/sci/ - Science & Math

this is pathetic lol, last thread died at 87 posts

>what are you working on?
Not working on anything except grading exams.
>what are you reading?
Real Analysis by H. L. Royden. Trying to prep for next semester.
>dumb question you need answered:
Is there a cheaper option for Maple/Mathematica?

>>10595700
The thread isn't too slow, the board is just faster than it should be.
>>10595713
https://alternativeto.net/software/mathematica/
https://www.topbestalternatives.com/mathematica/
https://www.physicsforums.com/threads/free-alternative-to-mathematica.756789/
https://alternative.me/mathematica

>>10595738
thanks! have you used any of these before? any reccomendations? it seems like there are so many, i wonder which one is most popular. ive been trying octave for a few days and it seems to be everything i need.

>>10595713
octave is free and isn't so bad at all, I've used a bit in the past and it was ok/above ok compared to mathlab :))

>>10595744
If Octave works for you, you can try Mirai Math as a frontend.
But it's really a matter of what it is you want to do. Just open the first link, select free software (not open source) and check out the websites to see what they can and can't do.

>>10595713
SciLab instead of Matlab

anyway
studying generating functions for a midterm
trying to understand analysis for a final

we're doing graphs now in combinatorics and they seem fun
algebra is as good as pased desu

>pure mathsss
Imagine dedicating your life to something that is literally defined by how useless it is.

>>10595798
>i've made piece with it. why can't you?

>>10595803
>piece

>>10595798
that's why i'm going into cryptography

>>10595623

Is there any established theory of diophantine quadratic surfaces?

From what I can gather, their aren't many diophantine equations which we know anything about. I can't find anything on mathscinet.

>>10595713

> Is there a cheaper option for Maple/Mathematica?


Sagemath, duh

What's a good graph theory textbook?

>>10596144
There's one book published by Dover (I think the author's last name is Trudeu) that is pretty neat and you can read it pretty fast just to get a very broad overview of graph theory.
Bollobás's Modern Graph Theory is one of my favorite books ever, you should definitely check it.
If you're interested in more advanced topics I suggest Algebraic Graph Theory Norman Biggs but beware that it doesn't have any excercises, but you might as well look for some online.
I'm currently working through Lovazs' Large Networks and Graph Limits but I'm kinda struggling because I don't have enough measure theory under my belt

>>10595623
this is why i tell you to take hrt and become femal

>>10595623
discussion topic: Was Mathematics as a whole invented or discovered? Can you break it down by topics?

Personally, I choose to believe that Mathematics was more discovered than invented.

>>10596906
how can you ""discover"" something that doesn't actually exist?

>I'm thinking of a pink elephant with wings. Wow, what an amazing discovery I made!!!

how do i not get motivated while studying a different degree but needing high grades to change to maths next year?

>>10596906
I can understand saying that theorems are discovered, since they express relations between already given objects, but I'm pretty sure you have to be completely out of your mind if you actually think that definitions and axioms are discovered.

>>10597066
If they work, how are they not discovered?

>>10597031
That's why it's called self-discovery anon. :^)

>>10597070
How does the definition working imply it precede the construction?
What autistic definition of discovery are you even working with?

>>10595623
where is the screenshot from?

https://www.strawpoll.me/17898588
>>10597176
Kodaira's Complex Manifolds and Deformation of Complex Structures.

>>10596906
Anything that uses ZF is discovered

Anything that uses C is invented

>>10597317
This

>>10597226
thanks

>>10597317
>>10597373
none of it is discovered you damn choicelets

>>10595807

>>10597317
Beautiful

>>10595623

The following question can almost as easily be binned in the stupid question containment thread, but it's a slight and sincere curiosity, and so I put it here instead.

Is there ever a non-pedantic, non-trivial reason to speak of (or, operate with) a 1x1 matrix [math]qua[/math] matrix, as opposed to a mere scalar or: number?

>>10597751

To clarify, the supposed matrix's entry is something from [math]\mathbb{C}[/math], so please no cute replies about an entry which is itself a matrix (or else another abstruse object), etc.

>>10597751
>non-trivial
You're asking for way too much.
But U(1), etc, sometimes shows up.

>>10597751
define "matrix qua matrix"

>>10597751
I guarantee that there are no non-trivial reasons, assuming a quick hop across an isomorphism is trivial.

>>10596865
post your discord tranny

Does anyone know of a good geometry book? I am looking for something about basic geometry (I think the correct term would be Euclidean geometry) that gives a more rigorous treatment. I want very clear definitions and proofs of everything.
I haven't found anything like that. Most books seem to be aimed to high schoolers and lack rigor.

>tfw got a B in real analysis because I sperged out on the oral exam
Life is tiresome, gotta do better on advanced real analysis I (measure theory and functional analysis)

What makes somebody good at maths compared to the general public who just espouse that mathematics is too hard?

>"Maths is hard"
>*high fives* the next person who says the same thing

>>10598147
Orality is much like a science too my friend. There are rules and tips to place your voice better and speak more confidently, rules and tips to articulate your discourse, rules and tips to persuade and move the jury, etc
You can work on that too. It may seem less satisfying to you than studying a "real science", but it will take you further in life.

>>10598227
Yeah but I am unironically a diagnosed autist that panics and stutters when I get stressed

>>10598135
Seconding this

>>10597751
If you count inducting on dimension of the matrix and hence using the 1x1 case as the base case as non-trivial then yes

Otherwise there's no point, no.

brainlet question incoming
how do I solve sums? for a lot of them, it's easy to guess how it's gonna act asymptotically and to verify it. but what if I wanted to sum, say
[math]\sum_{k=2}^{n}k(n-k+1)[/math]
I know it will be [math]\theta(n^3)[/math], I could easily prove that by, say, induction, but I'd like to be able to know the exact form.
desu, I don't even need it for anything, but would like to be able to do that.
Are there some cookbook approaches? Anyone know a sauce for where I can read about or practise this?

>>10595623
what's [math]m[/math]?

>>10598734
probably 'the number of the parameters of M roughly computed'

>>10598731
sum k(n-k+1) =
sum kn - sum k^2 + sum k

proceed from there

>>10598749
ok, I'm not THAT much of a brainlet
>proceed from there
please, go on

>>10598756
https://en.wikipedia.org/wiki/Summation#Powers_and_logarithm_of_arithmetic_progressions

>>10598731
>is there a cookbook way of converting series into closed form
No. Not at all. Not in the slightest. Boy does everyone wish there were.
We could probably have solved the generalized RH by now.

