/sci/ - Science & Math

First for Jewish mathematicians

>>11411492
This clown is a meme. Everybody should stop talking about him.

>the past thread lasted less than 2 days
I'm sorry, but half of you guys will have to leave.

>>11411552
>This clown is a meme.
What do you mean?

reposting from /sqt/
>>11407754

>>11411492
why does he look like papa franku?

>>11412037
Because all asians look the same

>>11411897
Do you know what the closed sets for the zariski topology on C are? Do you know what they are on C^2?
Here's a hint: how big can the zero set of a single variable polynomial be?

>>11412223
think i got it, thanks.

redpill me on the divide operator

>>11412234
What could you possibly mean by this inane, hopelessly nonspecific post?
Division of what? Numbers?

where should a mathematical brainlet with basically a pre algebra level knowledge of math start with learning this? i want to mentally rewire myself into a STEMlord

>>11412251
Have you checked /sci/ wiki?

>>11412240
What is the mathematical definition of a/b where a and b are integers? How does that work in mathematics? What if it is an impossible calculation? Try something else? pathetic

>>11412251

>>11412326
>Have you checked /sci/ wiki?
/sci/ wiki is a meme.

>>11411492
If I had a formula for the nth prime number, would that be significant? Could it be used to prove or disprove anything significant, like the Riemann hypothesis?

>>11412338
>If I had a formula for the nth prime number, would that be significant?
No, because one already exists.

>>11412356
Really? Do you have a link?

>>11412338
Is it easy and convenient to compute?
If so, absolutely. I'll just let you know that, if it's a polynomial, it doesn't work and you fucked the proof up.
Otherwise it might be useful for this and that.

>>11412330

Is this the math curriculum at MIT?

>>11412618
It's the official /mg/ curriculum.

>>11412618
MIT is a trade school for hacks and engineers. That's what you'd find at a real school like Harvard.

>>11412251
What the fuck do you mean by "pre-algebra". Algebra is already the starting point. If you mean you can't do 5 + 5 or 4 × 2 and that kind of stuff then consider finishing elementary school before posting on /sci/.
If you can do that then start with a easy pre calculus book like Sheldon Axler's. It's starts with just elementary stuff if I remember correctly. If you get stuck then just go to khan academy. When you are reading the book keep a paper or a notebook and solve the problems yourself but don't get discouraged if you can't even do the first step. Just think, write some garbage, try to find how to make progress. After a couple minutes read the solution and try to understand why he is doing what. At the end of each chapter, like half the problems have solutions... I think? So try to solve them by yourself without looking at the answers. If you can't get them, then re read the sections of the chapter you don't understand and re read the problems he has already solved.

And also libgen is a good way to get books. Axler pre calculus is on there as well.

>>11411492
I'm taking calc 1 with analytical geometry this semester as a prerequisite for my physics major and boi I'm loving it. We just finally finished up accumulation functions and we're moving on to integrals. I can't wait to start doing more interesting stuff. Accumulation was kind of dull and lasted a long time, though some parts were fun. Like when I finally got that R(x) = Rf(left(x)) I was like YOOOOOOOOO. It was crazy.

I'm really hyped guys. I can't wait for it to get more intense.

>>11412330
I would have fucking killed myself if i had to learn delta epsilon shit back in high school

what books should i use for relearning calculus, ODEs, PDEs, and maybe linear algebra? took the classes at my university a few years ago but mostly fucked around and want to strengthen my foundation of these before going on to higher mathematics.

>>11412330
has any autist actually attempted this? would it be abuse to force my son to take this path?

>>11411552
Even before IUT he was a well known Arithmetic Geometer and Did a lot of work concerning grothendiecks conjectures in the field

>>11412684
I keep seeing libgen suggestions, but can't find a working link. Can you help, anon?

>>11412722
Stewart for Calculus

imagine announcing your own death in your own Wikipedia article's talk page.

https://en.wikipedia.org/wiki/Talk:Boris_Tsirelson#Death

pretty based I have to say

>>11412727
LIB-GEN LINK! LIB-GEN LINK!

>>11412727
nigga dont you have google, bing, or duckduckgo?

>>11412727
http://libgen.is/
Here you go anon, I am the one you were replying to.
And just in case the link doesn't work, this site has a lot of "other" libgens. They are the same but sometimes one works and the other doesn't.
https://librarygenesis.net/
It also contains a guide on how to search books but to be honest, libgen doesn't exactly have the best searching engine. Most reliable method is to go to Amazon, find the book you want(and 99% of the time, it is on Amazon) and look at its ISBN-13 number and directly copy paste the whole number. If that doesn't work, then copy paste the title,if you get no results, then erase the title's last words and try again. And if that still doesn't work then try searching the authors' name. It's kind of tedious but I have found pretty much all books I wanted on Libgen.

>>11412333
It helped me

>>11412329
This is bait.

>>11413205
Ty, anon. You're terrific.

>>11413372
Does it matter if it's bait or not? You have no answer. If the result of a/b has to be an integer, there is no algebraic procedure for impossible results.

Do you guys know of a resource for a quick review of the most common methods of solving ODEs and PDEs?

I don't want anything rigorous. Just a review to get up to speed for numerics classes in the next semester.

>>11412655
>implying ivy league is not full of hacks

>>11413439
I mean analytical methods, not numerical methods, btw, if that was not clear.

>>11413441
>be masters students at state university math program
>dean calls every graduate student to a mandatory meeting
>Browse around the room
>Of the roughly 40~60 people there, only 10 were Americans and at least 20 were Chinese
I get that its because their countries pay for their students to come here but for fucks sake

>>11412251
>algebra
Oh, so you already know group and ring theory, good, you're in the right path.

Protip: don't use the word algebra if you're referring to high school shit

>>11412618
It's the curriculum at IMPA, that image was made by Misha.

>>11412558
It definitely won't be a polynomial. I actually haven't fully worked it out yet, but I am close. It will be somewhat unwieldy and full of floor functions. I don't think it will be very convenient to compute.

But I am also wondering if there is some established way to take the limit of such a function, to infer something about the distribution of primes. (e.g., to check that twinning occurs out to infinity, or the Riemann hypothesis.)

