/sci/ - Science & Math

About to start a math P.h.d. program, any advice?

>>9933729
If you are a woman, learn to suck a good dick. If you are a man, learn to work so hard that you wish you could just suck dick instead.

I was thinking of getting into actuarial science. Just wrapped up calc. 2 in a math BS. Anyone have experience with actuary exams? I was thinking about starting to study for exam p (on probability) without any background in statistics.

Good day, lads. Here hear my story for a sec, thank you:

>be me, economics undergrad
>study in the best uni for economics in my country but secretly hate economics
>have a "data science" minor and love it
>kinda ok with math and statistics
>finish undergrad choose Masters
>I want to do data science yay
>me is best so apply solely to the best uni in the country to the hardest faculty
>applied math, informatics and also fundamental math just in case
>don't pass in the first ones because it's so hyped everyone gets there
>accidentally pass for fundamental math

I'm scared shittles now, I don't know how I would be able to stomach Lie groups, Lie algebras and their applications, fundamentals of analysis on varieties, additional chapters of measure theory, the homology theory, qualitative theory of dynamical systems, spectral theory of operators, limit theorems of probability theory, theory of random processes and theory of records in the first semester with my tiny economics infected brain. Should I off myself right now or are there some books like math for dummies I should look into first?

>>9933878
>start off balls deep into applied math territory
>try to go even deeper into applied math
>out of nowhere you are going to fuck off to the other fucking extreme of the math spectrum and do measure theory, etc.

That is like if Donald Trump came out today as a communist and announced he is Ocasio Cortez's running mate for 2020. Off yourself right now, or try again.

>>9933878
ur gunna b ok brah
just werk hard

>>9933606
>formerly >>9916453
u mean

I was having trouble with this question

As Thanksgiving is rapidly approaching, many turkeys are understandably worried. Several of them have gotten together and convinced humanity to accept the following challenge (rather than settling things with the sword).
The turkeys will create a polynomial P(x) such that, no matter what integer k the humans give them, the output P(k) will be an integer. If they can do this with one of the coefficients of P(x) being 1/2013 then no turkeys will be eaten for the rest of 2013.
Can the turkeys succeed? More generally, if you give them finitely many years (say n+1 years) can they create a similar polynomial which has 1/2013, 1/2014, …, 1/(2013+n) as coefficients?

I know one solution is P(x)=x(x+1)(x+2)...(x+n-1)/n. There are solutions with lower degree but don't know what they would be

>>9933892
>>9934002
I don't know, friends, will I be able to keep my sanity after all this? My dad (who works in bioinformatics) keeps telling me I could come back to applied math easily if I'll survive this. Is that right?
>mfw I just wanted to write some models in R :'(

>>9934011
>There are solutions with lower degree but don't know what they would be
Well, to optimize you really can hope for heuristics until you want to do a weird computer search. Your solution of [math] x(x+1)...(x+2012)/2013 [/math] will be of degree 2013. I can improve that to 1201. Consider the polynomial [math] \frac{x^{1201} - x}{2013} [/math]

How did I find it? Euler's theorem.

>>9933878
>the homology theory

Spoiler: There is much more than one homology theory

>>9934055
>>9934011
Ah, even better improvement. Try [math] \frac{x(x+1)...(x+60)}{2013} [/math] with degree 61.

>>9934088
Yeah I just copied their information from the booklet, it's most likely something like "intro to.."

>>9934013
You will have to dedicate all of your time to studying. There is so much background you are missing in the first place so every class will be an uphill battle. Will you keep your sanity? Depends on your current work ethic. But that is not really the problem I'm trying to highlight. Are you really going to go through hell only to then immediately change back to applied math after you are out? Why? It will be a huge waste of time for you then. You will learn so much shit only to forget it right after.

If I was you, I would try to find a better use of my time.

How easy/hard is nelder and mead simplex method?

>>9935497
Piss easy.

>>9935497
It's one of the worst and most most ridiculously naive and outdated algorithms available in literature.

I can describe it to you in 3 greentext lines

>Start with simplex
>Flip vertex across face or shrink simplex
>Accept new vertex only if it's lower than others.

I suppose this >>9935477 was better asked here.

>>9935727
You must be out of fucking mind if you think I’m gonna read all of that shit

>>9935510
>>9935499
Am I correct in saying that with f(x, y) = x^2 + (y + 2)^2 – 15,
the initial simplex (a triangle), consists of the three given non-conlinear points.
(1, 0), (0, 0), (0, 1)
We start by arranging them in "nonimproving" order, and that order in this example, (assuming searching for a min), is given by
-15 < -14 < -4, related to
f(0, 0) < f(1, 0) < f(0, 1) ?

Can someone with a Master's degree in math field publish? I plan on doing research on my off time.

Post examples of mathematicians dunking on one another

https://projecteuclid.org/download/pdf_1/euclid.bams/1183538669

>>9936353
did you have a thesis advisor or do you have any sort of academic contacts still? If so I would contact them and ask.

>>9936390
I've still got contacts but they research in fields I find boring. Also one of them may be a malicious actor posing as a good contact.

How do I work a problem set from a text book that doesn't have a published solution set and ensure I'm answering them correctly when self studying stuff I have no teacher to confirm if I answered a problem correctly?

>>9936340
Anyone?

>>9936399
>How do I work a problem set from a text book that doesn't have a published solution set and ensure I'm answering them correctly when self studying stuff I have no teacher to confirm if I answered a problem correctly?
post your solution here, or on stackexchange

give me ideas for my bachelor's thesis

>>9936531
prove collatz conjecture by induction

>>9936531
http://www.openproblemgarden.org/
Prove one of these unsolved problems

>>9936531
paraconsistent arithmetic

>>9936510
>problem 1
>What is 1+1
I think it's 3

>>9936399
Pick up a problem book or something, like RP Burn A Pathway into Number Theory.

>>9936531
one of the weaker Goldbach conjectures

does that anime avatard fag still post here

>>9936884
He’s dead, just like every cool anon here. I feel sorry for assholes that’s still lurking in this general.

Ex-Math Major . Study
>https://en.wikipedia.org/wiki/Holomorphic_function
>https://en.wikipedia.org/wiki/Invariant_(mathematics)
To make cool headset glass apertures.

>>9936896
this general is dead as fuck

what are some operand/functor that are non-binary or lack unarity?

actually what the fuck is a non functor operand
do they exist

>>9936884
>fag
Why the homophobia?

>>9937130
Because gay is wrong

>>9937180
Why?

>>9937181
Faggotry is intrinsically disordered.

>>9937181
Gee Anon, I don’t know. Maybe because anal sex is 16 times more likely to give you Aids and HIV than vaginal sex?

>>9937244
Gee Anon, I don't know, doesn't heterosexual couples do anal? Is a exclusive gay thing?

Also, transfusion is 70 times more than anal sex, should we stop donating blood?

>>9933606

hope this is the right place for this
>can anyone explain the difference between periodic histograms and normalized histograms

inb4 brainlet im aware im just stuck and burnt out, thank you for your time.