>>10598767
yeah, I know there isn't a general way to do that, I also heard that we can only approximate even the harmonic series. What I meant by a cookbok approach was something that works for certain cases.. surely, there must be a way to sum [math]\sum_{k=a}^{n}k^b[/math], or isn't there (for positive bs)?

>>10598783
https://en.wikipedia.org/wiki/Faulhaber%27s_formula

>>10598763
>>10598788
thanks, these look like some good sauces, would love to get moar though

>>10595807
based

Just because a short exact sequence has no homology (trivially), does it also mean it has no cohomology? Everything just points at that it doesn't, but i just did an example and it did, so im not sure now

>>10598248
You can fake it with enough practice talking math, like if you have to TA courses

>>10599170
oh nevermind, just found out the sequence has non-trivial third cohomology from the ext term

>>10598731
No, for more or less the same reason that there is no recipe for computing integrals.
There are various tricks but no general method

Could somebody post the meme with the topics to study in high school, as sophomore, etc?

>>10599362
>Could somebody post the meme with the topics to study in high school, as sophomore, etc?

That springer graduate text in mathematics series has more than 300 books what the FUCK

>>10599418
You could be done in 6 years if u do one a week (with some breaks)

>>10599418
A bunch cover the same topics as different ones. I estimate it should be around 50.

why are cs tards so obsessed with constructive mathematics?

https://en.wikipedia.org/wiki/Joshua_King

>Joshua King came to Cambridge from Hawkshead Grammar School. It was soon evident that the school had produced someone of importance. He became Senior Wrangler, and his reputation in Cambridge was immense. It was believed that nothing less than a second Newton had appeared. They expected his work as a mathematician to make an epoch in the science. At an early age he became president of Queens’; later, he was Lucasian Professor. He published nothing; in fact, he did no mathematical work. But as long as he kept his health, he was an active and prominent figure in Cambridge, and he maintained his enormous reputation. When he died, it was felt that the memory of such an extraordinary man should not be permitted to die out, and his papers should be published. So his papers were examined, and nothing whatever worth publishing was found.

>>10599550
Constructive proofs tend to be quite algorithmic; they also permit computer-assisted proof verification.

>>10599762
but non constructive proofs permit computer assisted proof verification too

>>10599550
Constructive proofs have P R A C T I C A L A P P L I C A T I O N S and offer models and examples for making algorithms.

Can someone tell me why the following chain of equalities is wrong? Given that f, f^{-1} are integrable.

[math]\displaystyle{\int f^{-1}(x)dx = \int f^{-1}(f(x)) \cdot f'(x) dx}[/math] because of substitution (I think this is the problem)
[math]\displaystyle{= \int xf'(x)dx}[/math]
[math]\displaystyle{= xf(x) - \int f(x)dx}[/math]
[math]\displaystyle{= xf(x) - F(x)}[/math] using integration by parts

Where is the mistake? The answer is supposed to be [math]\displaystyle{xf(x) - F \circ f^{-1}(x)}[/math]

>>10595798
Inventing technology is more useless to me. I would much rather find out interesting theorems and die in the streets. I hate money and society, why should I contribute to others tangibly?

>>10595817
>Sagemath

>>10595798
Imagine dedicating your life to something that other people deem to be useful instead of enjoying your own life

>>10600235
>>10600239

>>10599362
>meme
It's the official /mg/ curriculum.

Please someone help. I'm tasked with showing that the cocycle [math]\varphi[/math] in pic related is not a coboundary, but I keep getting that it is. I don't see a contradiction.

>>10599605
holy based

>>10600172
What's wrong with Sage?

>>10600084
you have to undo the substitution...

>>10595623
Can I get a hand with this problem.

I have a series of points scattered on the plane. These points form a shape, for example pic related a brain.

How do I generate the largest grid of squares such that the centre point of each square is within the scatter of points?

I'm trying to generate my own grid. I'm reading a tonne of papers that say they do it, but they never say how,

>>10595700
>t unsuccessful NEET
>doesn't even have friends to tell him it's finals

thread is shit until the "remember to work with physicists" post

>>10600600
>thread is shit until the "remember to work with physicists" post
Threadly reminder to work with physicists.

>>10595806
Anglosphere education.

>>10600431
If I had to take a stab at it its a partial differential.

A challenge to the algebraic geometers: name one (1) application of your autistic field. Hard mode: no speculative pseudo-applications (i.e. some random paper on arXiv where some academics say x and y could be used for robotics n shiet)

>>10600084
bounds...

>>10601212
>A challenge to the algebraic geometers: name one (1) application of your autistic field
Proving the Weil conjectures

>>10600138
This, we are absolute autists, we don't care about the real world and applications

>>10601212
These are sacred grounds, philistine. Leave while I still allow you.

>>10598135
Geometry revisited

>>10598219
Math isn’t as hard as people make it out to be.
It’s mainly taught like shit, and since it’s rigorously cumulative, one missing link in the chain of education can spell chaos later down the line.

Did anybody here work on the Kähler-Ricci flow by chance? Is there any nice example for, lets say, a compact Kähler threefold with finite maximal existence of the KR flow where it (the threefold + metric) still converges in some sense to a compact threefold with certain singularities?

>>10598135
Berger’s Geometry I and II

>>10600172
Fuck off.

Looking for a good differential equations book with mathematics students in mind, that means minimal on the physics applications, preferably short, insightful and clear

Daily Putnam Problem >>10602626

>>10599605
>the virgin newton
>the chad king

>>10595623
redpill me on deformation theory

>>10598135
Michel Audin's book is ok

>>10600339
what is $\phi$? For me it is unclear

>>10602868
Literally what it sounds like. Take a manifold (more usually a subset of R^n or C^n), assign a complex manifold to each point in a proper way, acquire results about how the complex structure locally fluctuates through classical and cohomological techniques.
6/10 in the autism scale.

>>10602894
i found the problem already - all vertices should have been identified

and as for what phi is, it's a 1-cochain on the torus

>>10600408
This

>>10598744
hmm that means nothing to me

>>10602900
wow this piece of rubber sure is stretching nicely!

>>10602953
Roughly, if we take a space along which M is deformed that exhausts the local deformations, it has dimension m.

