/sci/ - Science & Math

>>12291777
Based trips. Fuck foundations

>>12291777
Can anyone here help an actual fucking brainlet?

I need to turn this:
[math]xA^{-1}x+(y-hx)^TB^{-1}(y-hx)[/math]

Into this:
[math]x^T(hAh^T+B)^{-1}x+y^T(hAh^T+B)^{-1}y[/math]

I was given this info:
x and y are gaussian vectors.
h is a matrix that turns x into y:
[math]y = hx[/math]

A is a covariance matrix of the input, x
B is a covariance matrix of noise

I don't know if it's even possible, but that's the hint the instructor provided. I've tried versions where I change everything into either x or y, one where I rewrote the noise into y as:
[math]y = hx + z[/math]
where z is noise

None of them become what it should be.

>>12292028
Also, noise is gaussian.

>>12292028
It seems to me that it would suffice to show that
[math]A^{-1} = C + h^T C h[/math], for [math]C = (hAh^T + B)^{-1}[/math].

This condition seems to imply [math]A = hAh^{T}[/math]. Is [math]h[/math] invertible with [math]h^{-1} = h^T[/math]?

Actually, nevermind, this condition is probably false.

>>12292119
I don't think it's meant to be invertible. It is "just a matrix".

Give it to me straight...

I haven't touched mathematics for 10 years.

Assuming I have zero high school mathematic knowledge, can a motivated person learn how to answer these questions within three days?

>>12292028
>>12292119
I keep ending up with
[math]x^Th^TB^{-1}hx+y^T(hAh^T+B)y[/math]

Later on, when I plug it into a gaussian integral identity and integrate over x, I end up with the probability distribution in almost the right format, except it's trying to say that:

[math]det(hAh^T+B) = det(hAh^T)[/math]

Is this even possible? I've been looking for a property or identity specific to covariant matrices that allows this to happen, but I can't find anything.

>>12292028
>>12292119
I keep ending up with
[math]x^Th^TB^{−1}hx+y^T(hAh^T+B)y[/math]
Later on, when I plug it into a gaussian integral identity and integrate over x, I end up with the probability distribution in almost the right format, except its trying to say that:

[math]det(hAh^T+B)=det(hAh^T)[/math]

Is this even possible? I've been looking for a property or identity specific to covariant matrices that allows this to happen, but I can't find anything.

>>12292028
>>12292119

Let's see if the math tags work this time.
I keep ending up with

[math] x^Th^TB^{−1}hx+y^T(hAh^T+B)y [/math]

Later on, when I plug it into a gaussian integral identity and integrate over x, I end up with the probability distribution in almost the right format, except its trying to say that:

[math] det(hAh^T+B)=det(hAh^T) [/math]

Is this even possible? I've been looking for a property or identity specific to covariant matrices that allows this to happen, but I can't find anything.

>>12292143
No, those will take a bit of learning to answer. Here's a more attainable question for someone of your level: Say I take a number, if it is odd, I multiply it by 3 and add 1, if it is even, I divide it by 2. If I repeat this process on any positive whole number, will the chain always go to one?

So for instance 5:
5 - 16 - 8 - 4 - 2 - 1
20:
20 - 10 - 5 - ... - 1

Will this hold for any positive number I choose? If you can answer it you'll be ready to learn highschool math.

>>12291777
H0T DAMN I'M SPOOKED

>>12292156
I couldn't even do that shit back when I was in high school.

>>12292143
They are quite easy, but without experience and knowledge no chance you will get evrything right. Although if you start reading about graphs you probably will score some questions.

So if you add the digits of any number in base 10 you get a new number. If that number is divisible by 3, the original number is also divisible by 3. I've looked up why this works and it makes sense, but what other base/divisor pairs does it work for?

>>12291777
>Against foundations edition

So basically fuck Nikolaj edition.

>>12292167
Most generally, I believe this always works for [math]n-1[/math] in base [math]n[/math]. I think(but am not sure) that [math]n-1[/math]'s prime factors also work.

>>12292183
Now that I think about it. This is a direct consequence of Fermat's Little Theorem

>>12292028
Looks like the decomposition of sum-of-squares into its error and data variance components.
If I recall you'll need to use the fact that the error and input are uncorrelated, but otherwise it's a general statistical identity that doesn't depend on normality of x and y.
(There's a geometric motivation that goes something like this: visualize the vectors in N-dimensional space, so that uncorrelatedness becomes orthogonality, and the decomposition becomes an application of the fundamental theorem of linear algebra to h, i.e. it projects the input x onto im(h).)

>>12292160
She's bullying you, it's a famously unsolved problem.

>>12292214
I tried that. It's how I got to this >>12292155

>>12292250
Fuck you anon, I'm a man.

>>12292250
>She
I hope you die a horrible painful death

>>12292169
You got me wrong buddy, I fully support OP.

>>12292274
Oh sorry, my mistake.

>>12292324
Sure seems like things are going that way at the moment

>>12291777
w-will anyone spare m-me a crumb of written reference and l-learning material to measure theory in the form of a b-book?
p-please anone...

>>12292363
Cohn.
Read this https://i.imgur.com/loGKqbK.png whenever you want to ask /sci/ for recs, it's basically a compilation of generic /sci/ recommendations.

>>12291777
I'M IN AS LONG AS WE ALSO KILL ALL CATEGORY THEORISTS

>>12292379
t-thanks anone...

>>12292363
1. Google "Measure theory textbook"
2. Download one and read it
3. if you don't like it go to step 1

Please give me a quick red pill on elliptic curves.

If I want to understand them to an extent where I can crack elliptic curve cryptography, will I need to learn all of algebraic geometry up to millennium problem material?

ok bros i know this is basic and easy but i have some doubts and i need someone to tell me what do now

>>12292447
Should have just divided every addend separately I think. No need for substitution

Here's a question for you /mg/: at what point did you stop feeling like a brainlet?

I am self teaching myself analysis and I keep seething over the fact that every theorem I encounter, no matter how convoluted, has always been figured out by some rando in the 1830s.

>>12291845
>Uses foundations to bash foundations

>>12292557
It's only getting worse. The more you know the more you are aware of how much you don't know. Before I started with math I felt like a brain Chad. Now I know I'm a massive brainlet.

Do you guys know where to see real analysis and proof material? I want an idea on what I'd be getting into studying a math major

>>12292250
Are you serious? Motherfucker i've been building a python function all day around it wondering why the fuck nothing is working. This would explain it.

>>12292617
It's called the collatz conjecture

[math]\bullet[/math]What textbooks, papers or text did you read today?
[math]\bullet[/math]What non-textbooks did you read today?
[math]\bullet[/math]Did you write something today?
[math]\bullet[/math]Did you do some programming today?
[math]\bullet[/math]Did you build something today?
[math]\bullet[/math]Did you clean up something today?
[math]\bullet[/math]Did you plan something today?
[math]\bullet[/math]Did you manage to work off some bureaucracy/paper work today?
[math]\bullet[/math]Did you practiced any skills today? If so, which?
[math]\bullet[/math]Did you do sports/cardio/weightlifting today?
[math]\bullet[/math]What were you eating today?
[math]\bullet[/math]How much sleep did you get yesterday?

