the ass again later

[Anonymous No.9841206]

>>9841161
If you're going to make up nonsense at least collect like terms

[Anonymous No.9841275]

>>9841198
I'm calmer now, I'll just read some books on trigonometry.

[Anonymous No.9841455]

>>9838336
Given that you understand the basics of Topology, Analysis, and Algebra, I would recommend you look at the more advanced sections of your undergrad books and try to figure out something more advanced which you want to learn. Find buzzwords and wikipedia them until you find something that catches your fancy. At least for me, you need to have a goal, a source of motivation to slog through the theorems and proofs because quite frankly, reading textbooks is boring. So, pick something that's beyond your understanding but can at least get the gist of what its about and then sort of patch your understanding up to that thing. Also, for the thing you want to learn, just pick a theorem and work solely on understanding why that theorem is true. Learn everything required to learn that theorem. Here's a secret: there's no reason to learn every single theorem in a book. Just learn what you need to learn for your goal. Then, when you need to go back, it's easy to patch up what you missed.

I'm a PhD student in math and have reached the point where this is the only viable way for me to learn math. Because of that, I retain significant more motivation than ever before to learn new math because everything I learn now is directed by a goal of understanding specific at the end.

[Anonymous No.9841610]

>>9841155
[math] (\cos(x),\sin(x)) [/math] is the point on the unit circle when you have covered distance x on it, starting from (1,0).
This is literally all there is conceptually. It's simple as fuck.
For example, why is [math] \cos^2(x)+\sin^2(x) [/math] always equal to 1? It's because (by definition) [math] (\cos(x),\sin(x)) [/math] is always on the unit circle which means (by definition) that it has length equal to 1.

The identities can all be derived by using the following:
[math]
e^{ix}=\cos(x)+i\sin(x)\\
e^{i(x+y)}= e^{ix} e^{iy}\\
\tan(x)=\frac{\sin(x)}{cos(x)}
[/math]

[Anonymous No.9841979]

>>9841455
Not op but thanks desu

[Anonymous No.9842283]

>>9841455
>Here's a secret: there's no reason to learn every single theorem in a book.
New PhD student here. I'm really having trouble switching to that mindset, though I know it's not realistic to try to read books cover to cover. How do you not get overwhelmed by the stuff you don't know when reading the sections you need if you didn't take the time to think about the proofs ?

[Anonymous No.9842434]

Am I insane or do mathbb letters have colors associated to them.

I have no idea where I got this in my head, but for some reason Z should be green, F should be red, S should be yellow, Q should be beigeish, N should be gray.

Where did these associations come from? Did I just make them up?

[Anonymous No.9842448]

>>9842434
Synesthesia.

[Anonymous No.9842502]

>>9842434

pretty sure that's a sign you might be a homo

[Anonymous No.9842576]

Is anyone interested in a group reading of Chitikila Musili's book on algebraic geometry and compiling a document with errata and some solution to exercises?

[Anonymous No.9842587]

>>9842576
>Indian author
dropped

[Anonymous No.9842589]

>>9842576
Did Musili tell you to compile an errata document and now you are trying to outsource it?

[Anonymous No.9842741]

>>9842448
I think you're right. I started thinking about it and realized I can instantly associate a color to pretty much every letter.

[Anonymous No.9842745]

>>9838336

Pick the ones with the yellow covers. That's when you know their not fucking around.

[Anonymous No.9842760]

>>9842741
Being wrong isn't my style.

[Anonymous No.9842797]

>>9842283
>>9842283
Sounds like you have trouble with tolerating ambiguity. It might be too late for you. The fact that you were previously reading books cover to cover makes it sound like you haven't ever grappled with solving any problems for any length of time. You're starting to get to the point where all the problems that you should have not looked up, you did, so now there are no easy problems for you to spend time getting used to that feeling of frustration and unknown. Since you never developed this courage and resilience, you're like a person who has spent the last 4 years reading books about painting and now you're about to start painting and expecting too much out of yourself.

I'll try not to be too mean though, just remember that something can only ever be new once. The first time you see something just plow through it anyways and get some kind of big picture, blurry overview at least to get the general proportions down of how the concepts are roughly connected together. Then from there you can begin to better inspect how the pieces glue together and what the edges are like. Another thing, If you've ever driven a car, you don't have to know how an engine works to get somewhere. At the end of the day, what are you striving for?

[Anonymous No.9842814]

>>9838360
First chapters explain where a pussy is on the body. But each pussy smells a little different.

[Anonymous No.9842852]

>>9842589
Musili is long dead. The reason behind this proposal is that I looked for an errata and didn't find it, it is a personal thing but I thought maybe someone else is up to a refresh and would like company as I do. Say it is out of boredom and loneliness, no sense of accomplishment and things like that. I'm actually up to anything, but I had this book on the list.

[Anonymous No.9842871]

>>9842852
I see. I like your idea.

[Anonymous No.9842878]

Remember Atiyah's 2016 paper about there being no complex structure on S^6, but some people didn't like the proof?
https://arxiv.org/abs/1610.09366

He came back with an update:
https://books.google.ca/books?id=lZRdDwAAQBAJ&pg=PA128&redir_esc=y#v=onepage&q&f=false
https://mathoverflow.net/questions/304071/atiyahs-may-2018-paper-on-the-6-sphere

[Anonymous No.9842904]

>>9842434
You are literally insane. N is obviously a navy blue.

[Anonymous No.9842908]

>>9842878
Thank you, based Atiyah.

[Anonymous No.9842910]

Can someone tell me what the bottom formula in pic related means in plain English? Retard-friendly if possible.

[Anonymous No.9842916]

>>9842910
It's a normal distribution with the normalization factor that's missing...

[Anonymous No.9842952]

>>9842797
Well said. A way I used to get used to this kind of thinking was that I read the chapter first without paying too much attention to details and then moved onto the problems. Solving those forced me to look at the results presented so far and trying to figure out which ones I needed to prove the given claim. I suggest trying this to >>9842283 if he has time for such activity.

[Anonymous No.9843040]

>>9842878
>4-spheres has exotic smooth structures
>2-sphere is not parallelizable
>now 6-spheres don't have complex structures
What the FUCK do we do now??

[Anonymous No.9843077]

I hate this general.

[Anonymous No.9843162]

>>9839413
Axler's exclusion of determinants, while legitimate, is not consistent with literally every other linear algera course and courses that use determinants like vector analysis.

Lang is pure shit. I have heard good things about Hoffman and Kunze, that they cover a lot more material than other texts while starting each chapter off simply then adding rigor at a nice pace.

