/sci/ - Science & Math

I sometimes see talking people using the density of a set as a substitute for volume. "Oh, set X is dense in set Y, so intuitively almost every element of Y is X". But this makes no fucking sense, rationals and irrationals are both dense in [math]\mathbb{R}[/math], but you would never say "almost every real number is rational" due to the difference in cardinalities. What is the actual intuition for a set being dense in another set?

>>11584748
>density of a set as a substitute for volume.
That absolutely is false. You can have sets with arbitrary measure which are dense in R, obviously.

>What is the actual intuition for a set being dense in another set?
Distance. Every real number can be arbitrarily well expressed by a rational number, that is the single post important quality about the whole thing.
The same goes in general, every element of a set can be expressed arbitrarily well by an element of a set which is dense in that former set.

>>11584605
why do white people of 1940-1950s all look the same?

>>11584759
they're actually gray

>>11584605
post more historial math photos, they are comfy as shit

>>11584605
>Taniyama
Why did he kill himself bros?

Threadly reminder to work with physicists.

>>11584773
I've read shimura's recollections about him but I don't know

>>11584748
Chocolate milk is mostly milk, but the chocolate is dense in it.

>>11584605
Conferences in Japan are so comfy but why are Japs so bad at English? It makes it a chore to have even a basic conversation.

>>11584803
>why are Japs so bad at English
Because they aren't a soulless mutt colony.

>>11584803
>Not learning japanese
It's unironically the best language to learn in mathematics after english

>>11584781
>>/sci/image/nyWMJSWzlXvV2WYxL60AmA

>>/sci/?offset=96&ghost=yes&task=search&search_text=why%20the%20homophobia

>>11584877
Damn, that's the first time I felt actual sadness seeing an image here, feels bad man

How can I prove using induction that for all [math]n \in \mathbb{N}[/math]:

[eqn]\sum_{k=2}^n \frac{1}{k^2} < 1[/eqn]

Most induction problems I've encountered would be solved adding the [math]n+1[/math]-th term on both sides
[eqn]\left( \sum_{k=2}^n \frac{1}{k^2} \right) +\frac{1}{(n+1)^2} < 1 + \frac{1}{(n+1)^2}[/eqn]

and then proving that
[eqn]1 + \frac{1}{(n+1)^2} < 1[/eqn]

but this is obviously wrong. What else can I do?

https://www.youtube.com/watch?v=pimTWIXgi-E

How can I prove using induction that for all [math]n \in \mathbb{N}[/math]:

[math]\sum_{k=2}^n \frac{1}{k^2} < 1[/math]

Most induction problems I've encountered would be solved adding the [math]n+1[/math]-th term on both sides

[math]\left( \sum_{k=2}^n \frac{1}{k^2} \right) +\frac{1}{(n+1)^2} < 1 + \frac{1}{(n+1)^2}[/math]

and then proving that

[math]1 + \frac{1}{(n+1)^2} < 1[/math]

but this is obviously wrong. What else can I do?

>>11584820
why?

>>11584877
Yes those are my posts, what of them?

>>11584925
Approximate it with an integral. It's long and I don't want to type it out so here's a video on it:
https://www.youtube.com/watch?v=3Y132LG_-nk

>>11584971
It's for an introductory algebra course. I'm not supposed to use calculus.

>>11584748
A dense set X in Y could be thought of as "being everywhere". If you were in a field and found that there are dandelions everywhere, it wouldn't typically be because every square inch of the field is covered by dandelions, but because the field is covered by small patches each containing at least one dandelion. In a similar sense, X can be thought of as being everywhere in Y.

>>11584925
Try to prove some other bound like [math]\sum _{k=2}^n \frac{1}{k^2} < 1 - \frac{2}{(n+1)^2} [/math] by induction, obviously.

Any fun books just on solving inequality?

>>11584925
Not by induction but the infinite series starting from k=1 converges to pi^2/6

>>11585037
It's called the Basel problem.
Euler's proof uses induction I think but it's really involved though.

