/mg/

[Anonymous No.11947815]

math, generally
nth edition

n-1: >>11940745

[Anonymous No.11947830]

gay

[Anonymous No.11947834]

>>11947830
*liberated from the womb

[Anonymous No.11947846]

>>11940795

[Anonymous No.11947870]

I just picture it in n dimensions and then let n=10.

[Anonymous No.11947881]

[Anonymous No.11947884]

Scientifically, how high does your IQ need to be to make novel contributions to mathematics?

[Anonymous No.11947887]

>>11947815
blackboard N is a set, not an ordinal
delete this shit and rebake it

[Anonymous No.11947903]

>>11947815
>Elliptic curves

[Anonymous No.11947915]

whats your favourite number
mine is 11

[Anonymous No.11947929]

>>11947915
8

[Anonymous No.11947937]

>>11947929

[Anonymous No.11947939]

>>11947929

hello professor baez

[Anonymous No.11947941]

>>11947915
11 is also my favorite number. more specifically, 11j in the quaternions

[Anonymous No.11947943]

what universities have you been to?

[Anonymous No.11947946]

>>11947929
8 is a weird number when it comes to 8 dimensional things. it's a very odd and prime feeling even, as well, 2^3

[Anonymous No.11947962]

>>11947884
>differential calculus
i think i couldve proved/discovered this 20 years into the future
>renaissance math
im shit at polynomials

[Anonymous No.11947970]

FUCK YOU ALL DELET THIS SHIT

[Anonymous No.11947987]

>>11947941
What about the sedenions?

[Anonymous No.11947997]

>>11947987
also the sedenions, yes

>>11947970
why anon, why why why????

[Anonymous No.11948003]

>>11947884
Where is this table from?

[Anonymous No.11948016]

>>11947943
>Dox yourself
You're glowing bro

[Anonymous No.11948078]

for v1,v2,v3... spanning V, the a's in a1v1+a2v2+a3v3..=0 if and only if there is a unique way to write each v in V as a combination of v1,v2,v3...
is this correct?

[Anonymous No.11948303]

>>11947887
Ordinals are sets. Your formalism is bad.

[Anonymous No.11948314]

>>11947815

[Anonymous No.11948317]

>>11947915
mine is 15, unrelated to your digits

[Anonymous No.11948370]

Fucking logarithms reee

[Anonymous No.11948404]

>>11948370
t. my little sister.

[Anonymous No.11948444]

>>11948404
nah, just a depressed retard trying to study and learn so that way I can at least be a depressed smart person.
Its just natural logarithms and eulers number that kinda confuses me
I'll get it though

[Anonymous No.11948458]

>>11948444
I'll tell you what I always tell my little sister:
You aren't confused. There isn't anything to understand. It's just formal manipulation,

[Anonymous No.11948464]

>>11948458
Show pics

[Anonymous No.11948467]

>>11948404
god i wish had an imouto to teach math to and do other activities with

[Anonymous No.11948506]

>>11948404
Your little sister looks pretty cute anon

[Anonymous No.11948555]

>>11948467
>other activities
Gentlemen...

[Anonymous No.11948561]

>>11948555
Like volleyball. y'know?

[Anonymous No.11949284]

>>11948317
>not prime
>a multiple of fucking 5
What's wrong with you anon

[Anonymous No.11949469]

>>11947815
Is there a pastebin or anything for this general with a list of good textbooks to pirate for someone starting out?

[Anonymous No.11949475]

>>11947915
1488
2147483647

[Anonymous No.11949554]

is there any way to show that a matrix doesnt have a square root? specifically
000
100
010

i dont wanna just do a system of equations

[Anonymous No.11949565]

>>11949554
we have [math](P^{-1}AP)^2 = P^{-1}A^{2}P[/math], use this to deduce that a matrix has a square root if and only if e.g. its Jordan normal form has a square root etc.

[Anonymous No.11949568]

>>11949554
A square root needs to have rank 2 or 3.
It can't have rank three, because then it's invertible.
It can't have rank two either, proof left to the reader (pain in the ass but easy).

[Anonymous No.11949569]

>>11949565
whats P and A?

[Anonymous No.11949570]

>>11949568
what does rank mean? why cant square roots be invertible?

[Anonymous No.11949574]

>>11949570
>what does rank mean
Dimension of the image.
>why can't square roots be invertible
Because if [math]A[/math] is invertible [math]A^2[/math] is too.

[Anonymous No.11949578]

>>11949574
why does a square root need to have rank 2 or 3?

why can't A^2 be invertible?

[Anonymous No.11949585]

>>11949569
any square matrices of the same dimension, P invertible

[Anonymous No.11949587]

>>11949578
I'll be honest, the first post was reasonable, but these questions are getting really stupid really fast.
>>>/sci/sqt
>>>/wsr/

[Anonymous No.11949589]

>>11949565
the matrix he wrote down is already in jordan normal form, this doesn't help
>>11949554
Let A be the matrix you wrote down, suppose B is a square root.
Observe that [math]B^6 = A^3 = 0[/math], and [math]B^4 = A^2 \neq 0[/math].
What can we say about the minimal polynomial of B? It follows from the above that
it should be a factor of x^6, and it doesn't divide x^4. But minimal polynomial of 3x3 matrix has degree at most 3, contradiction.

[Anonymous No.11949594]

>>11949587
I^2 is invertible and I^2 has a square root

[Anonymous No.11949605]

>>11949589
>factor of x^6
>doesnt divide x^4
but 3 is a factor of 6 and 4=!3*n

[Anonymous No.11949607]

>>11949605
wait im retarded 3 does divide 4 because thats not how polynomials work

[Anonymous No.11949618]

>>11949589
how do you know there isnt some polynomial of degree 3 or less that is a factor of x^6 but doesnt divide x^4? it could be a really weird polynomial that can be multiplied into x^6 but not x^4, how do we know it doesnt exist?

[Anonymous No.11949648]

>>11949565
>A is nilpotent
>diagonalizing makes it a diagonal matrix of eigenvalues
>A's eigenvalues are 0
>A is diagonalized to T=0
whut? my book hasnt covered diagonalization yet btw

[Anonymous No.11949854]

>>11949648
A nonzero matrix with all zero eigenvalues will have generalized eigenvectors and corresponding nonzero entries in its Jordan form. It can't be similar to the zero matrix.