>>11413439
Differential equations with boundary value problems by Zill

Dont know shit about pdes kek

>>11413478
Economically speaking, US universities are too big for just their own academics. You depend on the brain drain. Seriously, compare the total size of math departments around your country to some rough estimate of the number of mathematics graduates interested in pursuing academia.

Now, instead go look at the floor of quant hedge funds and you will likely see many more whites than non-whites. I'm sure this is a mystery that will take Perelman tier intelligence to solve, but for some reason, universities are not good at incentivizing people to go into academia unless they are from some dirt poor country.

>>11413516
There already exist "formulas" for the nth prime, but it always turns out that they're just disguising brute-force checking under a pile of arithmetic operations. Not only are they not "very convenient" to compute, they're almost always flat-out slower computationally than just listing all the primes until you hit the nth.
I don't even need to see it to guarantee you this is what you're doing.

>>11413536
>listing all the primes until you hit the nth
Is this even possible? Don't you have to check all natural numbers for divisibility by the known primes? (Or at least, check all multiples of 6 +/- 1?) . If I know all n-1 primes, can I figure out the nth prime with existing methods?

>>11413532
>universities are not good at incentivizing people to go into academia unless they are from some dirt poor country.
Look at it like this, Most STEM degrees (excluding math) have some sort of job work they can do straight out of the gate. They get some level of respect at their jobs and its enough that they can live on their own.

What does Academia offer?
4+ more years of effective poverty for a PHD
However a serious chunk of the academic disciplines PHD holders are a joke now. They just churn out paper after paper that has no use, these papers do not push the boundaries of knowledge, nor do they offer anything of substance. If I recall, we've reached a point where most academic papers published have simply not been read after their publication date. I mean, nice job showing a different proof of schwarz inequality, but literally no one cares, but hey, gotta keep pumping out papers for the next 10 years to get tenure.

>>11413547
What work can physics majors do straight out of the gate?

>>11413536
Kind of, yeah. I am trying to use the theorem here:
http://farhi.bakir.free.fr/index_fichiers/Fibonacci_2.pdf
which generates the complement of a sequence.

So if I have a sequence for multiples of 2, I can generate the complement of it (odd numbers).

Same for if I have a sequence for multiples of 2 and 3 (just multiples of 6)- the complement would be co-primes to 2 and 3.

In this way I can generate a formula for co-primes to the first (n-1) prime numbers. The nth prime number is the 2nd co-prime to the first (n-1) primes.

Do you have a link to some of these already existing formulas? When I look here:
https://en.wikipedia.org/wiki/Formula_for_primes
all of them seem to either have an unknown parameter, or give non-prime values some of the time, or something like that.

>>11413610
>Same for if I have a sequence for multiples of 2 and 3 (just multiples of 6)- the complement would be co-primes to 2 and 3.
Woops, made an error here- I meant to say multiples of 2 OR 3, which is not just multiples of 6.

I was wondering if this proof is correct. Is it wrong at the very beginning because it's negating the wrong thing? Or is it acceptable since the question isn't an if-then proposition?

>>11413437
You're literally talking about where the definition of rational numbers came from. Yes, in a system where your image is restricted to integers, you won't have closure through division hence why rational numbers came to exist as a mathematical classification. Unless you're genuinely trying to argue that in real life there are hard discrete definitions between all possible measurable objects then your objection is really silly.

>>11411492
I would like to talk about non-convex optimization but I doubt anyone here cares or knows anything about it.
Eitherway I've been working with 0th order optimization methods like proximal methods and monte-carlo approaches for large-dimensional problems for highly non-convex functions. I showed that these methods reduce to gradient-based approaches in specific circumstances, but in practice the gradient-based methods always seem to converge faster. (the connection to non-convex optimization is that a local convexity assumption is made, I haven't been able to relax that yet. The goal is to consider a 0th order global optimization scheme and its convergence bounds).
Perhaps someone has some intuition as to why gradient methods happen to work so well in non-convex optimization, or perhaps an idea for a 0th order global information scheme to accelerate convergence?

>>11413749
Just pointing out that divide is quite an "unnatural" operation compared to others. And I don't think it is adequately defined to match its complexity.

>>11413819
Division is unnatural? In what sense? Discrete division with a modulus is very natural. You've got 10 barrels of hay to split between 4 farmhands, you give each of them 2 and leave 2 additional as remainder or if you're talking continuous division you split the bales into halves and parse them out. What exactly do you mean that it isn't "adequately defined to match it's complexity?" What in your mind would be an adequate definition?

>>11413888
Assuming infinite granularity of the number lines makes it trivial, but for any segmentation- tessellation problems occur. The conditional linkages between factors is given no conventional expression and remains glossed over. Things like Riemann's hypothesis will never be solved simply because the tools do not exist.

>>11413958
>Things like Riemann's hypothesis will never be solved simply because the tools do not exist.
whoa whoa whoa whoa whoa
What about all the cranks and number theorists beating the fucking shit out of Robin's Inequality? I mean, when 4/5 papers on arxiv's number theory section has some fucking angle on that inequality, we must be close to an answer


right?

>>11413510
Algebra absolutely does refer to high school algebra as well. Stop the gatekeeping.

>>11413819
You seem very confused. Go read a book that builds up the reals from the Peano axioms. That ought to help.

>>11413958
>infinite granularity
>segmentation
>tesselation problems
>conditional linkages

Mathematicians don't make up words for fun but because it simplifies whatever they are trying to convey. That's the opposite of what you are doing. Please use conventional language instead of this mumbo jumbo.

Why does it take like a dozen axioms to define the reals? Why can't it just be like three?

>>11414012
Do you mean the ZF axioms? Some of them are redundant; Dana Scott came up with a reduced set of axioms and axiom schemes.

>>11413987
I appreciate the reference, but it is YOU that is confused, friend. Division is a different beast to the axioms you mention.

>>11414017
Division is not built into the Peano axioms, but on your way to defining the reals you will come across the rationals and their operations, which will include division.

>>11413510
>algebra
Oh, so you already know derived categories and dimension theory, good, you're on the right path.

Protip: don't use the word algebra if you're referring to undergrad shit.

That's how stupid you sound.

>>11414023
The axioms you use to define numbers are inherently independent of the operations used to connect them (or at least they should be).

>>11414032
>derived categories
That's a pretty weird example for a subject in algebra.