1 - 1: https://youtu.be/lNAMY_otcM4
1 - 2: https://youtu.be/8oU0F3d-H4U
1 - 3: https://youtu.be/EHwTEqwgYtE
1 - 4: https://youtu.be/pmZK6TCaI7o
1 - 5 (corregido): https://youtu.be/f1QjzRby62s
2 - 1: https://youtu.be/CEmqZNhlSqs
2 - Ejercicio 1: https://youtu.be/OP44XBx0Fv4
2 - 2: https://youtu.be/TUceh9nC_uk
2 - Ejercicio 2: https://youtu.be/tcNNW2y-Cus
2 - Ejercicio 3: https://youtu.be/wJCOzlod15c
2 - 3: https://youtu.be/lYOEVjGg1OY
2 - Ejercicio 4: https://youtu.be/LmAw5Sy0p-8
2 - 4: https://youtu.be/Konj8Hkifnw
2 - Ejercicio 5: https://youtu.be/1GS-b4OyMLI
2 - 5: https://youtu.be/Ssj9P3RiAHM
2 - 6: https://youtu.be/nEETZlbC-Is
3 - 1 (corregido): https://youtu.be/jGnGwII71zM
3 - 2: https://youtu.be/7kO8-7WVfVo
3 - Ejercicio 1: https://youtu.be/XsShQ_ceKkc
3 - Ejercicio 2: https://youtu.be/HBfcmyUgdnI
3 - 3: https://youtu.be/Ikb27u8rbuY
4 - 1: https://youtu.be/lqHvWmeDrIQ
4 - 2: https://youtu.be/xFoO6QVTNi4
5 - 1: https://youtu.be/OGMEMrVRFos
5 - Ejercicio 1: https://youtu.be/YkI0knASwEk
5 - 2: https://youtu.be/3IuTylXDrdE
5 - Ejercicio 2: https://youtu.be/rBv2AvBcVNQ
5 - Ejercicio 3: https://youtu.be/gXxON3zm-ZM
5 - Ejercicio 4: https://youtu.be/CeRi-Tr3iK4
5 - Ejercicio 5: https://youtu.be/KxC_QNf0ASQ
6: https://youtu.be/c1nfWqrNNZI
6 - Bonus track: https://youtu.be/LvECD3TcbKo
7 - 1: https://youtu.be/-HtCWLAwFh0
7 - 2: https://youtu.be/jB3Qj7BZb9c
7 - Ejercicio 1: https://youtu.be/FgzsC1M69yg
7 - Ejercicio 2: https://youtu.be/fC-pFDyjX7k
7 - Ejercicio 3: https://youtu.be/3WzhDagC-7A
8: https://youtu.be/3ClWGJduvts
9 - 1: https://youtu.be/JVnovIVGLL4
9 - 2: https://youtu.be/IBeO1FEFl5I
10 - 1: https://youtu.be/g1lQC-Kncdo
10 - 2: https://youtu.be/MNwbuLSwHoc
11: https://youtu.be/5fDqac5h2Co
12: https://youtu.be/JYR9Mxxz9_w

Do any of you guys have a crush on a mathematician from any time period?

>>12293375
Abel without a doubt.
no homo

Do any of you guys know how to increase the working memory? If I simply had a better working memory I could without a doubt become a leading mathematician in the world.

>>12293375
Galois without a doubt.
Full homo

>>12293408
Too much of a baby face. Underdeveloped phenotype.

>>12292761
Garbage language

>>12292617
lmao you actually fell for it? Jesus Christ

>>12292617
https://www.youtube.com/watch?v=7CcjvMXdwQk
Now that you've heard of the collatz conjecture, you have seven days to solve it. Good luck...

>>12293470
she a cunt teacher form my uni, the calsses have several mistakes. i just posted it here because i have to log in every 4 minutes to see that list otherwise

>>12292447
>integral with u and x
OH NO NO NO

>>12292447
First integral should have a dx, and you need to convert all of the ‘x’s to ‘u’s noylt just some of them. Also du can't be equal to something without any ‘d’s in it. You need to find dx in terms of u and du and substitute that in.

Hi anons,
I have a set of X,Y coord of human body parts in a computer program, (pic related)
Is there a formula to get the "direction" of the body? (Ex. where the chest is pointing out based on coords of shoulders)
I don't need an explanation, just a term i can search on google.

>>12294122
I would make a ray orthogonal (90 degrees) from the line connecting the shoulder points, then use the wrist, elbow, and other joint locations to figure it out based on how you can move your body. This will probably fail on a contortionist, but for a normal person it should be fine.

Hi. Given two random variables X, Y and their distribution functions, how can i find, for example, the probabilities that X>Y, X>Y^2, X>3-Y ???????
thank you mathchads


>>12293417
he was literally 14 in his portrait, brainlet

>>12294376
Integrate the joint distribution over the region where X>Y

>>12294425
thanks anon

>>12294003
just use multivariable calc

>>12292363
Stein Shakarchi real analysis

with a solid background in maths, what is the most interesting way to start exploring physics (in a nontrivial way)? Would quantum theory be a good place to start? Peter Woit's book seems interesting

>>12294872
Calabi-Yau manifolds?

>>12294003
w-whats wrong with that....

>>12292734
Yesterday..
>∙What textbooks, papers or text did you read today?
I read some Harvard students course notes, but it was a bit shallow. He was probably young when he wrote it and I'm a tad beyond that.
It was on group and set theory.
∙What non-textbooks did you read today?
I read a few pages from a book on motivation
∙Did you write something today?
Only copied over some notes from said notes.
∙Did you do some programming today?
x
∙Did you build something today?
x
∙Did you clean up something today?
:/
∙Did you plan something today?
The next day. Today I have to work despite it being Sunday.
∙Did you manage to work off some bureaucracy/paper work today?
I procrastinated on it again..
∙Did you practiced any skills today? If so, which?
I met some people irl that I didn't know which is always good progress I think
∙Did you do sports/cardio/weightlifting today?
Haven't done sports in weeks
∙What were you eating today?
coffee and chocolate
∙How much sleep did you get yesterday?
I slept long so a bunch - but at what cost

>>12292734 (You)
Yesterday..
>∙What textbooks, papers or text did you read today?
I read some Harvard students course notes, but it was a bit shallow. He was probably young when he wrote it and I'm a tad beyond that. It was on group and set theory.
>∙What non-textbooks did you read today?
I read a few pages from a book on motivation
>∙Did you write something today?
Only copied over some notes from said notes.
>∙Did you do some programming today?
x
>∙Did you build something today?
x
>∙Did you clean up something today?
:/
>∙Did you plan something today?
The next day. Today I have to work despite it being Sunday.
>∙Did you manage to work off some bureaucracy/paper work today?
I procrastinated on it again..
>∙Did you practiced any skills today? If so, which?
I met some people irl that I didn't know which is always good progress I think
>∙Did you do sports/cardio/weightlifting today?
Haven't done sports in weeks
>∙What were you eating today?
coffee and chocolate
>∙How much sleep did you get yesterday?
I slept long so a bunch - but at what cost