I learned linear algebra with Friedberg, Insel, and Spence and it's probably my favorite undergrad text so far but expect a lot more out of you in terms of proofs. There's also a solution manual online.

[Anonymous No.9843209]

>>9840705
*blocks your path*
https://leanprover.github.io/

[Anonymous No.9843224]

>>9842910
>SVM kernel
kek
exp is just the function which is the exponentiation of e (https://en.wikipedia.org/wiki/Exponential_function).).
If you don't know what the exponential function or the normal distribution is then you're going to have a hard time with SVM/machine learning.
Chapter 2 of bishop should explain this stuff in a way relevant to what you're doing.
http://users.isr.ist.utl.pt/~wurmd/Livros/school/Bishop%20-%20Pattern%20Recognition%20And%20Machine%20Learning%20-%20Springer%20%202006.pdf

[Anonymous No.9843234]

>>9842910
Think of k as a measure of similarity between x_i and x_j.
The (euclidean) distance between the two is used as the x value for a function like pic related, and k is the y value.

[Anonymous No.9843339]

>>9841275
Dope, that's the way to go

[Anonymous No.9843646]

>>9843040
Did your physical intuition fail you?

[Anonymous No.9843666]

>>9842434
N is red, Z is grey, Q is blue/purple, R is black, C is yellow/orange, F is green, S is yellow.

[Anonymous No.9843687]

>>9842908
What the hell am I looking at?

[Anonymous No.9843695]

>>9843687
The Euler of our time

[Anonymous No.9844023]

Does the average PhD students in math still struggles with High school Mathematical Olympiads questions?

[Anonymous No.9844038]

>>9844023
Probably. Thank you for reminding me about the IMO

>http://www.imo2018.org/
>site isn't working
Fucking gypsies...

[Anonymous No.9844045]

>>9844038
? It works just fine for me.

[Anonymous No.9844046]

>>9840645
I use UML to write diagrams, then type it out for brainlets (a.k.a. supervisors) to understand.

[Anonymous No.9844051]

>>9844045
Really? I get a
>This Domain Name Has Expired - Renewal Instructions.
generic page on my end.

Pic related.

[Anonymous No.9844057]

>>9844051
Yup. Try using a vpn.

[Anonymous No.9844093]

>>9844023
I probably would, but I didn't start applying myself until second year of grad school. Most of the smart grad students I've met did all the extra shit since middle school, and study for fun.

[Anonymous No.9844131]

>IMO
Anyone seen this https://www.imdb.com/title/tt3149038/ ?
How cringe is it?

[Anonymous No.9844161]

>>9837232
I got a quadrature scheme of order [math] k [/math] with nodes [math] x_1,...,x_n \in [0,1] [/math] and weights [math] w_1,...,w_n [/math]
such that
[math] \sum_i w_if(x_i) = \int_0^1 f(x) dx+ c\cdot f^{(k)}(\xi) [/math]
for some [math] \xi \in [0,1] [/math]

The quadrature scheme has an underlying interpolation polynomial [math] p_f [/math], such that [math] p_f(x_i) = f(x_i) [/math] for all [math]i = 1,...,n [/math] such that [math] \sum_i w_if(x_i) = \int_0^1 p_f(x) dx [/math]

Now I want to show that the arc length of [math] p_f [/math] is also an approximation of order [math] k [/math] to the arc length of [math] f [/math], in the sense that

[math] = \int_0^1 \sqrt{1+f'(x)} dx =\int_0^1 \sqrt{1+p_f'(x)} dx+ c\cdot f^{(k)}(\xi) [/math]

I have numerically verified that this seems to be the case, but am stuck on the proof.

[Anonymous No.9844460]

>>9844023
yes

[Anonymous No.9844546]

>>9843162
what about strang?

[Anonymous No.9844628]

>>9844131
It’s pretty meh

[Anonymous No.9844642]

>>9844023
The whole game of the IMO is that the writers submit problems that are engineered to be solved by some combination of 1-3 tricks, and your job is to figure out what tricks are needed. If you don't have a large enough toolbox of tricks you're simply not going to have any idea what to do with a lot of them.
There's a reason all the kids who succeed at them spends hundreds of hours practicing old problems and going to training sessions.

[Anonymous No.9844700]

>>9844642
Those tricks are of great values. What’s important here is the attempts in solving the problems, even if they’re unsuccessful. The Poincare Conjecture wouldn’t be solved if Perelman hadn’t use Ricci flow trick.

[Anonymous No.9844900]

https://web.archive.org/web/20170423133403/https://crazyproject.wordpress.com/aadf/
This website contains most solution to Dummit Foote Abstract Algebra book. Are there anymore website like this but for different math books?

[Anonymous No.9844904]

https://arxiv.org/pdf/1807.00797.pdf
>Black holes and class groups
>Nathan Benjamin, Shamit Kachru, Ken Ono, Larry Rolen
>(Submitted on 2 Jul 2018)
>The theory of quadratic forms and class numbers has connections to many classical problems in number theory. Recently, class numbers have appeared in the study of black holes in string theory. We describe this connection and raise questions in the hope of inspiring new collaborations between number theorists and physicists.

[Anonymous No.9844927]

>>9844904
Threadly reminder to work with physicists.

[Anonymous No.9845039]

>>9844927
I don’t understand this meme. They’re both seems like they couldn’t solve shit.

[Anonymous No.9845075]

>>9844700
>Those tricks are of great values
This is bullshit.

I'm not arguing with you that there is value in learning to work IMO problems, and high schoolers do learn some useful math skills from it (the canonical inequalities are heavily covered, you become extremely adept at inducting and elementary combinatorics, stuff like that) but you cannot possibly tell me there is "great value" in knowing a bunch of substitutions for 3-variable cyclic inequalities or how Vieta jumping works is good for anything other than olympiad problems.

[Anonymous No.9845246]

have mathematicians statistically measured the best mathematicians like a statistically best mathematician?

[Anonymous No.9845250]

>>9845246
That's dumb

[Anonymous No.9845253]

>>9845246
knock yourself out bud
https://en.wikipedia.org/wiki/Erd%C5%91s_number

[Anonymous No.9845324]

>>9844161
taylor expansion, brainlet

[Anonymous No.9845484]

>>9844904
>>9844927
Unironically fuck off. Black holes don't exist.

[Anonymous No.9845489]

>>9845484
>Black holes don't exist.
What do you mean?