>>9937287
That's why faggots are not allowed to donate blood dipshit.

>>9933808
Your uni probably offers a class called Mathematical Statistics or, it may offer a math class called probability. Take those. I’m a stats major and it’s recommended to take Calc 3, Linear Algebra, and a math Probability class before taking p exam

>>9937287
How retarded are you?

>>9933606
[eqn] \vec{F} [/eqn]

>>9937196
Proof?

Does anyone know why TeX does not work?

>>9937432
adblock

>>9937443
thanks anon!

Suppose i have a (time independed) Lagrangian [eqn]L(q + \epsilon \kappa, \dot{q} + \epsilon \dot{\kappa})[/eqn]
which comes from [math]L(q,\dot{q})[/math] after the transformation [math] q \mapsto q + \epsilon \kappa (q)[/math]. If i want to Taylor expand it around the small parameter [math]\epsilon[/math] i'll get the following:
[eqn]L(q + \epsilon \kappa, \dot{q} + \epsilon \dot{\kappa}) = L(q,\dot{q}) + \epsilon \left( \frac{\partial L}{\partial q} \kappa + \frac{\partial L}{\partial \dot{q}} \dot{\kappa} \right) + \mathcal{O} (\epsilon ^2)[/eqn]

The [math] \mathcal{O} (\epsilon)[/math] terms are given by evaluating the derivative of [math]L[/math] wrt [math]\epsilon[/math] at [math]\epsilon = 0[/math] correct? Can someone elaborate how i get the [math]\kappa[/math] and [math]\dot{\kappa}[/math] terms?Am i just evaluating [eqn] \left( \frac{d (q+\epsilon \kappa)}{d\epsilon} \right)_{\epsilon = 0} [/eqn] ? If thats so, shouldn't it be [eqn] \frac{\partial L}{\partial (q+\epsilon \kappa)}[/eqn] from the chain rule? Sorry for the Brainlet question my brain has been shut off.

Why does 3/4 of 1 = 3 divided by 4?

>>9937608
existence of multiplicative identity

>>9937512
>Can someone elaborate how i get the k and k˙ terms?Am i just evaluating
Think about an easier example: 1/x. If I want so compute 1/(x+\epsilon y) for small epsilon I have
[eqn] \frac{1}{x+\epsilon y}\approx \frac{1}{x}+\left(\frac{d \frac{1}{x+\epsilon y}}{d\epsilon} \right)_{\epsilon \rightarrow 0} \epsilon +\dots [/eqn]
but using the chain rule and defining z=\epsilon y, the derivative can be rewritten as
[eqn] \left(\frac{d \frac{1}{x+\epsilon y}}{d\epsilon} \right)_{\epsilon \rightarrow 0} \epsilon =\left(\frac{d \frac{1}{x+z}}{dz} \frac{dz}{d\epsilon}\right)_{\epsilon \rightarrow 0} \epsilon=\left(\frac{d \frac{1}{x+z}}{dz}\right)_{\epsilon \rightarrow 0} y \epsilon [/eqn]
The idea in the Lagrangian is nearly the same.

>>9937658
i see, thats what i was thinking but in that sense you have a [math]dz[/math] or in my problem [math]\partial (q + \epsilon \kappa)[/math] in the derivative

I want to learn as much analysis as possible. What are the essential books in their respective fields (i.e functional analysis, Fourier analysis, Harmonic analysis, measure theory, etc? (besides meme Rudin)

>>9937443
how do I fix it without having to disable everything? any way to whitelist the TeX stuff?

>>9937921
Just whitelist /sci/. It;s not like the adds on this site are intrusive anyway. It's just as small add on the bottom of the page.

>>9937675
>i see, thats what i was thinking but in that sense you have a dz or in my problem ∂(q+ϵk) in the derivative
Yes, but the derivative of L(q+epsilon) with respect to (q+epsilon) is the same as the derivative of L(q) with respect to q.

>>9937737
why do you hate yourself so much? Analysis is so fucking dull and boring..
Anyway, Analysis by Tao is a good intro, then you could try Princeton Lectures in Analysis by Stein and Shakarchi

I trusted you /mg/! ((

>>9938293

I'm a hipster I guess. Everyone and their mother likes algebra/topology; I feel like going against what's trendy. Truthfully though, I'd like to learn everything despite I know that's basically impossible.

>>9938328
Guilty as charged.

>going on my 4th year of my fin. math degree
>do bretty gud on real analysis, time series, probability, multi. var. calc and proofs
>think to myself that I ought to try topology, it's one of my electives

what the FUCK is going on, is this what brainletism feels like? I'm using General Topology as a reference textbook

Can someone please help me out? It's a proof about the divergence of 1/p. I can't understand how they made the log disapear.

>>9938432
https://en.wikipedia.org/wiki/Taylor_series#Natural_logarithm

>>9938442
Thanks, I'm trying to study number theory on my own but I keep seeing cal 2 stuff that I haven't taken yet.

>>9933808
i was curious about actuarial science as well, and looking at the subject matter for P, it seems right up my alley, thanks for reminding me

have a thicc gif

why does this error keep showing up
Although everything works properly I'm bothered by the tons of errors I get every time I compile the pdf

>>9938499
Her thighs has enough meat to feed a nation

How do people decide which graduate schools they want to apply to?
I don't have one highly specific topic I want to research, and without that metric all my options seem to more or less blend together. I have no idea what anyone is looking for when they decide that they like the look of the shitsville math department better than the look of fucktown.

>>9938677
Just read about the faculty culture, how many members work on areas related to those that you're interested in, faculty size, scholarships, workload (are you going to TA some classes as a requirement? How many?), email some profs about the topics that you're interested to hear if you're a good fit for that faculty, are you going abroad or staying in the USA?
Those we're some of the things that a friend of mine who just graduated considered before selecting a graduate program

>>9933780
unironically good advice

>>9937957
Thanks, I feel really stupid

>>9938556
At least show the whole fucking error message. Also
>{f,g,e,t}
Was that intentional?

>>9938431
see >>9935727

Have you ever felt guilty about downloading math books illegally from libgen?

>>9939084
>Have you ever felt guilty about downloading math books illegally from libgen?
In first world countries they're legal to download, only illegal to upload.

>>9939087
But the authors need money to feed their families too

>>9933892
>measure theory is the extreme of abstraction
fucking ameritards I swear

>>9939084
>>9939091
The fuck? They're getting very cushy sinecures from either the university or the government, depending on which country they live in. ALL scientific writings should be free for everyone, since even in the US, the university system is highly interlocked with and benefits greatly from the commonweal.

>>9939091
Unless you're James Stewart, nobody makes any actual money off math publishing. Not enough volume. For 99% of books on libgen, even if we assume that every pirate equals one lost copy and the author gets 100% of sales (both ridiculous assumptions) they're not losing more than a few grand on any given book.
And there's clearly no ethical issue at all with pirating papers since the authors never see any of that paywall money anyway.

Learning Linear Algebra with Axler's, what is a good companion to it that will teach me how determinants work?