>>10602436
i want yuugi to sit on my face

>>10599605
Guys...

I'm a bit confused, for a a general one parameter flow on a smooth manifold [math]\phi :\mathbb{R}\times M\rightarrow M [/math] what does it mean for a vector field [math]X\in \Gamma (TM)[/math] to be invariant with respect to the flow?

>>10603394
If [math]Y[/math] is the generating vector field for [math]\phi[/math] then [math][X,Y] = 0[/math].

>>10603409
Hmm, I'm not too sure, I mean a more general flow, I,e a smooth action of the Lie group [math](\mathbb{R},+)[/math]. In particular my problem has a flow acting on the tangent bundle of a manifold [math]\phi:\mathbb{R}\times TM\rightarrow TM, \phi (t, (p,X_{p}))=(p,e^t X_{p})[/math] which I don't think is the usual flow generated by a vector field.

>>10603422
Represent elements of the Lie algebra as vector fields.

>>10603432
plz be more explicit thnx

>>10602436
kasen is my friend!
we love to study riemannian geometry together!
sectional curvatures with kasen!!!!

How the fuck do you raise a number to an imaginary power?

>>10595623
Where is somewhere that can explain to me how to find eigenvalues and eigenfunctions for absolute dummies? I'm talking like holding the hand of a parkinson patient retarded

>>10603531
for z, w complex, we define z^w = e^(w log z)

>>10603533
addy thing does stretchy and no turny
maybe try gilbert strang's Lin Alg lectures on MIT OCW? they're very good

>>10603534
>w log z
w without i? So like, if w was 3i, then it would be 3 log z?
Thanks, got a link to a proof?

>>10603533
Weil's Basic Number theory

(eigen = number in German, text is in English tho)

>>10603538
what the fuck are you on about?
read my fucking lips
if z and w are COMPLEX NUMBERS, i.e. z = a + bi, and w = c + di, then we DEFINE z^w = (a + bi)^(c + di) to be the quantity e^((c + di)*log(a + bi)).
There is no "proof" to a definition. It makes no sense to take something to a power of i, so we have to define what it should be.
This is the obvious definition, since by log rules you want to have log(z^w) = w*log(z), in which case e^(log(z^w)) = z^w.

>>10603538
if you want an example, here: 2^i = e^(i*log(2)) = cos(log(2)) + i*sin(log(2))

>>10603546
Wouldn’t you just be left with e raised to a complex number? How you do resolve that?

>>10603549
>>10603552
Oh I see, you use euler’s identity

>>10603545
>Weil's Basic Number theory
what is this? I didn't find anything eigenvalue when I command find for it

http://tomlr.free.fr/Math%E9matiques/Weil%20-%20Basic%20number%20theory%20(Springer)(338s).pdf

>>10603535
I'm referring to the mechanical process of calculating it anon

>>10603556
>oh i see, you use euler's identity
dude please wait until you finish the prerequisites for complex analysis before you start trying to study it

>>10603561
I asked a very basic question because I was curious, fucking excuse me

>>10603559
yes, strang's lectures teach you how to calculate it
i mean come on now. you take a fucking determinant and solve for the roots of a fucking polynomial. then you solve a system of linear equations. 10th grade math at worse.

>>10603562
sorry i was mean :) hope you enjoy your stay!!!
btw remember to post these sorts of questions on r/mathhelp, this sub is for serious math discussion :)

>>10603569
Now was that so hard?

how's the new book about IUT?

>>10600138
this

>>10599550
they are dumb fags who cant into real math

>>10603562
nah go off yourself plebian.

Im reading a basic geometry exercise. They say an isosceles triangle has x+7 and x+9 as sides. It task you with finding area, perimeter, and all 3 angles. Is that doable? Isnt there info missing?

Daily Putnam Problem >>10603810

>>10598135

The Heath Edition of Euclid. Many anons will tell you that this is a poor recommendation. They are wrong, and history proves them to be wrong.

Just skip the historical commentary (runs about 250 pages in V.I of Heath). Instead, simply grab the basic ideas (postulates) stated around page 150, and then take the actual text starting around page 250 and personally engage with it. Do not simply read it. Using the copy you have at hand, draw pictures, imitate what you're reading on paper, and think.

>>10603771

You have said that an isosceles triangle has two sides, being x+7, and x+9.

Therefore, the triangle's third side must be either x+7, or x+9. Here, there are two cases. So, the thing to do is to treat both cases, for completeness of presentation (unless some observation reduces it to one case that I've missed). I refrain from further comment.

>>10603857
That was my logic too. But im supposed to give numeric answers for those questions, and not algebraic expressions. That is not doable, right?

>>10595798
Aplied maths junior spoted

>>10603865
Why wouldn't be doable? I doubt they want numeric answers as you claim, since it is impossible to find x with only that. What they probably want is for you to find area, perimeter and angles in terms of x.

Area: just use pythagoras to find the vertical and use the area formula
Perimeter: add the three sides together
Angles: you already know the sides so this should be easy

>>10602481
seconding

>>10602900
what can it prove?

>>10603422
This gives a vector field on [math] T(TM) [/math] rather than on [math] TM[/math]. It generates the vector field
[eqn] V(p,X_p) = \frac{d}{dt} \phi^t(p,X_p)\vert_{t=0} =(p,X_p,X_p) [/eqn]

>>10603531
carefully.

>>10596906
>observe thing that has already existed forever
>languages available suck at describing it and communicating about it
>invent language to describe it and communicate about it
>+10,000 years
>"Was this language invented or discovered???"
Bro.

One of the best books that I've read. I'd be willing to say it's superior to Atiyah-Macdonald. It certainly contains almost all the material in A/M except the few digressions into Dedekind rings and the Hilbert Polynomial, which could be read independently, and on the other hand contains material on homological algebra, like derived functors and projective/injective modules. At times it felt like it was just copying A/M but the proofs and explanations are more wholesome and complete, so you're basically getting the same treatment but better. Almost at no point was a step in a proof unclear to me. There are barely any results left as exercises. Probably one of my favourite aspects are the introduction before any chapter - I've gained a lot of intuition that I previously didn't have about certain constructions and results.

There exercises are more interspersed to solidify your understanding before moving on to the next chapter. There are fewer exercises, but to be fair many of A/M exercises were algebraic geometry (at the level of schemes) in disguise, and since the book devotes its second half to AG, it is reasonable.