[Anonymous No.9845496]

Please help I am brainlet

I'm solving polynomials

I have the equation

3x^2-18x-48=0

I first factor out the 3

So I get 3(x^2-6x-16)

The software I'm using tells me to factor out a three and I get completely lost.

It ends up 3(x+2)(x-8)

Can someone explain how you factor out a 3 from 3(x^2-6x-16) and how you end up with the above 3(x+2)(x-8)

I understand how to solve from that point, I just don't get how they got there

[Anonymous No.9845507]

>>9845496
End your fucking existence if you can’t even solve a simple fucking quadratic equation

[Anonymous No.9845516]

>>9845507
>>9845496
nvm, I understand now.

The wording confused me with a factoring out a three.

[Anonymous No.9845524]

>>9845496
I'm not an english native speaker, but we call it "finding the nullpoints". Your equation can be written like "ax^2+bx+c. You find nullpoints when your equation is 0. So you use the well known formula [-b+-sqrt(b^2+4ac)]/2. When you solve your equation you get 8 and -2. Try it out.

[Anonymous No.9845530]

>>9845524
This is the brainlet way of solving the quadratic, a non-brainlet just notices that 2-8=-6 and 2*(-8)=-16 so x^2-6x-16=(x+2)(x-8)

[Anonymous No.9845538]

>>9845530
This guy thinks.

[Anonymous No.9845546]

>>9845530
That's because the numbers are "nice". sometimes it might have ugly numbers and you will have to write it down. I'm giving him the brainlet way because not even brainlets could fuck that up.

[Anonymous No.9845558]

>mfw I spent years thinking Banach spaces and Hilbert spaces were some 2000IQ+ tier elite math shit
>finally get to babby's first functional analysis class
>It's just more fucking norms and vector spaces
>mfw

[Anonymous No.9845564]

>>9845558
same thing for c*algebras, but they are my limits

[Anonymous No.9845570]

>>9845558
How silly.

[Anonymous No.9845577]

>>9845524
wtf x^2+1 has roots +-1 now
>>9845546
>not even brainlets could fuck that up

[Anonymous No.9845708]

Is computer science harder than maths guys?

[Anonymous No.9845752]

>>9845708
Yes, math is built on the foundation of computer science.

[Anonymous No.9845780]

>>9845752
>Yes, math is built on the foundation of computer science.
Other way around.

[Anonymous No.9845822]

>>9845780
You must be fun at parties

[Anonymous No.9845824]

Anyone have other insecure mathoverflow/stackexchange posts? They're fun to read

https://mathoverflow.net/questions/289259/the-derived-drift-is-pretty-unsatisfying-and-dangerous-to-category-theory-or

[Anonymous No.9845868]

>>9845824
The suicidal thoughts of anime brainlets are a lot funnier to read.

[Anonymous No.9845890]

>>9845822
Yeah, saying things like "The Earth is flat", "Einstein was wrong", "Holocaust didn't happen" is probably a hoot at every party that you go to.

[Anonymous No.9846012]

>>9845577
Try again. That function shouldn't even touch the x axis. That means your solution is a complex number. In this case it is +-i. Don't be discouraged if you feel like a brainlet, you just have to go slow at first.

[Anonymous No.9846018]

>>9846012
go back to your original post and look closely at what you wrote retardo

[Anonymous No.9846019]

>>9844546
bump

[Anonymous No.9846175]

>>9844900
I don't know about websites. Online you can find pdf with solutions to exercises from Atiyah, or books with exercises and solutions such as Altman's. Also, as you probably know, there is MSE.

[Anonymous No.9846185]

>>9846018
That post was obviously wrong. It's -4ac.

[Anonymous No.9846186]

>>9846185
still forgetting something

[Anonymous No.9846194]

>>9844546
Strang is engineering-tier.

[Anonymous No.9846366]

>>9845489
Exactly what I said.

[Anonymous No.9846370]

>>9844900
munkres topology
https://dbfin.com/topology/munkres/
https://drexel28.wordpress.com/tag/munkres/

atiyah's commutative algebra
https://dangtuanhiep.files.wordpress.com/2008/09/papaioannoua_solutions_to_atiyah.pdf

[Anonymous No.9846376]

>>9845824
literally all the responses to Cleo's posts or the meta posts aimed at >her

[Anonymous No.9846463]

>>9846376
Who's Cleo?

[Anonymous No.9846468]

>>9846463
newfag

[Anonymous No.9846476]

>>9846468
see
>>9846463

[Anonymous No.9846486]

>>9846476
see
>>9846468

[Anonymous No.9846491]

>>9846463
>Who's Cleo?
https://math.stackexchange.com/users/97378/cleo

[Anonymous No.9846492]

>>9846486
I asked a question. Please answer it, faggot.

[Anonymous No.9846497]

>>9846491
Ah, a stackexchange user.

[Anonymous No.9846503]

>>9846497
just browse by highest voted answers for maximum keks

[Anonymous No.9846551]

Suppose i have 1000 sets containing A and or B and or C. Suppose i know the quantities of {AB}, {AC}, {BC}, {A} (just A), {B}, {C}, and {ABC}. what statistical test would i use to determine the significance of the relationship between the pairs and between the three?
For example, to be able to predict if a set containing A will also contain B, or B and C, etc?

[Anonymous No.9846560]

>>9845890
>implying the earth is round and the holocaust happened.

[Anonymous No.9846612]

>>9846551
chi-squared

[Anonymous No.9846633]

>>9845484
>Black holes don't exist.
This

[Anonymous No.9846642]

How hard compared to in person cal 2 would an online linear algebra class be from the same school?

[Anonymous No.9846785]

>>9846642
>>>/sci/sqt

[Anonymous No.9846807]

>>9846612
independence or the other one?

[Anonymous No.9847419]

Let's say I have a differential equation on the format:

y'' +k*y=0 (for this example, let's just assume k>0)

Wherever I look, it is always said that k must be n2, n=0, 1, 2..., for this function to be periodic in 2pi. I'm not sure if I'm just experiencing a huge brainlet moment or what but why the fuck does it need to be so? wouldn't any k make it periodic, since the solution will be linear combination of sine and cosine anyways?

[Anonymous No.9847423]

>>9847419
Oh, I get it now. The period will be 2pi/sqrt(k) which will only be 2pi periodic if sqrt(k) is an integer. Sorry for wasting two posts on this thread

[Anonymous No.9847502]

>>9837232

Is there a good textbook that presents multilinear algebras (especially exterior algebra) in a unified framework? Preferably with strong geometric developments.