Basically asking because I'm currently studying linear operators and I saw that the determinant of a matrix is equal to the product of its eigenvalues. What the fuck?

>>9939948
The determinant is invariant under transformations. If you choose a basis that diagonalizes your operator (an eigenbasis), then the determinant would simply be the product of the diagonal elements, I.e. the product of the eigenvalues.

>>9938499
Sauce?

>>9939948
speaking of eigenvalues the trace (sum of all main diagonal elements in square matrix) is always equal to the sum of all eigenvalues

eigenvalues are weird

I'M IN A READING SEMINAR WITH A POSDOC THAT IS SO FUCKING HOT AND I CAN'T FUCKING CONCENTRATE IM BASICALLY DROOLING THE 2 HOURS AND DON'T GET ANYTHING FUCK MY LIFE WHY DO I HAVE TO BE A FAGGOT

>>9940247
>be straight
>no attractive women in my department
homos btfo

>>9938343
You are not a hipster, just not knowledgeable enough to see how fucking hard analysis can be, but that + geometry is the best, most beautiful and most useful branches of math.

>>9940247
Don't worry anon, the Mary Ellen Carter will rise again. https://www.youtube.com/watch?v=Fhop5VuLDIQ

>tfw you take LaTeX a little too far

https://arxiv.org/pdf/1808.04902.pdf
>Mackey 2-functors and Mackey 2-motives
>Paul Balmer, Ivo Dell'Ambrogio
>(Submitted on 14 Aug 2018)
>We study collections of additive categories M(G), indexed by finite groups G and related by induction and restriction in a way that categorifies usual Mackey functors. We call them `Mackey 2-functors' and provide a large collection of examples. We then isolate the initial such structure, leading to what we call `Mackey 2-motives'. We also exhibit a convenient calculus of morphisms in Mackey 2-motives, by means of string diagrams.
>many beautiful figures

>>9940356
every day I become a little more convinced the entire philosophy of modern category theory is
>if I draw enough arrows nobody will want to bother checking my work

>can't be bothered to calculate shitty integrals
>put whatever wolframalpha gives me as answer ans call everything proof by inspection and hoping nobody will find out

>>9940454
try this for a feel
>be dickhead freshman and bomb all my math courses
>get my shit together and ace every course after this, but never fix very weak foundation
>find out a few weeks ago that the GRE is basically a glorified calculus test
>now frantically trying to patch up the fact that I never learned how to do anything in multivariable calc or differential equations

>>9940356
I cannot even consider how one LaTeXes this. Also is cat theory worth going into for a physicist?

>>9940596
You'll need a little bit of it. Not really worth "going into" in the sense of studying it in any great depth.
Category theory is very much like set theory. There's a basic language that everyone who does any math needs to know how to speak, and then there's a huge amount of additional theory that nobody outside of foundations research cares about.

>>9940601
That pretty much covers it, thanks.

>>9940302
Why is Stan Rogers so appealing to homos?

https://www.youtube.com/watch?v=TVY8LoM47xI

>>9940637
>>9940302
>>>/lgbt/

So for this integral I know that if I substitute the 1/2 for anything with abs value between 0 and 1 it will evaluate to 0, 1 and it's not defined while > 1 it will be nonzero.

However I don't understand how the results are obtained when I try to explicitly evaluate the antiderivative to get nonzero.

>>9940746
http://www.wolframalpha.com/input/?i=int+(+1%2F2+*ie%5Eit+%2F+(1%2F2+*e%5Eit-1)+)+dt,+t%3D0..2pi

http://www.wolframalpha.com/input/?i=int+(+1+*ie%5Eit+%2F+(1+*e%5Eit-1)+)+dt,+t%3D0..2pi

http://www.wolframalpha.com/input/?i=int+(+2+*ie%5Eit+%2F+(2+*e%5Eit-1)+)+dt,+t%3D0..2pi

>>9940746
[eqn] \int _0 ^{2 \pi} \frac{i e^{it} }{2 \left( \frac{e^{it}}{2} -1 \right) dt = \int _0 ^{2 \pi} \frac{(e^{it})’ }{2 \left( \frac{e^{it}}{2} -1 \right)dt = \int _0 ^{2 \pi} \frac{z }{2 \left( \frac{z}{2} -1 \right) dz= \oint _{\mathbb{S}^1} \frac{dz}{z-2} =0[/eqn] because the function [math] f(z) = \frac{1}{z-2}[/math] is analytic on the unit circle.

>>9940746
[eqn] \int _0 ^{2 \pi} \frac{i e^{it} }{2 \left( \frac{e^{it}}{2} -1 \right) dt = \int _0 ^{2 \pi} \frac{(e^{it})’ }{2 \left( \frac{e^{it}}{2} -1 \right)dt [/eqn]
[eqn] = \int _0 ^{2 \pi} \frac{z }{2 \left( \frac{z}{2} -1 \right) dz= \int_{\mathbb{S}^1} \frac{dz}{z-2}[/eqn] sorry for the TeX

>>9940770
>>9940746
[eqn] \int _0 ^{2 \pi} \frac{i e^{it} }{2 \left( \frac{e^{it}}{2} -1 \right) dt [/eqn]
[eqn] = \int _0 ^{2 \pi} \frac{(e^{it})’ }{2 \left( \frac{e^{it}}{2} -1 \right)dt [/eqn]
[eqn]= \int _{\mathbb{S}^1} \frac{dz }{z-2}=0[/eqn] AAA PHONE TEX IS IMPOSIBLEE

>>9940771
Okay I wrote it down

Can I skip Applied Linear Algebra and just learn Matrix and Finite Vector Spaces?

>>9940892
What do you mean by “applied”?

>>9940988
Never mind

>>9938677
To extend this >>9938720 you might also want to look into what sort of city you'll be staying in and the surrounding area. Grad school can be a bitch but if you're living in a shitty place because rent is too high or if you hate the city and/or climate then you're gonna have a much worse time.
>>9938467
Techniques in continuous mathematics are useful in discrete settings and vice versa since you can use one to try and approximate the other. It's actually a pretty common technique to use an integral to get an upper or lower bound on a series. This book
https://books.google.com/books?id=7g1ABAAAQBAJ&pg=PA105&source=gbs_selected_pages&cad=3#v=onepage&q&f=false
covers some of the techniques and ideas.
>>9937737
Not sure why everyone hates Rudin (I enjoyed it) but Stein has some good books, Simon has some good books, and Tao's notes are also good.

>pic related
Is the below "proof" of fact 3.1(1) correct? I've been studying formal language theory but, as this is the first time I deal with this kind of recursive definitions, wich are far more complicated than the ones seen in basic maths, I'm not sure whether this is ok or not.

