/mg/ - math general

[Anonymous No.15061257]

Discuss maths
Previously: >>15043101

[Anonymous No.15061264]

>>15061257
>Discuss maths
no. we talk sports now

[Anonymous No.15061278]

>>15061264
Baseball statistics?

[Anonymous No.15061285]

I hate math but I’ve decided to learn it so I can get better than my friend’s brother, one of the most pretentious faggots I’ve ever met. I plan on studying for at least 14 hours every day. What books should I start with?

[Anonymous No.15061305]

every math class should make use of programming

[Anonymous No.15061325]

>>15061285
Do you have preexisting knowledge of any of the following:
Precalculus
Single-variable calculus
Multivariable calculus
Linear algebra

[Anonymous No.15061335]

>>15061285
Amann Escher's Analysis series

[Anonymous No.15061356]

>>15061257
>AD 2022 ai is not that great at math
OP, the next few versions are going to terrify you to the bone. Lol

[Anonymous No.15061440]

>>15061335
Why is this being shilled lately? Is it better than Rudin? Rudin seems more concise.

[Anonymous No.15061456]

>>15061440
It is an actual analysis book and not a glorified advanced calculus book like Rudin.

[Anonymous No.15061466]

>>15061356
How long have you been saying that? 100 years?

[Anonymous No.15061470]

Don't let my thread die math bros :(
>>15060167

[Anonymous No.15061475]

>>15061440
>Rudin seems more concise.
No. Rudin is elliptic. Leaves out a ton of rigor for the sake of brevity. Amann-Escher's approach is much more rigorous all while being very comprehensive.

[Anonymous No.15061494]

>>15061440
It's hard to be worse than rudin..

[Anonymous No.15061524]

>>15061456
>>15061475
>>15061494
How long should I expect to be kept busy by Amann/Escher? I need a good real analysis refresher for next winter. Also is the German version better or the translated one?

[Anonymous No.15061525]

>>15061257
10% * 100 = 10
100 - 10 = 90
10% * 90 = 9
90 + 9 = 99

[Anonymous No.15061597]

Is the matrix for this, inconsistent? I can't really get it through my head, I can the answer that a = 2 but my teacher said the matrix is still inconsistent.

[Anonymous No.15061603]

>>15061597
I think I understand, if a is 2, then the matrix has a solution, if a is not 2, then it does not have a solution

[Anonymous No.15061630]

Is this solution correct? >>15060103

[Anonymous No.15061652]

>>15061525
This sort of proves the ship of Theseus paradox to be true it's not all the same anymore

[Anonymous No.15061664]

>>15061652
In no way does it prove that.

[Anonymous No.15061729]

>>15061257
can somone explin to me why this method works

1+(2 /x-2) find if Function Increasing or Decreasing

this wierd mathod : if inc or dec :
we take two x from the domain (−∞,2)

X1 < X2 < 2 and we fill it up to become as the original expression

X1(-2) < X2(-2) < 2 (-2) ..... X2 means bigger then X1 i think

X1-2 < X2-2< 0

1/(X1-2) > 1/(X2-2) ....... 1/0 i dunno it doesnt matter muhh

1/(X1-2) *2 > 1/(X2-2)*2

2/(X1-2)+1 > 2/(X2-2) +1 .... so from this the function is Decreasing from bigger to smaller ??????

IS THIS MATH I DONT KNOW , never mind i think i got it they tried to confuse me but at the start they made X1 < X2 < 2 which by itself say its decreasing so the other bullshit doesnt matter

[Anonymous No.15061749]

>>15061729
Did you forget to take your meds, or did you take too many?

[Anonymous No.15061754]

What if there were no paradoxes? What then?

[Anonymous No.15061770]

ok so I was studying gfology and I'm trying something but it doesn't go anywhere.
Deriving the following is straighfoward from LHS to RHS. But what about the other way around?
[eqn]\zeta '(s)=\sum_{n=1}^\infty \frac{\log n}{n^s}[/eqn]

[Anonymous No.15061775]

>>15061729 >>15061749

i think i like how my country teaches math it fill it up with bullshit to force you think cognitively to find the hidden truth in it , white people math keep you retarded lol kill yourself

1+(2 /x-2) from this domain (2,∞) , 2 < X1 < X2 is it decreasing or increasing how will i know without inputting a number in the expression or cheating by looking at it grapth

PS i write this "X1 < X2" first then put the 2 depending on the domain

[Anonymous No.15061830]

>>15061524
I don't know. I shill it all the times but I have never read it.

[Anonymous No.15061853]

>>15061729 >>15061749 >>15061775
eureka i figured it out

1+(2 /x-2) find if Function Increasing or Decreasing from this domain (2,∞)

2 < X1 < X2 ....by you filling up the inequality your finding the Y

2/(X1-2)+1 > 2/(X2-2) +1 .

Y1 > Y2 meaning its decreasing in both domains (−∞,2) u (2,∞)

[Anonymous No.15061876]

>>15060025
>>15060039
I know it's minor but I'm glad you guys didn't give me the easy way out.

[Anonymous No.15062439]

>>15061524
a few months for the first two books
>>15061830
cringe

[Anonymous No.15062447]

Will learning multi-variable calc make a master in single-variable calc tough problems ?

[Anonymous No.15062503]

>>15062447
No.

[Anonymous No.15062643]

Can any probability bros give me a hand? I'm reading about convergence in Probability Essentials by Jacod and Protter. For their proof of a.s. convg implies convg in probability, they give this proof. I feel like a moron but why is the limit of that faction equal to zero? Since Xn converges to X a.s. then that would be true a.s., not for all omega, right?

[Anonymous No.15062751]

>>15062643
You already said your answer. X_n converges to X
making the absolute difference zero. And 0/1 = 0.

[Anonymous No.15062774]

When doing self-study what's your process for exercises? I've been going through discrete mathematics by Rosen to prepare for next semester and I feel like I'm giving up too easily on the problems. If I can't do a problem or at least start a solution within maybe 3 minutes I move on to the next problem or go back to the text quickly and reread the section. I've now tried forcing myself to think about each problem for atleast 15 minutes before skipping but I'm burning out. How long do you give yourselves before skipping exercises? Am I just a fucked zoomer that needs to force himself to think?

[Anonymous No.15062976]

>>15062774
>How long do you give yourselves before skipping exercises?
I try to do the harvard putnam problem of the day every day.
Sometimes I'll spend a few hours beating my head against the wall until I get somewhere.
Usually if I'm doing book exercises, I skip the easy problems (ones where I can do a rough sketch of the solution in my head) and only focus on the tough problems.
I am confident I can grind out number crunching and basic algebraic manipulation so once I can tell that is all a problem is, I skip it.

If you are first learning the material, just try to get comfortable with the concepts to the point you know them by heart or could just re-derive them if you forget the exact details.
The easy first problems are usually just for familiarization with concepts. The harder problems are usually to let you figure out which tricks to use.

I'm more interested in the essence of a problem. Whenever a clever trick is required is what I like. I try to identify what properties of the problem might be useful for forming a heuristic that tells me when I should consider the particular type of trick.

[Anonymous No.15063152]

why is discrete maths so hard bros

[Anonymous No.15063467]

It's obviously possible but how would I go about counting all functions from N to N that acts like the identity function except on an arbitrarily large but finite amount of elements of N?
Is there a good scheme for enumeration or am I stuck with using the following:
{Send 0 to 1, else identity}
{Send 1 to 0, else identity}
{Send 0 to 1 and 1 to 0, else identity}
{Send 0 to 2, else identity}
...

[Anonymous No.15063473]

People who watch Institute for Advanced Study videos and hate the crappy audio, Adobe has released a free program for upscaling human voice components of audio.