I have only (fully) read the first half of the book devoted to commutative algebra, but I already know the second half, devoted to scheme theory, is not going to disappoint. If you are looking to learn commutative algebra, I recommend you look into this book over Atiyah/Macdonald's.

What are some non-meme books to learn the entirety of linear algebra and calculus?

>>10604325
learning the "entirety of algebra and calculus" is already a meme.

i guess linear algebra done right by axler and spivak's calculus or apostol's calculus are what you want. unfortunately the latter has a shit libgen edition

>>10604329
>apostol's calculus
seconding this

>>10603562
>trying to guilt trip genuine sociopaths
Imbecile.

>>10604392
>>>/squidink///

>>10604329
>LADR
>niggas recommending GTM all the time
Is Sheldon literally shilling here?

>>10604421
Is Sheldon a meme? First couple of chapters are obviously meant for brainlets

>>10604440
>picks up a book on basic linear algebra
>feels insulted when it contains basic linear algebra

okay, generating functions are really cool
like dude
really cool

If X,Y are two martingales with respect to the same filtration, then X+Y is also a martingale.

But can we give an example of two martingales X,Y, over different filtration, such that X+Y isn't a martingale?

I've had no luck finding examples so far, though I know that such X,Y can't be independent.

Hey guys, brainlet here.

Do you know a good calculator for permutations?

I have to "calculate" the number of possible passwords, for a password that has a length of 8, only contains {0,1} and the 1 appears 5 times.

Ofcourse I already tried it.

I got 56 as answer.

>>10604599

Any scientific calculator has a "combination" and "permutation" function, I'm pretty sure. On my Casio calculator, it's on the multiplication and division buttons and you have to press shift to use them. They read as "nPr" and "nCr". For your problem, you would input "8C5" which reads as "8 choose 5".

>>10604444
I don't feel insulted, it's considerably easier compared to Shilov or Kunze. That isn't a problem, personally I dislike that the rigor is dialed down considerably (for example fields are only mentioned in a small note in chapter 1), the book would still be suitable for the intended audience with some basic discussion of fields and the concept of vector space would be properly defined.

>>10604903
>implying i've read any book i recommend

>>10604325
Paul’s online math notes is the most rigorous piece of mathematics you’ll ever come into contact with

>>10604920
hmm, I'm thinking based

I admit I'm not a big fan of algebraic topology but computations are pretty fun desu. Feels like I'm dropping nuclear bombs on these spaces with long exact sequences, Kunneth theorems, derived functors, etc. Unfortunately I'm not very good at visualizing the spaces in question.

On that note, I'm trying to compute the cohomology ring of the space [math]X[/math] which is the space that glues a torus [math]S^1\times S^1[/math] with another torus, along the first copy of [math]S^1[/math]. I'm thinking of trying to do it both via long exact sequence of the pair and via Mayer-Vietoris.

I have some questions for some of you n-dimensional wizards:

Consider the pair [math](X,S^1_1)[/math] where the subscript is there to indicate it's the first copy.
>Is the torus modulo the first circle, [math]S^1_1\times S^1_2 / S^1_1[/math] just [math]S^1[/math]?
I'm pretty sure it is but:
>Is the space [math]X / S^1_1[/math] then the wedge sum of the circles [math]S^1\vee S^1[/math]?

If those two things were true, then we have the LES of the quotient (assume integer coefficients):

[eqn]0\to \tilde H^1(S^1\vee S^1)\to \tilde H^1(X)\to \tilde H^1(S^1)\to \tilde H^2(S^1\vee S^1)\to \tilde H^2(X)\to \tilde H^2(S^1)\to \tilde H^3(S^1\vee S^1)\to \tilde H^3(X)\to \tilde H^3(S^1)\to 0[/eqn]
Noting that [math] \tilde H^n(S^1\vee S^1)= \tilde H^n(S^1\vee S^1)\oplus \tilde H^n(S^1\vee S^1)[/math] and [math] \tilde H^1(S^1)=\mathbb Z[/math] and [math]0[/math] otherwise, then the sequence becomes:
[eqn]0\to \mathbb Z^2\to \tilde H^1(X)\to\mathbb Z\to 0 \to \tilde H^2(X)\to 0\to 0\to \tilde H^3(X)\to 0\to 0[/eqn]
Which in particular means that [math]\tilde H^1(X)=\mathbb Z^3[/math] and [math]0[/math] otherwise, which just looks utterly wrong given that it's at least a two dimensional object.

>>10605178
>it's a torus glued to a torus along S^1
Picture a Torus. Take a non-trivial simple loop along it (one that's easy to imagine). Picture another one, but highlight the other non-trivial simple loop. Glue them together.
So essentially, it looks like a donut that goes through the hole of another donut.

>>10605226
wut

>>10605238
THE OTHER NON-TRIVIAL LOOP LAD, NOT THE SAME ONE.

>>10605251
but it's the first copy for both innit? shouldnt then it be the same loop?

>>10605254
>but it's the first copy for both innit? shouldnt then it be the same loop?
SAME SAME LAD, IT'S JUST EASIER TO PICTURE IT THE WAY I'M EXPLAINING.

>>10605257
> EASIER TO PICTURE IT THE WAY I'M EXPLAINING
I think it would be easier to picture it if u drew a picture
regardless, the quotient of torus/circle is still a circle right? And the quotient X/circle is the wedge product of circles?

im an undergrad pleb who will be taking real anal and algebra at the same time. the uni i go to uses the quarter system, how doable is it for me to get A's in both classes assuming those are the only two i will take

>>10604321
I also like this book (from the german school)
but you can't compare it to AM (or the more recent Altman).
They are essentially different.

>>10605303
I can and will. They are essentially undifferent. If you say they are, then you haven't read it past the content page. It's almost theorem for theorem, lemma for lemma the same. Only difference is that the topics are shuffled around. Like for example, the chapter on primary ideals is extremely reminiscent of AM's.

>>10605257
Ok, i get it now. However, when I contract the circle to a point in the torus, then I get a pinched torus. If I have any loop that went around the circle I just collapsed previously, then I can contract it at the pinch point, so the pinch torus is still homotopy equivalent to a circle, so nothing essentially changes

>>10604181
I was helping a friend with a teacher's certification exam and she's adamant they require numeric answers. Im kind of glad to know Im not that much a brainlet to not be able to solve that. I tought maybe I was missing something really really obvious. Arriving to algebraic expressions is piss easy tho. Thanks anon.