>>11414035
False. Numbers are defined by their set, order type, and operations.

Does anyone else here feel that the "schizos" are actually more intelligent and grounded than the so called "mathematicians"? I've been reading a few debates, and it seems like the schizos BTFO the mathematicans every time.

>>11414040
Why do you think so?

>>11414047
Please point me to a schizo v mathematician debate.

>>11414043
So I can redefine a number by defining an independent operation (let's say :x:) that, for example, accumulates the two adjacent numbers. Because that doesn't sound right at all. The existence of a potential operation does not change the number or its definition.

>>11414048
Because it, technically speaking, is an extremely important construction in homological algebra.
But it's also category theory, which isn't "quite" algebra. At least I wouldn't say category theory is a subject in algebra.
It's not wrong, it's just a weird example.

>>11414057
With the naturals, integers, and rationals the simplest construction is fairly obvious, but there are still some choices you need to make.
The reals don't have a canonical construction: you can use Dedekind cuts or Cauchy sequences to define them.
Therefore there is, from a foundational point of view, no one set of real or rational numbers. The real numbers are any ordered ring that behaves like the real numbers, i.e. is isomorphic to some previously chosen instance of the real numbers.

>>11413560
Go work for helion energy.

>>11414065
Category theory is algebra, in my opinion.

>>11414068
I appreciate the references, Anon. You are making me stronger than you can possibly imagine.

>>11414069
> Education and Experience: M.S. or greater in Nuclear Engineering, Experimental Plasma Physics or in a closely related discipline and five or more years of experience or an equivalent combination of education and experience.

>MS or greater

>>11414101
you don't know anything about job applications, those aren't deal breakers. Its just them greatly exaggerating the job's requirements in hopes of either getting top quality undergrads or very rarely someone who actually fits the bill but is willing to take a smaller paycheck because they are that desperate for a job

>>11413747
negating the wrong thing.

How do i learn to write proofs in a week

>>11414477
The same way you learn calculus in a week

>take diff equations class
>prof is 80 year old boomer
>assigns 20 problems each session, all due the next one
>Starts every class by saying some weird joke, then proceeds to do random examples on the board while barelly ever looking back at us
>erases every example from the board as soon as he finishes
>constantly makes mistakes that we have to point out
>yet he will count whole problems wrong because we didnt simplify fractions

Help

>>11414508
sounds like my old ODE professor, is his last name Peterson?

>>11413436
You are welcome anon.
Now go and study math.

>>11414012
Because the closedness relation can only be stated by ranging over subsets of the object itself

https://en.wikipedia.org/wiki/Tarski%27s_axiomatization_of_the_reals

>>11414554
>no archimedean axiom
I'm extremely interested.

any good resources for learning to deal with inequalities (in particular with respect to delta-epsilon formalism)? I still look at limit proofs and throw my hands up in frustration when I can't follow them.

I've taken differential/integral/vector calculus, linear algebra, and ODE/PDEs. Is that enough for me to start learning about Lagrangian and Hamiltonian mechanics? Also, are there any books on that subject that you guys recommend?

Why are these implicit derivatives different? All I did was move (4-x) to the other side

>>11414884
Obviously not, you need at the absolute least extensive knowledge of differential topology, symplectic geometry, Lie groups, calculus of variations and torus actions on manifolds.

>>11414934

>>11412251
Go through these and you'll be good. Should only take you a month or so to get through each book

Oh, God, why? Why did you make my life so miserable? Why did you make mentally unstable people being my progenitors? I can't take this shit anymore, all I wanted to do was study math and live peacefully. If there really is a God out there, he's too cruel.

What's everybody's favourite maths textbook?
I think I'd have to go with Neukirch's Algebraic Number Theory. I was really sceptical at first with how he introduces class field theory abstractly but it ends up making the structure extremely clear. Lots of exercises too. I started reading it after an undergraduate and a graduate course in algebraic number theory.

>>11414603
almost surely Axiom 2, paired with some of the algebraic axioms can be proven to be equivalent to the Archimedean property. It is an intrinsic property or [math]\mathbb R[/math].
>>11414884
Enough if you only want a basic understanding; for a yukarifag-level of comprehension you'd have to know >>11414934, though it doesn't hurt to take an undergrad course in analytical mechanics if your physics department offers it, so you can gauge your interest and see if you care about the mathematics behind it.

What does the study of mathematics impart to subsequent generations/students of a school in real-world terms?

>>11415104
They should stop teaching algebra and start teaching financial math

>>11415064
Yeah, Yukarifag does have an elementary understanding of the basic results of hamiltonian dynamics.
>>11415107
They should stop teaching children algebra and start teaching them how to cheat in poker and have sex with your mother.

For Limit Comparison Test of Improper Integrals:
1) How do we decide which is f(x) [numerator] and g(x) [denominator]?
2) How do we decide whether or not to choose a bigger or smaller function to compare to the original?

>>11415164
Uhhh, used a pretty bad picture. Here's a better one that's more related and obvious to what I'm talking about, sorry.

>>11411552
If you're not a math phd working in the same field as him you have literally no right to criticize him.

>>11415107
I would agree to algebra and financial mathematics. That way the abstract measurer and the communal measurer are one and the same, and the shared fields woud allow for everything to be distributed in terms of stress.

Being aware of financial concerns (i.e. the grains of sand we share for optimal waste reduction) is of great communal benefit and algebra helps separate an observer's world view into discrete parts and join them.

Personally I have always felt like geometry belonged to the arts department.

>>11412330
Cool, is there a specific book on delta-epsilon formalism or is it just called baby rudin?

>>11415178
Sure, we'll just let the number theorists bashing each other's brains in with Robin's inequality keep pumping useless papers that get us no closer to the Riemann Hypothesis

Who was the best mathematician to come from here? Poincare? Laplace? Cauchy?

whats the point of studying abstract algebra

>>11415231
laplace

>>11414057
Actually, yes that is the case with many situations. For example if you were to try to define the number ln(z) where z = x + iy, there needs to be an explicit choice which is made as to what range for your Arg(z) that you are considering. The number ln(2+3i) is explicitly defined by the operation and the limited boundary of rotation we have chosen for the image of ln(z). In fact many numbers are defined explicitly by operations like √2. The number √2 is nothing but the positive number whose square is 2. We define √2 by the results of an operation performed on it, and then numerically come to an approximate decimal expansion through a variety of ways.