>>11585037
Come on guys, I don't think I'm expected to just plug [math]\pi^2/6[/math] and say problems solved

>>11584925
Try proving some inequality of the form [math]\sum _{k = 2}^n \frac{1}{k^2} < 1 + f(n)[/math], then the induction step becomes [math]f(n) - f(n+1) > \frac{1}{(n+1)^2}[/math] or something similar enough (note: typos might have been made).
>how do I choose f(n)
Try random stuff like [math]( \frac{n}{n+1})^2[/math] until something works.

>>11585046
The approach is probably, that you find a closed expression for [math]a_n[/math], and proof that it's correct, and that it stays below 1.
I'm not doing the googling for you. Do that yourself.

>>11585066
Should've been a minus f(n) on the first one.

>>11585066
Sorry, I didn't understand the second part of what you wrote

>>11584925
>>11585066
Just use:
[math]\sum _{k=2}^n \frac{1}{k^2} < 1 - \frac{1}{(n+1)^2} [/math]
Base case is easy. Induction step:
[math]\sum _{k=2}^n \frac{1}{k^2} + \frac{1}{(n+1)^2} = \sum _{k=2}^{n+1} \frac{1}{k^2}< 1 [/math] qed

>actually, it's Cauchy–*Bunyakovsky*–Schwarz inequality

>>11585086
That's just running around circles

>>11585086
wtf is this lmao

>>11585098
>>11585107
Prove this:
[math]\sum _{k=2}^n \frac{1}{k^2} < 1 - \frac{1}{(n+1)^2} [/math] (1)
Using induction. Don't care about the main problem.
Then begin to prove this:
[math]\sum_{k=2}^n \frac{1}{k^2} < 1[/math]
At the main induction step, use the result from (1).
Done.

>>11584925
>>11585037
>>11585066
>>11585086
>>11585119
I can't believe that /mg/ is having trouble over this. I'm disappointed.

>>11585119
How do you know the first equation is right?

>>11585119
His problem probably is, that what has to be shown only follows, if (1) is true for all n, and proving (1) for all n isn't easier, or is it?

>>11585079
What second part?
You choose some [math]f(n)[/math], show that [math]f(2)<1[/math] (the base case of the induction) and then you show that [math]\sum _{k=2}^n \frac{1}{k^2} < 1 - f(n)[/math] implies that [math]\sum _{k=2}^{n+1} \frac{1}{k^2} < 1 - f(n+1)[/math] (which is the inductive step)
I know it sounds like I'm sending you on a wild goose chase, but it's genuinely the only way of using induction that comes to mind, besides giving a general formula (which I've honestly never heard of but might exist).

>>11585129
Enlighten us then, o chosen one

>>11585137
Also, f's nonnegative, obviously.

>>11585137
But when you do [math] 1 - f(n)[/math], shouldn't the [math]n[/math] in the Sum symbol become [math]n-1[/math]?

>>11584925
Are you sure it's induction?
If there is an obvious induction solution, I have a feeling that it would have been listed here:
https://proofwiki.org/wiki/Basel_Problem
What you are trying to prove is that sum is [math]\le \frac{\pi^2}{6}-1[/math].

>>11584925

Maybe I'm dumb, but wouldn't it work if we exponentiate on both sides, bc then we would get prod(n+1)<e*(something smaller than 1)

>>11585180
wat

>>11584925
Prove that $$\frac{\sum_{1 < i_1 <...< i_n}i_1^2...i_n^2}{(n!)^2} < 1$$ by induction then use it to prove what you want

>>11585199
Like the we have to prove: [eqn]
\prod_{k=2}^n e^{k^{-2}}<e
[/eqn]
and so we get:
[eqn]
\prod_{k=2}^{n+1} e^{k^{-2}} = \prod_{k=2}^{n} e^{k^{-2}} * e^{(n+1)^{-2}}<e * e^{(n+1)^{-2}}
[/eqn]

>>11585225
>$$\frac{\sum_{1 < i_1 <...< i_n}i_1^2...i_n^2}{(n!)^2} < 1$$
Learn LaTeX first man

>>11585240
Ah shit, I see the error

>>11585243
[math]test[/math]
$test$
[eqn]test[eqn]

>>11585225
[math]\frac{\sum_{1 < i_1 <...< i_n}i_1^2...i_n^2}{(n!)^2} < 1[/math]

>>11585250
it should be only up to [math]i_{n-1}[/math] in the sigma notation tho

undergrad here. my reu got cancelled so what do.

i can either self study measure theory as a follow up to my two semesters of analysis or self study more in depth group theory (group representations, group actions, etc) as a follow up to my two semesters of algebra. any reccs?