[Anonymous No.11949941]

>>11949854
>all zero eigenvalues
>corresponding nonzero entries
wuht

[Anonymous No.11949953]

>>11948467
>an imouto to teach math to
Good luck with that lmao.

[Anonymous No.11949958]

>>11949941
Ah yes the trivial solution, aren't matrices grand? I got a B in intro linear algebra because I think I was probably too careful with the simple things so I didn't have enough time to learn the more interesting things very well. I should've made more time. I got lost around the time they started talking about "proj" and so on but because I had such good form on the easy stuff I managed to squeak out a B.

[Anonymous No.11949967]

>>11949958
but... but...
you said it cant be the 0 matrix
but diagonalization would make it the 0 matrix
cuz the eigenvalues are 0

[Anonymous No.11949981]

>>11949967
Oh I'm a random anon hijacking the conversation. I just applied and reapplied the formulas with OCD-like focus. I even tried deriving formulas from other formulas, sort of like proofs. If you want a B listen to me.

[Anonymous No.11949984]

Good afternoon, /mg/!

Some more postdoc positions, it seems:
Northeastern University (wherever that is)
https://www.mathjobs.org/jobs/list/16080
https://www.mathjobs.org/jobs/list/16102
Göttingen
https://www.uni-goettingen.de/de/305402.html?cid=100713

[Anonymous No.11949990]

>>11949984
Noon, lad.

[Anonymous No.11950009]

what happened to workingwith physicists

[Anonymous No.11950012]

>>11949984
please stop posting this you make me feel bad

[Anonymous No.11950022]

>>11950009
I'm not much into physics or the sciences in general.

[Anonymous No.11950029]

>>11950022
Why not?

[Anonymous No.11950032]

>>11950022
threadly reminder to work with physicists

all the math that will ever exist is a solution to field equations
mathematical functions do not take form in reality without space, matter, time, consciousness. they would be relegated to abstract nothingness without physics

[Anonymous No.11950048]

>>11950032
>they would be relegated to abstract nothingness without physics
theoretical physicists have already done that to themselves

[Anonymous No.11950052]

>>11950048
i wish you werent stupid

[Anonymous No.11950055]

Please work with economists, I beg you.
We don't even want you guys to solve some convoluted n+1-dimensional conformal topological field theory on a G_2 manifold, it's just stochastic dynamical systems and convex analysis.

[Anonymous No.11950059]

>>11949990
Any new insights, Lad Tepes?

>>11950012
No need to feel bad, anon.

>>11950032
>they would be relegated to abstract nothingness
Oh how I wish that was me.

[Anonymous No.11950061]

>>11950055
i've bought some bitcoin and other shitcoins recently, does that count?

[Anonymous No.11950082]

>>11949618
come on now anon

[Anonymous No.11950084]

>>11950061
It doesn't.

[Anonymous No.11950093]

>>11950082
is it obvious or are you just assuming?

[Anonymous No.11950102]

>>11950029
Just not my thing. I took physics and chemistry classes in my undergrad because it required a certain amount of credit hours for the natural sciences and while I did enjoy them, they just weren't the same as math.

[Anonymous No.11950123]

>>11950052
see >>11950052
but feel free to at me when we see the first evidence of SUSY

[Anonymous No.11950128]

>>11950123
see, that's not what i'm even calling you stupid for, and the fact that you think that SUSY is relevant here is why you're stupid

[Anonymous No.11950137]

>>11950128
>talking about abstract nothingness
>mentions abstract nothingness that physicists came up with
>no that doesnt count
this is why no one likes dealing with physicists

[Anonymous No.11950142]

>>11950137
*facepalm*

[Anonymous No.11950148]

>>11950137
abstract nothingness means incomprehensible
physicists making unverifiable equations are comprehensible
whether they have use or veracity is irrelevant here, the general aim of physics and the physical universe is still valid

for the record
>OOGA BOOGA THEORY NO RESULTS IN 30 YEAR
have some PATIENCE you subhuman ape, 100 years, 1000 years is a pittance in reality

[Anonymous No.11950156]

>>11950093
what can the decomposition of such a divisor into irreducible factors be ?

[Anonymous No.11950172]

>>11949941
Not all matrices are diagonalizable. Having all 0 eigenvalues doesn't mean you have the zero matrix.

[Anonymous No.11950260]

Dedekind BTFO.
https://www.youtube.com/watch?v=LSWIFXP2r14

[Anonymous No.11950291]

>>11950156
Well, obviously x^n n<=6 is a factor of x^6. But how can we know others don't work? Well I thought of a proof:
>In any two polynomials multiplying to an x^6 term, it has a smallest term for each. They only match up once and no other term has their power, so they can't fit pure x^6.

So, B's existence implies the existence of a minimal polynomial. But a minimal polynomial for B cannot exist. Thus B's existence implies a contradiction to truth. So B should not exist.

Cool proof Anon. I liked what you did with numbers. What if B's nonexistence and existence were both contradictory? Not saying it is, but what if?

[Anonymous No.11950294]

>>11950260
Thank you, I am now dumber after watching that.

[Anonymous No.11950296]

>>11950172
Oh I got confused. I thought P-1 and P were diagonalization matrices. I don't get what you're doing then

[Anonymous No.11950308]

>>11950296
There is like an «almost diagonalization» for matrices which are not diagonalizable called the Jordan canonical form. That's what the initial discussion was about.

[Anonymous No.11950320]

>>11950308
Oh. How does Jordan form help me show that
000
100
010 has no sqrt?
I can flip the bases into b3 b2 b1 and get
010
001
000, which I believe is Jordan. But how does that help?

[Anonymous No.11950356]

>>11950320
There are more zeroes in that Jordan form matrix, making it easier to check whether the quadratic variety of square roots has points on it. (You get a nicer generating set for the ideal.)

[Anonymous No.11950363]

>>11950356
Sadly I don't know what a quadratic variety or generating set or ideal is

But thank you all for the help. Goodnight mg, I'm gonna work on my book for now

[Anonymous No.11950364]

>>11950260
>dedekind cuts are not valid
>stops talking about dedekind cuts and makes up a new contstruction
based gabriel

[Anonymous No.11950427]

>>11947834
>the womb
I will play TBOI now

[Anonymous No.11950431]

>>11947915
-1/12

[Anonymous No.11950541]

>>11950363
Night, lad.