>>10605297
>assuming those are the only two i will take
kys, theyre piss easy

>>10604289
The OP works in just about every case.

tell me about grothendieck

>>10605609

>>10605609
Pure math is autism, but its good autism.

>>10605669
tell me about pure math, I'm a simple engineering sophmore who has only done up to diffeq and calc3

>>10605178
The torus mod S^1 in the sense you want is equivalent to S^2 wedge S^1.

http://www.kurims.kyoto-u.ac.jp/~motizuki/news-english.html
>2019-05-01
>(Papers) Revised version (list of revisions):
>The Mathematics of Mutually Alien Copies: from Gaussian Integrals to Inter-universal Teichmuller Theory.
>Added \S 3.11

http://www.kurims.kyoto-u.ac.jp/~motizuki/Alien%20Copies,%20Gaussians,%20and%20Inter-universal%20Teichmuller%20Theory.pdf
>§3.11. Mathematical analysis of elementary conceptual discomfort
>We conclude our exposition, in the present §3, of the main ideas of inter-universal Teichmuller theory by returning to our discussion of the point of view of a hypothetical high-school student, in the style of §1. Often the sort of deep conceptual discomfort that such a hypothetical high-school student might experience when attempting to understand various elementary ideas in mathematics may be analyzed and elucidated more constructively when viewed from the more sophisticated point of view of a professional mathematician. Moreover, this sort of approach to mathematical analysis of conceptual discomfort may be applied to the analysis of the discomfort that some mathematicians appear to have experienced when studying various central ideas of inter-universal Teichmuller theory, such as the log-and Θ-links.

help please

>>10605178
>Unfortunately I'm not very good at visualizing the spaces in question.
No one is, for the record. Despite what some may claim.

>>10605178
Isn't that space just the circle times the wedge sum of two circles

>>10596144
The trudeu one is really good, but focused on beginners. If this is you, I can't recommend it enough.

>>10599364
>>10599362

Lol. very few people can cover this amount of material in undergrad. This meme is worthless.

>>10599550
By constructing a solution you usually get an algorithm for it at the same time. Plus its computable.

>>10601958

> Math isn’t as hard as people make it out to be.
yes

> mainly taught like shit,
yes

> it’s rigorously cumulative

The absurd build up they do in school from adding numbers, to equations, to inequalities, to polynomials to differential calculus is.

They could far improve math education by doing proofs and logical thinking with topics that require little to no commutative knowledge:
- geometry
- graph theory
- first order logic
- simple group theory


The real reason this won't happen is that K-12 teachers aren't intelligent and can't think for themselves. They have literally zero understanding of what math is and think its for adding up money. They need memorized problems and solutions more than the students.

>>10603531
>still thinking numbers are "imaginary" and not logical constructions inside arbitrary algebraic systems.

never gonna make it.

>>10606159
>Lol. very few people can cover this amount of material in undergrad.
Speak for yourself.

>>10606168
>commutative knowledge

>>10606051
>help please
What have you tried?

>>10606178
was about to add: inb4 elitists tell me I'm an idiot.

If you were really smart and did all this, you would readily acknowledge this as for only the most remarkable students. The fact that you can't shows that you just are LARPing.

The very first things says "analysis in R^n" which is pretty much 3 years of most undergrad, 1-2 if in honors.

>>10606181
lol. slip of the tongue

cumulative

>>10606186
>The very first things says "analysis in R^n" which is pretty much 3 years of most undergrad, 1-2 if in honors.
Which school for brainlets do you go to?

>>10606190
look at this faggot. larping about his math skills on an online forum.

math 55 at harvard doesn't cover even cover half of that "freshmen" material.

>>10606194
>look at this faggot. larping about his math skills on an online forum.
"her" math skills, actually.

>>10606200
Thanks. Now I really know this conversation is worthless. bye

>>10606186
>"analysis in R^n" which is pretty much 3 years of most undergrad
im fucking sorry?
we're talking about mathematics majors here, right

>>10606184
I ran a few experiments...

>>10606178
Not even most professional mathematicians actually understand the material from "senior-specialist" in depth

>>10605297
you're only gonna get indignant replies ITT, most of us did those alongside multivariable calc, differential equations and/or stats. They're babby shit.

>>10606194
These days most harvard undergrads who are grad-school bound take only graduate math courses (besides math 55, which basically exists so they can prove they're not full of shit).

At this point the "standard" path is to enter undergrad having already learned 'undergrad math' and to enter grad school having already learned 'grad level math'.
The basic reason being the powergap between something like hartsgorne and actually doing interesting research is now large enough that if you're an algebraic geometer and you first learn about schemes in grad school, then you've already shot yourself in the foot for post-docs.

On the subject of that particular image, it's always been obvious it was made by a differential geometer (and one with a rather narrow worldview at that). But the general idea in terms of how advanced of material a student should be engaging with is correct.

>>10606661
A differential geometer who doesn't understand everything on that list either (A) has incredibly narrow interests, or (B) is trash.

>>10606186
What does "analysis in R^n" mean? If you're including functional analysis between real spaces then I guess. Otherwise I'm pretty sure even the most brainlet of pure math courses finish with vanilla real analysis by their second year.

>>10606910
What's vanilla real analysis?

>>10606904
How are étale cohomology, algebraic K-theory or class field theory of interest to someone specializing in geometric analysis or dynamical systems ? Stop LARPing and get a grip
Math does not end with complex geometry and mathematical physics

Daily Putnam Problem >>10607140

Daily Putnam Problem >>10607175

I need a crash course on probability before my final on Friday
holy fuck I skipped every class this semester because the homeworks were easy as shit and now I'm regretting it
kill me

>>10607222
Enjoy summer school, retard.

>>10606916
Real analysis done without measure theory, topology or banach spaces, I think.
>>10606888
>made by a differential geometer
I thought that too, but the analysis is extremely weak, and SDG doesn't show up entirely.
I think he just really, really likes pure differential, algebraic and complex geometry.

Let's say I have N cups and M marbles. All of the marbles are put into cups randomly, with repetitions. How do I find the expected value of the number of cups with at least one marble?

is computability fundamentally related to countablility in some way? it makes so much sense but im a brainlet

What's the next step in the sum /b/?

>>10607660
If you can solve something in a countable amount of steps you can usually arbitrarily approximate it.
Emphasis on usually.
>>10607670
Probably x^n^4.
>>10607430
Ask on /sqt/.