2020/04/20 - The legendary day where PhD mathematicians of /mg/ got obliterated by a simple induction problem

Based, now /pg/ is the new king of generals of /sci/, bow down to your physicists overlords, filthy mathematicians

>>11585258
What's reu?>>11585258

>>11584925
Wtf /mg/:
[math]\frac{1}{k^2} \le \frac{1}{t^2}[/math] whenever [math]\displaystyle t \in [k-1,k][/math], hence [math]\displaystyle\frac{1}{k^2} \le \int_{k-1}^k \frac{dt}{t^2}[/math], and therefore:[eqn]\sum_{k=2}^n \frac{1}{k^2} \le \int_1^n \frac{dt}{t^2} = 1 - \frac{1}{n}[/eqn]

>>11585024
cauchy schwarz master class

>>11585269
research experience for undergrads. basically a paid position to do research, typically at a different university than your own. I was supposed to be paid to do math for 8 weeks but here we are

>>11585270
See: >>11584981

>>11585265
Makes me wish I was >>11584877.

>>11585279
yea my bad, I didn't read beyond that post

>>11584925
Lemme see if I can get LaTeX working...
What about trying to use [math] \frac{1}{k^2} < \frac{1}{k(k-1)} [/math] and then trying partial fraction decomposition?

>>11585279
>>11585286
Well come to think of it, you can prove [math]\sum_{k=2}^n \frac{1}{k^2} \le 1 - \frac{1}{n}[/math] by induction

>>11585325
Yeah, turns out the f(n) is a lot stupider than I guessed it would be.

>>11585309
It actually works out. No induction necessary

>>11585309
This is the solution. It's super simple and I can't believe /mg/ didn't fucking realize it lmao

>>11585345
>OP asks for a solution using induction
>a solution not using induction gets posted
>This is the solution. It's super simple and I can't believe /mg/ didn't fucking realize it lmao

>>11585401
>I can't solve it
>Fuck, let me make some excuses here to save face
Heh, brainlet

>>11585412
The classic "make dumbass post and then start shitposting to cover when you realize it"

I'm the guy who asked about the induction problem. Thanks to all who helped (except the guys who provided integral solutions), but I think >>11585325 nails it the best. Thank you.

Oh and also thanks to >>11585066 for providing insight

>>11585430
>>11585445
https://www.math.upenn.edu/~peal/files/Proof.by.Induction[2018][Eng]-ALEXANDERSSON.pdf

Problem 8

>>11585430
I should be thanking you to exposing /mg/ like that, you proved the majority here are brainlets, now /pg/ can claim the throne of /sci/

>>11585341
What the fuck is this? A series of equals into equals an inequality? Clean up that logic bro.

--

>>11585552
>durr transitivity hard

Say that I have a non-increasing sequence [math](a_n)[/math] which converges absolutely to 0, and in fact I know that [math]\sum_{n=1}^\infty |a_n| = 1[/math]. If I only take the first [math]N[/math] terms of this sequence, how close to it (in terms of, say, the norm on [math]\ell^1[/math]) am I guaranteed to be? That is, what can I say about the tail term [math]\| (a_n) - (a_1, \ldots, a_N, 0, \ldots ) \|_1
= \sum_{n=N+1}^\infty |a_n|[/math], and how can I characterize it?

>>11585623
To clarify, I know that the term *eventually* gets arbitrarily small, but I would like to understand it for some fixed finite [math]N[/math].

>>11585623
>how close to it (in terms of, say, the norm on l1l1) am I guaranteed to be?
For an arbitrary sequence, you are guaranteed to be strictly within 1 of it. No closer.
Select some arbitrary integer M. Define the sequence
a_k = 1/M, 1 <= k <= M
a_k = 0, otherwise
The first N terms of this sequence sum to N/M, which you can shrink to any epsilon you want by blowing up M.