[Anonymous No.9847585]

>>9847502
>geometric
>>>/x/

[Anonymous No.9847589]

>>9847502
Winitzki's Linear algebra via exterior product should present almost anything in a very elementary way. The discussion is limited to linear/multilinear algebra, but it has the merit of presenting all usual operators (contraction, Hodge's star and so forth), which I don't see in many other books.
Multilinear algebra is used everywhere, differential geometry, Hodge theory, algebraic geometry, algebra etc, so if your question was if there is a decent book that includes all of that I'm quite positive there isn't, you should refer to different books according to your needs.

[Anonymous No.9847591]

>>9847585
Don't be an asshole Anon.

[Anonymous No.9847593]

>>9847591
>Don't be an asshole Anon.
I'm not an "asshole".

[Anonymous No.9847694]

>>9847593
You're a sphincter. Same shit.

[Anonymous No.9847713]

>>9847589
Thank you. This looks good.

>Multilinear algebra is used everywhere, differential geometry, Hodge theory, algebraic geometry, algebra etc, so if your question was if there is a decent book that includes all of that I'm quite positive there isn't, you should refer to different books according to your needs.
Not gonna lie I was hoping for that. Essentially a collection of all the fundamental operators possible with multilinear forms. But it sounds ridiculous now.

Do you happen to have a good recommendation for Hodge theory too?

[Anonymous No.9847724]

Some people say string theory is unfalsifiable because we don't have the right technology yet. What kind of technology is needed?

[Anonymous No.9847733]

>>9847724
Your mom’s virginity is unfalsifiable. Face it, string theory didn’t predict shit and incoherent with our observation. So it’s false.

[Anonymous No.9847736]

>>9847733
>incoherent with our observation
How so?

[Anonymous No.9847826]

>>9847713
>Do you happen to have a good recommendation for Hodge theory too?

Unfortunately no. I had the pleasure to follow a course in differential geometry, where the teacher gave us a brief exposition of Hodge theorem in order to prove Poincaré duality (in particular, that the pairing is not degenerate). If I'm not wrong the reference he gave us was Warner, and said that the theory is easy modulo some hard analysis (tipical nonsense involving weak solutions to PDE).

[Anonymous No.9847839]

>>9847724
ST is not unfalsifiable.

Think about it, all of ST is built off of data to begin with. It is its own verification.

When you do computations you get exact results back equal to lower order approximations. When it doesn't fit a new prediction there are countless things you can adjust.

People, including ST researchers, just get scared and go "well these abstractions seem far removed from the math I did in undergrad, are we sure we can still go back from this", but it doesn't work that way. The work done in ST will never be declared "useless" when someone finds a grand unified model because it helps us to understand and do computations with gauge groups that underlie well established theories. What I mean by this is; we still build bridges and aeroplanes with Newtonian mechanics.

[Anonymous No.9847844]

>>9847713
>>9847826
I just thought that maybe you could be interested in Janich's Vector analysis.

[Anonymous No.9847849]

>>9847724
No, string theory is unfalsifiable because it is infinitely adjustable. It has sufficient free parameters that you can tweak to fit any data.

[Anonymous No.9847851]

>>9847724
>>9847733
>>9847736
>>9847839
>>9847849
By the way, this is not the physics general.

[Anonymous No.9847852]

>>9847826
Yeah I've also only had exposure on its applications in differential geometry. But thanks anyway.

>>9847844
Looks very promising, thank you Anon.

[Anonymous No.9847858]

>>9847851
>By the way, this is not the physics general.
String theory is math, not physics.

[Anonymous No.9847871]

>>9847858
>String theory is math, not physics.
It's too unrigorous to be called mathematics. It's a LARP either way.
Go away.

[Anonymous No.9848472]

>>9845558
>more fucking norms and vector spaces

That doesn't mean the theory is simple..

[Anonymous No.9848627]

In the famous SICP book (computer science), one of the exercise was to write a recursive function to generate a list of every subset of a list. I tried to translate my solution in mathematical notation and i would like to prove it : [math]\mathcal{P}(\{x_1,x_2,...,x_n\})=\mathcal{P}(\{x_2,x_3,...,x_n\})\cup \{x_1\cup X:X\in \mathcal{P}(\{x_2,x_3,...,x_n\})\}[/math]
Where should i start? Should i use induction?

[Anonymous No.9848636]

>>9848627
Ok, i don't know why my latex code is broken, here is an image.

[Anonymous No.9848642]

>>9848627
>>9848636
I feel stupid, i think there is nothing to prove, that's really intuitive.

[Anonymous No.9848682]

How do I learn to learn math whilst enjoying it?

I'm getting very bored reading textbooks and doing exercises. There has to be a better way to learn Math, really I just hate reading math textbooks but enjoy doing interesting exercises. I have taken two semester of real analysis and abstract algebra.

Is it viable to try to learn math by picking out cool topics and trying to learn them? I'm sick of learning things by linearly following a book. Any advice would be much appreciated!

[Anonymous No.9848881]

>>9848682
http://www.openproblemgarden.org
Here, these are unsolved problems recommended for undergraduates. Make it your goal to solve it. Learn all the necessary math to solve these problems. You don’t need to learn all the theorems in a book, just theorems you needed to achieve your goal. I would eat my left nut if you managed to solve even one of these unsolved problems.

Or pick up some problem books recommended by /sci/ in the wiki like Putnam.

http://4chan-science.wikia.com/wiki/Mathematics

[Anonymous No.9848888]

>>9848682
you can talk to faculty to get involved in their research. do that and it should work well, it's a different and fun way of doing math

you also don't have to learn linearly, but you need to go about it methodically and using books/papers anyway

[Anonymous No.9848907]

>>9848881
don't give useless advice

[Anonymous No.9848918]

>>9848907
Your degree is useless

[Anonymous No.9849082]

https://arxiv.org/pdf/1807.01536.pdf
>Quantum Langlands duality of representations of W-algebras
>Tomoyuki Arakawa, Edward Frenkel
>(Submitted on 4 Jul 2018)
>We prove duality isomorphisms of certain representations of W-algebras which play an essential role in the quantum geometric Langlands Program and some related results.

[Anonymous No.9849290]

are linear/non-linear optimization classes continuations of matrix/linear algebra?

[Anonymous No.9849348]

>>9848881
bad advice

[Anonymous No.9849500]

>>9849290
Most linear programming algorithms are about arrays representing geometric objects.

Non-linear programming algorithms use ideas from about every math field you can think of.