[Anonymous No.15063489]

Learning matrix transformations in a plane tomorrow.

[Anonymous No.15063789]

Find the exact volume of the solid formed by revolving the region bounded by the graphs of: y=4-x^2 , y=0, x=0 about the line x=3

the answer is 24pi right?

[Anonymous No.15063800]

>>15063789
shell method with r= 3-x, h=y

if i wanted to use the washer method, how would the integral be set up? because this doesnt work

[Anonymous No.15063873]

bros, use the shell method to find the volume of this solid generated by revolving the plane region about the y-axis.

[Anonymous No.15063875]

>>15063873
forgot the picture

[Anonymous No.15064063]

what is the goal of a formal system.

[Anonymous No.15064263]

>>15061853
why was this a eureka moment for me shouldnt it have being obvious to figure out the reason is simple he you need to find the y to know if it's increasing or not , not the value of y but if the y1 is bigger then y2 so this operation came to be a fast way without calculating
2 < X1 < X2 ........2/(X1-2)+1 > 2/(X2-2) +1 ........... Y1 > Y2

is this good to force student to figure shit out themself am i smarter now i just feel stupid it should have being obvious , is there any cure for bad cognition

the variable interact with inequality sign and by me adding numbers to it , it change to fit it , i only noticed this now why not before when i was solving it ,i think its because i made a risk a fast conclusion i did not look at what i was thinking if i did i would have known that iam not seeing the interaction , is that what cognition is how do i learn it

[Anonymous No.15064298]

>>15062774
>How long do you give yourselves before skipping exercises?
At least one day. Preferably several days if the problem is hard.
Nothing says you have to do all the exercises in order. If you're stuck on exercise 10 after half an hour, move on to 11 and try 10 again later

[Anonymous No.15064737]

>>15061257
Which programming language do you use /mg/? I use J.
Don't tell me you fell for the abstract math meme.
here are some red pills: https://sites.math.rutgers.edu/~zeilberg/OPINIONS.html

[Anonymous No.15064748]

Twenty Pieces of Advice for a Young (and also not so young) Mathematician:
https://sites.math.rutgers.edu/~zeilberg/Opinion92.html

[Anonymous No.15064761]

>>15064737
Julia?

[Anonymous No.15064764]

>>15064063
A way to mathematically analyze what it means for a statement to be provable. I.e. the completeness theorem says for a sentence s and a collection of sentences T, [every structure satisfying every sentence in T satisfies s] if and only if [there is a proof of s from T]. In order to prove this rigorously, you need a way to formalize proof

[Anonymous No.15064766]

>>15064761
J

[Anonymous No.15064875]

what are the best websites to discuss maths and research

[Anonymous No.15065093]

>>15064875
4chan

[Anonymous No.15065199]

What to do during vacation? Study?

[Anonymous No.15065241]

>>15061257
Say that Y conditioned on X=x has a distribution G, with x as a parameter, furthermore lets say that X has a distribution H. How do you compute the characteristic function of Y in this case (without first determining Y's distribution)?

[Anonymous No.15065265]

>>15064875
Reddit. If you dont like that, you can ask them for other forums.

[Anonymous No.15065684]

>>15061770
It's an absolutely trivial exercise in calculus

[Anonymous No.15065784]

Currently working on matrix transformations in a plane.

[Anonymous No.15065919]

What will /mg/ think if I write a solution set to Amaan & Escher?

[Anonymous No.15065984]

>>15065919
It better have everything, and it better be good.

[Anonymous No.15066071]

Working through the Jay Cummings proof book.
It's all clicking bros

[Anonymous No.15066135]

>statistics courses are run by the computer science department instead of the math department
>data science courses are run by the math department instead of the computer science department
???????

[Anonymous No.15066147]

>>15061597

[Anonymous No.15066205]

Anyone pls help me, I am extremely shit at abstract algebra that too in units like relation, set theory etc

How should I study this ? Now able to grasp things, proof particular relation, sets pls help

[Anonymous No.15066232]

Can a manifold with a finite fundamental group of even order be orientable?

[Anonymous No.15066242]

How would one solve this without l'hopital? I got stumped

[Anonymous No.15066315]

>>15066242
Whenever you see one of those limits with a square root then you will have to multiply with the root conjugate
[eqn]
\frac{y - 4 \sqrt{y} + 3}{y^2 - 1} = \frac{y - 4 \sqrt{y} + 3}{y^2 - 1} \cdot \frac{y + 4 \sqrt{y} + 3}{y + 4 \sqrt{y} + 3} = \frac{y^2 - 10y + 9}{(y-1)(y+1)(y + 4 \sqrt{y} + 3)} = \frac{y-9}{(y+1)(y + 4 \sqrt{y} + 3)} \overset{y \to 1}{\longrightarrow} \frac{-8}{16} = - \frac{1}{2}
[/eqn]

[Anonymous No.15066323]

filtered by chapters 5&6...

[Anonymous No.15066338]

>>15066315
That is exactly what I did actually, but I made the stupid error of just powering everything by 2, so 4sqrty became 16y, instead of redistributing correctly which is what you did

[Anonymous No.15066407]

>tfw self learning math progress stagnated for a month because I downloaded tinder and got excited about women
sorry bros, I'm back to the eternal beauty of math now

[Anonymous No.15066453]

Hello friends I am starting my Journey into Geometric algebra (vectors), What shouldst i bringeth with me in this quest of mine?

[Anonymous No.15066494]

Bros, how do you solve to get 100% number value if the given is only like < 100% and has num value? gib formula please

example: if 30% is 57.2, get the 100% value of it

[Anonymous No.15066506]

>>15064875
thats like asking whats the best place to discuss vidya anon. That's too broad

[Anonymous No.15066568]

>>15066494
Use decimals, not percentages.

57.2 = 0.3x

Solve for x.

[Anonymous No.15066577]

>>15061257
How fast would the series in the OP pic converge toward 0 if you did this x many steps? Does it matter how big the number you start with, or is it linear or does it turn exponential in the end?


kinda like (a*0.90*1.10)^x
t. don't know how to compile or make an equation for it.

[Anonymous No.15066601]

>>15066577
>kinda like (a*0.90*1.10)^x
wait am i retarded? is it just a*0.99^x

[Anonymous No.15066609]

>>15066323
There's no such thing as a filter, do some other kind of math for a few days and come back to it later and you'll see some of the concepts will make more sense to you.

[Anonymous No.15066670]

>>15066601
yes

[Anonymous No.15066874]

I don't know how to get the angle from this, I'm stuck
Any help would be welcome

[Anonymous No.15066994]

smooth solution
[eqn] We consider the Navier-Stokes equations in 2D in vorticity-stream function form:
\begin{align*}
\frac{\partial \omega}{\partial t} + u \frac{\partial \omega}{\partial x} + v \frac{\partial \omega}{\partial y} &= \nu \left( \frac{\partial^2 \omega}{\partial x^2} + \frac{\partial^2 \omega}{\partial y^2} \right) + f \
\frac{\partial \psi}{\partial x} &= -\omega \
\frac{\partial \psi}{\partial y} &= u \
\frac{\partial u}{\partial x} &= -\frac{\partial \psi}{\partial y} \
\frac{\partial v}{\partial y} &= \frac{\partial \psi}{\partial x}
\end{align*}
where $\omega$ is the vorticity, $\psi$ is the stream function, $u$ and $v$ are the velocity components, $\nu$ is the kinematic viscosity, and $f$ is the external force.