>>12292734
Yesterday..
>∙What textbooks, papers or text did you read today?
I read some Harvard students course notes, but it was a bit shallow. He was probably young when he wrote it and I'm a tad beyond that. It was on group and set theory.
>∙What non-textbooks did you read today?
I read a few pages from a book on motivation
>∙Did you write something today?
Only copied over some notes from said notes.
>∙Did you do some programming today?
no
>∙Did you build something today?
no
>∙Did you clean up something today?
:/
>∙Did you plan something today?
The next day. Today I have to work despite it being Sunday.
>∙Did you manage to work off some bureaucracy/paper work today?
I procrastinated on it again..
>∙Did you practiced any skills today? If so, which?
I met some people irl that I didn't know which is always good progress I think
>∙Did you do sports/cardio/weightlifting today?
Haven't done sports in weeks
>∙What were you eating today?
coffee and chocolate
>∙How much sleep did you get yesterday?
I slept long so a bunch - but at what cost

>>12292143
open university?

>Ayo, professor! Give me the whitest white guy you got

>we got you bro

https://youtu.be/-ysVGWtAjio

https://www.youtube.com/watch?v=IT-O-KSWlaE

>>12296085
Why the anti-Caucasian sentiment?

https://youtu.be/JCM7M7XfSFg

can someone explain this to me or am I too brainlet?

>>12296116
nonwhites love white countries and white women. They want them all, so they hate on white men. Simple as, folks

>>12292605
A Real Analysis book? Like Abbott
There's also a lof of Why Math? books
>>12292617
Fuckin lmao

Don't get me wrong, I fucking love algebraic topology, but seeing shit like this makes me question everything.

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

>>12292383
This. Category theory is a bookkeeping tool, and should stay that way.

Any good books on elliptic curves from a pure math standpoint? I don't particularly care about cryptography.
Bonus points if it touches on the modularity theorem

>>12291777
Why don't we have a computer find a contradiction in ZFC already?

>>12294872
lagrangian mechanics from a practical perspective

>>12296301
Ed Nelson almost nailed down Peano arithmetic but (((they))) got him.

Anyone tried the MIT/edx course on probability? I want to run through of basic probability before moving on to heavier stuff that I need to learn

>>12296285
Doesn't seem so bad. Thought it was going to be about the Warsaw circle before I clicked through.

>>12296444
(((Chinese Australians)))

>>12296448
I’ve been working through the old course on ocw, it’s the best I’ve found for an introduction. Tsitsiklis is a good lecturer

>>12295558
Yeah, how'd you know?

>>12296487
Will give it a shot then. Thanks!

>>12291777
2 + 2 = ?

My math professor says 4, but my gender studies professor says its 5. Who do I believe?

>>12296513
1=S(0)
2=S(1)
3=S(2)
4=S(3)
For all n,m
n+S(m)=S(n+m)
n+0=n.
Thus we see
2+2=2+S(1)=S(2+1)=S(2+S(0))=S(S(2+0))=S(S(2))=S(3)=4.
Thus 2+2=4.

>>12291777
fuck this 150 iq shit how do i do long division?

>>12296578
Mach leading terms, subtract, continue.

>>12292344
hallo nikolaj

>>12296533
>n + 0 = n
sorry but if you leave 4 chickens without doing anything to them there will be 5 chickens sometimes even 6

>>12292734
Today I skimmed some textbooks on machanics and it was inspiring. I feel like the physicists gave up too much of it to the robotics people and engineers in general. Why is that? Is mechanics solved to such a degree that it's boring from a physics perspective?

Otherwise I had to work, so I didn't do much. I'll go to bed soon and get enough sleep - I promise.

book recommendations for weak turbulence theory? or non linear dynamics in general?

>>12296925
what about apples?
sometimes there might only be 3 or 2 by the time you check them again

Brainlet here.
How can I ensure pic related is exact on degree 2 polys?

You did communicate your PhD thesis with interpretive dance, right?
https://www.youtube.com/watch?v=MASNukczu5A

>>12298387
I thought that was pretty epic. Interpretive dance is extremely cool as well because it activates all of your limbs and organs. You can do brain dances and subtle dances with muscles that others don't or barely witness. It would be truly cooler if each body motion in the dance actually represented a mathematical operation or entity. But this was still cool.

>>12298295
Just say f(z)=z^2b_0+zb_1+b_0, substitute that in and solve.

>>12298295
let a_0=a_1 = 0
a_2 = f'(x_0)/f(x_2)

>>12291777
Probability has always been my weak suit and right now I'm taking a course on computer system performance analysis.

We just got into "Generating Functions" and I'm completely lost. It feels like there is just so little content that intuitively explains this stuff.

Like for example there's an exercise wherein we are supposed to find the generating function for
[math] Y = X_1 + (1/2)X_2 [/math] where [math] P\{X_1 = -1\} = P\{X_1 = 1\} = 1/2 [/math] (i.e., a coin-toss) and [math] X_1 = X_2 [/math]

There's tons of stuff about generating function that sum for example coin tosses and dice rolls, but then we've got a constant in front of one of them and I'm just lost. Feels like I can't wrap my head around what I'm supposed to be thinking.

>>12299028
sad story bro

>>12299028
it's just sums bro
shut up and calculate

>>12299052
Sure it's just sums but I've been staring at generating functions and I can't understand where the fuck I'm even supposed to start

>>12299057
Start with trying to find the generating functions for [math]X_1[/math] and [math]X_2[/math]. Then consider whether or not they are independent. If they are, things will be easy for you. If not, it's a little more difficult but you have a finite number of possible values so it shouldn't be that bad.

>>12292408
yes.

pack it up boys its solved https://arxiv.org/pdf/2008.13643.pdf

>>12299149
Guaranteed someone on /mg/ will seethe over this

>>12299057

Ngmi, basicslly it asks for
00
01
10

In whatever flavor of math you subscribe too

>>12299149
>The Collatz tree proves to be a Hilbert hotel for uniquely numbered birds. Numbers divisible
by 2 or 3 fly off. An infinite binary tree remains with one “upward” and one “rightward” child
per number. Next rightward descendants of upward numbers fly off, and thereafter generation
after generation of their upward descendants. The Collatz tree is a Hilbert hotel because its bird
population remains equally numerous
Jesus christ they type like retards

Is there anything good in between May and Hatcher for topology? The former is maybe too concise for me while the latter is absurdly bloated. My background is basic undergrad algebra (D&F) and Munkres for basic point set and algebraic topology.

>>12299149
The Collatz conjecture is "proved" every couple years. It'd be nice if this one was real, but it's been up five days and no actual mathematician I know has said anything about it so it's probably not valid.