[Anonymous No.9849549]

According to Godel Incompleteness theorem, it's impossible to prove certain problems. Can we prove that such problems to be unprovable?

[Anonymous No.9849650]

>>9849549
you can find two models of your theory, one where the theorem holds and one where it doesn't.

[Anonymous No.9849684]

Yo /mg/, I'm looking for some good theorem for interpolation errors in more than one dimension.

In one dimension we've got the usual interpolation error
[eqn] | f(x)-p_n(x) | \leq C \sup_x \left | f^{(n+1)}(x) \right | [/eqn]
for any interpolation polynomial of at most degree [math] n [/math].
I'm aware of the Bramble Hilbert Lemma, but it just specifies, that there exists a polynomial of degree [math] n [/math], but I need a result that works for any interpolation polynomial, so something along these lines:

For a lipschitz domain [math] \Omega [/math] there exists a constant [math] C=C\left(n,\Omega \right) [/math] such that for any [math] u\in W_{\infty}^{n+1}(\Omega ) [/math] and any polynomial [math] p\in P_{n} [/math] with [math] p(x_i) = u(x_i) [/math] for all [math] i=1,...,\frac{(n+1)(n+2)}{2} [/math], we have
[eqn] || u-p|| _{W_{\infty}^{0}(\Omega )}\leq C\left\vert u\right\vert _{W_{\infty}^{n+1}(\Omega )} [/eqn]

[Anonymous No.9849688]

>>9849684
the last formulation is a bit akward.
[math] \{x_i\}_i [/math] should be any collection of points that define a polynomial in [math] P_n [/math] uniquely

[Anonymous No.9849742]

>>9849684
>>9849688
I think I found a solution.
[eqn] ||u-p||_{W^0_\infty (\Omega)} \leq (1+\Lambda(\{ x_i \}_i)) \inf_{v\in P_n} ||u-v||_{W^0_\infty (\Omega)} [/eqn]for the lebesgue constant [math] \Lambda [/math] which is only dependend on the inerpolation nodes.
Now I can use Bramble Hilbert to get
[eqn]
|| u-p|| _{W_{\infty}^{0}(\Omega )}\leq C\left\vert u\right\vert _{W_{\infty}^{n+1}(\Omega )}
[/eqn]
for any interpolation polynomial, where [math] C [/math] is only dependend on [math] \Omega,n [/math] and the interpolation nodes

[Anonymous No.9850555]

I dont understand what it means for an object to be "nice."
I see that word everywhere. What does it mean?

[Anonymous No.9850564]

>>9850555
>I dont understand what it means for an object to be "nice."
https://en.wikipedia.org/wiki/List_of_mathematical_jargon#Descriptive_informalities

[Anonymous No.9850566]

>>9850555
It has some kind of desired properties. This depends on the context, obviously.

[Anonymous No.9850685]

Why haven't you solved the Collatz Conjecture yet anon?

[Anonymous No.9850760]

>>9850555
It means that it has all the properties required for some relevant theorem(s) to be applied.
Like for example, a function may be called "nice" when it's infinitely differentiable, or real analytic, or whatever.
It essentially means "don't worry about checking the properties required to apply the usual theorems".

[Anonymous No.9850845]

>>9850555
I dont understand what it means for a function to be "well behaved."
I see that term everywhere. What does it mean?

[Anonymous No.9850979]

>>9850685
>Why haven't you solved the Collatz Conjecture yet anon?
I have.

[Anonymous No.9851005]

>>9850685
Because it’s a boring conjecture. Who give a shit if n eventually become 1?

[Anonymous No.9851123]

>>9848682
https://ncatlab.org/nlab/show/HomePage
go nuts :^)

[Anonymous No.9851270]

>>9850979
>I have.
Mathematicians use "we", not "I".

[Anonymous No.9851327]

>>9850685
Because I don't care about engineering problems.

[Anonymous No.9851367]

>>9851270
We fucked your mom senselessly last night

[Anonymous No.9851541]

redpill me on stacks

[Anonymous No.9851568]

I understand why Galois theory shows there is no solution by radicals to some (degree 5 and above) polynomials. Why does that mean there is no general solution though? Is it not feasible that there could be some general way to write out a solution involving things other than radicals? Is this just a meaningless concept?

[Anonymous No.9851705]

>>9850685
I'm trying. But it's pretty hard.

[Anonymous No.9851706]

>>9851568
>Why does that mean there is no general solution though?
It doesn't.

[Anonymous No.9851944]

I want to show /sci/ something harder than the Riemann Hypothesis

[Anonymous No.9851960]

>>9851568
Solution by radicals is the only thing we know how to do aside from numerical approximation shit.

[Anonymous No.9851967]

>>9851568
>Is it not feasible that there could be some general way to write out a solution involving things other than radicals?
https://en.wikipedia.org/wiki/Bring_radical#Solution_of_the_general_quintic

[Anonymous No.9852563]

So /mg/, I got a job. Thanks for the years of fun and fuck you for the years of shit. The best of luck to everyone on their stuff! Bye bye <3

[Anonymous No.9852841]

I have the functional equation [eqn] f(x) = f(x^2) + f(x^3) + f(x^6) - 2 + 2x [/eqn]

I want to get an asymptotic formula for the coefficients of the Taylor series expansion of the solution. What methods exist for this?

[Anonymous No.9852885]

>>9852563
Bye wagecuck.

[Anonymous No.9852898]

>>9852563
>years of shit
this general started late summer last year, newfag

[Anonymous No.9852931]

>>9852898
>this general started late summer last year
newfag

[Anonymous No.9853006]

>>9838941
this

[Anonymous No.9853246]

Really stupid question, but how do I know when a problem is linear least squares vs. nonlinear least squares? I'm kind of worried that I might be applying Gauss-Newton when I don't need to, but I don't know how to be sure.

[Anonymous No.9853432]

>>9853246
Read your damn textbook retard.

[Anonymous No.9853876]

>>9853432
I don't have one. I'm self taught and writing a program to do tomographic reconstruction as a hobby. I'm basically minimizing an L2 norm, which as far as I can tell is nonlinear, right?

[Anonymous No.9854333]

>>9853876
Just read your goddamn book or wikipedia that shit

[Anonymous No.9854752]

>>9838444
I read Sauer as an undergraduate, and I would recommend it because it had examples in matlab rather than maple. You could also read the fucking wiki, which has recommended texts for nearly every undergrad science/math/engineering course.