We seek a solution $(\omega, \psi, u, v)$ that is smooth and bounded on the domain $\Omega = [0, L_x] \times [0, L_y]$. We introduce the norms
\begin{align*}
| \omega |\infty &= \max{(x,y) \in \Omega} |\omega(x,y)| \
| \psi |\infty &= \max{(x,y) \in \Omega} |\psi(x,y)| \
| u |\infty &= \max{(x,y) \in \Omega} |u(x,y)| \
| v |\infty &= \max{(x,y) \in \Omega} |v(x,y)|
\end{align*}
and
\begin{align*}
| \omega |2 &= \left( \iint\Omega |\omega(x,y)|^2 dx dy \right)^{1/2} \
| \psi |2 &= \left( \iint\Omega |\psi(x,y)|^2 dx dy \right)^{1/2} \
| u |2 &= \left( \iint\Omega |u(x,y)|^2 dx dy \right)^{1/2} \
| v |2 &= \left( \iint\Omega |v(x,y)|^2 dx dy \right)^{1/2}
\end{align*}
to measure the smoothness and boundedness of the solution.

We can rewrite the Navier-Stokes equations in the following form:
\begin{align*}
\omega^{n+1} &= \omega^n + \frac{\Delta t}{2} \left( L_1(\omega^n, u^n, v^n)
[/eqn]

[Anonymous No.15066998]

anyone have tips for getting my mandelbrot zooms more views? i tried using clickbat title and thumbnail
https://www.youtube.com/watch?v=jeRsjAg3rNY

[Anonymous No.15067076]

Examples for real-valued functions that are differentiable but not continuously differentiable and that do not feature trigonometric functions in their terms?

[Anonymous No.15067081]

>>15066494
rule of three

[Anonymous No.15067088]

>>15066242
substitute y with x^2, then cancel (x - 1) and use polynominal division of the term in the denominator, then apply the limit

[Anonymous No.15067093]

>>15064875
instagram and youtube kids

[Anonymous No.15067097]

>>15064737
mostly Python for serious stuff and C for fun. I want to learn Java eventually

[Anonymous No.15067241]

>>15061285
>I hate math but I’ve decided to learn it so I can get better than my friend’s brother,
one of the best reasons I've heard to study mathematics.

[Anonymous No.15067318]

>>15061257
Everything after Pythagoras is a mathēmatikoi cope. He had it all figured out. Numbers are the essence of the universe.

[Anonymous No.15067387]

>>15066232
bump

[Anonymous No.15068159]

>>15062643
In the 1 norm it’s zero. But thank you for posting this i had no idea you could use LDC theorem in probability. But I guess it makes sense since probability is just a measure. Very cool.

[Anonymous No.15068514]

Anyone wanna help me with some Linear Algebra problems? Eigenvalues/Eigenvectors and vector space axioms. I'm kinda fucked here. Willing to pay XMR.

[Anonymous No.15068541]

whats the best way to get work noticed as a amateur

[Anonymous No.15068545]

>>15067318
>mathēmatikoi
speak english, faggot

[Anonymous No.15068551]

do you know any books about foundations of maths that declare all the primitive notions and axioms they will be using at the beginning
i have principia mathematica.
I'll take anything, but i would prefer ones without so much uneeded information, it's better they get straight to the point.

[Anonymous No.15068554]

Do I understand little o notation correctly? I couldn't find a formal definition of little o notation in the context of analysis so I am unsure if this is correct.

[Anonymous No.15068602]

>>15061257
Hey lads, I have a math related question. Here in Denmark we have a tradition of eating vanilla rice porridge with cut almonds, but one of them is whole and whoever has it in their dish it receives a prize (usually some chocolate). And each year, we have the same damn question of *if* there is an optimal spoonful to have the best odds of getting the whole almond.

For the sake of ease, I'll just rephrase this question to simplify it:

>Of 10 cards in a deck 1 of them is an ace, you win if you have the ace at the end of the game
>You are playing against 4 other people (5 in total with yourself)
>You may draw the first card or after any player (including yourself) has drawn a card
>You can only draw 2 cards in total
>After everyone has drawn 2 cards and the deck is empty, the game is over
>The player revealing the ace at the end of the game wins

Question: Is there an optimal draw?

[Anonymous No.15068614]

>>15068554
It's usually a [math]\mathcal{O}[/math] , but yes

[Anonymous No.15068620]

>>15068602
IF the cards are truly randomly distributed, then every time someone takes a card they have exactly 1/10 chance of getting an ace. So there is no optimal draw. Your only hope is that the cards may not be truly random, so that the order makes a difference. For example, maybe the whole almond is heavier and more likely to be near the bottom, so it is better to wait near the end. But that is a physics question.

[Anonymous No.15068621]

>>15068614
awesome. thanks

[Anonymous No.15068631]

>>15068554
That isn't strictly correct since [math]\mathcal{O}[/math] in that expression is meant to represent higher order terms. So [math]x + \mathcal{O}(x)[/math] would mean x + some other terms in x, probably not what you want to say.

What it should be is [math]\sin{x} = x + \mathcal{O}(x^3)[/math], and that makes it clearer in the limit that those terms vanish quicker than x.

[Anonymous No.15068690]

Just learned about generating functions.

[Anonymous No.15068765]

>>15068620
>IF the cards are truly randomly distributed, then every time someone takes a card they have exactly 1/10 chance of getting an ace
That was also the arguement my dad made, guess he is right. Thanks for the answer!

[Anonymous No.15068809]

>>15061475
or better yet spivak

[Anonymous No.15068852]

I'm already done proving tx = xt^-1
I'm having trouble proving that t^n = 1.
When I expand it, it's just t = (xy)(xy)(xy)... (n times).
What should I do here?

[Anonymous No.15069029]

>>15068852
>t = xy
>(so that *if* n = |xy| < infinity, then ... )
you are already done

[Anonymous No.15069047]

>>15068631
That's big O, not little o, brainlet. his statements are correct.

[Anonymous No.15069076]

>>15068554
>a formal definition of little o notation

[Anonymous No.15069318]

>>15066232
Yes; Gompf's construction allows us to construct sympletic 4-manifolds with arbitrary (finitely generated?) fundamental group. The symplectic form induces a global volume form (wedge it with itself), so the manifold is orientable.

[Anonymous No.15069361]

>>15065919
Why is this being memed so hard lately? Also how do I do pic related (g)? Induction on m?

[Anonymous No.15069395]

>>15063152
What are you struggling with? I guess it's because there's no cookbook for general discrete problem and one has to use different tricks taken from other parts of mathematics to proceed with the problems. A bit like why number theory is so hard, but in a different way.
>>15066407
How did it go? Was the tinder run any fun?
>>15067076
You know the x^2 sin(1/x) example right? What's the core of why it works? Surely you can think of a periodic function that can be used for this same trick, without using sin. Using sin is just convenient.
Then it's a question what you mean about "do not feature trigonometric functions", but that's just my autism kicking in.
>>15068541
Noticed by whom? If it's really worth anything, send it to a professor in the area.
>>15068690
Which application did you learn about? One in probability, combinatorics, or somewhere else?
>>15069318
Cool! Thanks for the answer. I thought it wouldn't work, but couldn't think of a counterexample myself.
Homology is the go to for orientability then, if one wants a huge hammer for the job.

[Anonymous No.15069399]

>>15069361
hint for g: look at the roots.

you can also do it by induction but it's worse

[Anonymous No.15069607]

>>15069361
I feel like you can prove this in the same way that you "prove" the binomial theorem? Like, you just compute all the possible X^(m-k) terms' coefficients manually. In particular you must pick k elements that are in {-X_i}, and because our ring is presumably noncommutative we have them in increasing order from right to left. The sum of all such elements is exactly (-1)^k * s_k.

No induction neccesary

[Anonymous No.15070319]

>>15069395
>tinder
it was fun for about a day or two, but then I realized I'd have better chances cold approaching people on the street than meeting someone from the platform. doesn't help that ~95% of the girls are total basic thots with tattoos who smoke and drink.