>>10599364
Memes aside, what's the actual OFFICIAL /mg/ certified curriculum?

If it is khan acad -> spivak and then wherever your interest lies (or uni tells you to), it's pretty shit. We should have an official curriculum all the way from 1st year highschool to senior grad.

>>10607714
Wouldn't it be easier to make a list of topics we believe everyone here should have some grasp of and recommend books?

>>10596144
we're using Harris' and it's great on theory, but doesn't give a fuck about you learning how to solve graph theory problems

>>10598135
I had an elementary geometry course in uni that was really formal and rigorous. Great experience, I enjoyed it a lot.

Edwin Moise's Elementary Geometry from an Advanced Standpoint is great, but not probably what you're looking for. I'd use it as a supplement to any other standard elementary geometry book.

Just if, by the chance, you happen to be chilean, 'Geometría Elemental' by Arenas, Masjuán and Villanueva is unironically the best treatment of geometry I've seen so far. No pdf version available so far unfortunately, although I could get my hands on that soon.

>>10607714
I think people should properly learn analysis before doing or even instead of rote calculus

It weeds out brainlets

>>10601212
not an algebraic geometer, I despise them too, but one has to give them credit for the weird applications to number theory, arithmetic geometry is a thing on its own

>>10604325
you can't "learn the entirety", but I assume you mean "traditional uni lin alg and calc"
I'd really suggest reading Axler's Linear Algebra followed by Hoffman & Kunze. LADR is unbeatable at explanations but it's kinda incomplete. Hoffman & Kunze cover more topics. For Calculus, try Spivak's Calculus and Bartle & Sherbert's Intro to Real Analysis.

>>10606168
>commutative knowledge
>muh algebra
you're right tho, teaching simple group theory may not be a good idea unless there's a good grasp of the motivations behind it

>>10595623
How do I get laid

>>10607875
https://en.m.wikipedia.org/wiki/Lie_theory

>>10607797
bitter toyman

>>10607875

>>10607875

>>10606888
I believe this for the very top top mathematicians. I don't believe the vast majority of even tenured professors followed this path.

https://arxiv.org/ftp/arxiv/papers/1905/1905.00255.pdf
>A Simple Proof for the Four-Color Theorem
>Wei-Chang Yeh
>(Submitted on 1 May 2019)
>The four-color theorem states that no more than four colors are required to color all nodes in planar graphs such that no two adjacent nodes are of the same color. The theorem was first propounded by Francis Guthrie in 1852. Since then, scholars have either failed to solve this theorem or required computer assistance to prove it. Hence, the goal of this paper is to provide the first correct proof of this 170-year-old mathematical problem composed with the human brain and without computer assistance in only five pages.

>>10607660
Countable infinities are the only infinities we can actually get our hands on. It's because, in some more rigorous sense, they're "approximated" by finite values, which are the only things we can actually compute. This is opposed to larger infinities, which are approximated by other infinities.

>>10609033
Why are topologists still butthurt about Appel and Haken's proof of the four color theorem?

>>10609378
why arent you?
its not a convincing proof to say "its true because a computer checked it"

>>10609402
>its not a convincing proof to say "its true because a computer checked it"
Humans are just biological computers.

>>10609378
The last steps of the proofs rest on checking an astronomically high (by human standards) number of configurations automatically and without real understanding of why they work. It's a bit unsatisfying.

Fwiw people have had the similar misgivings about the "proof" of the classification of finite simple groups up to isomorphism, which didn't rely on any computer proof assist. Some cases haven't been dealt with in public paper yet (as far as I'm aware) and we don't have a clear picture of why the classification holds yet (although people are working on it) so despite having most of the proof some feel it's not enough.

>>10609003
Tenured professors are often from an older generation. Prospects are looking direr for us milleniumlets.

>>10599438
This is a retardedly high speed for seriously reading a mathematical book. You might as well skim everything and only remember bits of notations here and there.

>>10609409
irrelevant, we still explain the steps we go through in proofs.

So the other night while I was preparing for finals I was sitting in the computer lab in the engineering hall at my school. Some random kid I knew was messing around in a python terminal, multiplying huge numbers together for shits and giggles. He entered in 9999^9999 and it spat out this enormous number that was several pages in length in half a second. I sort of questioned whether the answer was correct because it seemed unlikely that it could calculate such a large number so quickly. All I remember was the last 12 or so digits of the was 9 repeated. Is there some sort of proof you could use to check what the ending digits in 9999^9999 would be?

>>10609591
>So the other night while I was preparing for finals I was sitting in the computer lab in the engineering hall at my school. Some random kid I knew was messing around in a python terminal, multiplying huge numbers together for shits and giggles. He entered in 9999^9999 and it spat out this enormous number that was several pages in length in half a second. I sort of questioned whether the answer was correct because it seemed unlikely that it could calculate such a large number so quickly. All I remember was the last 12 or so digits of the was 9 repeated. Is there some sort of proof you could use to check what the ending digits in 9999^9999 would be?
what's the tl;dr?

>>10609591
> Is there some sort of proof you could use to check what the ending digits in 9999^9999 would be?
> pow(9999,9999,10**10)
> 9999989999L
Exponentiation isn't a particularly complex operation. Just split the exponent into powers of two and use x^(a+b)=x^a*x^b, x^2n = (x^n)^2. IOW, keep squaring x to get the x^(2^n) terms then multiply the terms corresponding to 1-bits in the exponent. If you just want the last few digits, you can reduce intermediate results modulo 10^k, as (a*b)%m=((a%m)*(b%m))%m (which is why the 3-argument pow() exists; pow(x,y,m) is more efficient than (x**y)%m as the former reduces intermediate results modulo m rather than generating a 40,000-digit number then reducing it at the end).

Cayley's Theorem isn't just a theorem. It's a way of life.
t. Geometric Algebraist.

I have a diff eq final in 6 hours and I have no idea how the fuck to solve literally anything without referencing examples

Fuck this class so much. I need like a 50 something to pass but its gonna be close

x^5 = 6 mod 101

I made another thread, but didn't see this maths general. Can someone help me solve this? I know there are 5 solutions but how do I get them least residue?

>tfw running out of paper

>>10610073
Just use laplace transform properties of derivatives. It's not hard.