>>12299354
Munkres also has an algebraic topology book.

are all groups of the same size isomorphic to each other?

>>12299379
no you fucking retard

>>12299379
why can't you just arbitrarily assign elements to each other? That's what Cantor's diagonal argument looks like to me.
t. undergrad

>>12299398
meant to reply to you >>12299388
sorry

>>12299401
Do you know what an isomorphism is?

>>12299402
groups whose elements may be bijectively assigned to one another are isomorphic, right?

>>12299149
>https://arxiv.org/pdf/2008.13643.pdf
If it's not Vixra, it's not true

>>12299407
https://en.wikipedia.org/wiki/Group_isomorphism
Ask for a refund from your college

>>12299407
[math]\phi:G\to H\text{ is an isomorphism if } \phi \text{ is a bijection and } \forall a,b\in G,\ \phi(ab)=\phi(a)\phi(b).[/math]

>>12299407
imagine being this far into the semester and not understanding that isomorphism needs to respect group structure

>>12299419
>>12299418
>>12299410
sheeeeiiit thanks boys

>>12299354
You should take a look at Bredon's Topology and Geometry.

>>12299418
oh so it has to be a bijection and a homomorphism? I'm assuming you left out that the right side of that equation enforces that between phi(a) and phi(b) is group H's operation (or I'm just unfamiliar with how it's usually written)

>>12299459
yes
yes

>>12299149
When a mathematician makes a false proof do they get shunned from mathematics or can they just move on

>>12299518
They can move on, especially if the mistake is subtle and a few other people initially thought it was correct.

>>12299536
This is what always confuses me when people speak about mathematical truths. It would seem that ever theorem and proof we have still admits the possibility of falsehood.

>>12299550
Can you elaborate? I'm not sure I understand what you're confused about. Just because someone was incorrect about something doesn't change the truth of the matter.

>>12296505
I can tell by the TMA layouts

>>12299550
Proof checkers fix that, I wish they were more widely used. Agda is my favorite.

>>12299825
The proof checker could also contain an error, or there could be a hardware problem giving a false positive verification. I'm not saying they're useless, but they're not real-life oracles.

>>12299825

> Proof checkers fix that

>>12298885
how do I do this?

>>12299379
Some profs really don't emphasize enough the structure preserving part of isomorphism

>>12299906
Some profs shouldn't be allowed to teach algebra.

>>12292605
Krantz wrote a book called Real Analysis and Foundations in an attempt to bridge the divide between normal calculus textbooks and hard edged books like Rudin's Principles of Mathematical Analysis. An alternative to Krantz could be Geoff Smith's Introduction to Algebra and Analysis which is pitched at a similar level but more broad in scope.

>>12299906
it's not my professor's fault, I just didn't properly read the notes before starting the homework

>>12296290
Silverman's trilogy seems to be the standard, but Cassels and a few others have books on the subject.

>>12299028
Generatingfunctionology by Wilf has an excellent reputation while still providing intuition, so I heartily recommend it.

>>12299996
Do you mind being more specific? Searching isn't giving me much

Did any of you have courses that used the usually recommended memebooks? Or even attempt to self learn through them?

>>12300050
What about Mathematician's Delight

I'm trying to find a ring [math]R[/math] with unity and a maximal ideal I such that [math]R/I[/math] is not an skew field. I tried with [math]R[/math] being the set of matrices with elements in [math]\mathbb{Z}[/math], but I'm but sure how to build the maximal ideal. Any ideas?

>>12300050
My old prof loved all of Rudin's books and also the Axler linear algebra one. He always said that matrices were "for high school kids"

>>12300050
Used Rudin PMA, Munkres Topology. I TA'd for a course that used Axler. They're fine books, if you work through them you will have a decent understanding. With these charts it matters less what book you use, and more about how much you stick with it.

>>12300050
>those linear algebra books
Disgusting. Any self-respecting mathematician would derive all of linear algebra on his own.

what the gfuck do you get if you SVD a transition probability matrix of a markov chain?

>>12300159
Stale meme

>>12300050
We're using Hammack's "Book of Proof" in an introduction to proof's class I'm in. It's pretty good.

>>12300278
have you tried it in a one or two-dimensional case?

For starters, I'd try to find if you can form a transition matrix with det=0 and then you'll have a good idea

>>12300282
It's not a meme and I'm not joking. Linear algebra is a subject that any person interested in maths should be able derive and prove the most important results on their own.
That said, of course you need a starting point, so I would suggest the definition of a vector space, the definition of a matrix and the determinant. The rest follows quite trivially and it's fun to do it on your own, plus much more educational.

>>12300278
have you tried it in a three or two-dimensional case?

For starters, I'd try to find if you can form a transition matrix with det=0 and then you'll have a good idea

>>12300290
yes i've tried it one a very basic 2-dim one. didn't know what the fuck i was looking at though, which is why i asked here. i compared to the asymptotic distribution but they were not even close to being similiar

>>12300289
It's definitely a stale meme, I've seen it said repeatedly for along time
In any case LA was where I learned to try to prove theorems by myself and it was fun, yes

>>12300298
I've never seen anyone else say it but me.

Multi-armed bandit problem, what is it about?

>>12300302
Well that just makes it sad for both of us

>>12300308
Idk why you're so uptight about it bitch boy. I made a simple observation about linear algebra and you're getting all pissy on me.

you have 2 minutes to explain to a non-mathematician the rational points on the unit circle are dense in the unit circle

>>12300326
Strech it and use the result for intervals in R

>>12300063
Determinant nonzero might be a maximal ideal

Let [math]x \mathrel\epsilon \phi[/math]. Since [math]\phi = \{\}[/math] we know there is no such [math]x[/math], what is its value after the binding? Is it [math]\mathrm{nil}[/math]?

>>12300357
>binding
u w0t m8

>>12300346
I changed my mind it's not additive

>>12300311
Relax man, I wasn't trying to be rude. I did see the sentiment a lot though and I disagree with it, tho

>>12300326
All of these except the one about calculus and analysis were my posts.

am i missing something obvious with this definition of a "bottleneck" in Graph Theory?
for a set of vertices S, we can define the set of neighbors N(S) = {r | {r,s} is an edge for some vertex s in S}
then S is a bottleneck if |S| > |N(S)|
how can S have more adjacent vertices than the set of its neighbors? aren't they at least equal?

>>12300406
read carefully
o=o=o

>>12300424
thanks anon. i think I had it in my mind that S was a single vertex rather than a set of vertices. i've been trying to draw an example so I can visualize it, does this look right to you?

>>12291777
I'm looking for books that would be enough to cover calculus BC and algebra for my embedded software projects. No bully

>>12300049
In increasing order of difficulty: Rational Points on Elliptic Curves, The Arithmetic of Elliptic Curves, and Advanced Topics in the Arithmetic of Elliptic Curves. All are by Joseph Silverman. Cassels' book is entitled Lectures on Elliptic Curves and is published by Cambridge.