I don't need a "math gf" but it would be nice to meet a person who wasn't wilfully destroying themselves.

Also, the whole dopamine rush of flicking through a hundred girls every few minutes doesn't feel like it would be "healthy" in the long run.

But really, the worst part is that I broke my habit of self-learning some math almost every day, so I will have to rebuild that, and it's not so simple. Especially now that I feel like /learning math/ is a kind of escapism to me. But I have no idea what the non-escapist thing to do would be in my life.

[Anonymous No.15070567]

What are you anons studying during the break? (assuming you have a winter break) I'm starting on Topology without tears

[Anonymous No.15070645]

>>15061257
Can I work out the arc length of a semi-ellipse (like part of a track on a half completed oval) with only the chord length (C)? I know C = 150m.
Distance from centre of the arc to the chord is about 33m.

[Anonymous No.15070920]

>>15070319
>doesn't help that ~95% of the girls are total basic thots with tattoos who smoke and drink
Do you live in a muslim country? Here in Eastern Yurop, almost everyone drinks and cured alcoholics are a big part of the rest.
I don't reckon tinder is big in muslim countries though.
>>15070645
Ever heard of search engines?

[Anonymous No.15070970]

>>15070319
I'm sure you'll eventually meet one, provided you groom yourself and aren't a cunt obv. Most people like to be around passionate people, largely doesn't matter what your passion is. I doubt anyone would look down upon yours as a kind of escapism.

[Anonymous No.15070987]

>>15070920
Yeah and they give me autism like this

[Anonymous No.15071085]

I'm doing a PhD and last week my advisor just told me to prepare to write my thesis.
But I have 0 publication? Is this normal in math?

[Anonymous No.15071087]

>>15071085
What ranking are you? Low end to mid unis just want to puff up their PG student numbers; the supervisors also love the hundreds per 30 min session they do when "supervising" you in weekly meetings. Be prepared for a lot of arse licking.

[Anonymous No.15071089]

>>15071087
Not that anon but where to look up ranking?

[Anonymous No.15071094]

>>15071087
USNews says my school is in top 25 in the US for math.

[Anonymous No.15071104]

>>15071089
Depends on your uni, but here is subject related rankings. QS is a bit annoying because they hide some of their metrics to make it "fair" but it could be bullshit for all we know. Unis use it for marketing anyway, and prestige.
https://www.topuniversities.com/university-rankings/university-subject-rankings/2022/mathematics
Generally, if you are not in the top 100 in the world, you will be brought into PhDs for the sake of bringing "fresh blood" and "new ideas" to the faculty for about 4 years until you die off in obscurity and shitting temp jobs/marking that you will probably hate. The pay is alright but it's nowhere near a proper career, and forget about tenure.
Ones to look out for legitimacy would be THE and the more established rankings.
https://www.timeshighereducation.com/world-university-rankings/2023/subject-ranking/physical-sciences#!/page/0/length/25/subjects/3075/sort_by/rank/sort_order/asc/cols/stats
Now, they're bringing in Sustainability Rankings but they're probably just bullshit marketing, even if we are going to new ways of teaching, learning, research, and operations. I know the maths department at my uni are trying hard to be sustainable and underpin other sciences with that ethos. I don't really know how though.

[Anonymous No.15071122]

>>15071087
>Be prepared for a lot of arse licking.
Do you mean I have to go out of my way to please people to get postdoc jobs?

[Anonymous No.15071127]

>>15071122
Yep. My co-supervisor was buddying up to my supervisor, who just moved and became the head of the department. He was a fellow doing really shitty tutoring that he hated, until finally he was good friends (even though I think he didn't really like the head) and now he's running his own courses and got upgraded to lecturer. It's not that great after he's been here for years and years, but it's how it works.

[Anonymous No.15071979]

/mg/, I come to you in a time of need. Please recommend me some books on Set Theory. Both naive and axiomatic models are fine, but preferably the latter since I already own a book of the former.

[Anonymous No.15072313]

>>15071979
I just have Cantor's book. Go to the source material.

[Anonymous No.15072332]

>>15071979
Kunen

[Anonymous No.15072584]

>>15068159
it's used all the time

[Anonymous No.15072720]

>>15072313
Wouldn't that be old as fuck and hard to understand?
>>15072332
Thanks, Kunen's book is actually not all that expensive if I want to buy a physical version.

[Anonymous No.15073067]

>>15071979
I recommend Azriel Levy's Basic Set Theory, it's not so expensive and it's a pretty formal treatment of 'classical' set theory subjects. Might want to polish your formal logic background first, though.

[Anonymous No.15073078]

>>15071979
Foreman, Kanamori. Handbook Of Set Theory (2010)

[Anonymous No.15073313]

>>15066242
>without l'hopital

[Anonymous No.15073320]

>>15070319
faggot

[Anonymous No.15073350]

>>15070319
>MUH TRAD CATHOLIC GF

Friendly reminder that compulsive masturbation and perpetual isolation ARE ways of destroying yourself.

[Anonymous No.15073407]

>>15066242
[math]\frac{y-4\sqrt{y}+3}{y^{2}-1}=\frac{\left(\sqrt{y}\right)^{2}-4\sqrt{y}+2^{2}-1}{y^{2}-1}=\frac{\left(\sqrt{y}-2\right)^{2}-1}{y^{2}-1}=\frac{\left(\sqrt{y}-3\right)\left(\sqrt{y}-1\right)}{\left(y-1\right)\left(y+1\right)}=\frac{\left(\sqrt{y}-3\right)}{\left(\sqrt{y}+1\right)\left(y+1\right)}\overset{y=1}{\rightarrow}-\frac{1}{2}[/math]

[Anonymous No.15073436]

>>15066994
post machine broke

[Anonymous No.15074101]

>>15066609
There are entire books about filters in math.

[Anonymous No.15074109]

>>15066323

I think Hatcher's Algebric Topology is a better book if you want to learn about cell complexes

[Anonymous No.15074121]

>>15074101
Cheeky anon.

[Anonymous No.15074325]

Read Badiou

[Anonymous No.15074582]

>>15064875
there is a global math discord that is pretty active. There are also ones specialized for topics like algebraic topology or algebraic geometry which are research level

[Anonymous No.15074879]

>>15074109
Hatcher's good at conveying the intuition, but i find that the formal details are often missing

[Anonymous No.15074896]

Let [math]\Gamma[/math] be the free group generated by [math]a,b[/math]. Let [math]\{ \delta_g\} _{g \in \Gamma}[/math] be the standard basis of [math]\ell^2 (\Gamma)[/math]. Consider the group von Neumann algebra [math]L(\Gamma)[/math].

What's an example of a (non-trivial) projection in this algebra? For example, is the projection onto [math]\mathbb{C} \delta_{a}[/math] in the algebra? Or anything of this sort?

[Anonymous No.15075230]

terminology and symbols are my nightmare

[Anonymous No.15076264]

>>15068614
>>15068631
Nope
>>15068554
That $f = o(g)$ means $f/g \to 0$. For example $f(x) = f(0) + o(1)$ iff $f$ is continuous at zero. That $\sin(x) = x + o(x)$ means $(\sin(x) - x)/x$ has vanishing limit at zero.

[Anonymous No.15076476]

I watching a video by The Math Sorcerer and he recommended two books for beginners; Discrete Mathematical Structures and Discrete Mathematics with Applications by Sussana Ebb. What do you anons think about these ones? I dropped out of school after 8th grade and haven’t touched math in 15 years so I’m unsure what course to take.