>>11415231
Galois. Any other answer is fucking wrong

>>11412234
It's not real, you're really just dealing with rings have multiplicative inverses for all elements besides the additive inverse

>>11415392
additive identity*

>>11412358
>Really? Do you have a link?
https://en.wikipedia.org/wiki/Formula_for_primes

>>11415209
>Cool, is there a specific book on delta-epsilon formalism or is it just called baby rudin?
Rudin is a meme.

Something I thought was neat in Linear Algebra was the fact that the polynomials are isomorphic to a vector space. Is there a good use for conceptualizing the polynomials in this way?

>>11415645
Let [math]a_1,...,a_n,b_1,...,b_n,c_1,...,c_n,d_1,...,d_n[/math], with the [math]a_k[/math] different from one another and the [math]b_k[/math] as well.
Prove that there is exactly one polynomial P of degree 2n-1 or less such that for all k, [math]P(a_k)=c_k[/math] and [math]P(b_k)=d_k[/math].
This is much easier done with linear algebra

>>11415167
We tend to rewrite that condition [math] f \sim g[/math].
Then if you start from f, you look for any g equivalent to f that you know is (or isn't integrable). Who goes on top is quite a detail, pick whichever function makes the algebra easier.

>>11415045
I'm reading it right now as I'm getting back into maths after a 3 years break.
I took algebraic number theory classes back then but I still struggle with the exercises (I'm probably quite out of shape).
For instance he asks to prove in paragraph 4 of chapter 1 that (p) is a prime ideal of [math]\mathbb{Q}[\sqrt{d}][/math] iff the equation [math]x^2 = d mod p[/math] which I can only tie to more advanced techniques that come later in the book. He proves the same thing himself as an exemple a few paragraphs after that.
Was there an elemental way of doing that that I'm just too thick to see or should I not worry that I can't solve all the problems right away?
I feel I'm spending a lot of timeon those and I wanna get back into shape as quickly as possible as I'm applying for a PhD in june.

>>11413547
Just write a mediocre paper now and then, and let your advisor steal it, this incentivizes him to keep you around so you can work on a passion project.

>>11415392
>>11415395
Based
>>11415352
2^0.5 isn't a number though, you're writing out an operation to a number.

>>11415949
>4 isn't a number though, it's just the operation 2^2

>>11415968
But it is the number because you directly referenced it. As you previously mentioned, root 2 has no exact solution, so by calculating it you are only producing a set of near numbers

>>11415975
√2 does have an exact solution. It's √2. √2 doesn't have an exact decimal expansion but that doesn't mean it doesn't have an exact solution you literal brainlet.

Can (t-20)^2 be rewritten as (t-20)(t+20)?

t^2-40t+40?

it can only be (t-20)(t-20) right?

>>11416058
No.

>>11414930
bump

It was all good until I divided out the [eqn](x^2 - 4)[/eqn]

>>11412234
>>11412329
That's a good question. Here is the main formal definition of a/b.
First we take the integers for granted, including the operations + and * (times).
Then we look at the set of pairs of numbers (a,b) where a,b are integers and b!=0. We define an equivalence relation on this set of pairs ~ by requiring that
(a,b)~(c,d) if and only if ad=bc.
You can verify that this is indeed an equivalence relation. (use the fact that in the integers, ab=0 implies that a or b =0).
Now look at the equivalence classes of the equivalence relation. We write [(a,b)] for the equivalence class of (a,b), and it consists of (a,b), (2a,2b), (3a,3b) and infinitely many other elements.
With this, given integers a and b, with b nonzero, we define a/b to be [(a,b)] and the operations +, * as [(a,b)]+[(c,d)] = [(ad + bc, bd)],
[(a,b)]*[(c,d)] = [(ac,bd)]. You have to verify that these operations are well defined, meaning that taking different representatives of the same equivalence class gives you the same result, but that's easy. These operations define the field of rational numbers Q.

Guys, I think I fucked up.
In the last semester I spent all my time on math, did it 24/7 for 3.5 months, I think I only took a couple days off.
Now I can't bring myself to do literally anything not only math, any other activities too when I try to do them there is a thought that pops in my head that says "what's the point? you will achieve #1 here, then what?" In the last week I also became much less tolerant I explode (inside) at everything. I read yesterday that these are the signs of a beginning depression. What do I do?

>>11416139
learn category theory

>>11416139
>Now I can't bring myself to do literally anything not only math
? Do you mean you can't do math anymore or all you can do is math?

If its the latter, congrats, you're on your way to mastering the discipline

>>11416147
no, I can't do math anymore or any other thing

>>11416149
get a gf and leave all this math nonsense behind

>>11416157
yeah having someone to talk to would be nice, I guess one part of the problem is that I have not communicated with pretty much anybody in the past 2 years.

>>11416170
some campuses offer free consoling services were you can just go talk to a grad student who is training to become a therapist, Id start there

>>11416178
I did that in the very beginning I don't remember the exact reason but I went there in the first semester, they don't do shit they only listen and don't offer any solutions

>>11415982
Show me the exact solution then if you think you're so smart.

No 2^0.5 isn't the EXACT solution because it designates a calculate TO generate a solution.

>>11415551
All of those seem to either have an unknown parameter, or give non-prime values some of the time, or something like that.

>>11416208
No it doesn't. Literally write the following lines
> x^2 - 2 = 0
> x^2 = 2
> x = +/- √2

Or if you'd like, take a square with sides of length one and draw a line from one opposing corner to another. That length is a number called √2. Whether the number can ever be exactly evaluated in a decimal expansion is totally irrelevant to whether it is a number which only requires an exact analytical solution. √2 is an algebraic number that is the positive solution to the algebraic equation:
> x^2 - 2 = 0

>>11416115
>that's a good question
It isn't. If you wanna spoonfeed retards, do it in /sqt/.

>>11416115
Finally, someone with some intelligence on /mg/. I enjoyed the formal definition you posted.

However, I can't help but notice that this definition is quite loose, in that all you really have defined are the equivalent forms. What I am looking for is a mapping of valid parameters for (a/b=c where a,b,c are integers).