>>12300493
https://www.mathinenglish.com/PWB/SkillsI.pdf

>>12300055
That's not really a textbook though. And it isn't memed

can somebody even prove this? am I literally retarded?

>>12300553
oh i forgot to mention F(x) is a the distribution fucntion so it is a non decreasing function wich image is between 0 and 1

>>12300540
Thanks a lot, I hope you would get AIDS.
On topic, is Khan academy a meme or it would be sufficient for this problem?

>>12300553
Holy fuck learn to use [math]\LaTeX[/math] jesus. also don't know

>>12300553
>pic

>>12300564
>calculus BC and algebra for my embedded software projects.
Yeah, should be. If you need something specific, google "calculus textbook pdf" and grab any of them, they're all basically identical. As for "algebra", you're gonna have to be a lot more specific.

>>12300579
>If you need something specific, google "calculus textbook pdf" and grab any of them, they're all basically identical.
I remember huge flamewars years ago over which to pick of Courant, Thomas, Apostol, Spivak and the like, all joined however in their hate of Stewart
Wonder what was that all about

>>12291777
how do you find the diameter of a pentagon pls help me i am so stupid :(

1. The distance between the farthest corners of the pentagon.

2. The diameter of the largest circle that fits inside the pentagon.

3. The diameter of the smallest circle that fits around the pentagon.

4. The distance from the base to the opposite corner of the pentagon.

>>12300667
>The distance between the farthest corners of the pentagon.

>>12300676
thank you senpai

>>12300688
In general for a set X the diameter of X is defined to be the supremum of the distances between any two points in X.

anyone have a good book on optimization?

Anyone working with p-adics here and can give me an example of a nice application? I mean, besides them being a cool concept.

>>12299560
I probably can't specify what I'm confused about in a rigorous way, since I don't know anything about epistemology.

>Just because someone was incorrect about something doesn't change the truth of the matter.
hmm. I guess if we assume the existence of some sort of being, e.g. god, with the ability to always make logically sound conclusions, then there is a truth value to mathematical knowledge. The thing is, if we don't make this assumption, then I don't see why we privilege such knowledge over other kinds of scientific knowledge.

In the physical sciences we have experiments that might give evidence of certain theories, and if we repeat an experiment enough and continue to get the same result, then we begin to think of that theory as true. It seems like mathematical knowledge is something similar, but instead of doing physical experiments we have people logically work through the proof and verify whether it is sound or not. This is a similar sort of test to a physical experiment in that it can give contradictory results (people can make mistakes working through the proof), but it is with enough repetition (people finding the proof sound) that we can take this as evidence of an underlying truth.

>>12300553
This is the wildest typesetting I've ever seen lol. Also, how are we meant to interpret the integral on the LHS? Does this mean something like 'integrate with respect to the measure for which F is a distribution function'?

>>12300553
heh, I just realized it's an integral

>>12300591
All of those are good choices. Spivak's the best IMO.

Fuck Stewart.

>>12301029
what do you even mean? F(x) = P(X=<x)

>>12299560
Are you retarded?

there you go sensitive fags. this doesnt mean you would know the answer though

>>12301123
looks horrible. please learn latex

>>12301133
based double dubs

>>12301123
ok
have you tried to partition the integral in [math](-\infty,0][/math] and [math][0,\infty)[/math]?

>>12301133
it was originally on latex i'm assuming
>>12301173
yes i still dont know how am i supposed to integrate that shit. the simples step is rewriting right part as infinity-Fx*dx integrated in all numbers. fucked shit is you are nto allowed to do that although it's a basic itnegration property because it's an undefined integral

Is it a good idea to study calculus and precalculus side by side?

>>12301193

precalc is basically not needed for calc since they go over limits and stuff in calc books.

I did precalc and calc at the same time in highschool, shit was retarded

>>12301184
rewrite the infinity limit to [math]n[/math] as [math]n \rightarrow \infty[/math]
now anon, what's the "similar" rule to derivative chain rule in integrals?

>>12301102
>All of those are good choices. Spivak's the best IMO.
>Fuck Stewart.
That seems to be the position the shitshow eventually condensed into, yes.
To this day though I haven't seen anyone that actually used the books. See >>12300050

>>12301218
>chain rule
you must mean product rule unless you're clinically disabled

>>12301355
whatever mate you get the idea

>recommend a book to someone on /mg/
>now there is a request on the copy of the book that I have borrowed from my university library
>have to return it or pay a fine
hmm

>be unable to solve a problem
>don't want to move on and give up
i hate math

Is this the reddit formula?

>>12301658
Move on and come back later.

>>12301686
It's pretty cringe. I know someone who got it tattoo'd on after doing first year maths.

>>12301735
Why does everyone pretend it's super complicated or contains a lot of insight on mathematics when neither of those things really apply?

>>12301777
People like pretending to have lots of super complicated insight and other people who actually know shit don't like calling them out on the posturing. Especially if it's just to impress noobs and redditors

>>12301735
>I know someone who got it tattoo'd on after doing first year maths.

>finally figured out how to solve a problem I've been stuck on since yesterday
>it turned out trivial
I want to die

Might be a long shot bros, but I really need help with this question in logic. Any ideas?

[math]\text{Consider the function } f : \mathbb{N} \to \mathbb{N} \text{ where } f(n) = 1 \text{ if $n$ is the Gödel number of a theorem offormal arithmetic (i.e., a statement that can be proven in formal arithmetic), and } f(n) = 0 \text{ otherwise. Prove that there is no numerical Turing Machine that can compute }f. [/math]

Obviously, you show that f cannot be partially recursive (and thus there's no Turing Machine) by relating it to the function in the halting problem. You probably use Godel's first incompleteness theorem as well, somehow. Unfortunately, I have literally no idea how to do this.

>>12301892
You need to keep track of your struggling process and use this situation as a learning opportunity to see where your thinking went wrong. What was the problem?

Can't stop listening to
https://www.youtube.com/watch?v=RY7FpB9BZH4
on loop

>>12302051
i want to pound your trannypussy with my dick

>>12302075
Not a tranny even though I am actually a very cute and funny.

>>12302079

omg! I don't give a fuck

What's a good undergrad thesis for CS? I'm in a third world shithole and my professor's are absolutely clueless about the mathematical parts of CS (most of it). I prefer something mathematical btw.

>>12302477
distributed systems, dependent type theory, or something closer to chips

>>12301899
This is trivial, assuming formal arithmetic is consistent.

Let n be the Gödel encoding of the embedding of the statement "format arithmetic is consistent". Assume f is computable, just compute f(n). If it returns 0, then arithmetic is inconsistent which violates the assumption. Otherwise you know that there is a proof in arithmetic that arithmetic is consistent. This violates Gödel's incompleteness theorem.