That recursive definition of regular expression can be described as follows:
[math] \begin{align*}
p &\to x \mid (e) \mbox{ (where } x \in V \cup \{ \underline{ \epsilon}, \underline{\varnothing}\} \mbox{ )}\\
f &\to p \mid f* \\
t &\to f \mid tf \\
e &\to t \mid e \cup t
\end{align*}[/math]

This is what I've done:
Observations:
> [math] |f| \geq 1[/math] and [math] |t| \geq 1 [/math]
> The final symbol of [math]f[/math] can be any element of [math]\{ *, (, x \}[/math]

Proof:
Let [math]t_1[/math] and [math]t_2[/math] be regular terms and let [math]f_1[/math] and [math]f_2[/math] be regular factors such that [math]t_1 f_1 = t_2 f_2[/math]. Induction on the length of [math] t_1 f_1[/math]:

Base case: [math]|t_1 f_1| = 2[/math]. Then [math] |t_1| = |f_1| = 1 \implies t_1 = a_1 \land f_1 = a_2[/math]; analogously [math] t_2 = b_1 \land f_2 = b_2[/math] (where [math]a_1, a_2, b_1, b_2 \in V \cup \{ \underline{ \epsilon }, \underline{ \varnothing }\}[/math]); then [math]a_1 a_2 = b_1 b_2[/math] wich implies [math]t_1 = t_2 \land f_1 = f_2[/math].

Assume the result is true for [math]|t_1 f_1| = n[/math].

Suppose [math]|t_1 f_1| = n + 1[/math], then [math]a_{n + 1}[/math] is [math]*[/math], [math])[/math] or some [math]x[/math].
First case: [math]a_{n + 1} = *[/math], then [math]f_1 = F_1 *[/math] and [math]f_2 = F_2 *[/math], where [math]F_1[/math] and [math]F_2[/math] are regular factors; thus [math]t_1 F_1 = t_2 F_2 \implies t_1 = t_2 \land f_1 = f_2[/math] (by the induction hypothesis).
Second case: [math]a_{n + 1} = x[/math], then [math]f_1 = f_2 = x \implies t_1 = t_2[/math].

>>9941840
Continuation:

Third case: [math]a_{n + 1} = )[/math], then [math]f_1 = (e_1)[/math] and [math]f_2 = (e_1)[/math], where [math]e_1[/math] and [math]e_2[/math] are regular expressions.

As [math]f_1 \neq f_2[/math] if and only if (1) [math]f_1[/math] and [math]f_2[/math] have the same length and differ in some symbol or (2) [math]f_1[/math] and [math]f_2[/math] have different length. The first case cannot be possible as it contradicts the hypothesis [math]t_1 f_1 = t_2 f_2[/math], so [math]f_1[/math] and [math]f_2[/math] must have different length, namely, [math]|f_1| = k_1 \neq k_2 = |f_2|[/math].

Now suppose, without loss of generality, that [math]k_1 > k_2[/math], then [math]a_{n + 2 - k_1} = a_{n + 2 - k_2} = ([/math], thus [math]f_1 = ( s f_2[/math] where [math]s[/math] is a string on [math]V \cup \{ \underline{\epsilon}, \underline{\varnothing}\}[/math], wich contradicts the definition of regular factor.

What bothers me the most is the fact I'm using the induction hypothesis only once.

I came across a nice puzzle recently. For you math-riddle-fans out there:

There is a table of length 1 meter. On the table there are 100 ants. Independent of the other ants, each ant either walks left or right, 1 meter per minute. If two ants collide, both will change direction. If an ant reaches the end of the table, it just falls off the table. How long does it take at most, until there is no ant left on the table? How are the ants distributed on the table at the beginning?

so scholzefags, what's the error in IUT?

>>9941923
If they're all walking it takes at most one minute

>>9942070
correct!

So, how big does a prime p have to be for the discrete logarithm problem to be impossible to solve modulo p ?

>>9933606
Why exactly is calculus so vital for almost all higher maths?

>>9942292
>Why exactly is calculus so vital for almost all higher maths?
Why exactly do you think it is?

>>9942292
if by "calculus" you mean "elementary real analysis" then it's because everything in math ends up being connected to everything else, so of course the elementary properties of an object as fundamental as the real line are going to come up

>>9936356
what a fucking pleb that reviewer is

>>9942036
There isn't any. Mochizuki is correct.

i hate to be that guy, but would anyone know of any books to self-teach vector calculus from for a student fresh out of high school ap calculus?
the real analysis type books on the wiki look good for a second pass on the subject, and paul's online math notes felt a little barebones to me. should i just shut up and flip to the corresponding sections in simmons or something

So I have to give an expression for An in terms of An−1 and An-2, that works for all n >=3.

I've worked out these as the values
A1 = 10
A2 = 120
A3 = 1200
A4 = 14000
A5 = 144000
A6 = 1728000

I understand that a1 = 10 and a2 = a1 * 12
a3 = a2 * 10, a4 = a4 * 12, it's just alternating what it's being multiplied by depending on if it's even or odd, but how can I write this as an expression? I'm a brainlet.

Help me out brehs, what math is needed to know to pass a GED exam?

>>9942956
[math]
A_n = \frac{A_{n-1} * A_{n-2}}{A_{n-3}}
[/math]

>>9943119
Have they killed [math] tags?

>>9942292
It's not

>>9943120
No, turn off your ad blocker.

>>9942947
if you know linear algebra you could try analysis on manifolds by munkres (it's even a bit too computational and not so rigorous) and complement it with calculus on manifolds (if you use this one alone it's too terse and might be had for you), they are pretty cool together IMO

>>9943119
>in terms of An−1 and An-2

>>9942956
>I understand that a1 = 10 and a2 = a1 * 12
a3 = a2 * 10, a4 = a4 * 12, it's just alternating what it's being multiplied by depending on if it's even or odd, but how can I write this as an expression?
A_n =
A_{n-1} * (5 * [1+(-1)^n] + 6 * [1+(-1)^n]) + 0*A_{n-2}

>I understand that a1 = 10 and a2 = a1 * 12
>a3 = a2 * 10, a4 = a4 * 12, it's just alternating what it's being multiplied by depending on if it's even or odd, but how can I write this as an expression?
A_n =
A_{n-1} * (6 * [1+(-1)^n] + 5 * [1+(-1)^(n+1)]) + 0*A_{n-2}

>>9942956
An-1 is An-2 * 10 or An-2 * 12
Then whichever of 10,12 you didn't multiply An-2 by to get An-1, you multiply An-1 by to get An.
So shouldn't it be An-2*120 in any case?

>>9943125

Why isn't topology taught before analysis? It seems much more intuitive.

>>9940481
>pulling your hair out to be some PhD's slave for the next couple of years
That's why I gave up on graduate school.

>>9943911
Topology generalises analysis

>>9943918
No it doesn't. Analysis and topology are two distinct subjects, related, but not sub/super sets of one another. Topology is the study of space itself. Analysis is the study of how objects of different form may change in some sense, within a space.

>>9943918
Yeah, but I like the topological definition of a limit better.

>>9943917
You can tell yourself that, if it makes you feel better. People suited for graduate school should ever need to pull their hair out. If fact shouldn't be terribly stressful at all.

>>9943932
People content with slavery shouldn't ever need to pull their hair out either.

>>9943944
>he thinks grad school is slavery
t. brainlet labrat

>>9933606

If you are so smart why you didnt chose a degree with actual employment?