>>11416257
I will spoonfeed you in his place just this once, but please leave afterwards kudasai.
[math](a, b)/(c, d)=(a, b)*(d, c)[/math]

>>11416273
You just said what the other guy said, that I was replying to. Delete your post, retard.

>>11416273
And you even got it wrong. Stupid nigger

>>11416280
>>11416284
Not either of them but the pairs (a, b) represent rational numbers a/b and he just told you how to divide them. Division has been fully formalized, now you can fuck off and leave us alone.
You could also read about this in the beginning of the "fields" section in literally any introductory algebra text.

>>11416184
Yeah, that's the point.
The idea is to have you work through it.
Much like a math problem, having someone else hand you the solution does not promote actual progress

>>11416284
>nigger
Why the racism?

>>11416378
Dear dribbling retard,

>(a,b)~(c,d) if and only if ad=bc
defines equivalent fractions, nothing else. This does not answer my points.

>(a,b)/(c,d)=(a,b)∗(d,c)
is completely wrong, in both notation and form. Which is what you posted.

It is clear to me that you have no idea what you are talking about, so why don't you let the actual high IQ individuals talk about this. Now please never return to this place as we're not daycare for cretins.

Regards,
160+IQ Anon

>>11416284
>>11416411
>/mg/ has actual pre-schooler anons who don't know how to divide fractions

>>11416401
Who says I was being racist?
>>11416225
Draw using what medium? Listen pal, I know your tiny mind struggles with this, but the exact solution does not exist. Even if you had infinite time to compute it, you would still not achieve it.
>>11416432
Tell me about it. You ask one simple question and no one can answer it.

>Do you think the divide function in mathematics is properly defined such that all resultant behavior is index defined?
>2/3 is equal to 4/6 huehuehue ME SSHHMART *dribbles* U DUMB HEHEHEHE

Honestly, this place could be renamed to undergrade midwits general and nothing would change.

>>11415045
Additive Number Theory imo,the first volume excellently introduces the subject

>>11415383
Based

>>11416411
>>11416438
don't listen to the dumb weebs, your questions are good. Keep it up

If something as simple as a divide operator isn't properly defined, does that make mathematics a schizo subject?

>>11415711
There is an elementary proof of this but I don't quite remember it. You only need to look at the minimal polynomial, I think, and play around with it for a bit. No big tools required.

>>11415383
maybe if he didnt die so young he would have been, but laplace and cauchy mogged him

bros, how do i get letters of recommendation, the last time i talked to any of my undergrad teachers was six years ago

>>11416438
You don't seem to know what the word number means.

>>11416532
Shoot one of them an email and see if they'd be willing to write you a letter of recommendation or meet up with you in person.

>>11416469
What is "improperly defined" about division you schizo? Have you ever once in your life considered that maybe the literally 10s of thousands of mathematicians who don't seem to have your personal issue with division or "definition of numbers" understand something you don't?

>>11416411
>>(a,b)/(c,d)=(a,b)∗(d,c)
Care to explain what is wrong with that? It's just [math]\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b}\cdot\frac{d}{c}[/math] written differently (pairs instead of fractions)

>>11416469
Remember the set of rationals we constructed as the set of equivalence classes of pairs of integers (a,b) where b is nonzero.
The integers can be realized as a set of rationals of the form (a,1).
For two fractions (rational numbers) x=(a,b) and y=(c,d), their ratio x/y is defined to be
(a,b)*(d,c) = (ad, bc).
What about this is not properly defined to you?

>>11412329
int a = 2, b = 3;
a/b = 0

>>11416558
>Understand something you don't
Other way round bucko

>>11416587
>>11416558
>>11416546

Why don't you all stop replying to an obvious troll so people can actually talk about maths?

>>11415975
>root 2 has no exact solution, so by calculating it you are only producing a set of near numbers
Near to what?

>>11416668
To each other

Is it too late to apply for maths PhDs? are there any countries still taking applications?

>>11416739
the whole of europe

>>11416739
Japan. Visited Okinawa last year and if I recall they mentioned that they accept applications until April.
It's first come first serve though.

>>11416739
Germany especially has really lenient deadlines.

How do we get from the definition of variance Var[X] := E[(X - E[X])^2] its definition with the integral?

Is anybody here active on stackexchange or overflow?

>>11416950
okay it follows from
E[X^k] = int[R] (x^kf(x)dx)
why is that though?
I know that E[X] = int[R] xf(x)dx

>>11416974
Use LaTeX

>>11416990
I know that [math]E[X] = \int_{-\infty}^{+\infty}xf(x)dx[/math]
how does it follow that
[math]E[X^2] = \int_{-\infty}^{+\infty}x^2f(x)dx$?[/math]

>>11416990
I know that [eqn]E[X] = \int_{-\infty}^{+\infty}xf(x)dx[/eqn]
how does it follow that
[eqn]E[X^2] = \int_{-\infty}^{+\infty}x^2f(x)dx?[/eqn]

>>11416990
I know that

[math]E[X] = \int_{-\infty}^{+\infty}xf(x)dx[/math]


how does it follow that


[math]E[X^2] = \int_{-\infty}^{+\infty}x^2f(x)dx?[/math]

>>11411492
Suppose I have a formula for an increasing sequence of positive integers, a(n). Is there any way to turn that into a counting function, c(x), such that c(x) estimates the number of a(n) values below x?

>>11417015
WHY THE FUCK THIS SHIT IS NOT WORKING

>>11417020
I know that [math]E[X] = \int_{-\infty}^{+\infty}xf(x)dx[/math] how does it follow that [math]E[X^2] = \int_{-\infty}^{+\infty}x^2f(x)dx?[/math]

>>11417003
Bro, you just posted cringe.

>>11417022
Surely the 6th attempt will work

>>11417024
>>11417025
YOU NIGGERS DON'T HELP

>>11416739
It doesn't work like this in other countries but in America, the length of the deadline is inversely proportional to the quality of the school. Only shit tier schools keep their applications open past mid-January, and most of the really top-tier schools close before Christmas break.
So unless you're willing to go abroad it's in your best interest to wait a year now even if you _could_ get in somewhere.