>>12292605
Book of Proof by Hammack, it's free on his website and too many universities use it and it's on amazon in hardcover for $35, then get Understanding Analysis by Abbott off of amazon for $40 or pirate at http://gen.lib.rus.ec/

You now know what you are getting into as a math major, work through both of those boooks and you will thank the good anons on 4chan for helping making your life 4 times easier in university

>>12302477
What kind of shithole are you talking about? It changes a lot what can be done or not.

>>12302495
im not the original poster and also i might be retarded but:
the statement "formal arithmetic is consistent" is unprovable by godel incompleteness
there's no proof so f("formal arithmetic is consistent") = 0
how is that a contradiction

>>12294872
Classical Mechanics by Taylor -> Analytical Mechanics by Lemos -> Electrodynamics by Griffiths -> Quantum Mechanics by Shankar ->
Modern Quantum Mechanics by Sakurai 3rd Edition -> Thermal Physics by Reif -> Solid State Basics by Simon ->Stars and Stellar Processes by Guidry -> Modern relativity by Guidry -> Nuclear Physics by Krane

>>12302493
I've managed to delved in a bit into Coq using the book: Software Foundations. Almost done with part 1. How can I manage to dig in some open problems in dependent type theory, or if that's not possible, implement/create some stuff with it?


>>12302505
I'm in the Philippines. And desu the research here is not that great, the journal here for CS is quite meme-y lmao.

>>12302510
I think you're right, his case is not water tight.
f returning 0 would just mean it's not a theorem. There's several options for why, e.g. the negation is a theorem, or it's undecidable.
So from this we don't know that arithmetic is inconsistent.

>>12302510
>how is that a contradiction
You need to assume that formal arithmetic is consistent. Otherwise, the constantly true function would satisfy all the prerequisites.

Gödel's incompleteness says that consistence of a reasonable enough system is not provable inside that system *provided it is consistent*.

>>12302526
Read the github discussions on Coq, Agda, Lean, Idris and join their google groups and zulip chats and get to know the people.

>>12302526
>How can I manage to dig in some open problems in dependent type theory
Learn a bit of realizability, category theoretic models and the like. An interesting open problem is the compatibility of dependent type theory with classical logic in a strong enough way.

why can't my AA proff look like this? AAAAAAAAAAAAAAAAAAAAAAAAAAAAA

>>12301899
https://math.stackexchange.com/a/269941

>>12302682
i would be busy cooming and i wouldn't learn much with those videos

>>12302682
isn't that literally just an actor?
that would explain it

>>12302537
I don't see how this answers the question. The claim was
>Assume f is computable, just compute f(n). If it returns 0, then arithmetic is inconsistent
but it appears that if consistency is merely unprovable (which it is, but that's beside the point), then this is also a way to have the function return 0. So it can't be concluded that returning 0 means arithmetic is inconsistent.

>>12302877
does it really matter?

Any tips to master real analysis?

>>12302919
yes? it goes a long way to answering the question

Any advice for math majors who want to continue their education a bit without grad school? Just graduated and I really regret not taking more difficult/interesting courses like combinatorics, algebra, topology, analysis, number theory etc since I was a math/econ major and didn't really challenge myself other than one quarter of an honors analysis course. Can I just pick up textbooks and try things out or is this just way too difficult without an instructor?

>>12302935
Triangle inequality, triangle inequality everywhere.

>>12303070
this, sometimes holder's too

>>12303089
sometimes releaser's too

>>12302477
probabilistic programming/bayesian computation (variational inference, MCMC)/statistics on switching linear dynamical systems are all interesting 'mathy' topics if you like probability.

>>12301218
i dont get it

>>12300817
Not a single analytic number theory chad here? C'mon now and help me out.

>>12295096
you never mix 2 name variables, in rigourous maths you either do with x/cx, or directly tranform into u/du, never mixing both

>>12303325
i wanted to remove the Xs with the du but thats wrong and i was retarded

>>12303089
for me it's jensen's

>>12303253
>probabilistic programming
This is cool but is it promising?

>>12302935
IFT

hey everyone :) i was wondering if anyone would help me find this book, "Calculus Two: Linear and Nonlinear functions" by flanigan and kazdan for free. i can't find it on either b-ok nor libgen. i would be willing to return the favor if anyone did. picrel is one of the covers.

>>12304047
Have you tried the irc and such?

>>12304052
um i don't know what irc you mean. hopefully I'm not too dumb?

>>12304047
Here you go bro
https://archive.org/details/calculustwolinea00flan/mode/2up

>>12302898
You can resolve that the usual way, by feeding n to both f and 1-f.
In more detail: since both are computable, assuming the consistency of formal arithmetic, exactly one will return 0 and the other 1. This would make formal arithmetic consistent and decidable (by generalizing n to any sentence of arithmetic), contradicting the first incompleteness theorem.

>>12304064
thank you :) but i maybe should have mentioned i found that link and i think that's a paid link only?

>>12304073
No you need to create an account and then you can "borrow" the book for 14 days for free.
I just tried it myself and it works.

>>12302898
You can resolve that the usual way, by feeding n to both f and 1-f.
Since both are computable and total, assuming the consistency of formal arithmetic, exactly one will return 0 and the other 1. This would make formal arithmetic consistent and decidable (by generalizing n to any sentence of arithmetic), contradicting the first incompleteness theorem.
(Which is slightly stronger in that it prohibits even the partial functions [math]f[/math] that return 1 iff their argument is provable, for which the above proof can still be used, although you'd need to do some bookkeeping to account for the nonhalting cases, and appeal to Godel's completeness theorem to show that the effective domains of f and 1-f cover all the sentences of arithmetic.)

>>12304080
wow thanks i must have missed that. for me, it says it will only let me borrow for one hour though...

>>12304170
TRUMP 2020

This is just the Taylor expansion of log right

>>12304178

andy sixx shit log?

ANALysis is based

>>12304173
um ok. but thank you!

>>12303389
Yes. In my field we use it all the time. There are a bunch of advantages to bayesian methods in some contexts, and there's lots of interesting work being done in the methods themselves.

>>12304205
c quoi?

>>12304178
Disregard please

Just rename it to CSnigger general. It's not a math thread anymore

>>12303253
Do I need measure theory based probability for that? I don't have a background in probability yet. But I'm wrapping up my Analysis background.

>>12300817
They are related to solving single variable polynomial congruences in the ring of integers.
For example, consider the problem of degree 2.

First, applying the chinese remainder theorem you can reduce the problem of solving module a general positive integer to solving the system of the same congruences but with module varying over the prime powers of the original module. In other words, we can assume the module is a prime power.

Now you can apply Hensel's Lemma (plus a few occasional details) to "lift" solutions module [math]p[/math] to module [math]p^n[/math] in a way that you describe all solutions for the prime power once you have all solutions module the prime itself. This procedure is closely related to p-adics, you can translate what is being done here as solving a quadratic equation in the p-adic ring [math]\mathbb{Z}_p[/math]. The remainder by the [math]n[/math]-th power of [math]p[/math] is the [math]n[/math]-th component (maybe there's a special name I don't recall now) of the [math]p[/math]-adic solution, which also corresponds to the [math]n[/math]-th insertion that characterizes this solution as a [math]\mathbb{Z}[/math]-module morphism into a projective limit (you can construct [math]\mathbb{Z}_p[/math] as a projective limit of modules [math]\mathbb{Z}/p^n\mathbb{Z}[/math]).