[Anonymous No.9854825]

>>9851960
Apparently not. Look at the other post I replied to.
>>9851967
Thanks

[Anonymous No.9854833]

>>9853876
https://en.wikipedia.org/wiki/Linear_least_squares_(mathematics)
https://en.wikipedia.org/wiki/Non-linear_least_squares
Linear least squares is fitting a line to your data. You might perform a non-linear transform on your data (with "basis functions") so the actual curve fitted to your data is not a line (but is a line fitted to the transformed data).

Non-linear least squares is fitting something other than a line to your data directly.

[Anonymous No.9854855]

I just had a bit of a query for some resources/direction if any of you guys had any to give?

I'm in my second year at uni, and one of my tutors just seems to have such a solid grasp on Mathematics. It of course has to do with the fact that he holds a double degree in Mathematics and Philosophy - but I think that really just inspired him to understand it from the ground up. Maybe his passion for Philosophy lead him to be influenced to reading the originals, making an effort to understand the original papers, as they were released, in their own context.

I'm studying Data Science (hold the memes), and I don't want to be one of those people who is clueless of the Mathematics/Statistics behind each of these methods which are commonplace today. As it currently stands I have a decent grasp on Calculus, have been 'as far' as differential equations with no problems really. I've taken a whole class which dives pretty in-depth into regression, its assumptions, its shortcomings, calculus of it, matrix algebra of it - but everything seems so scattered and concepts seem hard to link up at times.

But every time I've learnt this stuff the questions seem to be based around some pretty obvious applications. I can understand them from a very specific 'tool based' approach, but the fundamental way of thinking has sort of skipped me.

Just focussing on the subset of Statistics, how would I go about getting a ground up knowledge of the field? Do I really have to knuckle down and just read page by page through a text book? Try get my hands on the original papers? Are there any (auto)biographies on some of the OG's that give some insight into their thinking and are easier to approach?

[Anonymous No.9854903]

>>9854855
There are some books on statistics in >>9841145. Just download it from libgen.

[Anonymous No.9854913]

>>9854903
Cheers, I'll have a look through now.

I'm currently 20, and to my own demise (and maybe growing up on the internet) have unfortunately not grown up being much of a reader. Is it really just as trivial as sitting down, and going through chapter by chapter slowly, making sure you understand everything being said? Should you just skim through and focus less on the details and just try absorb the main parts? Is there any specific 'roadmap' for approaching a fundamental knowledge of Statistics which would be optimal?

[Anonymous No.9854925]

>>9854913
I prefer to sit down and make sure I'm understand shit. But, if you felt unmotivated doing so, then by all means skim it through and absorb the main parts.

>Is there any specific 'roadmap' for approaching a fundamental knowledge of Statistics which would be optimal?
Don't know. Sorry buddy.

[Anonymous No.9854940]

>>9854925
Just out of curiosity, do you take notes when you read through a textbook? In a seperate notebook, underline stuff/notes within the margin of the book, or just none at all?

I just find it hard to concentrate, always seem to be 'reading' something but turns out I've been absorbing nothing and have to skip back a paragraph or two to before it was when I 'zoned out.' And it just leads to frustration, and when sitting there, reading through at that rate it seems that it'd take me an eternity to just get through one book.

[Anonymous No.9854958]

>>9854940
No, I just read it. That sort of stuff happens to everyone.

[Anonymous No.9854967]

>>9854958
Hmmmmm, I might spend awhile finding a good roadmap of books to go through, and then devote like an hour before bed or something each night, be rigorous, and hope it works.

[Anonymous No.9855016]

>>9854913
>>9854940
Do the exercises.
Taking notes is good too, but don't do it blindly; think about what you need to write down.

[Anonymous No.9855026]

>>9855016
Will do. I think the way I'm going to approach it from now on is reading, maybe underlying something that stands out to me in pencil if/when it happens. And then yes, doing the exercises.

Just need to make myself a bit of a roadmap now, and start my own little collection. Need a fucking statistician lol

[Anonymous No.9856352]

>>9850845
differentiable/continuous everywhere would be my guess

[Anonymous No.9856430]

[Anonymous No.9856838]

do y'all know anything about quantum computing?
shit looks pretty neat but its kind of fucky getting into it

[Anonymous No.9856859]

>>9856838
fuck off back to >>>/g/

[Anonymous No.9856863]

>>9856859
shut up nerd

[Anonymous No.9856893]

>>9856838
https://www.youtube.com/watch?v=mIULkvTGk2U

[Anonymous No.9856901]

>>9856893
sounds like a bunch of hoopla to me, and then who cares if its practical or not like what are you a fucking engineer??
the mathematics behind it looks to be fascinating

[Anonymous No.9857047]

>>9856901
>then who cares if its practical or not
Optimization is a math subject too you know

[Anonymous No.9857056]

|x|=? when x^2=x

x^2/x=1, x=1
OR
x^2-x=0, x(x-1)=0, x=0,1

Two different results and my mind is blown. How does this happen? I'm a dumbfuck, not seeking homework help

[Anonymous No.9857061]

What's another trig-related & compelling, multiple solution question such as:

>A sinusoidal function has x-intercepts at -45o, 45o, 135o, . . . What could its equation be?

I'm thinking of possibly a question that would have one drawing a triangle or an equation out that doesn't have one concrete answer

Any ideas? Nothing too complicated. Thanks

[Anonymous No.9857105]

>>9857056
I hope you're trolling. If not, you really are a dumbfuck.

Above the "OR" you are dividing by x, which assumes x is nonzero, hence you drop a solution to the equation x^2 = x.

[Anonymous No.9857108]

>>9857061
>degrees
>in current year

why are you interested in coming up with a problem? even in pure math, we try to have some sort of motivation.

[Anonymous No.9857115]

>>9857108
it's sort of a 'test your peers with a higher-thinking question and get a question back' kind of deal...

[Anonymous No.9857141]

>>9857115
give them this. it is intended for highly gifted middle school students. i couldn't solve this until my 3rd year as a math undergrad. The solution is 3 lines.

[Anonymous No.9857148]

>>9857141
Thanks but I need something in trig

[Anonymous No.9857160]

>>9857148
this can be interpreted as a trig question

hint:
a^2 + b^2 = 1
is pythagorean theorem

[Anonymous No.9857170]

>>9857160
I guess that works... I was thinking of a more 'applicable' trig question- more along the lines of applying sine and cosine laws, closer to Grade 11/12 Trig

Like so:

>A sinusoidal function has x-intercepts at -45o, 45o, 135o, . . . What could its equation be?