[Anonymous No.11950890]

Let [math]a, b[/math] be positive integers such that [math]a, b \leq 2020[/math].
Prove that [math]|a - b \sqrt{2}| \geq \frac{1}{5050}[/math].

[Anonymous No.11950933]

>>11950890
You have to pick b so that b√2 is as close to an int as possible

Modular arithmetic?

[Anonymous No.11950949]

>>11950260
based

[Anonymous No.11950958]

>>11950890
>fucking diophantine approximation
Thank you very much, but I'm not interested.

[Anonymous No.11950974]

>>11950958
There is a one-line solution which requires no knowledge beyond high-school algebra.

[Anonymous No.11950982]

I stumbled upon something odd. Normally when dealing with piecewise PDEs you
just solve the equation in all intervals and are done. That works as long as you have
continuous solutions. Example:
[eqn]\left(-\frac{1}{2} \partial_x^2+\Theta(x)\right)\Psi(x) = E\Psi(x)[/eqn]
Now, consider instead
[eqn]\frac{1}{2}\left(- \partial_x^2+ x^2+\Theta(x)\right)\Psi(x) = E\Psi(x)[/eqn]
This one has discrete [math]L^2[/math] solutions, and I just aligned them
so left and right never meet energetically.
I lack the expertise to formally prove that no solutions exist,
so I am not sure what to take from this.

[Anonymous No.11951007]

[math](a+b)^n = a^n+b^n[/math]
suck my dick polynomial faggots. nothing in real life has more than one answer, you can't be more than two things at once, it's a hoax promoted by the same people that believe lines are real

[Anonymous No.11951009]

>>11951007
True mod n.

[Anonymous No.11951052]

>>11951007
Based.

[Anonymous No.11951067]

>>11951007
BASED

[Anonymous No.11951081]

>>11950974
>one line
That's impressive, I thought you'd at least have to get some nice approximations for square root of 2.

[Anonymous No.11951103]

>>11951007
>keeping that nth power bullshit
[eqn](a+b)^n = e^{n\ln(a+b)}\approx 1+n\ln(a+b)\approx 1+n(a+b)[/eqn]

[Anonymous No.11951221]

>>11951007
>implying I would work in characteristic zero
Brainlets can't into arithmetic

[Anonymous No.11951235]

>>11951009
* for prime n.

[Anonymous No.11951252]

>>11951007
>lines are real
the linear spook has gone on for too long
all things are jaggedy or curves

[Anonymous No.11951258]

>>11951235
Are you super sure it doesn't work for non-prime n?

[Anonymous No.11951289]

>>11951258
Give me an example where it does.

[Anonymous No.11951312]

I have never been on /sci/ before but want to check 2 questions with you guys and didn't want to start a new thread.
X / 1.3 = (100/120)2 and 5.6 x (10.5/9.8)3
I got 1.0833 for the first one and 5.999 repeating or 6 for the other one. Am I wrong here?

[Anonymous No.11951317]

How do we know theres a unique binary for every decimal? Or generally unique base n for every base m

[Anonymous No.11951401]

>>11951317
Binary expansion of reals is not unique. For instance .0011...=.01.

[Anonymous No.11951408]

>>11950890
>>11950974
this is 2 minutes of boneheaded manual checking if you've taken a baby number theory class, I spent 10 minutes trying to figure out what the epic asspull competition solution is supposed to be but my IQ is too low

[Anonymous No.11951413]

[Anonymous No.11951470]

learning number theory makes me depressed, we are frauds humans are just pathetic apes

[Anonymous No.11951472]

What's a good book on graph theory?

[Anonymous No.11951486]

>>11951413
What math do I need to know to solve this?

[Anonymous No.11951501]

>>11951486
>>11947903

[Anonymous No.11951507]

>>11951486
addition and multiplication

[Anonymous No.11951512]

>>11951486
Numbers

[Anonymous No.11951554]

>>11951512
which ones?
The highest I have ever counted to was 100

[Anonymous No.11951557]

>>11951413
Elliptic curves.

[Anonymous No.11951558]

>>11951554
1, 2, 3, 4, 6, 7, 8, 9

You don't need 5 or 0, though.

[Anonymous No.11951631]

>>11951486
Elliptic curves, number theory, and Diophantine analysis.

[Anonymous No.11951643]

>>11950890
im getting fucking filtered by this question
can somebody give a hint? and maybe recommend some painless suicide methods for if i can't get it after that

[Anonymous No.11951652]

>>11951643
>>11947903

[Anonymous No.11951674]

I just got declined for bsc pure math, but they placed me into bsc applied math. is this good or...?

[Anonymous No.11951679]

>>11951643
Plug the max and min values of a and b into the equation.

[Anonymous No.11951680]

>>11951674
depends if you want to be an abject failure of a "human"

[Anonymous No.11951685]

>>11951680
ok, but seriously.

[Anonymous No.11951686]

>>11951685
Did I stutter?

[Anonymous No.11951690]

[math]K={\mathbb{Z}_2}/\langle x^2 +x +1 \rangle[/math] satisfies a field with four elements, right?

[Anonymous No.11951692]

>>11951686
I don't know, did you?

[Anonymous No.11951695]

>>11951692
Yes, but shhhh

[Anonymous No.11951707]

>>11951401
1/4=1/8+1/16+1/32....
cool

[Anonymous No.11951709]

>>11951690
yeah, its pretty easy to show that the polynomial is irreducible
and since its quadratic, the only elements in K are classes of linear functions in Z_2[x], which there are only 4 of

[Anonymous No.11951715]

>>11951674 anyone...?

[Anonymous No.11951717]

>>11951289
n=2

[Anonymous No.11951750]

>>11951674
>>11951715
Depends on whether or not you're ok with doing applied math. Are you?

[Anonymous No.11951762]

>>11951750
I guess so.
Are the job prospects as good as pure maths?

[Anonymous No.11951768]

>>11951762
Better by a million miles

[Anonymous No.11951769]

>>11951289
(a+b)^4 = a^4 + b^4 + 2a^2b^2
do you even know the binomial coefficients?