Daily Putnam Problem >>10610385

>>10609422
>>10609402
Explain to me how wasting years of your life checking 1,476 cases by hand is any different from wasting years of your life trying to understand Mochizuki's proof of abc. Then explain to me why you'll take some crusty old academic's word that something is true on faith, but not a program that has been independently verified by humans and proof assistants and that you yourself could easily verify too.

>it's a bit unsatisfying
I think this is the real reason why there's so much controversy about it and computer assisted proofs in general. Mathematicians want to have a short, ingenious explanation as opposed to a laborious proof by cases. It's more of an objection on aesthetic grounds than anything else.

I for one think this mentality is old-fashioned and counterproductive, even bordering on luddism. It seems foolish to think there will ever be a "simple" explanation for things like the classification theorem or Goldbach's conjecture.

>Graduating with a bachelor in Mathematics this month

So what now?

>>10610488
i accept that the proof is true, but its not a good proof since independently checking it requires the same computer power

yes, its an aesthetics criticism, because its a fucking ugly way to prove something

Remember to work with Engineers

>>10610505

>>10595713
>>10595623
>>dumb question you need answered
i had a thought and so far cant find any answers
if you were to build a horizontal road/bridge/piller from one point on earth out to space, and then walked along it how would the changes in gravity effect you? at a certain point would it start to feel like you were going up hill? would you get to a point you couldnt move any further
pic related

Opinions on AoPS books? AoPS in general?

>>10609033
> Written in Word
> Nobody is going to take it seriously

>>10611418
Come on no one in /mg/ going to IMO 2019?

>>10611652
>math olympiads
>functional equations, algebraic manipulation, autism tier spatial visualization and combinatorics
Hard pass. Honestly fuck olympiads, who actually likes those things other than combinatorics.

>>10611661
Come on don't be a cuck, the kids love that kind of shit. It's fun for the whole family.

>>10609591
(10000 -1)^9999 will have 9999 as its last four digits by high school algebra.

>>10611652
4chan is a website for people aged 18+.

>>10600374
>what's wrong with sage?
you don't follow the news, do you?

>>10606012
>Scholze is a dumb high schooler: the post

>>10612285
What news, other than William Stein is bitter as fuck?

>>10596144

Bondy Murty is by far the best one.

Avoid reading anything by Bollobas please, don't let student from Cambridge tell you otherwise.

How do career prospects look like in your field? Is there any chance to get a tenure before 40 if you're not a Scholze?

How is the teaching/administrative burden? Do you get any vacation?

t. considering moving from the totally fucked up Germany to Murrica

>>10612477
If you are even considering making mathematics your career then you should accept that your life will be full of poverty and suffering.

>>10612283
The leader and deputy leader are typically mathematicians with an important position in their country's olympiad foundation. I'm literally hoping that /sci/ is not just a board of fakes and that there's at least a couple of peope doing interesting stuff.

>>10606012
>Often the sort of deep conceptual discomfort that such a hypothetical high-school student might experience when attempting to understand various elementary ideas in mathematics may be analyzed and elucidated more constructively when viewed from the more sophisticated point of view of a professional mathematician.
Truly the Galois of basic number theory.

>>10612692
olympiad isnt "interesting stuff"
its gay competition math

>>10612819
Yeah, that's true and everyone knows that. But I have yet to meet a mathematician without a rich olympiad history who was not also a complete dead-end loser.

Even people who do not compete as kids, if they are worth their salt they eventually get into competition math because it is fun and in Europe, you really have the true greats making problems. Everyone who likes math likes those problems. The only reason I can think of for why someone would not like those problems is because they are simply too dumb to solve them.

>>10603207
Underrated.

>>10612819
based
most kids there are smug af but grow up to be depressed and addicted to drugs because higher math is hard for them and they can't cope with it
t. knows people who went to them

>>10612828
>agrees its gay
>”its fun”
what did he mean by this

>>10612898
Many things are gay and fun. Here's a red pill for you: math in general is very gay and very fun. Hope you don't find out too late!

>>10612477
Learn to code.

>>10597031
who told you that math doesn't exist?

>>10612828
this is moronic
for instance, i am very very opinionated about math. i fucking despise combinatorics and algebra, can't understand why anyone would bother with discrete probability, etc. etc.
and yet i absolutely love analysis and (modern) geometry.
liking high school competition math might make you a good combinatorist or some dumb shit, but it has no bearing on your analysis skills
of course, in america we have the putnam for uni which does have analysis (but also lots of other things)
i don't know my dude, sounds like you need to get out of your little circlejerk if you think that all mathematicians unironically enjoyed competition math. there are just so, so many better and more fun ways for people to spend their time.

>>10613153
You are getting too fixated on the topics. The thing is that just by virtue of knowing math, you already know all there is to know about elementary algebra, geometry, number theory and combinatorics. Everyone knows everything about all of those topics almost by default. From birth. Because of this, olympiad problems are literally just top tier problems with virtually 0 pre-requisites. And the problems are fucking good. The mathematical form of crack cocaine.

I cannot comprehend why someone would not enjoy this.

>what are you working on?
Finishing up my linear algebra course and trying to learn more about SVDs also preparing for research this summer
>what are you reading?
Reading, Writing and Proving by Ulrich Daepp and The Game of Cops and Robbers on Graphs by Anthony Bonato
>dumb question you need answered:
What is a good text to read about Singular Value Decompositions? My professor said we won’t have bough time to get to it but it seems like a fairly important topic.

Daily Putnam Problem >>10613291

>>10613225
kys retard

What is the most complex task or branch a four function calculator is suited for?

haven't done math in three weeks, give me something to warm up with.

>>10610073
Are you from north Europe?

>>10611174
I think the original two-volume AoPS set is the best resource for high school math I've ever seen (provided you are good at math). It covers everything a good high schooler should know pre-calculus and then some, and it's perfectly possible to literally teach raw students shat straight out of eighth grade directly from it if they're talented (this was what I did in a gifted high school many moons ago when these books were only a few years old). It also does a wonderful job of approaching contest prep properly by teaching reasoning methods for approaching weird problems instead of teaching you to recognize piles of retarded ugly tricks (looking at you, all 300 books by Andreescu).
Never read any of the other volumes. They seem kind of redundant except maybe as a source for additional problems since everything relevant is already covered in the general problem-solving books.

It's true that [math]\mathbb RP^n / \mathbb RP^{n-1}\cong S^n[/math]. Is it also true that [math]\mathbb CP^n / \mathbb CP^{n-1}\cong S^{2n+1}[/math]?