[Anonymous No.9857186]

>>9857170
Try actually solving the problem I gave you, using trig identities.

Make the substitions:
a = cos x
b = sin x
c = cos y
d = sin y

The difficult part of the problem is realizing that the point (a,b) lies on the unit circle and is 90 degrees rotated away from the point (d,c). Once you find this fact, the second set of equations can be derived.

There is also an alternative solution, (the 3 line one) which uses matrix algebra. That solution is the one which took me so long to find. The longer solution is a trig problem.

You should try actually solving a problem rather than just looking at it blankly.

[Anonymous No.9857222]

>>9857186
Matrix algebra? Just multiply the first line by c^2
a^2c^2+b^2c^2=c^2
b^2d^2+b^2c^2=c^2
b^2(d^2+c^2)=c^2
b^2=c^2
and you're pretty much done.

[Anonymous No.9857239]

>>9857222
This doesn't prove the third equation in the second set of equations. It proves the first two though.

You can prove both at once using orthogonal matrices and uniqueness of inverses.

[Anonymous No.9857249]

>>9857239
It does prove the third, b=+-c so ab+cd=+-ac+-bd=0. This "proof" is more elementary too.

[Anonymous No.9857252]

>>9857249
i think you lose parity of the signs. maybe you can solve it in the way you describe, but there needs to be more detail. I think that adding in that detail makes it no more elementary than the other proposed solutions.

[Anonymous No.9857261]

>>9857252
Elementary in the sense that an arithmetic problem has an arithmetic solution.

[Anonymous No.9857266]

>>9857261
Sure. One of my friends in my department really likes solutions which are answered in the same way that they were posed. I think that there is an elegance in that, but my personal preference is to bring in seemingly unrelated mathematics and solve a problem in a novel way through.

[Anonymous No.9857276]

>>9857266
True, it's always nice to have different types of solutions for the same problem.

[Anonymous No.9857592]

>>9857141
This good?

[Anonymous No.9857626]

>>9857141
Holy shit I teach middle school math, seriously. I'll give them this tomorrow.

[Anonymous No.9857828]

>>9857141
ac = -bd
a^2 c^2 = b^2 d^2

a^2 c^2 + b^2 c^2 = c^2
b^2 d^2 + b^2 c^2 = c^2
d^2 + c^2 = c^2 / b^2
1 = c^2 / b^2
b^2 = c^2
b = c or -c

The rest is trivial substitution.

This is piss easy.

[Anonymous No.9857865]

>>9857828
http://www.openproblemgarden.org
Good, now go solve some unsolved problems.

[Anonymous No.9858086]

>>9857141
>elegant
>two vectors on the unit circle, and their dot product is 0
>(c,d) is orthogonal to (a,b), so it is either (-b,a), or (b,-a)
>plug and chug for the remaining 3 equations
if you used anything else, then you got 0 points on this question,

[Anonymous No.9858103]

>>9858086
>vectors
>dot product
>in middle school

[Anonymous No.9858314]

>>9858086
>if you used anything else, then you got 0 points on this question,
this desu

[Anonymous No.9858325]

[Anonymous No.9858349]

>>9857626
I do as well. A good challenge.

[Anonymous No.9858369]

>>9858349
>>9857626
Who the fuck has school in the middle of july?

[Anonymous No.9858387]

>>9858369
Asian schools.

[Anonymous No.9858403]

>>9857592
looks valid to me.

>>9858086
this solution is a re-wording of the "orthogonal matrices" mentioned here: >>9857239

Pic related is my solution.

[Anonymous No.9858864]

>>9858103
yes? you didn't have that in middle school?

[Anonymous No.9858937]

it kinda sucks that sci is so slow in the summer, but im kinda glad that the mg spammers are gone for now

[Anonymous No.9859013]

turbo brainlet here taking Trig at 22

how the FUCK do I find the Y values of these points? I understand how to get the X values

[Anonymous No.9859025]

>>9858937
>the mg spammers
Who?

[Anonymous No.9859108]

>>9859013
Hey I'm math Chad doing my PhD at 22. You have a function which takes in x and gives out y, yes?

If you have x, then plug it in to the function, compute it, and get y.

[Anonymous No.9859111]

>>9859013
by key points they mean corresponding points on y=-2*cos(x-pi/5)+3 after its transformation from y=cos(x)
so e.g. where will the (pi/2,0) of y=cos(x) be on the y=-2*cos(x-pi/5)+3 ?
it will be where the argument of that cosine in y=-2*cos(x-pi/5)+3 is equal to the argument of that untransformed cos(x), which is pi/2 for the point (pi/2,0). So: x-pi/5=pi/2 and thus x=7*pi/10.
and the values? just input the "transformed" arguments into the y=-2*cos(x-pi/5)+3
so for corresponding point of (pi/2,0) input 7*pi/10 into y=-2*cos(7*pi/10-pi/5)+3 = -2*cos(pi/2)+3 = 3
so here you have your corresponding point (7*pi/10, 3)

[Anonymous No.9859112]

who /financialmath/ here

where my time series niggas at

[Anonymous No.9859116]

>>9859112
I’m not a nigger

[Anonymous No.9859117]

>>9859116
yet here you are, basketballius

[Anonymous No.9859119]

>>9859112
financial math is not really the type of thing discussed on /mg/, it is an application of some small subset of math and not math itself. for an example of typical discussion on /mg/, we can see that several people discussed this problem: >>9857141 and solved it in a number of ways just for fun. finance is not mathematics in this sense.

[Anonymous No.9859125]

>>9859119
>it is an application of some small subset of math and not math itself
define "math"

[Anonymous No.9859131]

>>9859125
Philosophical arguments, but with only logos. No pathos or ethos based arguments. Math consists of taking assumptions and expanding on those assumptions in a rhetorical style mentioned above.

If you are interested in fundamentals of mathematics, the wikipedia page on ZFC is a good starting place:
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory

[Anonymous No.9859222]

>>9859108
>>9859111
Thank you anons

My professor didn't explain this well at all

[Anonymous No.9859237]

>>9859222
its ok, sometimes people who work with something for a long period of time tend to forget to explain detail because of being too used to it.