[Anonymous No.11951772]

>>11951768
Guess I'll be accepting my offer. Thanks! :)

[Anonymous No.11951775]

>>11951762
Are you joking?

[Anonymous No.11951776]

>>11951775
Why would I be?

[Anonymous No.11951777]

>>11951631
So is number theory just solving the weird equations you make on scientific calculators when bored in highschool math class?

[Anonymous No.11951780]

>>11951777
trips of truth

[Anonymous No.11951782]

>>11951777
yes

[Anonymous No.11951784]

>>11951762
Much better. If you have no desire to pursue academia, then I see little reason not to do applied math. You'll have a wide array of job prospects with an applied math degree (even better with a master's), whereas pure math is pretty much exclusively academia.

[Anonymous No.11951787]

what's a good site to drill a few calculus problems each day without running dry? don't need convoluted word questions, just looking to practice the techniques like an 8 year old chink

[Anonymous No.11951790]

>>11951787
no such 'site' exists. google college course webpages for calc and do the homework sheets on the webpages. also buy schaum's outlines in advanced calculus, etc.

[Anonymous No.11951797]

>>11951787
https://sites.rutgers.edu/joseph-guadagni/135-2/

[Anonymous No.11951798]

>>11951787
khan academy
Lamars math notes

[Anonymous No.11951804]

>>11951787
[math] \frac{d}{dx}\left(\sin(\cos(\tan(\arccos(\arctan(\arcsin(\ln(x)))))))\cdot \frac{x^2}{e^x}\right) [/math]

[Anonymous No.11951812]

>>11951804
Cute function.

[Anonymous No.11951818]

>>11951776
Its like asking which would get you more pussy playing tennis or being the starting runningback for a national championship college football team. Its fucking stupid and you’re a retard for not doing research on this by yourself. Yes, Applied Math is a very good degree with good job prospects you nigger.

[Anonymous No.11951820]

>>11951652
>>11951679
okay, just give me the suicide methods
i passed all my undergrad algebra, analysis, topology classes with flying colors and even did well in the grad classes ive started to take
but i suspected all along that i could only solve exercises and not any problem that was remotely creative and not a problem from my classes.
this problem singlehandedly proved my suspicion right
goodbye mathematics, goodbye cruel world

[Anonymous No.11951826]

>>11951820
Bye, lad.

[Anonymous No.11951840]

>>11951777
How can number theorists ever recover?

[Anonymous No.11951845]

>>11948444
Anon:

Think of log base 10. 10^-1= 0.1, 10^0=1, 10^1=10, 10^2 = 100, etc, so log10(.1)=-1, log10(1)=0, log10(10)=1, log10(100)=2, etc. For numbers between this, your calculator can figure out the exact exponent. eg log10(50) is about 1.699 because 10^1.699...=50; you can't easily calculate that yourself, but since 10 < 50 < 100, you can at least know log10(50) is between 1 and 2.

Natural logarithms are just base e = 2.718... . So ln(1)=0, ln (2.718...)=1, ln(7.389...)=2, ln(20.085...)=3, etc. Again, calculating exactly is tough, but at this point it's all about symbolic manipulation.

On that note, logarithms have really convenient math properties. As useful practice, I'd encourage you to try proving these yourself -- they're helpful for understanding and not too hard.

ln(e^x) = e^ln(x) = x. (True for most, but not all, numbers, at least without getting into complex analysis. Think about which ones may not work here by looking at their graphs and seeing where each function is defined.)

log base a (x) = ln(x) / ln (a). Note that you don't need ln on the right side, log x over log a in any base yields log x base a. Try proving by putting both sides e^(...) and applying exponent rules.

ln(x^y) = y*ln(x). This is a crucial property for proofs. Also, again, you don't need ln (aka log base e) here -- all of these properties are general properties of logarithms.

ln(xy) = ln(x) + ln(y). This is where slide rules came from: before calculators, really big, precise multiplications could be done easily by taking the log of the two inputs, adding them, and de-converting, using pre-calculated logarithms marked out on the slide rule.

ln(1/x) = -ln(x). Follows from prior rules, try proving.

Now, you may be wondering: why this 'e'? Honestly, the answer takes calculus (or at least a good answer, anyways, IMO). Teaser: d/dx a^x = a^x * ln(a). Also e^(i*pi) + 1 = 0, and a million other important identities

[Anonymous No.11951864]

>>11950890
What does this have to do with math?

[Anonymous No.11951916]

im so pathetic bro. im a math "major" but i cant even solve a random problem on a mongolian fishing forum by some animeposter

[Anonymous No.11951937]

>>11951916

[Anonymous No.11952040]

>>11951937
Don't start with 2, that's bullshit.

[Anonymous No.11952055]

>>11952040

It's more honest than starting with zero, since to start with two at least ensures a partition of primes and composites.

[Anonymous No.11952073]

just tell me how to do it. you got me.. you've humiliated me. just let me know how

[Anonymous No.11952085]

>>11950933
>>11951408
>>11951643
>>11951864
Here's the solution:
[eqn]|a - b \sqrt{2}| = \frac{|a^2 - 2b^2|}{a + b \sqrt 2}, [/eqn].
The numerator is an integer, and it cannot be zero, hence [math]|a^2 - 2b^2| \geq 1[/math].
The denominator satisfies [math]a + b \sqrt 2 \leq 2020(1 + \sqrt{2}) \leq 5050 [/math].

[Anonymous No.11952092]

>>11952073
>>11952073
recognize that abs(x - x * sqrt(2)) < abs(x + 1 - x * sqrt(2)) so the measure is minimized when a = b. Then the only interesting points are the max and min of the set, 1 satisfies the inequality, then the rest follow inductively up to the max, which also satisfies the inequality. This is not a formal proof.

[Anonymous No.11952097]

>>11952092
If you want to be really "rigorous", you could add abs(x - x * sqrt(2)) < abs(x - (x+1) * sqrt(2)) but I was lazy.

[Anonymous No.11952105]

pathetic
years of studying math
and i can't solve a simple problem
like working out for years but only being able to do one pushup

[Anonymous No.11952106]

>>11952105
try being smarter

[Anonymous No.11952112]

>>11952105
its inequality trash
its got nothing to do with proper math

[Anonymous No.11952114]

>>11952106
This has worked for me in the past.