>>11585641
*N/M provided N <= M, obviously

>>11585641
This seems corrects.

It also works in the other direction. You can blow up the first N coefficients to sum to any number just about 1 and thus have the tail be as tiny as you want.

>>11585641
>>11585659
thanks, good points. in what cases could the tail term be understood better? let's take an (a_n) with a_n > 0 for all n, I'm looking for some regularity assumptions on (a_n) to make the tail term behave "nicely" and be easier to bound

>>11584748
you're probably confusing dense and generic
people say generic, or open and dense, to mean that topologically almost every element of Y is X. it's kind of a substitute for measure. look into baire category theory.

>>11585667
not clear what you're saying. in your example the series was decreasting and summing to 1, so that's a nice falling extremely convergent series. 1/2^(-n-1) comes to mind.

>>11585623
what exactly do you mean by non-increasing? that a_m is never larger than a_n if m>n?

>>11585738
I just wanted some ideas about how to understand the tail term when a_n>0 for all n, which avoids extreme counterexamples like in >>11585641 >>11585659. for instance, the faster the series converges to 0 the smaller the tail should be, but how to quantify this more precisely?

>>11585752
yes

>>11585775
Sounds like this "smaller" notion is exactly just O behaviour.

>>11585667
There are endless conditions you could put on a series to get a bound on the tail, and they all result in different bounds on the tail. Your question is massively too broad to have a nontrivial answer.
I dunno if you're the same guy who asked the other series question last thread, but if you are (or even if not) you should try to understand that asking for nontrivial "bounds" on completely general (even a.c.) series is an impossible question. The family is too broad, and can converge arbitrarily poorly or quickly in infinitely many variations of shittiness.

If you have a specific series or family of series you want to say something about, then start there and try to be more general once you see what properties you do and don't need.
If the most specific thing you're trying to study is seriously "series which sum to 1" then whatever led you there was either a bad question or a bad approach to a solution.

>>11585797
O behave.

A guy just (indirectly) shitted on me because my school is 20 ranks below his.
I know I should study math for fun but that's hurt.
I can take most of the shit people throw at me on /sci/, but when it comes to real life, I can't.

>>11584877
>>11584894
lmao

>>11586075
I study at a literally who school on a third world country (a bit bellow 1300 in a global ranking I found, not even top 50 Latam). It's unlikely you're worse off than me, so don't be sad anon.

>>11585265
lol this is fucking embarrassing
I honestly think for problems involving any actual dirty work or any numbers at all /pg/ would be better at solving them than this retarded general

How do you work out fractional equations where the variable is on the bottom of the fraction? For example, simultaneous equations where the x and y values lie beneath the numbers

>>11586124
Depends on the problem, you may be able to do something as simple as just solving for 1/x etc by change of variable.
But after the fucking shameful display earlier in this thread I don't know if you'll get much help from these clowns.

How can something become a "theory"? For instance, why is it called "Inter universal teichmuller theory" and not "one application of teichmuller theory"?

Given a PDE and a state for time t = t_0 > 0 we can't usually determine the states for t < t_0, right?
Are there many PDEs that are time reversible?

>>11584894
why tho?

>>11586098
Thanks, anon.

>>11586122
Too bad they'll never hold a candle to us at not dying after 80 posts

>>11584820
kekest kek

>>11586163
I would prefer /mg/ dying rather than seeing half of the posts being unrelated shit.

>>11584820
How did you learn nihongo? How do you use in mathematics? Just reading textbooks? Are there any good Japanese texts that haven't been translated? Are there good papers that didn't get translated?

>>11586174
>How did you learn nihongo
Cringe lmao

I'm trying to recall a theorem, or the name of a theorem, that can be used to express a finite sum in terms of an integral.
It can also be used to represent sums as integrals over the floor function and the like. The proof basically hints at it being a variant of the fundamental theorem of calculus.
It roughly goes like

[math] \sum_{k=1}^{n-1} A_n \phi(n) = \cdots + \int \cdot [/math]

Anybody got a hint?