[Anonymous No.15076477]

>>15076476
Read how to prove it by Velleman

[Anonymous No.15076488]

>>15076476
https://www.youtube.com/watch?v=didXE0HkSC8
Here is the V2 video he did. It has more books for beginners and is probably the best beginner guide. If you really don't know any algebra at all, I'd highly recommend going through khan academy in addition to the two basic algebra books he recommends in the linked video. Books are the way to go when you reach higher level math, but at highschool/entry college math, khanacademy can't be beat as a perfect supplement to books.
If you do know algebra then I'd probably just do a proof book (Velleman's book is good), alongside a big calculus book like Stewart and pick up the trig/precalc along the way

[Anonymous No.15076489]

>>15076477
>>15076488
Thank you

[Anonymous No.15076515]

[Anonymous No.15076517]

>>15076515
fuck off, high-schooler

[Anonymous No.15076520]

>>15076515
6

[Anonymous No.15076563]

I have a question.

Correct me if I'm wrong but
(-2)^5 means (-2)(-2)(-2)(-2)(-2) = -32
But -2^5 means (-2)(2)(2)(2)(2) = -32

I understand how to do it, where the power sign is in relation to the parenthesis and whether or not the parenthesis exists determines which operation you do. but what I don't get is "why"? Why does this distinction exist? Is there going to be some kind of purpose for it once I get deeper into maths? Especially since most of the time it ends up being the same answer anyway. What's the philosophy behind it. I apologize for asking such a basic question.

[Anonymous No.15076567]

>>15076563
The notation is garbage. At all times exactly one of these two options is meant, not both:
>[math]-(2^{5})[/math]
>[math](-2)^{5}[/math]

[Anonymous No.15076570]

>>15076515
>pdf of a photo of a book
cringe

[Anonymous No.15076575]

Even if, technically, they're both just covering already explored topics, why has the Lean/CoQ community accomplished much more than the HoTT community?

[Anonymous No.15076635]

>>15076563
Those are two different expressions that evaluate to the same result; doesn't meant they are the same.
Le why does [math] \sin \pi [/math] exist if it is always 0?
Are you retarded?

[Anonymous No.15076637]

>>15076563
Also [math] -2^5 = -(2)(2)(2)(2)(2) [/math]

[Anonymous No.15076751]

I got a A+ for Calc1. Are you proud of me /mg/?

[Anonymous No.15076768]

>>15076515
9/2

>>15076520
idiot

[Anonymous No.15076789]

>>15074325
Kinda I want to

[Anonymous No.15076833]

Can anyone tell me what a fourier transform does to a function?

[Anonymous No.15076839]

>>15076833
It takes one function in L^p and maps it to a function in L^q where 1/p + 1/q = 1.

[Anonymous No.15076847]

>>15076476
Matousek is the best intro to discrete memes

[Anonymous No.15076856]

>>15076833
It decomposes the function into waves

[Anonymous No.15076858]

Thoughts on QFT?

[Anonymous No.15076891]

Just imagine if he lived longer.

[Anonymous No.15076962]

>>15076891
he'd just die over some other pussy

[Anonymous No.15077039]

Two questions.

If I find infinitely many linearly independent vectors, can I then assume that the dimension of the space has to be infinite, too? To specify, I’m unsure whether or not these infinite linearly independent vectors have to be contained in a subspace to draw this conclusion.

Do all vector spaces, the underlying sets of which have uncountably many elements and the underlying field is finite or has countably many elements, have an uncountably infinite dimension?

[Anonymous No.15077054]

>>15076858
It's cool.

>>15077039
Pretty sure yes it's infinite dimensional in both cases - but that's just a first feel.
Would have to look up how dimension (as cardinal/ordinal) is defined in the general vector space case to formalize why. The definition (possibly exactly in terms of independent vectors) might make the first one trivially yes.
The second one is probably resolved by assuming the negation of the conclusion (countably large dimension) and showing that then the number of elements is countable too.

>>15076575
But the HoTT community works with fairly new abstract identifications, I'm not sure what you mean by that formulation. Afaik the latter tries to make univalence work and possibly make it practical. They're not formalizing math with old tools like the Lean projects etc.

Btw. I find it funny how agda is not mentioned anymore. Lean won?

Also, this just came out fyi
https://arxiv.org/abs/2212.11082

[Anonymous No.15077055]

>>15076768
why is it 9/2

[Anonymous No.15077077]

>>15076515
>300000 Americans took a test with a 5-question-multiple-choice-test and only 3 got it right
That basically can't be true, statistically speaking

[Anonymous No.15077095]

>>15076515
It's three. The ratio of the circumferences is the same as the ratio of the radii.

[Anonymous No.15077096]

Has anybody ever tried to work out a foundation of physics with only finite differences, instead of fully fledged d/dt's?

(Possibly internal set theory people, but I'm not sure if I want to go there)

[Anonymous No.15077198]

>>15076515
If this isn't 3 then I'm a retard

[Anonymous No.15077569]

>>15076515
>implying there is such a thing as a circle
pi is not a number, infinity tards

[Anonymous No.15077589]

>>15077039
>If I find infinitely many linearly independent vectors, can I then assume that the dimension of the space has to be infinite, too?
that's literally the definition of infinite-dimensional spaces. a space is finite-dimensional if it has a finite basis. if a space is not finite-dimensional, it is infinite-dimensional. a finite-dimensional space cannot have inifinitely many linearly independent vectors, hence such a space is infinite-dimensional. subspaces are irrelevant here
>Do all vector spaces, the underlying sets of which have uncountably many elements and the underlying field is finite or has countably many elements, have an uncountably infinite dimension?
yes, if the space had countable dimension it'd be isomorphic (in particular would have the same cardinality as) [math]K^{\mathbb N}[/math], [math]K[/math] being your countable base field. but [math]K^{\mathbb N}[/math] is countable, as a countable product of a countable set

[Anonymous No.15077600]

>>15077589
actually i should've written something like [math]K^{(\mathbb N)}[/math] (i.e. [math]\bigoplus_{\mathbb N}K[/math]) to differentiate it from [math]\prod_{\mathbb N}K[/math], which is uncountable

[Anonymous No.15077601]

>>15061257
>>15061257
i didnt realized picrel was wrong until recently.
i have an statistics diploma and have been trading crypto since 2014.
im kinda retarded XD

[Anonymous No.15077607]

>>15077589
>>15077600
oh and [math]\bigoplus_{\mathbb N}K[/math] is countable not because it is the countable product of countable sets (that's uncountable), it's countable because all linear combinations in it have almost all coefficients equal to 0

[Anonymous No.15077619]

>>15061257
OpenAI hired a topologist from my math department last year. Keep in mind he's strictly theoretical. Any ideas why? What could he possibly contribute?

[Anonymous No.15077631]

>>15077589
>>15077600
aha interesting, thank you very much

[Anonymous No.15077681]

>>15077198
>>15077095


Google it, it's 3+1

[Anonymous No.15077686]

>>15076891
he'd just take more dicks up his boypucci

[Anonymous No.15077694]

>>15077601
>buy 1 BTC
>lose 97% of your portfolio
>but then gain 97% of what you still have back
>you're back at 1 BTC
phew

[Anonymous No.15077697]

>>15077694
This is how black folks feel

[Anonymous No.15077703]

Post most advanced math theorem you can prove from memory.

>Abel-Ruffini theorem

[Anonymous No.15077705]

>>15076891
If Galois didn't die in the duel, he probably would have been executed for being a political radical anyway.

[Anonymous No.15077714]

>>15077703
transcendence of Liouville constant

[Anonymous No.15077816]

>>15077705
That's what he studied solutions by radicals for.

[Anonymous No.15077935]

which one?