[Anonymous No.9859314]

Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive
Definition 2: A is an essence of x if and only if for every property B, x has B necessarily if and only if A entails B
Definition 3: x necessarily exists if and only if every essence of x is necessarily exemplified

Axiom 1: If a property is positive, then its negation is not positive
Axiom 2: Any property entailed by—i.e., strictly implied by—a positive property is positive
Axiom 3: The property of being God-like is positive
Axiom 4: If a property is positive, then it is necessarily positive
Axiom 5: Necessary existence is positive
Axiom 6: For any property P, if P is positive, then being necessarily P is positive

Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified

Corollary 1: The property of being God-like is consistent

Theorem 2: If something is God-like, then the property of being God-like is an essence of that thing
Theorem 3: Necessarily, the property of being God-like is exemplified

[Anonymous No.9859324]

>>9859314
>Theorem 1: If a property is positive, then it is consistent, i.e., possibly exemplified
Possibly exemplified? Go back studying logic dude

[Anonymous No.9859334]

Kill all physicists

[Anonymous No.9859351]

>>9859334
No I need them so I can use their findings as toy problems in my numerical analysis. Just let them do their thing and think they know anything. They can be useful.

[Anonymous No.9859428]

>>9859314
tl;dr "if I imagine something with properties that would make it exist, then it exists"

[Anonymous No.9859446]

is Kolmogorov good to learn probability from?

also, am working my way into analysis starting with some set theory, but I hear the modern thing is category theory. Recommend a book?

[Anonymous No.9859743]

>>9859446
there's no point learning category theory without knowing (classical) abstract algebra, and algebraic geometry/topology. Not only that, but you will most likely not understand anything, nor understand the motivation behind it. Further, analysis/probability are one of the subjects where category theory is the least beneficial, and hence the least used.

[Anonymous No.9859746]

>>9859446
>is an 85 year old math book good for learning?
I haven't read it, but no, it's too old.

[Anonymous No.9859836]

>>9859746
It’s a great book. It’s like Hardy/Littlewood/Polya’s Inequalities book but with probabilities.

[Anonymous No.9859840]

>>9838125
Typing /kiss in WoW doesn't mean you have boyfriends, kiddo

[Anonymous No.9859845]

>>9859743
It is also possible to learn category theory along topology, i.e. via convergence spaces. See Preuss's foundations of topoloogy.

[Anonymous No.9859890]

>>9859743
>there's no point learning category theory without knowing (classical) abstract algebra, and algebraic geometry/topology.

[Anonymous No.9859934]

>>9845496
>>9845516
you must become a master of the distributive property to do algebra, my son

[Anonymous No.9860153]

>>9860149

[Anonymous No.9860186]

>>9843077
Good. We feel the same about you

[Anonymous No.9860211]

What's the deepest math folklore you guys know?
I'm completely self-taught so I never got to hear all the juicy things that never get published because they are too speculative.

[Anonymous No.9860216]

>>9860211
read section 10.6 of Henri Cohen's 'Number theory vol.2. Analytic and modern tools' (its on libgen)

[Anonymous No.9860231]

>>9859836
>It’s like Hardy/Littlewood/Polya’s Inequalities book

what is the virtue of said book? I'm not attacking you, I'm the Kolmogorov guy.

[Anonymous No.9860240]

>>9860231
It's basically the Rudin of inequality

[Anonymous No.9860347]

>>9840171
I used this book for my real analysis in conjunction with Royden's book. It's ok it doesn't really give a grown up appreciation for measure theory so ymmv

[Anonymous No.9860358]

>>9842745
This
can confirm from experience

[Anonymous No.9860456]

>>9860240
ok, cool that helps. Thanks!

[Anonymous No.9860538]

>>9860216
Can you tease a bit what he's saying about them?

[Anonymous No.9860573]

>>9860538
>Can you tease a bit what he's saying about them?
He says it better than I can

[Anonymous No.9860648]

>>9859890
do you have a rebuttal ?

[NOT OP No.9860657]

>>9838459
>Liking your women LONG
WTF is wrong with that picture?

[Anonymous No.9860692]

>>9860648
There's no reason one would need abstract algebra/algebraic topology/geometry, categories are worth studying on their own merit.

[Anonymous No.9860698]

>>9860692
>categories are worth studying on their own merit.
I knew the larping was strong here but wew

[Anonymous No.9860716]

>>9860698
t. freshman

[Anonymous No.9860736]

>>9860692
trufax

[Anonymous No.9860744]

>>9860716
t. neet, self-taught """mathematician"""

[Anonymous No.9861037]

>>9842576
im game

[Anonymous No.9861097]

if one is """self-studying""" math, should they do the exercises which don't have solutions to them?
it's kind of weird learning a new topic and not being able to self-check what you've learned

[Anonymous No.9861108]

>>9861097
Yes, see >>9844900, >>9846175 and >>9846370. Also, R. P. Burn wrote problem books for analysis and Number Theory.Check it out.

Or pick up some problem contest books like Putnam.

[Anonymous No.9861134]

is second class honors 2nd division acceptable for phd?

[Anonymous No.9861288]

>>9861097
It might depend on the type of math and what you hope to get out of it.

For instance, if you're looking to gain general applied skill in (early) undergraduate linear algebra or calculus then you should do as many exercises as it takes for you to feel comfortable with the techniques and then do a few more on the harder scale (but beware that many textbooks contain extra problems that apply the technique to some science or something, don't bother with those unless you're particularly interested in that application). In addition, make sure to look for solutions manuals and if the textbook isn't jiving with you don't be afraid to choose a different one (millions of people have learned these topics and there are countless textbooks that take different pedagogical approaches to teaching it at different levels).

On the other hand if you want to gain conceptual theoretical understanding (perhaps you plan on entering a math program at a university or are just really interested in math) then you'll want to try and choose the problems that are the most important. Look at the theorems and claims involved. Often textbooks will expect that you've done certain problems that will give you insight or may in some cases even be pre-requisites to proving theorems later on. In this case don't be afraid to look at extra textbooks as references (but beware that different texts may use different incompatible approaches, such as slight variations of a theorem or definition). It might also help to look for 'lecture notes' (aka 'course notes') written by a professor for a course (these typically highlight the important material in the same way it would be taught in lecture, sometimes they contain mistakes though). Online lecture series can be pretty good too, as well as slide decks, and professor's webpages.

What are you studying, out of curiosity?

[Anonymous No.9861299]

>>9860744
Not that guy but you are wrong. Category Theory is studied for its own sake and there is a wealth of beautiful and rich theory there.

There is also a large community of mathematicians and computer scientists that study it from the programming language theory perspective as there is a powerful relationship between type theory, logic (classical and non-classical), and category theory. The Homotopy Type Theory project lies in this intersection and it's currently one of the most well funded areas of research in either field.

[Anonymous No.9862220]

>>9861134
What is this in British? A grade 2 pass?