>>11416990
[math] 2^2 = 4 \cdot 5[/math]

>>11417034
>assuming everybody is American

>>11416990
[math]E[X] = \int_{-\infty}^{+\infty}xf(x)dx[/math]

>>11417037
>explicitly specify that the post only applies if he's American
>complain that the post only applies to Americans
based retard

>>11417040

>>11417040
I think you've managed to break LaTeX embedding in almost literally every way it can break without getting it to work once. It's honestly impressive.

If I have a square Jacobian matrix, can I take its eigenvectors to determine in which directions the function is increasing and decreasing?

>>11417064
maybe

>>11417064
Yes.

So what's everyone's favorite theorem?

Mine is the Fundamental Theorem of Galois Theory. It is so strong, so useful, so pretty. It just keeps on giving.

>>11417015
[math]E[X] = \int_{- \infty}^{+ \infty} x f(x) dx[/math]

>>11417015
I know that [math]E[X] = \int_{- \infty}^{+ \infty} x f(x) dx.[/math] How does it follow that [math]E[X^2] = \int_{- \infty}^{+ \infty} x^2 f(x) dx?[/math]

>>11417081
Bravo!!
No idea though

>>11417081
Substitution, I guess.
Missing a divided by 2, tho.

>>11417077
>Generalized Stoke's theorem

>>11417081
Ahem, I'll give a most excellent explanation.
[math]E[g(X)] = \int g(x)f(x) d \mu (x)[/math]. That's the definition of expectation.

>want some math lecture in the background while im doing chores
>only youtube choices are random math subject IN HINDI or Wildberger
i want to die

>>11417170
I'd much rather learn Hindi than listen to that quack.

>>11413747
You don't want to negate the supposition, because that is what you're taking for granted to be true of x0. You want to negate the statement you want to prove.

>>11411492
>EE taking a shit ton of math classes for fun
>Taking algebra next semester
>Pass a transcript of all my registered credits to my dad so that he can pay tuition
>"Anon why the fuck are you taking algebra as a 3rd year engineering student? I learned algebra in highschool, I thought you where good at math!"

How do I explain to my lawyer dad that "algebra" is not what he thinks it is?

>>11417208
>in the room to your left you have to listen to a crack go on about how he proved the Riemann Hypothesis
>in the room to your right you have to listen to Wildberger discuss how infinite sets do not exist
>you must pick one and only one and stay in their for an entire hour
which do you pick?

>>11417077
Axiom of Choice iff Zermelo's theorem.

>>11417262
Wildburger. At least finitism is philosophically interesting.

>"What is the longest river in the world?"
>"What is the capital of vietnam?"
>"Who is Big Bird's friend on Sesame Street?"
The solutions to these questions can be computed with relative accuracy, and I think that's exciting. What is it about the structure of a question that affects speed and accuracy at which the solution can be reached by a computer? Where should I focus if I wish to study this kind of thing in depth? Linguistics? Theory of computation? Is there a Lang-tier text on this subject? I adore Lang's pedagogical style of his algebra text, and I really want to study this stuff in depth. I'm not a uni student but mathematics was my favorite hobby before it became my dedicated obsession.

>>11417077
Nyquist-Shannon sampling theorem

Do mathematicians still make basic, completely avoidable arithmetic/algebraic errors like us plebs do? Like forgetting a negative sign or bad handwriting making a z look like a 2 fucking everything up

>>11417320
we leave the arithmetic to physicists after waving our hands and exclaiming that the rest of the problem is trivial

>>11417281
Sounds like NLP. My friend who works in the field told me the classic introduction is "Handbook of Computational Linguistics and NLP". Haven't read it myself.

>>11417320
Absolutely. Doing analysis modules full of long strings of algebra helps, though.

>>11417320
Yes, except imagine the following two scenarios
>In scenario 1, you have effectivly proved a 300 year old theorem. To do this it took hundreds of pages to. However once or twice, you fucked up and fucked up bad. However, thankfully, since you're an ingrained part of the community, your colleagues come in and help you fix these problem areas.

>Scenario 2: Turns out a 40 year old inequality was incorrect this entire time because there was a major issue deep in the logic that everyone except 1 guy trying to learn it from another guy sees. This was an important inequality, so it was cited quiet often. This means you just invalidated a few hundred research papers, which is fine because they were built on bad math, but it still chaffs at the core

>Don't reply to the TROLL guys; having deep and interesting conversations about the fundamentals of mathematics is just RETARDED!

>Why yes, I do like to use /mg/ as my personal blog.
>Shallow trivia? What else would we talk about haha!

>>11417366
The fact that you never took a decent introductory analysis course is not our problem. Please stop trying to pass off your ill-posed questions as deep and interesting and go read a textbook. Tao's Real Analysis will help you out.

>>11417461
I did a maths degree, but I knew it was rubbish the whole way through.
>falling for the Tao meme
Big yikes buddy. That washed up schizo will never accomplish anything.

>>11417488
Where did you do your degree? What do you do now?

>>11417503
ITT tech

>>11417503
>Encouraging a blogpost
you r*dditors make me sick

Let's get things back on topic and talk about why the real numbers as a domain is poorly defined. Nested complexity with no mention of bounded complexity? Why are mathematicians so dumb?

>>11417579
There's nothing wrong with reddit.

>>11417579
>Nested complexity with no mention of bounded complexity
what does this mean? Please elaborate

>>11413819
funfact, if you strip the Peano axioms off multiplication, you're left with a decidable theory (i.e. Gödel incompleteness doesn't apply)

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

>>11411492
Are the formulas given on OEIS proven? If so, where can I find the proof?

>>11417641
>(i.e. Gödel incompleteness doesn't apply)
Why is this remarkable/fun?

>>11417641
Thanks Anon, that was a good read and very helpful. People like you make this general worthwhile.

>>11417600
A key point about the reals is that at any given point, you can increase the complexity (precision). This injection, whilst the very crux of the set, is very poorly defined on an operational basis. This becomes evident with any irrational numbers that feature- often treated as static where they really are dynamic. Things like Cantor's Diagonal Argument hinge off of this nested complexity being unbounded and static, thereby untouchable in terms of mathematical derivation and proof. Really the whole process of generation, complexity and indexing is mutable as long as the logic is congruent to itself.

>>11417641
>Peano axioms off multiplication
But doesn't addition naturally lead to multiplication or am I just being tarded?