[Anonymous No.15077997]

I enjoy physics as a hobby (always found it to be easy), but lost interest in math in 10th grade and currently it's giving me trouble, which books do I need to go through if I want to get back to calculus level and start from abbreviated multiplication formulas(7th grade)

[Anonymous No.15078070]

>>15073078
kek. death to the big publishers by the way

[Anonymous No.15078262]

>>15061285
>to learn it so I can get better than my friend’s brother, one of the most pretentious faggots I’ve ever met. I plan on studying for at least 14 hours every day. What books should I start with?
Listen if you just want to dunk on him at dinners or social events learn Probability and Combinatorics , those are the most likely to come up as relevant in common conversations.

[Anonymous No.15078328]

How many different ways can you visit 6 cities twice without visiting the same one twice in a row? I think you use the inclusion-exclusion principle here but I'm not sure.

[Anonymous No.15078353]

>>15078328

2631600

[Anonymous No.15078384]

Why is 1 not 0? Why is left not right?

[Anonymous No.15078404]

>>15078384
It's because they're fundamentally different things.
For numbers, they are a difference of quantities,
or perhaps a difference of position or order.
Zero inch mark on a ruler is a different spot than
the one inch mark, and you can clearly move
your finger between those positions.

For direction, the difference is more solidified
from another's perspective from yours. You may
see something going left, but the other would
see it going right. Change positions with the
other person and you'll see what the other sees.

[Anonymous No.15078440]

What is the simplest example of looking at something in a different way?

[Anonymous No.15078441]

Anyone here studied langlands program?

[A. No.15078501]

>>15078440
Ask someone else to look at it.

[Anonymous No.15078525]

>>15078440
Come back to it after sleeping.

[Anonymous No.15078539]

>>15078440
look at the probabilities in Plinko as coefficients of [math](1+x)^n[/math]

[Anonymous No.15078575]

>>15078539
that can't be the simplest example.

[Anonymous No.15078613]

Why is the limit not DNE? For positive infinity, it's 2, for negative infinity, it's -2, then the general limit should not exist

[Anonymous No.15078640]

Which Millenium Prize problem is next most likely to be solved?

[Anonymous No.15078671]

>>15078640
If older ones will last longer, then a newer one

[Anonymous No.15078741]

>>15078613
It's common to write positive infinity as just [math]\infty[/math] and use [math]\pm\infty[/math] for unsigned infinity.

[Anonymous No.15078801]

>>15078741
I see, that explains it, thanks man

[Anonymous No.15079027]

>>15078640
Idk I just wish to live long enough to see PvNP solved and hope to understand the proof.

[Anonymous No.15079119]

>>15078640
impossible to say. which ever one it is will require new mathematical method(s)

[Anonymous No.15079164]

>>15078353
Thanks for answering anon, could you explain how you got that?

[Anonymous No.15079170]

>>15076833
Takes a function, any function, after you assign one of its varriables as time, then transforms the Time domain into the frequency domain, which gives you the pure sine wave rates that reproduce the original function to any degree of detail.
Any function. ANY
It's sister function transforms Frequency into time.

The trick to moderm calculus on computers is that shifting the frequencies by a right angle, (think sin integrating into cos) and then transforming freq back into time is equivalent to integration. FOR ANY FUNCTION

https://m.youtube.com/watch?v=qS4H6PEcCCA

[Anonymous No.15079173]

>>15079164
Call the cities A,B,C,D,E and F and then use a pen and paper to write down all the possibilities. After that just count them.

[Anonymous No.15079233]

>>15077703
Fermat's Little Theorem, and I don't use any proofs listed on Wikipedia.

[Anonymous No.15079246]

>>15077703
Riemann-hypothesis, but I'll only use triangle property

[Anonymous No.15079549]

>>15079246
Is it futile to learn math if my IQ is only 110?

[Anonymous No.15079635]

>>15079549
Not him, but my IQ was estimated as "140 or higher" by psychologists (imo it's actually more in the ~130 territory) and I'd say for me it's 'futile' in some ways.
Much of math is about training and me, starting serious education at 19yo, I'm still a noob at 24.
That said, I enjoy studying math for the fun of it, and in that regard there's probably not much difference between 110 and 130 IQ, plus some math you learn, and the problem-solving skills you get from it, may be used in more brainlet fields like chemistry and CS, so that's nice.
Actual significant research is probably done mostly by ultra-talented geniuses (not quantifiable by IQ, but surely 170+) or people who started very young (the majority being both).

[Anonymous No.15079832]

What is the difference between existential axiomatics and constructive axiomatics? Can you give me an example of how these would look like?

[Anonymous No.15079842]

>>15078328
>I think you use the inclusion-exclusion principle here
Right. You have a set of six properties you want to avoid (P_k being "I went to city k twice") and it's not hard to count the set of arrangements which satisfy any subset of those P_k. Pretty standard inclusion-exclusion
Take the signed sum over all possible subsets of properties and if you did it right you should get >>15078353

[Anonymous No.15079861]

>>15079549
depends how you define "learn math"

[Anonymous No.15079868]

>>15079832
>difference between existential axiomatics and constructive axiomatics
Never heard these phrases, but you may have constructive axioms like the schema of specification
>If you already have some set, with a set of rules for their elements, you may postulate a set meeting these rules
and existential ones like the axiom of infinity
>there does exist some infinite set
or more pain-inducingly the axiom of choice
>for a family of nonempty sets, there is some function that picks an element from each

idk is that anyting like what you were asking about?

[Anonymous No.15079959]

>>15077703
like 90% of my undergrad algebra course, but that's not terribly advanced
finitely-generated modules over PID
existence of algebraic closure of a field
existence of universal covering

[Anonymous No.15080067]

>>15061285
Khan Academy

[Anonymous No.15080345]

>>15078613
What is a general limit?

[Hououin Kyouma No.15080356]

Why wouldnt this work?

[Anonymous No.15080363]

So I've gone through discrete math and how to prove it, I was thinking about going back to calculus for self study. I've done calc1-3 in uni years ago and know all the concepts but am still rusty and can't compute to save my life. Should I be good to just go straight to an " advanced Calc " or analysis book, or is having a strong base important enough to warrant going through something like Stewart or spivak again?

[Anonymous No.15080364]

If I complete every course on kahn academy, how deep will my understanding of math be? Good enough to get a 100% on the GED? Good enough to fly through college effortlessly?

[Anonymous No.15080371]

>>15078441

yes

https://www.quantamagazine.org/what-is-the-langlands-program-20220601/

[Anonymous No.15080373]

>>15080364

Khan Academy is high school level math

[Anonymous No.15080447]

>>15080345
It means two-sided limit.

[Anonymous No.15080468]

>>15080356
Actually that's pretty damn good. Nice work.

[Anonymous No.15080472]

>>15080373
No.

Khan Academy has Precalculus, Differential calculus, Calculus I, Calculus II, Integral Calculus, and Multivariable Calculus. It also has college algebra and linear algebra. It also has college statistics, and a lot more. Maybe you haven't taken a look at their library in a while. There's a shit ton of information there, not enough to "breeze" through all of college but it definitely covers some collegel level stuff.

It also has some college level history, biology, and physics now if anybody is interested in that.

[Anonymous No.15080479]

>>15080472
Adding onto this: It has college physics 1 and 2, it also has college biology. College chemistry. College environmental science. College microeconomics and macroeconomics. College US government and politics. College US history. College art history. College computer science principles,

[Anonymous No.15080481]

>>15080472
>>15080479
But you aren't supposed to *only* do kahn economy. For math, I'd recommend watching youtubers like professor leonard and the sort and going through a couple textbooks on top of khan.

[Anonymous No.15080482]

oh it has calculus AB and CD

[Anonymous No.15080836]

When you are trying to prove something for an exercise e.g. do you have a systematic approach for approaching these proofs or do you just listen to your gut feeling?