>>9943969
So if societal pressures convince me to go to college...
>Dude, you'll have a the degree to be able to get a stable well-paying job, you'll meet new friends, etc. It'll be great. Besides, what will your parents think if you don't attend. You don't want to be like those losers who didn't go to college.

Then I get to college, but it's not what I expected...
>What are you doing studying what you want to study instead of what I am paid to teach you? It's not my fault my class is taking up all your time.

Then I think about dropping out of college...
>What you're dropping out? How are you going to pay back those student loans on a minimum wage job? Besides those who went to college have already had a steady job for a few years, you would look even worse than those guys.

Even if I did go on to complete my Bachelor's, but decide not to go to graduate school, and go find a job...
>We like your degree, but what work experience do you have? Here is this pointless entry-level job that only pays slightly more. But hey, at least you have some flexibility over your income.

Or if I went on to graduate school...
>I know you aren't interested in this research at all, but you're basically at my complete mercy. I can terminate you if I want to, and there is really nothing you could do about it. All the work you have done up till now would have been for waste.

Sorry, but at every point in education, there is always some degree of coercion involved. If someone is unhappy with their education, but they are coerced into continuing, I view as a form of slavery (there's only a difference in degree, not in kind). Likewise, if someone decides to distance themselves from such a system, that doesn't necessarily make them a brainlet, especially when said person is reading graduate level books in their free time.

>>9944028
>he is american

Here is your problem

>>9944028
Well, that's certainly a pessimist's interpretation. I am an American math Phd student at an American University and I've found the entire experience to be pretty rewarding. Every subject in math has been pretty engaging and fun to learn, and now I'm paid to write about it. Judging by happiness, seems like a good deal.

how???

>>9944028
>>I know you aren't interested in this research at all, but you're basically at my complete mercy. I can terminate you if I want to, and there is really nothing you could do about it. All the work you have done up till now would have been for waste.


That isn't how research works in math.

>>9944228
Plug'em in and remember the relation between coefficients and roots of a polynomial

>>9944228
p(x) = (x - a)(x - b)(x - c)
= (x^2 - bx -ax + ab)(x - c)
= x^3 - cx^2 - bx^2 + bcx - ax^2 + acx + abx - abc

=>
a + b + c = 0
bc + ab + ac = - 2
abc = 2

>>9933878
Going the same route as you, just let us know how you're doing in the future generals. Are you Brazilian by any chance? The system you described is similar to ours.

Anyone with an idea how to do the implicit solution? I'm a brainlet that can only do general solutions for this question

>>9944601
literally just substitute it in??

How do I approach a professor to have a purely technical conversation about something that doesn't have to do with a course?

In my case I have basically did some experimental math, came up with a proven theory about some observations, plus developed some rather high quality software tools and I want to share my results I guess

>>9944028
if you are in college because society "pressured" you then you have no place in graduate school

>If someone is unhappy with their education, but they are coerced into continuing, I view as a form of slavery
literally just leave lmao like leave and never talk to them again you fucking retard

>>9944601
literally plug n chug

this is the worst general on 4chan

>>9944817
Really? You only need to ask him about that.

>>9944817
Just be confident bro, and keep visual contact while giving him a firm handshake.

>>9944817
Wow you Literally talk to him. this place is pathetic

Yea! Why even bother learning calculus when you can quite literally calculate any area of any shape... of a curve by using first grade geometry.

>>9944917
Oh yeah this seems way easier than an integral

>>9944917
Do count the squares to the top of the line or the bottom?

>>9944934

lol, why?

>>9944934

I wasn't being sarcastic btw,
there are many things I can do in life and
calculating an area under a curve might be one of them, but it's definitely something that real life problems never demand me to do.

>>9944874
>this place is pathetic
Why are you so unkind?

>>9944976
try reddit or >>>/a/
any of you brainlets going to post some math?

>>9945023
Why would anyone post math here? For that matter, why aren't (you) posting math?

>>9944280
>That isn't how research works in math.
Can you tell me how research works in math? As far as I can tell, it's "Pick one of the Hilbert/Millennium/DoD problems, find out you'll never solve it, start publishing about problems literally no one cares about (finding a solution for the problem is optional)"

>>9944028
Degrees are going out of style anyways. Due to the inflation of Bachalor's Degrees in the market place, and the prominence of indie learners, you're probably best off doing the following:
1. Grab a graduate list of textbooks and start working them meticulously
2. Start reading published papers now rather then later, as by doing this, you'll not only practice reading maths, but probably discover a discipline you want to focus on. Also take names of authors who catch your fance
3. While doing that, work on gaining contacts within the Mathematics community, starting with submitting questions on papers you read to relevant authors.
4. Repeat until one or more of those published Mathematicians wants to work with you to publish work.
5.(Optional if you want that degree)If you did well on step 1, you can rush a PHD in 2 years or less rather then 4 years since you can blitz past the qualifiers and prelim stuff. This is because the PHD degree is more akin to admission to a community rather then any true indicator of being a high performing member in maths.

>>9945319
How grad school works:

You take some general courses, see general topics you like.

You take some more specific courses, study some independently.

Take special topics courses, attend local seminars, go to research conferences, etc. To get an idea of what modern research is like in your field of choice.

Find some interesting open questions (either on your own or via a advisor) in your very specific field of choice and work on them.

>>9933878
>fundamental math
is that Mathematical foundations or like some physics thing?

>>9945348
The problem here is who the hell if funding that?

Math PhD programs are almost always fully-funded, generally all you have to do is work as a TA.

>>9938556
>only posting part of the code
>only posting part of the error
Look up the error on stack exchange. Read the documentation.

>>9939084
No, there's an abundance of shitty books out there and with the way the current book market is setup (i.e. geared for storybooks) it's near impossible to tell if a book is what you need until you look through it. For every useful book I download there are usually a handful of shitty useless ones that I'm really glad I didn't pay for. So, no, I don't feel bad. I feel bad for the consumers who buy tons of books off Amazon prime without adequate information and end up not using them in the end.

>>9945388
>geared for storybooks
What do you mean by this?

>>9945407
Most online book shops maintain a system where books are given a one dimensional rating that tells you "how good it is". This is good for storybooks where the rating captures the 'entertainment value' of a book but it's not good for a textbook where the questions you have are far more complicated.
>What pre-requisites does it have
>How salient are the explanations.
>How verbose/terse is the exposition.
>How formal is the notation.
>How rigorous are the arguments.
>Is it useful for self-study or meant to be used alongside lectures.
>Is some of the material offloaded into the exercises?
>Do the exercises have solutions
>What is the diagram count?
>Who is the intended audience (eg. math students, software engineers, chem students, etc..)?
>etc...

Different people look for different things in books. A book with a high degree of formalism, rigorous proofs, terse explanations, etc... that may be great for someone with a strong math background but may be awful for someone in an applied field who is completely new to the topic and requires less formalism, more in depth explanations, applications as examples, etc....

When I mentioned bad textbooks in my last post I wasn't saying that a book is inherently bad but rather that it's poorly suited to me (i.e. bad for me).