>>11416447
There are several books with that name retard, give the authors name

>>11416834
One needs to be japanese to study there though, right?

>>11417260
>Oh, yeah? Tell me more about groups and rings then dad

>>11417669
How is this "injection" poorly defined? How are irrational numbers "dynamic"?

>Really the whole process of generation, complexity and indexing is mutable as long as the logic is congruent to itself.

If not the rest of your post, this sentence all but convinces me you have no idea what you're talking about.

Writing down more digits of a real number doesn't increase its complexity in any meaningful sense.

>>11417680
Nope. Where I went (OIST) had fully-funded PhD positions that do not require you to teach; and even if you had to the classes were held in English, at least officially. Most of the students/faculties weren't Japanese either.
It certainly helps if you knew Japanese but it'd only be required when ordering food.

>>11417693
How hard was it to pass there? I'm not a genius and my grades are just average, but I'm fluent in japanese though

why is this so hard...

integrating the left side of the equation is a nightmare so the easier approach would be to use uniform convergence. But the issue with uniform convergence is that playing with |e^-t - (1-t/n)^n| is also just as difficult.

What do?

>>11417698
>integrating the left side is a nightmare
It literally isn't tho.

>>11417716
Use the power series for the exponential function and exchange sum and integral.

>>11417692
I'm not going to write a whole paper for you Anon, but you'll see that the generation part ties into the operational basis that I was talking about. There is nuance to my language; don't think I'm just mashing the keyboard at random. I would love to be more specific but I'm dancing around the subject because I'm stupid as to give up important ideas on a basket weaving forum.

>>11417698
Don't know what you mean by "pass", but I was there for a conference and wouldn't be 100% sure about the acceptance rate. I don't think knowing Japanese would matter much imo.
Might be a long shot but you can try reaching out to their admissions office, which you can find on their website.

>>11417692
>>11417731
*not
Mind the Freudian slip

What is Touhoufag's background?

Why is dynamical systems so underrated? No one talks about it in the math community, I rarely see comments around here as well.

>>11417747
Yukariposter is an EE
Remiliaposter is a physicist

>>11417747
Fuck off blogposter

>>11417724
excuse me for being retarded but don't you get:

\sum_{k=0}^{\infty}\left[\left.\frac{(-1)^{k} t^{k+p+1}}{k !(k+p+1)}\right|_{0} ^{\infty_ { 0 } ^ { \infty }\right]

which is unbounded when we plug in the bound of infinity?

>>11417782
>\sum_{k=0}^{\infty}\left[\left.\frac{(-1)^{k} t^{k+p+1}}{k !(k+p+1)}\right|_{0} ^{\infty_ { 0 } ^ { \infty }\right]
Cringe.

>>11417782
[math] \sum_{k=0}^{\infty}\left[\left.\frac{(-1)^{k} t^{k+p+1}}{k !(k+p+1)}\right|_{0} ^{\infty_ { 0 } ^ { \infty }\right] [/math]

do mathematicans have power levels?

>>11417731
Nutters being vague on purpose about their "discoveries" is something you see time and time again at the fringes of the maths community. I'm willing to bet you don't have any sort of degree or even read a textbook on set theory or logic. Don't fool yourself into believing that your uneducated mind is able to think up anything remotely new on such a delicate and well-understood topic.
Your home-brew confusion is never gonna turn into research.

>>11417798
>>11417782
Bro.

>>11417875
Good thing I'm not uneducated or unsuccessful then. Cope harder, midwit sheep.

What field of physics is the most mathematically innate?

>>11417857
Yep.

Level 5 - 10 - Analysts
Level 10 - 20 - Geometers
Level 20 - 30 - Algebrists
Level 30 - 40 - PDEs/Dynamicists
Level 40 - 50 - Algebraic Geometers
Level 50 - 70 - Number Theorists
Level 70 - 90 - Theoretical Physicists
Level 90 - 99 - Logicians/Set Theorists
Level 100 - Category Theorists
Level 105 - Combinatoricists

>>11417972
Swap PDEs with Combinatorics and we're good.

>>11417984
Bro, you need literally genius level intelligence to get into research-level combinatorics

>>11417262
tough choice, but I'd pick Wildberger since he's presumably saner than a literal schizo. Plus I've already had the chance to meet a guy who insisted he had a valid proof of RH using only elementary complex analysis, it was cringeworthy.
>>11417655
yes; look on the references for each sequence.
>>11417761
few departments/institutions do extensive research on dynamical systems and many that do are in non-English speaking countries (e.g. IMPA in Brazil)

>>11413205
>https://librarygenesis.net/the-best-android-e-reader-app-2019/
>The best Android E-Reader App is Moon+ Reader
I'm not sure...

>>11418001
You literally don't.

>>11418001
this fuckin guy.
combinatorics barely counts as math you pseud. although i will admit some of the proofs are pretty neat. thanks for letting all of us know that you are a stupid undergrad cs major

>>11418043
Why does /math/ hate CS majors, again?

>>11417972
Level 110 - Information Theory

>>11417945
Come. Let me show you

>>11418003
I'm on this sequence:
https://oeis.org/A060461
I clicked on the "refs" hyperlink, and all it gave me was a search with 9 other sequences. And I clicked on the name next to the formula (Charles Greathouse), and it just took me to what looks like the guy's personal profile on the site.

>>11418068
I'm coming, I'm cumming

>>11418068
Ok.

>>11414115
Have you seen it out there lately? Every data analyst, even at shit companies, has a masters.

>>11418146
What's an example of a 'shit company'?

>>11418148
Apple
Google
Amazon
Microsoft
The Linux Foundation

>>11418009
Honestly I don't use that site except for getting links to different libgen sites.
I don't defend or condone whatever else the website is saying.

>>11418154
And a good company?

>>11418176
Are you serious? No company is good, no company is your friend. Fight capitalism, fight the Government.

>>11418185
This but unironically.

>>11418176
>And a good company?
Cambridge Analytica

>about to post about a problem I was having
>as I was putting it into LaTeX I realized the dumb mistake I was making
many such cases

>>11418298
Can I get a hint?

>>11418302
Try to have fun.

>>11418306
Thanks.

>>11418068
Well what am I looking at here?