>>11586174
>How did you learn nihongo?
Imabi for grammar
Dictionary of japanese grammar (3 volumes) for reference
Remembering the Kanji I and III for Kanji
Several anki decks
But most importantly, studying everyday, not losing motivation
Other interesting books: making sense of japanese, rapid reading japanese, all about particles
>How do you use in mathematics?
Several great math books and papers in japanese, it'll also make it easier to immigrate there (you do want to live there, right? It's the best country in the world after all)
>Just reading textbooks?
Yeah, and manga and lit
>Are there any good Japanese texts that haven't been translated?
There are thousands
>Are there good papers that didn't get translated?
You're kidding, right?

>>11586212
nevermind, my browser history didn't forget

>>11586075
what a shitter
Honestly math is one of those fields where where you're studying is basically meaningless
enough stuff is out there for free nowadays that I doubt pouring resources into students really makes them much better. It comes down to building a good list of study topics for classes and having an engaging faculty with interesting research with which to involve their students. Since schools need mathlads to teach plebs calculus anyways none of that really costs anything extra on the school's part.
And even if a school somehow fucks all that up, teaching yourself isn't particularly hard compared to other subjects. It's not like there's any experiments or anything of the like as if you tried to teach yourself engineering or chemistry.

>>11586146
>dude can you just sum up the theory of inverse problems for PDEs for me
I can't.
Not only because it isn't my field, but also because I don't want to.

>>11584605
look at those nerds lmaooo

>>11586231
Forgot to mention it, but Groetsche did a computation of the inverse problem for the heat equation in one of his books about regularization.
Real simple stuff, a child could read it.

Can anyone please tell me the name of the website where you can download almost any mathematics textbook pdf for free? I downloaded 'Geometry, Topology and Physics' by Nakahara about a year ago and I completely forgot where I found it.

>>11586243
libgen.is

>>11584925
A retarded try using only elementary stuff. Let f(n) be the sum in question for compactness. We can show that f(n) < 1 - 1/n^2 for all n bigger than 2 by induction. It is true for n = 2. Assume it is true up to some n, and let's show it is true for n+1. We have f(n+1) = f(n) + 1/(n+1)^2 < 1 - 1/n^2 + 1/(n+1)^2 by induction. Next I claim 1/(n+1)^2 < 1/n^2 - 1/(n+1)^2 for all n bigger than 2. It is equivalent to show that 2/(n+1)^2 < 1/n^2 for such n. It is clearly true for n=2. For n>=3, we generally have (n+1)^2/(2n^2) = (1/2)*(1+1/n)^2 < 8/9 < 1, so my claim was true. This implies f(n+1) < 1- 1/(n+1)^2, which is what we wanted. Now your shitty homework is done with only elementary shit and also induction. Now go neck yourself or post body.

When an arc consisting of one side of a square is drawn on a circle that fits in the square as shown in the figure below, what proportion of the area of the circle is outside the arc?

>>11586253
Thank you!

>>11586212
This looks like Abel-Plana/Ramanujan summation

>>11586243
Some books aren't on libgen, but you can find them through other obscure methods

>>11586269
here's a hint
https://www.desmos.com/calculator/3ehiun1vxb
from there making some integrals to solve should be easy

>>11586269
Oh shit the math majors are weaponizing Voltorbs

>>11586301
this elucidates nothing

>>11586269
Compute the green area (circular sector), subtract the yellow are (circular sector again) and subtract the two triangles.
>can I do it purely analytically
No idea.

>>11586364
Anon pls
https://www.desmos.com/calculator/rl9xjnnqrn
There's an exact value if you use >>11586385
's method

>>11586385
Oh, the triangles you can compute with Heron. one side is the small circle's radius, the other one is the large circle's radius, the third one you compute with Pythagoras as square root of two times the smaller radius.
Not sure about the angles.

>>11586396
just use trig, it's 1-sqrt2-2

>>11586399
Yeah, that's right.
Cosine law gives the triangle's angles since you know the sides, and then you can use them to compute the two angles.