[Anonymous No.11952117]

>>11952106
Rude anon

[Anonymous No.11952118]

>>11952105
Protip: start by doing pushups with your knees on the ground.

[Anonymous No.11952119]

>>11952112
Shots fired. Will the analysts respond?

[Anonymous No.11952126]

>>11952119
By ignoring coping brainlets.

[Anonymous No.11952128]

>>11952112
Ur mom got nothing to do with proper math

[Anonymous No.11952139]

>>11948317
>15
Someone has a room temperature IQ.

By the way, two out of six permutations of the date of my birthday (ddmmyyyy)are prime numbers. how about yours, /sci/?

[Anonymous No.11952151]

>>11952105
Don't be so hard on yourself lad, we're all gonna make it.

[Anonymous No.11952169]

>>11952126
Like how you guys ignore real math?

[Anonymous No.11952172]

>>11952169
I'm sorry, not everyone is spergy enough for Topology, now run along and go back to drawing your Venn diagrams.

[Anonymous No.11952181]

>>11951787
look up challenging calc problems from books like spivak or David Patrick's Calculus, this will help the concepts stick better than mindless monkey drilling.

[Anonymous No.11952188]

Prime factorization seems to be a red herring.
Generalizing from (2,...,10^whatever) to any finite nonempty list [math](x_i)_{i\in I}[/math] of nonzero field elements, i.e. [math]x:I \to \mathbb{F} \backslash \{0\}[/math], we can show by induction on the size card(I) of I that the resulting value is
[eqn]\frac{ \sum_{P \subseteq I, card(P) \text{ odd} } \prod P }{ \sum_{P \subseteq I, card(P) \text{ even} } \prod P }[/eqn]
which also proves that it does not depend on the order of evaluation, since the xi's are arbitrary.
The answer to the actual problem probably involves some bullshit about Stirling numbers or Vieta polynomial invariants that I can't be bothered to look up right now.

[Anonymous No.11952189]

>>11952188
>Prime factorization seems to be a red herring.
Forgot to quote >>11952055

[Anonymous No.11952191]

>>11952106
i wasnt born smart enough
seriously
why didnt the math department vet me with an iq test before letting me take classes for two years
life wasted

[Anonymous No.11952196]

>>11952055
Prime factorization seems to be a red herring.
Generalizing from (2,...,10^whatever) to any finite nonempty list [math](x_i)_{i\in I}[/math] of nonzero field elements, i.e. [math]x:I\to \mathbb{F} \backslash \{0\}[/math], we can show by induction on the size [math]card(I)[/math] of I that the resulting value is
[eqn]\frac{ \sum_{P\subseteq I, \: card(P) \text{ odd}} \prod_{i \in P }x_i }{ \sum_{P\subseteq I, \: card(P) \text{ even}} \prod_{i \in P }x_i }[/eqn]
which also proves that the value does not depend on the order of evaluation, since the xi's are arbitrary.
The answer to the actual problem probably involves some bullshit about Stirling numbers or Vieta polynomial invariants that I can't be bothered to look up right now.

[Anonymous No.11952260]

imagine being filtered by a math question on 4chan
LMAO
well that's fucking me
fml
pure math is too high iq for me

[Anonymous No.11952267]

>>11952260
have you tried category theory?

[Anonymous No.11952512]

>>11952267
don't be mean

[Anonymous No.11952578]

>>11947915
2 gang wya

[Anonymous No.11952583]

I cant solve these problems either
but I dont care
I'm still a math major working as a statistician at a major firm
there's this joke in our depratment
how do you call someone doing analysis? an analyst
how do you call someone doing algebra? an algebraist
how do you call someone doing statistics? employed

[Anonymous No.11952616]

>>11952583
this is /mg/ not /boringworkg/

[Anonymous No.11952617]

The adjacency matrix of a graph feels like a natural thing to come up with - it's a succinct representation of the information encoded in the graph. That I understand. But as far as I'm concerned, that's all it "essentially is" - just a succinct representation. In that sense, I perceive it not as *a matrix*, but as *a table of numbers*, if you will. That is, I think of matrices as a compact encoding of *linear transformations*, and of the adjacency "table" as a compact encoding of *the edges of a graph*. Two fundamentally different objects, or so it seems.

My question is this: The theory of eigen-stuff makes sense to me when I interpret it in the context of linear operators on vector spaces. Why is it reasonable to apply it to the adjacency table? Is there a natural way to interpret the latter as an actual matrix representation of a *linear operator*, w.r.t to some basis of a vector space? If so, how?

[Anonymous No.11952624]

>>11952616
cope
I earn a six figure salary and deal with fun math as a hobby

[The Vagus Core No.11952641]

>>11947870
We just picture it in twin-prime dimensions and then let n = 2

[Anonymous No.11952653]

>>11952583
There is a joke in my head:
Three men go to a guru on a mountain for wisdom. The first man claims to be the tallest man in the world and goes into the room. "Who is the tallest man?" he asks, and the guru answers: "You are the tallest man in the world." The second one claims to be the fattest man in the world and goes into the room. "Who is the fattest man?" he asks, and the guru answers: "You are the fattest man in the world." The third man claims to have the shortest dick in the world and goes into the room. He returns shocked and asks his companions: "Who are these applied mathematicians?"

[Anonymous No.11952670]

>>11952624
post math not boringwork next time

[Anonymous No.11952727]

>>11952617
In spectral graph theory you often work with the Laplacian matrix (which can be constructed easily from the adjacency matrix). As the name suggests, the Laplacian matrix shares some properties with the Laplacian operator in partial differential equations. You may know that the solutions to some classes of PDE tell you a lot about the geometry of a manifold (e.g. index theorems). So roughly speaking, large parts of spectral graph theory can be seen as a discrete equivalent to differential geometry.

[Anonymous No.11952750]

>>11952653
lel

[Anonymous No.11952787]

>>11952617
In the simplest possible situation, the point is: if A is adjacency matrix, then the (i, j) entry of A^k tells you how many distinct paths you have from vertex i to vertex j. If you have matrices and matrix multiplication, then it feels natural to me to use all the eigen-stuff.
If you want to have a vector space here, its base would be [math]e_v[/math] for each vertex v, and then the adjacency matrix represents a linear transformation such that [math]A e_v = \sum e_w [/math], where w ranges over all neighbours of v. But I don't know how much it helps.