>>9945376
>The problem here is who the hell if funding that?
Step 1: Buy a fucking book for once in your life, if you're looking for confirmation your solutions are correct, stackexchange which is free

Step 2: Your local library or college library can get you archived publications and more reading material for fucking free. However lets assume for some reason, you're in the middle of fucking no where or your local library is literally cancer. If that is the case, arxiv.org is becoming the de facto website for publishing papers(Warning, there are cranks, they literally had to make a category so they could sweep people who claimed to solve the Riemann Hypothesis using arithmetic) and frequently, researchers will publish on their own webpage. All this for free.

Step 3: Playing the networking game is inherently free, reach out to researchers in the subfield your interested in by making sure that a) you read their paper b) your questions are not shitposts in mathematical notation. If this is the case, then you should recive a reply anywhere between a few hours to a few months.

4. Repeating a cycle means all you have to do is buy a new set of textbooks or obtain them via some other method, keep reading research papers, and reaching out. Since doing research with fellow mathematicans is free, you don't have to worry about costs here.

5. If you choose to do this step, there are frequently scholarships at universities that can only be accessed via a recommendation from a professor only, along with steep discounts if they get you into a research assistant possession (which means you get paid to do research with the researcher you reach out to).

So if you play the game right, you literally pay for your own textbooks(potentially free if you know what you're doing), scratch paper and marking utensil. Also TAships have become "Teach these 3 courses along with your 50 hours minimum per week study load" aka a scam

>>9945429
Lol I'm not talking about funding supplies. I'm talking about funding your entire life while you are doing math.

>>9945432
Literally get a real job, if you can't study/research math and enjoy it in your free time, then you're wasting your time doing any kind of full time graduate student work and it's just going to torture you.

>>9945432
There's the Erdős method:
1. Resign yourself to a level of living that is barley above the poverty line
2. Go to the salvation army and make use of their shelter, food and hygiene station for free
3. During the day, hit the library
4. Once you make your connections, literally bum a couch with your research professor

>>9945445
You can not have a full-time job and get nearly as much work done as a full-time student.

You're kidding yourself.

>>9945450
I would prefer to not be a bum.

>>9945456
>You can not have a full-time job and get nearly as much work done as a full-time student.

This is why PhD programs are fully funded in the first place.

>>9945456
>You can not have a full-time job and get nearly as much work done as a full-time student.
That's 'cause you're a brainlet who was never going to make it in the first place.

>>9945462
Says the faggot who can't even get into grad school.

>>9945467
>faggot
see >>9937130

>>9945467
>implying

>>9945459
>This is why PhD programs are fully funded in the first place.
Close, the only funded positions that are worth a damn are ones that are at a top 25 school in the US. That's because at those institutions, either you are fully funded and your job is literally to study, or you are a true teaching assistant in the sense that you spend 5 hours a week in a small room as proxy for some professor's study hours. In that case, yes such PhD programs are worth getting into, however unless you have a top notch math subject GRE score, you got 25 points or higher on the Putnam exam, or you have a social connection in (if that's the case, good luck with your first semester worth of classes), you will not be getting into one of these programs.

Anywhere else in the US at least, you're either tutoring 20+ hours a week which cuts into study time or you are working 50+ hours a week lecturing for different classes, essentially acting as a cheap professor with non of the power. In those cases, you're better off just getting a full time job and studying in your free time, as it's less strenuous and since you have no time constraint (aka homework and tests), you have more time to internalize concepts as needed

>>9945527
>however unless you have a top notch math subject GRE score
Said like someone who has absolutely no idea how to get into grad school. The math GRE is required, but it pretty much the least important part of your application.

>>9945532
>I don't know the difference between the Math Subject Exam and the Math portion of the General GRE
That's all you had to say

>>9945548
I said math GRE. Not math portion of the GRE.

At least 50% of the math GRE is just calculus. The rest is a mix of basic algebra, anaylsis, etc.

It speaks absolutely nothing to a students research ability, which is the most important of applying to grad school. And why the most important part of your application is Professor Recommendations, good grades in grad / grad-level courses, attending summer schools and REUs, etc.

>>9945450

This is actually a good idea. It's just that most you you can't give up the luxuries of life to pursue math. You don't need a girlfriend, a house, or any fancy toys to be satisfied.

>>9945348
>>9945429
please don't listen to this retard and think you can become some self guided wizard of mathematics with PHD level knowledge without going to school

brehs, i learned a little about groups today, what books would you recommend for going deeper?

>>9946035
Aluffi and/or rotman, depending on how deep you went.

>>9943062
pls respond

>>9946035
Dummit and Foote Abstract Algebra. That book has everything(and I do mean everything) and explain everything wonderfully.

>>9946122
>That book has everything(and I do mean everything)
It really doesn't, and if you think it does, you don't know group theory.

>>9945620
>Who is Ramanujan
>Who is Weierstrass

In both cases, they did some of their best work sans a PhD (Ramanujan died right after flunking school and Weierstrass only got his PhD AFTER his ground breaking research)

That said, how many people with a PhD have the knowledge to really push maths forward? I'd guess only 10%. Everyone else is literally chaff. A solid chunk will go onto publishing one or two inconsequential papers a year while playing the social game for tenure but contributing nothing of value to any discipline of math, others will realize they're wasting time researching math and just go into industry/government and leave the true research to the 10%. These people literally paid or worked the equivalent of at least 40k for a paper that has their name + PhD and they are doing nothing with it. This means that it's only a status symbol and nothing more.

>>9945450
You forgot about the constant supply of amphetamine.

>>9946134
‘Everything’ as in everything you’ll encounter about abstract algebra during undergraduate.

How?

>>9946143
>>Who is Ramanujan
>>Who is Weierstrass
literal mathematical geniuses.

>>9946911
>not being a mathematical genius

>>9947054
>not pretending to be a math prodigy

>>9946716
>what are partial fractions

Hello /sci/.
I dropped out of high-school to escape a bad situation many years ago.
Since then I've been feeling very lost and passionless.

Recently I've been watching some lectures by high-level math users where they dumb down the concepts that their equations describe for listeners outside of their field.

I don't know exactly how to word this but I think all this time I've been missing something math can give me, it really feels like water to a man dying of thirst.

Can anyone recommend me some downloadable pdfs, websites, or lecture series?
Thank you.

>>9947147

https://www.youtube.com/user/professorleonard57/videos

I have a similar life story as you, I started with the first video in his series not knowing any math and I started studying mathematics after I finished watching all of them pretending to be a student. Now I study mathematics with good results :)

>>9947168
This looks amazing, thank you very much.

>>9947168
MIT OCW much better

>>9947178

No problem, and good luck friend :)

>>9947182

It's very good, but I find the way this series is structured and the way this professor presents it to be very useful for someone who does not know anything about mathematics. It covers high school mathematics in depth rather than more complex material.

>>9938328
lmao the sauce is hilarious
https://www.breitbart.com/tech/2017/03/08/cia-keeps-database-of-japanese-style-faces-emoticons-to-use-tn-online-forums/

>>9943929
what is it?