[Anonymous No.15080849]

>>15080836
the only "systematic" thing I do is start trying to draw examples if I have a problem and after a few minutes my gut feeling for what to try is going
>uhhhhh
but that's only if no idea pops into my head. if something pops into my head I just go with it

[Anonymous No.15080850]

>>15080836
The best thing to start with would be to write down all the assumptions and conditions in the question in logical symbols. Then if necessary write down all the definitions that are being used in logical symbols. In many cases, it becomes quite easy to find the relevant tautologies, then.

[Anonymous No.15082089]

>>15081116
Would the jews really make a new thread 70 posts early just so they can stop seeing the Santa hat? Yes. Yes they would.

[Anonymous No.15082431]

>>15066323
Try Bredon. Lee is amazing if you already know the topic to some degree from my experience with his diffgeo books. Otherwise you got no clue why he does what he does.

[Anonymous No.15082435]

>>15082089
based jews, kill all avatarniggers

[Anonymous No.15082444]

>>15080479
>college physics 1 and 2, it also has college biology. College chemistry. College environmental science. College microeconomics and macroeconomics. College US government and politics. College US history. College art history. College computer science principles,
Is any of that stuff different from its similarly named high school-level equivalents? I don't remember taking any biology or general history classes past 10th grade or so.
Also, does Khan Academy have any practice problems or questions at all? I remember watching a few Khan Academy videos on YouTube, but I've never gotten into the website itself.

[Anonymous No.15082541]

>>15080447
How can you have a two sided limit at infinity? How do you approach infinity from right?

[Anonymous No.15082657]

>>15082541
>>15080447
My mistake. It's a one-sided limit only at the
infinities by default. If you have a finite number
to approach, say x->4, you can approach it from
the left and/or the right.

Further, the limit may not exist at those finite
numbers when you approach both sides of it at
once. The infinities are okay since they're at two
different opposite places and the limit exists for
them no matter what because they're one-sided.

[Anonymous No.15083144]

>>15077703
probably consistency of the continuum hypothesis with ZFC
(took a course on it at Oxford)
currently self-teaching myself the proof of its independence

[Anonymous No.15083159]

>>15079027
same here my friend

[Anonymous No.15083261]

>>15082089
What jews? You are mentally handicapped by prolonged self imposed isolation and exposure to pol memes. Go outside.

[Anonymous No.15083515]

Pic related.

How do I explictly calculate the Kleisli category of the given monad? I can somewhat understand what it means in abstract but there's an exercise I'm trying to do which tells you to use the properties given to give the Hom sets in the Kleisli category, identity, composition. I am stumped. Any hints?

[Anonymous No.15083715]

>>15065241
with the law of total expectation
[math]E[\exp(itY)]=E[E[\exp(itY)|X]]=E[\int\exp(ity)dG_X(y)] = \int\int\exp(ity)dG_x(y)dH(x)[/math]

[Anonymous No.15083825]

>>15083715
>[math] E[\exp(itY)]=E[E[\exp(itY)|X]]=E[\int\exp(ity)dG_X(y)] = \int\int\exp(ity)dG_x(y)dH(x) [/math]

[Anonymous No.15083907]

Came across something curious in my studies. If I wanted to investigate the potential for a relationship between the inverse laplace transform of F and the inverse laplace transform of F's antiderivative, the most obvious place to start is the "bad" method in picrel. The "good" method is provided by the textbook I'm reading, and I understand the proof. Wondering if I'm correct about the motivation for the bounds of integration being s and +infinity. Is the "good" method a mitigation for the fact that the "bad" method will not yield anything useful? Or is the "bad" method in fact a viable method which I have fucked up?

[Anonymous No.15084345]

Dumb question, but is there any point in still teaching Riemann integral in the basic courses? The only reason I see to not just go for Lebesgue from the beginning is that it's a perhaps a bit easier to understand Riemann, but that doesn't sound like a good enough reason.

[Anonymous No.15084368]

>>15083515
It already hints that algebras over that kinda (sending X to SX) are like “semi modules” over the semi ring S. I imagine a semi module over S is just an abelian group M with a choice of semi ring map from S to End_Z(M). Figuring out the morphisms should be straightforward.

[Anonymous No.15084372]

>>15084368
>over that kinda
should be “over that monad”, stupid autocorrect

[Anonymous No.15084564]

>>15078440
squinting

[Anonymous No.15085123]

>>15082444
>i dont remember taking any biology or history classes in college
.....
>does Khan Academy have any practice problems or questions at all?
Yes. They divide each subject, like lets say algebra, into multiple units. and every unit takes you threw every aspect a little bit at a time and tests you on everything one at a time.

[Anonymous No.15085131]

>>15082444
like for pre-algebra for example. they will have a unit for ratios, a unit for percentages, a unit for order of operations, a unit for variables and expressions, a unit for roots, a unit for pretty much everything.

and all of these units will have like 20 different videos and 20 different tests from easiest to hardest, 1 test for every video basically and at the end there will be a unit test. it covers everything. if you take your time and go in order and try to get a 100 on every test, you will have WAYYY more knowledge than a high school graduate.

[Anonymous No.15085142]

>>15085131
>>15082444
But still, whether or not you actually end up with an in-depth understanding of math (let alone actually 100% khan academy) is completely dependent upon your own discipline. It helps to look stuff up when you don't fully understand something after watching a video, use all the recourses at your disposal. It's best to combine it with youtube and maybe read a few textbooks, although that's only if you're really autistic like me.

[Anonymous No.15085527]

>>15084368
I do think that's correct. The Kleisli category is going to be free left modules over the semiring

[Anonymous No.15085678]

>>15061257
Does anyone know a good book about Grzegorczyk Hierarchy? Wikipedia said it is used to make arithmetic operators with just Successor Function and I like Successor Function because it writes the letter S a lot of times and if you write it in reverse polish it doesn't have parenthesis so you can enjoy looking at S more.

>0 S S S S S POP
>5

[Anonymous No.15086148]

>submit final exam with some question unattempted because I just wanted to be done with this semester
Post a pic for that feel

[Anonymous No.15086696]

say you're a retard and wanted to fully relearn mathematics from the ground up

does anyone have a clear list of things I just need to work through and the order in which to do so? Like a list of videos/textbooks that clearly show the basics and the direction I need to move in and where to start?

Again, assume I am retarded and know little, but wish to use this knowledge for a career in STEM.

[Anonymous No.15086706]

>>15085678
>Grzegorczyk
fookin' hell this guy has a fat wikipedia page

[Anonymous No.15086722]

Dyscalclia retard here
If 10 equals 100 then what is 586

[Anonymous No.15086730]

>>15086148
Passed with B-

[Anonymous No.15086890]

Does it actually make a difference where I eventually work as a mathematician?
I want to be a professor, but I want to move to Latin America.

[Anonymous No.15087060]

Do the computable reals form a linear continuum?

[Anonymous No.15087071]

>>15087060
No, nor do the definable reals or the analytical reals or the hyperarithmetical reals or any countable set of reals.
I forget where I read it but one of the consequences of Baire's Category Theorem is a proof that all dense sets with the least upper bound property must be uncountable.

[Anonymous No.15087082]

>>15087071
BCT is overkill for basic questions about continuums. Urysohn's lemma and IVT can be used to show that any continuum contains [0,1].

[Anonymous No.15087119]

>>15086148
I don't understand that feel at all. Try harder, you sub80 IQ untalented hack.

[Anonymous No.15087122]

>>15086890
if you cant figure out such a basic question on your own, you will never be a professor.

[Anonymous No.15087261]

>>15087071
Is there a countable dense subset P of the reals where any argument showing that P doesn't possess the least upper bound property must rely on numbers that aren't definable?