[Anonymous No.11953093]

>>11952105
>>11952260
Calm down.

[Anonymous No.11953106]

>>11953093
Fuck, this image quality is horrendous, why do I have this in my folder?

[Anonymous No.11953140]

How do anons get better at difficult/creative problem solving beyond getting good at the exercises on their homework? And how do you make the transition between doing exercises and doing research?

[Anonymous No.11953177]

>>11953140
Bigger, more elaborate exercises.

[Anonymous No.11953283]

>>11953140
Do some big exercises where you build the proof of a big theorem piece by piece. Then apply similar methods to whatever your research is about. You start with what you already know and start extending that by checking what consequences and examples you have, what happens if you add some assumptions, where it fails etc. Then you end up having some nice result that actually follows from these little ones after you put the puzzle pieces together and get your favourite painting or some cute animal photo.

[Anonymous No.11953322]

>>11952617
One example where it makes sense to use
it as a linear operator is probability theory. If you normalise the adjacency matrix A then it can tell you about random walks in the graph: the entry (A^k)_{i,j} is the chance that a walk of k steps starting in vertex j lands in vertex i.

[Anonymous No.11953328]

Reading this today:
https://arxiv.org/pdf/2002.03255.pdf
The abstract says something about dilating, so as an anime-loving transsexual I can't help being interested.

[Anonymous No.11953353]

>>11947915
1488
2137

[Anonymous No.11953362]

>>11953353
i see

[Anonymous No.11953431]

>>11953283
That just sounds like the scientific method of experimenting and disproving/proving informed guesses. Do you recommend any advanced problem solving books or others on research methods? I've heard Polya's one is good but I'm not sure how useful it is for research.

[Anonymous No.11953565]

>>11953431
It is pretty experimental, yes. The only thing I can recommend for certain is following one's own gut instinct. Study things, spot similarities, pursue. Be persistent and try to have fun. Maybe there are some useful texts on how to do research or how to solve problems, but I have read none and can't comment on those.

[Anonymous No.11953692]

Could anyone please reccommend me a book / website where I can exercise integrating? (preferably with answers providing steps)
And if you know a good one for diff eqs please share too.
(I'm thinking of simply practice with no theory or other text)

[Anonymous No.11953702]

>>11952617
Well yes, you can view it as an operator on the vector space generated by the vertices of your graph, or to phrase it differently, on the space of real valued functions on the set of vertices of your graph, whose interpretation can be understood in the other replies to your post.

Why should you expect eigenvalues to have a geometric interpretation ?
I guess maybe you shouldn’t at first glance (although once you see the interpretation in terms of random walks, it makes a lot more sense).
Still, having in mind the fact that the adjacency matrix is the same as your graph, you should expect all of its geometric properties to be encoded somehow in that matrix.
Moreover, isomorphic graphs have conjugate adjacency matrices. Hence, you expect the pertinent information to be conjugacy-invariant.
What are the first interesting conjugacy invariants of a matrix ? Its characteristic polynomial and eigenvalues. And so you look for an interpretation for these objects in terms of your graph.

[Anonymous No.11953715]

>>11953322
Normalization is just modern witch-craft.

[Anonymous No.11953722]

>>11947884

How would you go about learning 1950s-present day math? I'm still in highschool, and I'm not sure where I would even begin.

[Anonymous No.11953732]

>>11953722
>I'm still in highschool
Probably best to set your goals a bit lower, then.

[Anonymous No.11953752]

>>11953722
It's unrealistic for you to be able to do much past 1950 unless you do the equivalent of a bachelor's degree in math. There are isolated things you can learn here and there but if you have no understanding of what happened between 1850 and 1950 you'll be lost. And you're in high school, so you may not even know enough pre-1850 stuff.

[Anonymous No.11953791]

>>11953752
Ah. What pre-1850s stuff could I be missing? I'm guessing I should learn multivariable calculus first? If so, where should I learn it?

[Anonymous No.11953806]

>>11953722
>>11953791
you got memed into thinking that "modern" = "more valuable and respectable"
the biggest hurdle for a beginning mathematician is being rigorous and being able to tell the difference between proof and handwaving
just do the highschool olympiads from your country mate

[Anonymous No.11953814]

>>11953791
This has to be bait.

[Anonymous No.11953829]

>>11953814
Nope. I just want to learn more about higher level math and physics because they both sound interesting.

[Anonymous No.11953836]

>>11953829
Major in one of them.

[Anonymous No.11953841]

>>11953806
The olympiads aren't bad to do or anything but I want to chime in that you don't need to do this competition-style math in order to learn. If math is a sport those people are weightlifters, but some of us prefer to run marathons.

[Anonymous No.11953864]

>>11953806
but all competition math is handwavy too
they just reduce problems to other problems that they never prove

[Anonymous No.11953968]

What does it mean to define prime and irreducible elements with respect to conditions on the ambient ring?

[Anonymous No.11953997]

>>11953968
¿What are the conditions?

[Anonymous No.11954006]

>>11953997
An irreducible element is an (non-zero) element that can't be represented as the product of two units.
A prime element is an element such a|bc means that a|b or a|c.

[Anonymous No.11954019]

Let [math]f(n)[/math] denote the size of biggest possible subset [math]S \subseteq \{1, 2 \dots n \}[/math], such that for any [math]i, j \in S[/math], their difference [math]|i - j|[/math] is not a square.
What are the asymptotics of [math]f[/math]? no one knows
why is modern math so cucked, we are unable to solve such simple problems

[Anonymous No.11954028]

>>11954006
I think you made a mistake in your definition of irreducible, but in any case I don't understand your question. Those definitions are for all rings, they have nothing to do with a special type of ring.

[Anonymous No.11954043]

>>11954028
I guess it was 'ambient ring'. Does that just mean any arbitrary ring?

[Anonymous No.11954058]

>>11954019

[Anonymous No.11954074]

>>11954058

[Anonymous No.11954078]

Imagine getting filtered by an anime girl’s math problem
Well that’s my reality
It even had a one line solution
Pretty dire for me

[Anonymous No.11954082]

>>11954074
This is now a Chitose thread.