>>9947182

MIT OCW is lame and over rated

>>9942398
t. has an infinitesimally small penis

>>9947147
Although he may be a bit overhyped, I find 3Blue1Brown really good. He got a really good serie on linear algebra and manage to show a lot of stuff visually.
FlammableMath is quite funny, altough it's mainly just him integrating complicated stuff.
If you want lectures, i'd recommend the Graduate Mathematics. This dude post tons and tons of lectures on advanced stuff, but there is some that are accessible to non experts.
Some dude posted a huge dump of all kind of textbooks on /sci/, earlier. Here's the magnet : magnet:?xt=urn:btih:11c8b43e664983c0299c2858c2e213fd4c0b4f95&dn=MATHBOOKS&tr=udp%3a%2f%2ftracker.coppersurfer.tk%3a6969%2fannounce&tr=udp%3a%2f%2ftracker.opentrackr.org%3a1337%2fannounce&tr=udp%3a%2f%2fmgtracker.org%3a6969%2fannounce&tr=http%3a%2f%2ftracker.city9x.com%3a2710%2fannounce&tr=udp%3a%2f%2f9.rarbg.to%3a2710%2fannounce
Have fun.

>>9947147
Only if you promised to work hard, ok?

http://4chan-science.wikia.com/wiki/Mathematics
https://www.ocf.berkeley.edu/~abhishek/chicmath.htm
https://pastebin.com/V8WNshHV

You can download math books for free at:
http://libgen.io/

can anyone link me to some resources on simpification? I can do algebraic simplification but i'm learning calc now and i keep getting lost because of the large amount of steps involved, especially with multiple powers.

>>9947673

Well you must have some definition of a canonical form in mind?

What kinds of problems are these?

>>9947579
>TORRENT NOT FOUND: Please click Start Again to continue.
Why must you hurt me like this?

How does one memorize all this shit?

https://www.symbolab.com/cheat-sheets/Algebra

how do you make it come naturally to you otherwise?

>>9947784
Fucking kill yourself if you can't even memorize that shit. This is not stupid question thread.

>>9947789
sorry i was just asking for advice

>>9947791
Sorry friend, you either have it or you don't.

>>9948016
It's not a matter of whether you have it or you don't, it's a matter of whether you put in effort or you don't. Even a dumbfuck can memorize that shit.

>>9948066
>put in effort or you don't

>>9948066
Dumb post.

>>9947784
>>9947791
This is absolutely the wrong place to ask for advice on 3rd grade math. Fuck off

>>9938596
Or birth a nation

If I can learn mathematics up to early university level with just a reasonable amount of effort, is it likely that more advanced stuff won't be too terribly difficult either?

>>9948124
Difficulty of math blows up in finite time. The shit you learn during general education is there precisely because it's more intellectually palatable for the average Joe.

>>9948124
I believe there’s no such thing as difficult to understand subject, only lazy students.

>>9948205
I believe you're a dumb chink.

>>9948215
Such filthy language. Do you kiss your mother with that mouth?

WHO ????
H
O
ENS HERE

>>9947756
e.g (x^{3}+6x^{2}+5)(2x^{2}+8x)

>>9948268
There’s a wikipedia page dedicated to polynomial factorization. Lucky for you, there’s a formula for finding X of the third degree equation. The same holds for the fourth degree of equation. Not true for the fifth degree, as show by Galois.

>>9947784
What le FUCK

Why would anyone memorize that as a formula

All of the formulas here are direct consequences of, like, 5 basic rules- just learn them and you'll be ok

>>9948446
Hahahh you expect dumb undergrads to learn lasting information that will benefit their education instead of just hitting themselves with the textbook until they accidentally get an A- and then immediately forget everything

Magmas are underrated algebraic structures

They are strong enough to formulate the concept of a normal sub-magma

>>9948478

I would like to read a book that explores properties of magmas

Also I'd read one about latin squares

So im interested in GF(2)^k (where "^" is a cartesian exponent).

This is not a finite field, it's a commutative ring

does anybody know any information about this structure? does it have a name?

>>9948533
Robertson's Clepsidra.

>>9948538
>Robertson's Clepsidra.

Has anyone in /mg/ completed an undergraduate research seminar? I have a week to select a topic and I'm at a loss to some extent. I'm not sure if my topic ideas are too broad or too narrow.
I feel like any topic in my algebra textbook deserving its own chapter (e.g., grobner bases for ideals) would be too broad. At the same time, I feel like a proposed problem from MAA Math Magazine would be too narrow.
I'll talk to the professor that's running the course, but I wanted to see what /mg/ thinks in the mean time.

>>9948945
>grobner bases
It's Gröbner or Groebner.

>what /mg/ thinks
You can get a lot of mileage out of a single problem, especially if you try to solve it in its most general setting, like any proper mathematician would do.

>>9948945
I have no fucking idea what an "undergraduate research seminar" is, sounds kind of gay. Anyway, do whatever the fuck you want, the point is that you do something presentable and respectable.

>>9948404
>Not true for the fifth degree, as show by Galois.
Galois never showed that, and he couldn't have, since there is a formula the roots of any quintic.

>>9949157
Show me you cactus

>>9949199
>Show me you cactus
https://en.wikipedia.org/wiki/Bring_radical#Solution_of_the_general_quintic

>>9933606
Is there a finite nonabelian group all of whose irreducible complex representations are one-dimensional?

I suspect the answer is no, but I can't see how to prove it. I tried playing the row/column orthogonality relations and didn't get anywhere.

>>9949201
Tch. Fine, you win. Are you happy now?

>>9948533
Boolean rings

>>9948516
>>9948516
Nonassociative algebras are pretty much impossible to study in general unfortunately. There is some nice theory behind quasigroups though. You should look into those if you're interested in Latin squares.

>>9949217
>Are you happy now?
I was already now.

>>9949232

>Nonassociative algebras are pretty much impossible to study in general unfortunately

Sounds like a challenge.

What is a book about quasigroups? Are all quasigroups latin squares and latin squares quasigroups?

I want this book so badly but I can't find it

>>9949492
Pic related

The Cayley table for finite quasigroups is always a latin square, and conversely each latin square defines a finite quasigroup. Of course, there are infinite quasigroups too (e.g. the integers under subtraction).

>>9949492
>I want this book so badly but I can't find it
http://gen.lib.rus.ec/

If you don't care about Probability Theory, then leave this general.

>>9949593
>If you don't care about Probability Theory, then leave this general.
Probability theory is wholly irrelevant to most maths.

>>9949593
I don't care about probability theory and I'm not leaving

Be honest /mg/

>>9949748
I genuinely love mathematics.
(Why are (you) still here tho?)

i don't understand the proof of FLT. Too difficult.

>>9949853
See >>9948205

prove that Frey curves are semi-stable elliptic curves

>>9949890
>prove Fermat's Last Theorem LMAO

>>9949870
That chink is a retarded physishit. What does he know?