[Anonymous No.15087297]

>>15087261
I don't think the definable numbers are a closed subset of R anon. If you have some set of the definable members of R you can use it to define a slightly larger "2-definable" subset of R and repeat. This sequence of ever larger countable subsets of R seem to go on forever in the same way that the ordinal hierarchy does.
I'm guessing though since I do differential geometry and not logic.

[Anonymous No.15087636]

>>15087122
Answer it and stop being a retard

[Anonymous No.15087639]

>>15087119
>sub80 IQ untalented hack
You misunderstood.
I did so well, I didn't care about the remaining points. I just wanted to go home.
Retard.

[Anonymous No.15087642]

>>15086890
Why would you want to move to that shithole?

[Anonymous No.15087657]

>>15087642
I already live in a shit place (not financially, but more like politically), and the west fucking sucks.
Latin America seems like the best alternative culturally. A few of the countries there are very stable.

[Anonymous No.15087676]

>>15087657
what place?

[Anonymous No.15087680]

>>15071104
>my uni is ranked 101
Well fuck

[Anonymous No.15087689]

>>15087676
I'll just say "the Middle East"

[Anonymous No.15087700]

I miss /pdeg/. No I will not post another one, the effort posts kept getting swamped by people shutting on /pdeg/. No /mg/ is not sufficient because it’s overloaded with two types of people: a. Those who’ve been doing drugs for twenty years and are making a public profession at age 40 that they will finally learn how to add two numbers together, and b. Algebraic category theorists who think any math with a visualization is “too applied” or “not real math”.

[Anonymous No.15087789]

>>15087700
>Algebraic category theorists who think any math with a visualization is “too applied” or “not real math”.
Can't you make a visualization of algebraic category theory?

[Anonymous No.15087967]

As I crank my way through khanacademy, I have to wonder how much success and how much the entire program is carried by the indian having an actual fluent understandable voice. It sure helps a lot.

[Anonymous No.15087995]

>>15087967
He is American, born and raised. Still, there are real Indian channels which don't have as much of an accent like Presh Talwalkar, and that 3blue1brown rip off who made that Gaussian integral video.

[Anonymous No.15088573]

>>15084345
bump

[Anonymous No.15088729]

have the primitive notions for basis of maths in principia mathematica been improved since then.
because they seem like they are not the end.

[Anonymous No.15088937]

picrel is from a French commutative algebra textbook/set of notes that i can't find, does anyone recognise it?

[Anonymous No.15089554]

>>15088573
It takes a few weeks to define and that time is better spent on other topics if they are possible to develop with Riemann

[Anonymous No.15089563]

>>15087700
Me too anon. Me too.

[Anonymous No.15090120]

>>15087689
I don't know about Latin America, but you are better off moving to Russia, China, or India, since they have some accomplished mathematicians in their old top colleges (though these are very hard to get into). I suppose there is also Japan and Singapore, but I don't know much about them. I have never heard of Latin America being anything special in math; never really read a math book written by a professor from any Latin American university. It won't directly affect your career, but being in a prestigious university helps you connect with other mathematicians in academia.

[Anonymous No.15090997]

For ideals A, B, C in a commutative ring with unity, is this following equality true?
[math]A(B\cap C) = (AB)\cap (AC)[/math]

[Anonymous No.15091014]

>>15088937
Hilbert and Noether respectively above and below an inverted pentagram with an inscribed depiction of a goat is very odd, where did you find this?

[Anonymous No.15091015]

>>15061525
[math]
(100\% - 10\%)x \cdot 110\%\\
= (110\%)(90\%)x\\
= (110\% \cdot 90\%)x\\
= (99\%)x\\
[/math]

[Anonymous No.15091020]

>>15071104
>unranked in your first link
>800+ in your second link
uh oh

[Anonymous No.15091217]

>>15091020
For me
>151-200 in first
>301-400 in second

[Anonymous No.15091226]

>>15091014
bro, learn to read

[Anonymous No.15091236]

[Anonymous No.15091269]

>>15063467
find a way to pick n elements from naturals and order them in some way
hint: use binary as a subset selector
then go through them one by one selecting all permutations as functions except the identity

[Anonymous No.15091640]

>>15091236
I can't even trust this holy shit-bot in a can to do my
taxes.

[Anonymous No.15091678]

I think my big struggle is creative thinking. I was doing this thing today and one question that came up was (x^2-y^2)/(x-y) and it took me like 10 minutes to come up with the answer. I was thinking of all sorts of ways like multiplying both the numerator and denominator by (x+y) but that didn't work. There was also lots of time spent just staring at the thing expecting to magically think of a solution. Eventually I figured it out, but it took longer than I would have though given how simple the answer was. idk why I didn't think of doing it like that in the first place.

How do I become more creative with math?

[Anonymous No.15092061]

>>15091678
Ten minutes to figure out something that’s blitheringly obvious in hindsight isn’t even that bad. You can expect worse in the future.
I don’t know if this is exactly what you’re looking for, but you can try reading something like How to Solve It. Aside from that, you can make up for shortcomings in creativity with persistence and feeling comfortable with frustration.

[Anonymous No.15092062]

>>15091236
love how confident it is
and people want to use this to replace their doctor, lmao

[Anonymous No.15092071]

>>15091236
Two more weeks, chud. It will replace artists, programmers and mathematicians in two more weeks. It already passes the Turing test.

[Anonymous No.15092608]

>>15091678
Just keep trying to rewrite things in different forms. Whenever you see polynomials, try to find different ways that you can factor them. Think about different ways to make the terms. Learn some polynomial division.

As you learn more about math, you'll begin to see different trends more.

Just trying writing down things that you know are equivalent forms. Don't be afraid to pull things out or add random things so long as you don't to both sides.

[Anonymous No.15092649]

>>15091678
There's no general answer to your question, but I can tell you an approach that usually helps me, and did help me with your particular example: instead of treating the expression as a bunch of symbols to manipulate mechanistically, try to think of some interpretation of it that helps you reason intuitively. You can interpret this one geometrically, as the ratio of the difference between the areas of two squares, and the difference of their side lengths. That gave me the idea of expressing the side length of one square in terms of the difference from the other. Substitute y + d for x and from there it's straightforward.

[Anonymous No.15092668]

>>15076858
>>15076858
How did you like that book and do you recommend it to others?

[Anonymous No.15093295]

A natural number m is either a factor of a different natural number n or not. That is to say, factor(m,n) is a function with only two outputs.
Is there some kind of generalization of factorisation G such that the function G(m,n) has a continuous range of outputs?

[Anonymous No.15093878]

>>15093295
Not exactly continuous, but you could define G(m,n) by G(m,n) = {n/m}, where {x} is the fractional part of x.
This way, if m divides n, then we get 0. Otherwise we get some rational number between 0 and 1, both exclusive.
But I said "not exactly continuous" because you don't get irrational numbers.

[Anonymous No.15094360]

>reading Serge Lang's Algebra
>he suddenly tells me to read another book and do exercises from it
Why is this allowed?

[Anonymous No.15094434]

So a Laurent polynomial is a polynomial with any integer indices, be they positive, 0, or negative.
Is there a similar name for polynomials whose indices range all of R or even C?

[Anonymous No.15094600]

>>15094360
Holy shit, he does? It sucks for readers but that's amazing. What chapter does he do this in?

[Anonymous No.15094604]

>>15094434
Either "algebraic expressions" or "varieties over C". If you really want to see what you can do with polynomials, you gotta check out algebraic topology at some point.

[Anonymous No.15094607]

New thread

>>15081116

[Anonymous No.15095727]

>>15061597
>>15066147
Bumping this, I still don't understand