[Anonymous No.11954112]

>>11954078
it's alright
we are all gonna make it bro...

[Anonymous No.11954130]

>>11952727
>>11952787
>>11953322
>>11953702
Thanks y'all. I must admit I'm still puzzled, but you've given me food for thought.

[Anonymous No.11954155]

>>11954112
Thanks, lad.

[Anonymous No.11954199]

>>11951007
>>11951221
true in all fields of characteristic n.

[Anonymous No.11954202]

>>11954199
>field
meant integral domain

[Anonymous No.11954221]

>>11954202
>integral domain
meant euclidean domain

[Anonymous No.11954239]

>>11954019
because your problems are ugly as fucking sin, why would anyone want to solve them

[Anonymous No.11954249]

>>11954239
To quench one's desire for knowledge.

[Anonymous No.11954253]

>>11954043
Yes, when you have some ring element the ambient ring of that element is the ring it belongs to.

[Anonymous No.11954287]

>>11954239
>why would anyone want to solve them
here's an OEIS entry which mentions 6 papers on this problem http://oeis.org/A100719
here's a wikipedia entry https://en.wikipedia.org/wiki/Furstenberg–Sárközy_theorem
so i think there is a number of people interested in this problem

[Anonymous No.11954321]

>>11953692
bump

[Anonymous No.11954334]

>>11954321
https://www.amazon.com/Ordinary-Differential-Equations-Dover-Mathematics/dp/0486649407/ref=sr_1_1?dchild=1&keywords=ODEs+Dover&qid=1596137469&sr=8-1

[Anonymous No.11954365]

>>11954082
SLUTose

[Anonymous No.11954553]

>>11954365
rude

[Anonymous No.11954565]

Don't forget to wear a mask on campus in the fall, /mg/!

[Anonymous No.11954683]

>>11954565
I'm not one of the brave souls who volunteered to join our skeleton crew on camps. Stay safe friends.

[Anonymous No.11954786]

>>11954565
The government will give me two for free, but I thought I'd get myself one with a cat face. Assuming there is any need for me to be present.

[Anonymous No.11954793]

>>11954365
LACTose.

[Anonymous No.11954809]

>>11953322
this

think of the sum of columns as weight corresponding to the options in which directions you can go. If the j'th column has many 1's and few 0's, this means the j'th node is well-connected. where options at nodes matter, it will be a function of the columns

[Anonymous No.11954967]

good night /mg/
>>11954565
thank you for worrying for my health sir...

[Anonymous No.11954987]

>>11954967
Night, lad.

[Anonymous No.11955031]

Hi. Can you explain to me why
[math]
\triangledown \cdot \iiint \dfrac{ \bar{r}_0- \bar{r}}{ \left | \bar{r}_0- \bar{r} \right |^3} \, \text{d}x \, \text{d}y \, \text{d}z = 4 \pi
[/math]
Holds true? Note: r=(x,y,z)

[Anonymous No.11955042]

>>11955031
What have you tried?

[Anonymous No.11955046]

>>11955031
My physishit brain would say pull the divergence into the integral and use the identity with the Dirac Delta:
[eqn]\nabla \cdot \frac{\mathbf{r}}{|\mathbf{r}|^3} = \delta(\mathbf{r})[/eqn]

[Anonymous No.11955058]

>>11950890
uh so you minimize this with calculus and proe the minimum is that?

[Anonymous No.11955333]

wearing this when I meet up with my professor for a letter of rec for grad school

[Anonymous No.11955340]

wearing this when I meet with my professor for a letter of rec

[Anonymous No.11955345]

>>11955340
Did the prof notice? What impression did you have? That's so cool holy shit.

[Anonymous No.11955346]

>>11955340
Did you custom make this? I kind of want one.

[Anonymous No.11955352]

>>11955345
only spoke via email, meeting in person over Fall. took him for a graduate course and figured there's no better recommendation than the professor of a graduate course you took
>>11955346
no, bought it off redbubble
https://www.redbubble.com/i/mask/LATEX-Overfull-hbox-by-kp00/51224041.9G0D8

If you have the means to get something custom made instead then do it, the quality on the ear loops is bad.

[Anonymous No.11955388]

>>11955352
Would it be cringe to get one with Cauchy's integral formula on it?

[Anonymous No.11955409]

I want a really slick proof that a diagonal [math]n \times n[/math] matrix has at least as many zero entries as non-zero entries if [math]n \geq 2[/math].
Something like "[math]n^2 -n = n (n-1) \geq n[/math] if [math]n \geq 2[/math]" isn't going to cut it, I want it to be slicker. much slicker.
You guys can do it, I believe in you.

[Anonymous No.11955413]

There was a set theory book recommendation image posted here a few days ago. Anyone still have it?

[Anonymous No.11955428]

>>11955413

[Anonymous No.11955430]

>>11955413
Dozo.

[Anonymous No.11955437]

>>11955428
>>11955430
ty

[Anonymous No.11955439]

>>11955413
>>11955428
>>11955430
fucking why. set theory/logic is pure dry autismo that nobody cares about. the specialists can't even understand each other's papers, they only understand their own work and their advisor's.

[Anonymous No.11955440]

>>11955409
I mean. That's the proof. What else do you want.
You can say something like the first column has n-1 zeros and the top right is a zero.

[Anonymous No.11955450]

>>11955439
It's fun.

[Anonymous No.11955458]

>>11955440
You can, and that's an improvement.
But you can definitely do slicker.
For example, if we consider the matrix's entries to be indexed by [math]\mathbb{Z}_n \oplus \mathbb{Z}_n[/math], then, for [math]n \geq 2[/math], the map [math](i, i) \rightarrow (i+1, i)[/math] injects the the diagonal into the set of non-zero entries and proves the result.
Of course, I'm sure that even this is merely the tip of the slickness iceberg.

[Anonymous No.11955461]

>>11955458
>non-zero entries
Zero entries.

[Anonymous No.11955466]

>>11948003
https://www.unz.com/akarlin/intro-apollos-ascent/

[Anonymous No.11955474]

Hey I'm a big dumb. Whenever I need to do some math, I'll learn as much as I need to solve the problem and then I'll forget it.

However, I notice more connections and can skip steps when I actually remember the math.