There was an anon who wanted the magnet to the huge math book dump that I posted earlier, but the link was broken.
Here's the (hopefully) working one:
magnet:?xt=urn:btih:11c8b43e664983c0299c2858c2e213fd4c0b4f95&dn=MATHBOOKS&tr=udp%3A%2F%2Ftracker.coppersurfer.tk%3A6969%2Fannounce&tr=udp%3A%2F%2Ftracker.opentrackr.org%3A1337%2Fannounce&tr=udp%3A%2F%2Fmgtracker.org%3A6969%2Fannounce&tr=http%3A%2F%2Ftracker.city9x.com%3A2710%2Fannounce&tr=udp%3A%2F%2F9.rarbg.to%3A2710%2Fannounce

>>9941923

either 99 or 100 minutes. final guess

>take diff equations course
>no mention of numerical analysis whatsoever
>first assignment
>pic related

REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

>>9949899
>>>/pol/ was a mistake

>>9949899
>chink
Why the racism?

>>9949906
>7 days to download
Kill me

>>9950017
Because it is proper.

>>9949987
Nah, your father made a mistake when he blew his load inside your mother.

We should have never made mathematics available to the chinks. They are incapable of understanding it properly to begin with.
Fucking humanoid-insectoid race.

>>9950045
His father didn’t blow a load, he just took a shit and decided to adopt it

>>9950045
>>9950046
>>9950052

Go shit up threads elsewhere you untermensch scum

>>9950056
It's true though. China is supposedly the "oldest continuous civilisation" and yet Gauss (just as an example) alone achieved more than the whole of China in 5000 years.

>>9950118
Not saying he's completely false but he acted as if this was /pol/ and his shameless self-replies triggers me

Ancient China was a backwards place where philosophy was valued higher than natural sciences. Only people who dropped out of imperial exams chose to study """useless""" things like maths.

>>9949215
Rep theorists please halp

Let [math]R[/math] be a ring. Is the quotient [math]R[x]/R[/math] just the zero ring? Or am I being a brainlet?

>>9950546
>>9949215
Since your group is finite and you're looking for representation over [math] \mathbb{C} [/math] which is a splitting field, for any two conjugacy classes in your group there exists a finite representation of it over [math] \mathbb{C} [/math] such that its character takes different values for your two conjugacy classes.

>>9950667
R isn't even an ideal of R[x]

>>9950667
No. Maybe.

>>9950667
R is not an ideal of R[x]

>>9950673
ohhhh damn should have been the first thing to check.... but it seemed so obvious that it would be>>9950675

>>9950668
>>9949215
https://math.stackexchange.com/questions/358104/nonabelian-group-with-all-irreducible-representations-one-dimensional/358126

lads, what's the correct operation for this so i don't waste time drawing them out

>>9950691
Going from top to bottom there are only two sets of vertices that form diagonals parallel to the top or bottom sides. Multiply this by four for the four different angles of the sides and this gives us A = 8.

Each vertex creates a diagonal with the 5 vertices that are not adjacent to it. Multiply by the number of vertices and divide by 2 since each diagonal is connected to two vertices and this gives us 20 total diagonals. Subtract A to get B = 12.

>>9950691
Fix a side. Count. Remove duplicates.

Did that twink Scholze still not publish his rebuttal of IUT?

>>9933606
Trying to declare in Applied Mathematics at uni. I've finished up to vector calculus and currently doing linear algebra, I'm taking courses in combinatorics, applied complex variables, and numerical optimization/scientific computing. Anybody have recommendations in any of those fields, or just general advice? Heard good things about gilbert strang from MIT OCW?

EVERY proof of the Nullstellensatz I've seen uses the Rabinowitsch trick... Have the jews also taken over algebraic geometry?

>>9951152
No.

>>9950729
>Did that twink Scholze still not publish his rebuttal of IUT?

>>9951291
Fucking finally! Time to make myself some time to start reading the IUTT papers now.

>>9951369
Unless Klaus is blowing steam.

>>9951291
>>9951369
>>9951378
Why no update though?

>NEW !! (2018-06-28)

>>9933606
Alright lads daddy needs some advice.
>Econ undergrad
>What until near the end to take advanced micro theory with calculus
>Took calculus I freshman year and got a C
>Don't remember anything
Anyone know of a good refresher? I'm not sure what to expect as I'm not awful at math, but a bit worried as this shit always makes me a bit anxious.

>>9951291
So....it’s official? Mochizuki was right all along?

>>9949492
>>9949508
>>9949232
>>9948516
I didn't expect to see this conversation on /sci/ of all places. I just woke up so maybe this is obvious but my understanding is that the notion of a cayley graph for groups can be generalized to an automata (semi-automata?) for monoids or semigroups (honestly not sure since I've never seen it formalized anywhere. Does anyone know if there is something like that for quasigroups as well? does the graph representation for a group (eg. cayley diagram) require associativity in order to work?

I'll check out those books as well if I can find a copy somewhere because that shit sounds awesome and I'm interested in all the different interpretations and visualizations for algebraic structures.

>>9951708
>Does anyone know if there is something like that for quasigroups as well? does the graph representation for a group (eg. cayley diagram) require associativity in order to work?

You definitely need power associativity for Cayley diagrams to make sense, so probably not.

>>9951519
calc I? Just google some practice problems, doesn't it consist almost entirely of solving integrals, finding surface areas, and volumes of revolution? Theres stuff like linear approximations you might need to do as well, but those are pretty simple if you get the other stuff

>>9951291
Absolutely based if true.

>>9948236
Is this a meme?

>>9951291
Okay, this is based

>>9952189
"Repräsentierber"(sic!) broke the immersion

>>9952189
Nah, just some frenchfag bragging.

>>9951291
Who draws these?

>>9952189
Looks like Godel's denationalization argument.

>>9952304
You don't say.

>>9951291
It's the 22nd of August already. Where are the proofs?

https://www.youtube.com/embed/fNS7N04DLAQ?autoplay=1&auto_play=true
Subtitles at 20 seconds in
>For those watching via Nico-Nama, we support live comments with TeX formats.
WHAT THE FUCK!? What is this wizardry!?

Will gaijins like us ever catch up?

>>9952351
You got rused.
https://twitter.com/hashtag/iutabc?src=hash

>>9951291
>>9951579
>>9952205
hope

>>9950704
what do i google to understand this operation better

>>9952696
nevermind this

why should i read this as 3 ÷ (1/9) and not 3 ÷ 1 ÷ 9?

I thought in order of operations you just read shit in order if it's ambiguous

new thread when?

>>9952784
never its time to retire this shitty general

Is there any appilication or insight to gain with comma categories or is it only a funny but useless technical construct?

>>9951291
The madman has done it. I want a Mochizuki film desu.

>>9952706
>>9952696
Don't waste your time. No one would actually write that anywhere because it is actually confusing. Whoever designed that question is a retard.

>>9952836
Things like (co)slice categories and arrow categories are special cases of it, so it's at least useless to talk about all of these at the same time. I've never seen a good exposition on comma categories in their full generality though.

>>9953625
>>9952836
I view them as a generalization of natural transformation.