>>11584773
>>11584795
Come on now. There is a wiki page about him
https://en.wikipedia.org/wiki/Yutaka_Taniyama#Depression_and_death

is this correct?

>>11586414
I like how E and F are essentially bloat and it's already impossible to do with just A, B, C and D, but it's easier to tell then why it's impossible.
Unless you let the lines leave the box or something.

>>11584605
How difficult is it to have a 4.0GPA in math/physics/comp-sci at a globally top 100 public university?

>>11586455
>comp-sci
not hard at all compared to the other two

>>11586414

>>11586414
>>11586467

>>11586457
I apologise for asking my question in a bad way.

What I meant to ask is: what would a bell curve distribution of GPA look at a university. What percentage of undergraduate students have a GPA above a 3.9, 3.7, 3.5?

>>11586470

based opus magnum tier solution

>>11586467

cringe

>>11586494
opus magmun is a comfy game
just a shame i cant skip levels

Just ordered Topology by Munkres, which I will begin after I finish Principles of Mathematical Analysis by Rudin. What to expect? Is there any problem sets which deal with topology and probability? Gonna do measure theory at some point.

>>11586690
If you'll do it after Rudin you should grab something more advanced like Lee's Topological Manifolds

If you can't do differential calculus you can't be my friend!!!

>>11586806
Man even a monkey can do diff calculus with proper training

>>11586807
I think that anon is talking about people who never went to college.

>>11586806
functional analysis*

>>11586806
Derivatives can be fully automatized thanks to the chain rule, it always surprises me when students struggle with it. Just apply the rules nigga

What is the standard method to find a basis for a given vector space?

>>11586796
Oh, why, I thought the pre req was Rudin's analysis?

>>11586868
I don't think you need Rudin for Munkres, maybe even something along the lines of Abbott

>>11586863
Gram-Schmidt?

>>11586880
that begins with a basis you idiot
>>11586863
pick vector, pick vector outside of span, pick vector outside of their span, etc.
or take a finite spanning set, remove vectors in the span of the others

>>11586876
The local uni lists prereqs as all of baby blue AND measure theory.

>>11586910
>measure theory is a prereq for topology

>>11586910
topology is a prereq for measure theory
what measure theory does anyone do without the borel sigma algebra

>be stephen hawking
>dick stopped working way back in the 60s
>feels bad man
>actually can't feel anything at all
>spend decades becoming the world's foremost authority in astrophysics. Shits cash
>but when I go to the bar, no bitches want to put their tits in my face and motorboat me
>virgin 4 life
>come up with a plan
>years later
>the world is morning my death
>little do they know I'm still alive, but not for long
>my pal elon plays along, distracts the world with a cheap gimmick, a tesla in space
>little do they know there's a second payload
>I'm hurtling through space naked, with a specially designed helmet and oxygen tank.
>my body has been essentially dead since the johnson administration, so they didn't bother with heating anything but my head. It's very cheap to keep it alive.
>but millions of stem cells have been cultivating in my penis
>and 20 doses of viagra
>my spine is bent violently, I'm hurting penis first through the cosmos
>and suddenly I see it, or rather, the lack of it.
>nothing can escape the pull of a black hole, not even light
>I accept my fate and I mentally grin with anticipation
>I cannot feel it, but the world's greatest scientists have ensured me that my penis would be fully aroused for this moment
>I have accepted my fate. I am sacrificing myself for science
>The sensors in my body are relaying all the data back to CERN
>just a pale blue dot, lights years away
>finally we can answer the age-old question
>what happens when you hurl, pelvis first, towards a black hole
>and your penis enters the event horizon
>would you, for a brief fraction of a fraction of a second
>be fucking the very fabric of space-time itself?

>>11586918

Beautiful

Can someone link the books to read to go full math monk? I really want to make use of this qurantine time

>>11586937
No.

What is the standard book for functional analysis and algebraic geometry?

>>11586937
Assuming familiarity with proofs and set theory
Calculus: Spivak
Linear Algebra: Hoffman & Kunze
Abstract Algebra: Herstein or Dummit & Foote
Topology: Munkres
Number Theory: Niven & Zuckerman
Probability: Bertsekas & Tsitsiklis

>>11586937
Lang, full stop

>>11586937
You'd be lucky to read 2 textbooks and understand them during the quarantine, math books tend to be pretty time consuming.