I can usually pretty quickly understand something, but retaining it is not working out. Is there a way to retain something without just drilling a bunch of problem sets? It would be really inefficient to drill problem sets for something I may only use once again in my life.

[Anonymous No.11955479]

>>11955474
Actually understand the intuition behind why something is the way it is. Lower level math is mostly non-rigorous and unmotivated and as a result, it's less likely to stick.

[Anonymous No.11955528]

What are the prerequisites for measure theory?

[Anonymous No.11955532]

>>11955528
Analysis I and II (basically comfortable with most of Rudin) and basic point set topology.

[Anonymous No.11955533]

>>11955528
real analysis, if not simply 'mathematical maturity'

e.g. tao's two analysis volumes are prerequisite to his intro to measure theory.

[Anonymous No.11955535]

>>11955528
Same as for being a streetwalker: Giving up a little bit almost everywhere.

[Anonymous No.11955545]

>>11955533
Tao's sequence is really good.

[Anonymous No.11955555]

>>11955545
>>11955532

How does the Rudin 'sequence' compare?

[Anonymous No.11955585]

>>11955555
Holy digits.
Anyways, the biggest difference is that Rudin jumps right into the thick of things, whereas Tao takes a few chapters to really build up and develop things (like covering the reals and so on). I personally prefer the way Tao explains things, but either one is good. So, the first chapter of Rudin is akin to like the 4th chapter of Tao. Princeton Lectures in Analysis are also a good option.

[Anonymous No.11955612]

how many formulas do i need to memorize to learn calculus

[Anonymous No.11955635]

>>11955612
Zero. Understand it.

[Anonymous No.11955638]

>>11955635
This.

[Anonymous No.11955642]

>>11955528
Basic analysis really. It's kinda like general topology, there are a shiton of books who foccus on different things and so the motivation kinda depends on what you know, but the general theory follows from the definitions.

[Anonymous No.11955686]

>>11955612

[Anonymous No.11955731]

Is Lee's 'Introduction to Smooth Manifolds' good?

[Anonymous No.11955755]

>>11955439
>the specialists can't even understand each other's papers, they only understand their own work and their advisor's.
This is just not true, how did you even come up with that retarded opinion? My advisor has worked in several areas of set theory, and he even moved away from his advisors area. Each subfield of set theory has its own technical machinery it uses to solve problems. That can make it hard to be up to date with the latest research in every subfield. But there are lots of set theorists that move around.

[Anonymous No.11955801]

>>11955731
Pretty good. It still handwaves pretty important stuff sometimes. If you want s grounds up book that isn't a pussy about the nitty gritty topological details I recomend Tu's book.

[Anonymous No.11955829]

>>11955801
Intro to Manifolds?

[Anonymous No.11955882]

>>11955829
Yes

[Anonymous No.11955894]

hey /mg/, collegeanon here

I absolutely fucked myself in high school and had barely paid attention in my math classes, the most advanced thing I learned most likely being the difference between an x and y axis

what resources can I use to bring myself up to a better understanding of maths in general?

[Anonymous No.11955898]

>>11955894
I understand its a bit late to learn these things now but I'm really kicking myself for not paying attention more when I was younger and would like to do as much as I can to not be a brainlet when i'm 30

[Anonymous No.11955902]

>>11955352
would recommend clipping the bands behind your head with a paperclip, helps on the ears

>>11955894
>>11955898
Try Khan Academy.

[Anonymous No.11955921]

>>11955801
What? Where does Lee handwave?

[Anonymous No.11955976]

Good morning, /mg/!

A PhD position in Utrecht https://webspace.science.uu.nl/~meier007/PhDDetails.pdf

[Anonymous No.11955981]

>>11955976
morning, chad

[Anonymous No.11956017]

>>11954565
But Mr anime poster, there's no community transition where I live!

[Anonymous No.11956107]

>>11955976
>dank for coming to the e-interview anon, so where did you hear about this position?
>one of the tibetan cartoon posters on the learn to count section of my favourite mongolian tapestry weaving forum posted it

[Anonymous No.11956112]

Is there anything interesting/noteworthy between learning about distributions and stochastic processes?

[Anonymous No.11956212]

>>11947915
6, 28, 496, 8128...

[Anonymous No.11956230]

>>11956112
>between
What do you mean by this?

[Anonymous No.11956235]

What was the last time we got a brand new branch of Mathematics?

[Anonymous No.11956247]

>>11955981
Same to you, my friend.

>>11956107
>ach ja zat was me
But I recommend someone to send an application there. Gijs Heuts at least is a nice guy.

>>11956235
The last time would be IU-Teichmüller if you want to count that. The next time will be when I make my diary public, desu.

[Anonymous No.11956250]

category theorists are superior to everyone in this thread

[Anonymous No.11956286]

>>11956250
not me, though

[Anonymous No.11956316]

>>11956250
Are they really, tho?

[Anonymous No.11956333]

>>11956250
I am a category theorist

[Anonymous No.11956338]

>>11956250
>>11956333
Dilate.

[Anonymous No.11956512]

>>11954565
I wonder what the experience of the first weeks will be like for the first years this time.
Thinking back, it's where all the friendships started, that stood the test of time.
You can't really have that through Zoom and Skype.

[Anonymous No.11956520]

>>11956512
You don’t private message all the twinks on Zoom and tell them they look cute? That’s weird haha

[Anonymous No.11956836]

>>11956250
>>11956333
Dilate.

[Anonymous No.11956999]

>>11956512
>not going to a uni that doesn't give a fuck and has classes anyway
bruh

[Anonymous No.11957393]

>>11952139
>By the way, two out of six permutations of the date of my birthday (ddmmyyyy)are prime numbers. how about yours, /sci/?
none of mine, every number is even

[Anonymous No.11957435]

>>11957393
Based.
t. 28th of December -92

[Anonymous No.11957481]

>>11957435
I turned 6 on 06/06/06

[Anonymous No.11957507]

>>11957481
Hail Satan!

[Anonymous No.11957760]

>>11956999
I'm fortunately done with uni. It's become an extremely hostile environment for "white" men.
My Alma Mater has entirely moved to online classes, though.
Written exams are offline, but with extreme precautions.

[Anonymous No.11957760,1]

>>11955046
thats wrong tho. nabla*(r^-2)=4*pi*direc delta(r) so there i have the result :)