>>11418326
The Shadow World, by the looks of it.

>work on loop spaces
>eat chocolate and crisps
>feel your psycho-physical muscles grow instead of getting fat
Algebraic topology makes you strong.

>>11417116
thanks bro

>>11417798
You messed up the page for mobile users. Thanks a lot, asshole

>>11418333
Thats pretty gay brah

>>11418685
>for mobile users
Subhumans not needed, subhumans not welcome.

ITT:
We prove Riemann's conjecture one expression at a time.

>>11418770
Lemma 1. (Robin's inequality)

>>11418773
Is this peak midwit?

>>11417798
>>11417782
>>11417015
(you)

[math]\qquad\mathbb{YOU}\qquad\mathbb{HAVE}\qquad\mathbb{MADE}\qquad\mathbb{ME}\qquad\mathbb{STRONGER}\qquad\mathbb{THAN}\qquad\mathbb{YOU}\qquad\mathbb{COULD}\qquad\mathbb{POSSIBLY}\qquad\mathbb{IMAGINE}[/math]

>>11418770
Fuck Rainman.

>>11414068
this is somewhat inaccurate, because the reals can characterized as an ordered complete field, and that is enough to ensure that any two constructions satisfying that are uniquely order-isomorphic.

Waitlisted at UIC right now. Give me a reason not to off myself.

>>11418940
there aren't any
do it faggot

>>11418779
dude has a thought crossed your mind that I DID check the [math]TeX[/math] before posting and it still fucked me up?

>>11418940
Galois failed twice at École Polythechinique.

>>11419166
He was also 14

>>11419172
Age doesn't really matter, some people have simply faster development of the brain.

How come the US have 13 fucking fields medals? They're fucking dumb.

How come Germany, the land of the greatest mathematicians ever, have only 2?

How come Japan, the most intelligent people on earth in modern times have only 2 as well?

How come third world shitholes like Brazil, Vietnam, South Africa and Iran have fields medals?

That's why the Fields Medal is a joke and will never be in the same league as the Nobel.

>>11419217
>That's why the Fields Medal is a joke and will never be in the same league as the Nobel.
Don't forget the fact that its age restricted.

God forbid a 41 year old fucker solves the Riemann Hypothesis. Regardless its looking like Abel Prize will be a closer approximation of the Nobel Prize due to this fact.

Imagine having such a simplistic and reduced worldview, like >>11419217, where you strip all nuance for a few easy sentences.

You can almost hear the monkey sounds emanating from his very dumb comment.

Imagine having such a poor sense of humour and high sense of self-worth, like >>11419252, where you strip all nuance for a few easy sentences.

You can almost hear the monkey sounds.

>>11419217
Seethe.

>>11419252
>simplistic and reduced worldview
Isn't it the exact same thing you're doing in your post? Hipocrisy at its best.

>>11412333
No, it's not.

>>11419282
Yikes. Not even nearly the same thing. I thought mathematicians were supposed to be smart?

>>11419055
Use a lot of spaces. That's how I avoid most of my fuck ups.
t. different anon

>>11419401
Then explain this, retard:
>>11418829

>>11419417
Show me one single use of space in that, fuckface.

>>11419433
> \qquad

[math] \qquad \mathbb{YOU} \qquad \mathbb{HAVE} \qquad \mathbb{MADE} \qquad \mathbb{ME} \qquad \mathbb{STRONGER} \qquad \mathbb{THAN} \qquad \mathbb{YOU} \qquad \mathbb{COULD} \qquad \mathbb{POSSIBLY} \qquad \mathbb{IMAGINE} [/math]

Perfect.

>>11419446
Is a command that prints a space, not a space.

>>11419465
[math] \qquad \mathbb{THANK} \qquad \mathbb{YOU} \qquad \mathbb{BASED} \qquad \mathbb{ANON} [/math]

>>11419482
No problem, my friend.

Please stop FUCKING SHITPOSTING AND FILLING THIS GENERAL WITH DRIVEL! FOR FUCKS SAKE!

>>11419497
These are already ruined with all the Touhou shit.

>>11419507
Tohou poster contributes everytime with good posts on several areas of math that I doubt you double digit IQ brain can even comprehend.

>>11419511
He essentially just paraphrases textbooks lmao.

>>11419524
Holy shit LOLOLOLLOLOLOLOLOLOOLLOL

GET THE FUCK OUTTA HERE

I miss schizo Anon telling us how maths is wrong.

>>11419542
t. pathetic fanboy

>>11419551
Math is a human construct, if I define that math is wrong, then it is wrong by my construction.

>>11419558
t. High schooler 'mathematician'

You might be in for a huge awakening if you ever go to the stupids questions thread and see who answers almost all questions there.

>>11419568
By paraphrasing textbooks and/or not understanding the questions and just sending something random almost related stuff to maintain his beta orbiter fans' perception of him being some supergenius. It must be nice to be as stupid as you are. Makes life easy.

>>11419577
LOLOLOLOL

You are deluded, so he/she answers every single question, even the ones that are PhD levels just by paraphrasing books? How the fuck is one even supposed to do that? Can't you see you're the only one that hates him/her here? You're just doing it to be a contrarian, tohou poster is one of the finest on this board.

>>11419583
He fails to give actual answers quite often. Too bad your mental capacity is insufficient to notice that.

>>11419591
Of course he does, no one knows everything in Math you retard, von fucking Neumann said he knew only 30% of math at best, how do you expect anyone to be able to answer every single question?

It doesn't change the fact that he has an extensive knowledge and answers as much as he can. Being envy is bad for your health, kiddo.

>>11419599
You are simply pathetic. Try to stay consistent the next time you try to protect your crush's honour. I'm done with you. Protip: your overuse of words related to mental disabilities are actually reflections of your inner voice telling you how stupid your posts are.

>>11419606
>I have no arguments anymore so you're projecting your mental disease in me
Really? Is this the best you could manage? You're not even qualified to even lick tohou's poster shoes.

>>11419563
That's nice Johnny. Now go play with your GameCube while the adults have their conversation.

Can I create a new thread or is there someone here responsible for making it?

>>11419511
>>11419542
>>11419568
>>11419583
>>11419599
>>11419636
t. touhou

new thread

>>11419925
>>11419925
>>11419925