The final step on these reductions is solving module a prime, which can be done with the RESSOL algorithm.

Another application of p-adics on diophantine equations is the (Hasse's?) local-global principle. You can solve some diophantine equations by solving it in [math]\mathbb{Z}_p[/math] for each prime [math]p[/math]. Sometimes the equation is harder than the corresponding congruences, so this comes in handy.

>>12300817
They are related to solving single variable polynomial congruences in the ring of integers.
For example, consider the problem of degree 2.

First, applying the chinese remainder theorem you can reduce the problem of solving module a general positive integer to solving the system of the same congruences but with module varying over the prime powers of the original module. In other words, we can assume the module is a prime power.

Now you can apply Hensel's Lemma (plus a few occasional details) to "lift" solutions module [math]p[/math] to module [math]p^n[/math] in a way that you describe all solutions for the prime power once you have all solutions module the prime itself. This procedure is closely related to p-adics, you can translate what is being done here as solving a quadratic equation in the p-adic ring [math]\mathbb{Z}_p[/math]. The remainder by the [math]n[/math]-th power of [math]p[/math] is the [math]n[/math]-th component (maybe there's a special name I don't recall now) of the [math]p[/math]-adic solution, which is also corresponds to the [math]n[/math]-th insertion that characterizes this solution as a [math]\mathbb{Z}[/math]-module morphism into projective limit (you can construct [math]\mathbb{Z}_p[/math] as a projective limit of modules [math]\mathbb{Z} / p^n \mathbb{Z}[/math] [/math]).

The final step on these reductions is solving module a prime, which can be done with the RESSOL algorithm.

Another application of p-adics on diophantine equations is the (Hasse's?) local-global principle. You can solve some diophantine equations by solving it in [math]\mathbb{Z}_p[/math] for each prime [math]p[/math]. Sometimes the equation is harder than the corresponding congruences, so this comes in handy.

>>12291777
Computer Science major here, any good discrete mathematics book?

>>12303253
>>12304446
On topic, does anyone here have book recommendations for measure theory based probability books, strong on mathematical rigor, not encyclopedic (short is better desu, just the essential), that explains the intuition for someone with no experience on the area and with nice applications (may be through problems) in both 'mundane' (statistics, CS...) and in other areas of mathematics (I'd like to see some in number theory)?

red pill me on group actions

Not really math related
But any tips on studying math (mainly analysis and linear algebra), and dealing with procrastination/time wasting?

>>12304618
group is like "number five"
group acting on an object is like "five apples"

>>12304618
Groups are like people. You shall know them by their actions.

>>12304711

I just realized that I don't know how to prove [math] U \subseteq V \rightarrow W^{k,p}(U) \subseteq W^{k,p}(V) [/math] and even worse I can't find a proof of this statement anywhere online.

>>12304995
no nevermind this is not what I want to show.
What I want is:
[math] f \in W^{k,p}(V) \rightarrow f\vert_U \in W^{k,p}(U) [/math]

>>12305003
what is [math]W^{k,p}[/math]?

>>12305015
The Sobolev space, the functions in L^p which have weak derivatives up to order k who are in L^p themselves.

>>12305003
what do you want to prove? that the mapping is well defined?

>>12305043
yes! Obviously the derivative of the restricted function should be the restriction of the derivative but I can't prove this without going into weird mollifications.

>>12305046
Use small bump functions: ones that vanish outside of a small open ball.

>>12305061
That's what mollification means, you wild animal you.

>>12302682
God I want to fuck her so badly.

>>12305062
Well then use mollification duh. It's simple, I don't see what's your problem here bro.

>>12305061
So I have a situation like
[math]
\int_U u(x) \cdot 1_V(x) \cdot \partial_x \phi(x) \,dx [/math],
where phi is a test functiin and I can't use that u has a weak derivative because the indicator function of V is in the way. But when I try to mollify:
[math]
\longleftarrow \int_U u(x) \cdot (\eta_r \ast 1_V(x)) \cdot \partial_x \phi(x) \,dx
[/math]
I have to get to
[math]
\int_U u(x) \cdot \partial_x ((\eta_r \ast 1_V(x)) \cdot \phi(x)) \,dx
[/math]
which due to the chain rule leaves me with a difference
[math]
\int_U u(x) \cdot \partial_x
(\eta_r \ast 1_V(x)) \cdot \phi(x) \,dx
[/math]
where I get a derivative of the mollifier. Depending on some dimensions this derivative explodes as the mollifier concentrates in a small ball and the total integral doesnt vanish.

>>12305083
wtf I'm so dumb phi is already compactly supported in V so it just swallows the indicator function of V and the derivative goes over to u...

>>12304446
You definitely do not need measure theory (of course if you do want to do research professional in it you will). If you like variational inference you'll need a little calculus of variations. Other than that, you'll be fine math-wise to work on an interesting project.

>>12305092
What is 1_V and what is eta_r?

>>12305063
>ywn work through hard proofs with her and have sloppy passionate sex afterwards

>>12305063
>>12305127
she's a paid actress lol

>>12305170
That wont prevent me from wanting to bang her. This guy:>>12305127 is a retard though.

>>12305170
Wow you must be really smart for pointing that out!! Gold star!!
Kill joy faggot, it's the fantasy of it all. Bet you're fun at parties (oh wait, you don't get invited to any lol)

>>12305258
embarrassing post

>>12305258
Don't be so harsh, not everyone is as socially aware as (you). Remember, this is /mg/.

>>12304995
>>12305003
Let [math]C_C^\infty(V)[/math] be the space of compactly supported smooth functions on V. Since U is a subset of V [math]C_C^\infty(U)[/math] is a closed subspace of [math]C_C^\infty(V)[/math].

If F is a continuous functional on [math]C_C^\infty(V)[/math] then its also continuous on [math]C_C^\infty(U)[/math].

Elements of sobolev space are those functions f from L^p(V) such that the distributional derivatives of the functional [math]F(u)=\int_Vf(x)u(x)dx \ \ \ \ (u\in C_C^\infty(V)) [/math] on V are given by functions from L^p(V). By the second sentence F is also a functional on [math]C^\infty_C(U)[/math] and since the distributional derivatives of F on V are given by L^p functions the distributional derivatives of F on U are given by the restrictions of those functions,

So, I am having the biggest stinkiest brain-fart of my life.

There are supposedly 20 files in here, however the ennumeration indicates there should be 19

Am I becoming insane?

>>12305483
How many number are there between 1 and 19 (including 1 and 19)? What is 19-1?

>>12305483
01 - 20 is 20 files, right
now add 43 to both numbers

Friends, I didn't show up to my odes exam. It's over for me. I'm gonna drop the hell out of it. How screwed am I if I apply to a masters in the future but I've never "taken" odes?