>>10614101
no

>>10613225
they're not good, they're boring and ridiculously uninteresting. HURR DURR JANE AND ADAM PLAY A GAME!!! LOOOOL FIND F(X) :)))) HAHAHAHAHAH WHAT IS LE INTEGRAL :^) !!!!!!
this is what you people sound like
i care about the bigger picture, thank you very much. i care about theorybuilding, history, and context. math is living and flowing. competition math likes to pretend that it's so fun and quirky, but really it's just a lifeless emotionless husk.
you have to be one of those fucking reddit tier autistic morons who thinks that math is so fucking epic and loves numberphile and flammablemaths. not what math is, sorry. it's elegant, classical, and refined. go be a fucking physicist.

>>10595623
>Talk empirical science.
fire hot

>Trying to set up a study schedule so that I can get into the habit of studying math in 75 minute blocks
>Family keeps interfering in my study time by blaring the fucking TV. Fuck it, might as well give up trying to focus.
>When it's not the family, it's one of the numerous cats who starts calling out for no damned reason. Can't blame the cat because she's calling out for the kittens she lost 10 fucking years ago.
>When it's not at home, it's work when I suddenly get volentold that I'll be helping disabled fucks with their finals on the last study day that I have despite the fact that was never in my shitty part time job description
Is there a way to start building a flexible study habit with math? Any time I try to start building a ridged study habit, some fucking giant space flea appears out of nowhere and fucks up my day. Pic Related, me in the center.

>C in Calc 3

Should i just switch majors math bros?

>>10614327
>they're not good, they're boring and ridiculously uninteresting. HURR DURR JANE AND ADAM PLAY A GAME!!! LOOOOL FIND F(X) :)))) HAHAHAHAHAH WHAT IS LE INTEGRAL :^) !!!!!!

I think you are thinking about olympiads like the AMC. What I'm talking about are the real dick measuring olympiads made for the US, China and Russia to nuke each other and see who is big daddy without actually killing anyone.

>i care about the bigger picture, thank you very much. i care about theorybuilding, history, and context. math is living and flowing
Nothing wrong with that but you should read some Erdos.

>you have to be one of those fucking reddit tier autistic morons who thinks that math is so fucking epic and loves numberphile and flammablemaths. not what math is, sorry. it's elegant, classical, and refined. go be a fucking physicist.

Nothing to do with that actually. Competition math is a bit specific and actually requires a lot of dedication so that immediately disqualifies pseuds. I mean, sure anyone could break a couple of IMO problems but to actually break into these organizations you need more than that. What I personally like about competition math is that it is the only way to teach a math class in a room with only geniuses. Seriously, these lectures flow better than an actual college course because pretty much every kid sitting there knows more than you by nature of being a machine produced by the state to solve problems. There's no friction, only fun.

And that, I'd say, is priceless.

>>10614508
i have read some erdos thank you very much, and it was appalling how he lived.
i'm partial to the hardy lifestyle myself.

>>10613673
Prove that there are only 4 rings of order 4.

>>10614346
If you attend a decent uni they should have a library; otherwise look for a public one and make it a habit to study there. Studying at home is tough when you live with your family, even more so if they don't give a fuck about your studies.

>>10601212
Cryptography

>>10598227
Yeah, I bet your mom knows a lot about the science of orality.

How to measure the "predictability" of a set of data?

I need to benchmark a forecast of incoming contacts for the customer service of a medium-large company.
I've already set up reporting based on the forecast incoming vs actual at various rolling intervals, but as the different markets we support can be different in terms of volatility I think it would be useful to have a metric on the predictability or consistency of the actual incoming contacts per market.

We're a fairly new company & none of this reporting has been in place before

This is what I've thought of so far:
>Split historical data into buckets for days of the week, weeks of the month & months of the year
>Calculate the standard deviation of each bucket

Now I have measures of the volatility at a daily, weekly & monthly level.
The part I'm having trouble with is getting this down to a single metric, how to combine these?

Daily Putnam Problem >>10615013

>>10614536
Any other tips

>>10609591

How does one go about proving there is no constructive proof of a theorem? (for example the Brouwer fixed-point theorem).

>>10615232
Size reasons. The number of constructions will usually be less than the number of outputs

>>10615380
Could you expand on that what you mean by outputs?

>>10614346
Get a lock on your door
Buy earplugs (silicone is goat), can get good ones for 4$
If that's not enough, buy those construction site ear protectors and put it over the earplugs. Can get them for 15$

Use pomodoro method

>>10615232
Probably there's some theorem or heuristic where if it depends on the axiom of choice, there is no constructive method

>>10615397
Sure but how do you haven't just come up with a rubbish proof and you don't need the axiom of choice?

>>10615400
A lot of work has been done on this, why don't you read set/model theory? Obviously such proofs are not easy to come by. Regardless, you can pretty much discern without a need for proof which proofs (or statements rather) are constructive or not just by their nature. Fixed point theorems in analysis are notoriously non-constructive.

What's a good textbook for Data Analysis?
Something that includes stuff like Principal Component Analysis, Factor Analysis, etc. while also not being for brainlets who don't know basic shit like Linear Algebra?

>>10615443
Isn't banach's FP theorem constructive? Constructing the FP as the limit of the sequence [math]x_{n+1} = F(x_n)[/math]?

>>10615232
Show that it (constructively) implies the existence of some object which you know cannot be constructed. Depending how strict you are about what counts as a valid construction, this might mean something that requires choice, like a non-measurable set, a free ultrafilter, or a well-ordering of the reals, it might mean a function R -> R that is not continuous, or it might mean a function N -> N that is not computable.
>>10615600
Banach's is, Brouwer's isn't. Brouwer's fixed point theorem doesn't imply any consequence of the axiom of choice that isn't provable in ZF, but it does imply the existence of non-continuous functions.

why are there so many fixed point theorems?

should i get gud with Java bros? i already know Python and C++

>>10615692
Because they're for different things.
See the Brouwer fixed point theorem, the Arnold conjecture and the Lefschetz fixed point theorem and compare.

>>10615692
cuz fixed points are fuckin neat

have you seen this video?

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

>reading about a mathematician from poland
>turns out he worked with this other mathematician from.my country
>who happen to be my thesis director's phd assesor
jfc how deep the rabbit hole goes