>>12305642
knowledge of odes is not a very important thing unless you're going into the more physics-related fields of math
on the other hand if you drop out of courses, i'm worried about you...

Fellow Ameribros who went to uni in Europe especially Germany, how did you send your AP scores? Did you send them online somehow or did you get it printed and notarized? They say to just mail everything but AP scores are held/sent online in USA usually.

>>12305680
Turns out 4 math courses was a little much, especially with how little I cared about odes going in to it. The other courses are going well, so don't be too worried (yet)

What are the best programming languages for pure mathematical algorithms, where the main objectives are:
1. Building the algorithm almost from scratch in your own customizable way;
2. Comparing different ones in terms of time efficiency;
As opposed to just using it as a tool to compute/visualize things for research support?

For instance, I'd like to build one that takes a quintic single variable polynomial over the rationals as input and gives either a short proof through galois theory that it isn't solvable or an explicit solution in terms of radicals (maybe with auxiliary variables forbetter visualization, but not necessarily). The goal isn't just having an algorithm to get the answers, it's to build a functioning one and then evaluating it's complexity. I just think it's a nice exercise, and there are lots of similar ones you can do for different areas in math.
Notice that I don't want to focus on numerical stuff.

I know Mathematica and SAGE can be used for those things as tools, but I'm not sure if they're adequate for these distinct goals.

>>12305940
Coq?

>>12304557
Thank you very much for the explanation!

>>12305642
I disagree with >>12305680. ODEs are extremely important to nearly every field in analysis, PDEs of course, physics, differential geometry, dynamical systems. But don't worry, there are many excellent books that you can use to teach yourself. Arnolds ODE book is a personal favourite.

Also coming from someone who made the same mistake in the past: Do not take too many courses, take rather the courses you are REALLY interested in. After having a bit of experience in math (as in having studied a bunch of topics), self learning will be a much easier task so you will not miss out. And don't listen to any faggots telling you
>Take the pure algebra route LOL!
or
>Take this course without it you're not a real mathematician!
or similar, it's all bullshit.

>>12306202
>every field in analysis, PDEs of course, physics, differential geometry, dynamical systems
I uhh, don't really care about those fields.
>Do not take too many courses, take rather the courses you are REALLY interested in
That was the goal for the most part, odes was just the one course I was missing to make my degree "equivalent" to an honors degree.
>>Take the pure algebra route LOL!
Based

>>12306022

if you have ever tried to use coq for anything, you would know that it necessarily multiplies the amount of time required to do something 10-100 times. I estimate it would take years for a team of PhDs to figure out how to do Gallois theory in Coq.

>>12305940

SageMath already has a library for computing the Galois group of a polynomial

>>12306281
Well, as long as you don't close your mind off to anything analytically flavoured, fine. Unless your interests lie in linguisti- I mean archer- I mean category theory. Don't be memed into thinking that cats, at least without having a concrete application in mind, will lead you anywhere. It's a language. Just saying this because I've seen talented young mathematicians specializing in pure cats just to waste away and leaving math eventually.

>>12306303
I thought so, but I wouldn't use this function.
There are things I want to do with ease though, like algebraic/symbolic (rather than numerical) simplifications. I know Wolfram do those automatically, so I suppose Mathematica would too, but, on the whole, I wouldn't be using it like how I use Wolfram Alpha.

>>12306022
I think Coq is mostly used to compile programs, not run ever them.

>>12306305
You could defend ODEs without attacking purely abstract subfields like category theory for its own sake, but failed.
The problem you should be highlighting for him is that putting all your eggs in the same basket is too risky. Every mathematician should invest at least a bit of time learning the basics of a few fundamental subjects of common areas, ODE is a main one with lots of connections within analysis.

>>12306406
>You could
Yeah but I won't, sorry. Also not "defending" ODEs, but basically only attacking category theory or, rather, how many people approach it. Namely as a magical tool to somehow gain insight on a pure abstract nonsense level. Which never works, ever. Not for alg geo, not for logic (again, cat thy is a language), and fuck me in particular not in physics.

Also don't take the bantz to heart. The archery thing is stolen from "Categories for the Working Mathematician".

>>12306434
>Namely as a magical tool to somehow gain insight on a pure abstract nonsense level. Which never works, ever.
The same ought to apply to "pure" graph theory, as they don't even have the composition structure of categories. And yet Robertson and Seymour demonstrate that there are highly nontrivial results to be found. I don't think it's too far off the mark to call them "foundational".
As a matter of pragmatic advice to a working mathematician, digging at foundational structures (which seems to be language, in your case) is almost always counterproductive (the risk-reward ratio is far too high) and its discouragement is understandable (one can point to physics as a warning sign). But presenting the foundations as unquestionable (as Principia Mathematica and Bourbaki attempted to do) is fighting against two very fundamental phenomena: the Aristotlean tendency for humans to think scientifically about structures, and Godelian incompleteness which implies that the foundations can always continue to be analyzed. They're not insurmountable, but it would require nothing short of a major philsophical revolution.

>not for logic (again, cat thy is a language)
It might not be the dominant view, but it's not uncommon to hear logicians (e.g. Mathias) describe their subject as the formal study of language.

>>12304618
Groups are basically just ways to represent symmetries.
It doesn't matter you won't care about them until you use them lots.

>>12306573
Interesting points. Maybe I was a bit, let's say, ticked off by higher structure people lately. Haven't really thought about graph theory much to be honest, but if I understand correctly a lot of arithmetics is involved. So yeah, category theory is great for "talking" about foundations. But I'm genuinely worried that many mathematicians, in particular young students, see something in it that is simply not there.
I'll ask some guys from my departments graph theory about your points (as soon as home office is over lol), I'm curious about their perspective. I am working in hardcore technical differential geometry and quite a lot of my colleagues developed an extreme aversion to anything that contains the words category or higher structure.

>>12291777
I claim the following: Let [math] \Omega \subset \mathbb{R}^d [/math] have finite measure and [math] f \in L^1(\Omega) [/math] so that [math] f > 0 \text{a.e.} [/math]
Let [math] C > 0[/math].
Then [math] \inf_{m^d(A) \geq C} m^d(A)^{-1} \int_A f \,dx > 0[/math]

>>12307070
Honestly, I don't really care.
Let's just call it quits, nobody please make the next edition

>>12307370
Based.
Why don't we just all agree to stop doing maths and go out into the real world?

>>12307070
Sure, I agree

>>12307370
This.
I'll make one ~3 months from now to test the waters.

>>12307370
Ok, it would be better that way. I'm never gonna make it if I'm always distracted by /mg/ at work

>>12307410
Man, demons have some huge ass ears

>>12307370
I agree

>>12307370
Too late
>>12307507

>>12307519
B A S E D T O O K E R

>>12292143
These are all elementary questions. If you are truly motivated, 3 days is plenty of time learn how to solve this kind of stuff.