>>11586937
>Can someone link the books to read to go full math monk?

>>11586261
waiting for body post.

>>11586863
>What is the standard method to find a basis for a given vector space?
Depends on whether a basis exists.

>>11586993
>>What is the standard method to find a basis for a given vector space?
>Depends on whether a basis exists.
It does.

>>11586993
Suppose finite dimension

>>11586455
>>11586472
I'm doubling Math/Physics and had a 4.0 until the second half of my junior year. It's hard, but doable, especially if you plan out your schedule so you aren't overloaded (not all 3 credit hour courses are created the same) and you're wary of the shitty professors who set you up for failure. I'd say that the worst thing about a 4.0 is all the stress that comes with it. Once I ate my first A-, my college stress dropped significantly.

Also, GPA curves really depend on the school and professor. Some schools pride themselves on having the bell curve and mean centered at a C. Others curve tremendously, to the point where you're in the lower end of the class with a B. At my school, for instance, above 3.0 is considered pretty high for a physics major. Not so sure about math, but in the Complex Analyses/Functions course I'm taking, the test averages were 73 for the first and 76 for the second (and there was no curve given). In Mechanics, the test averages were so bad that the professor offered to drop 1 test.

I enrolled for my university's math program because I didn't know what I wanted to do with my life and thought "whatever I choose, it's gonna need math". I'm now finishing up my 3rd year and it just hit me: I fucking hate proofs. They are like these intricate logic puzzles and I just don't like them. I like practical, actionable knowledge and I am perfectly content with treating theorems and such as black boxes and means to an end.

I dunno I just wanted to type that out.

>>11587087
fair
Incredibly unbased, but fair

>>11587087
Have you tried physics? It's pretty much all applied math, especially vector calculus, differential equations, and probability/statistics.

>>11587087
should've been an engineer I guess :/

>>11587087
I hated proofs at first, but once I became comfortable with them, they're kinda fun. Lots of unintuitive memorization up front though, and you have to be fluent in notation.

>>11587087
Statistics is the worst. I don't doubt it's usefulness, but so many boring and tedious calculations, and you're always drowning in spreadsheets.

>>11587100

Since I am like 99% done my math major, I decided to double major with Computer Science mostly because of the same logic as math ("whatever i end up doing, i'll need to know how to program shit"). Admittedly, my math endeavors is helping a lot with CS. I kinda see why this board memes on CS. Not that it is super easy, but I guess it's like training with weighted clothing and now I'm taking them off.

Yeah I dunno I'm just kinda accumulating the most general skills and knowledge possible because I do not have a definitive end goal in mind.

>>11587117
based maths generalist

>>11586937
Here ya go

>>11587115
>Statistics is the worst. I don't doubt it's usefulness, but so many boring and tedious calculations, and you're always drowning in spreadsheets.

>having to manually enter in a data set of nx=100, ny=100 to do a confidence interval of two means or hypothesis testing

Don't know what's worse; weird and obtuse probability theory and having to memorize all the crazy pdfs/cdfs, or stats spreadsheets.

>>11587093
pure math is gay

>>11587175
yes and?

>>11587179
I hate homosexuals and things that partake in their nature

>>11587165
Just use R lmao

how should I learn physics? I feel that starting with mechanics and elementary calculus is a long slow road, can I just jump into something more rigorous or advanced? I’m thinking about books like Arnold’s Mechanics, is that realistic? It would shave off a whole year if I could just jump to that level

>>11587087
proofs get fun once u git gud

what do I need to understand gruntz algorithm? It’s used in most modern limit calculators, and I, trying to get through his thesis on it. I didn’t know what a hardy field was initially, for example, and honestly it still isn’t super clear.

>>11586690
How long did Rudy take?

I'm trying to think of a structure that would be a sort of path space.
The idea is to take a topological or metric space and consider all possible paths (here paths is also not certain yet. Maybe [math]C([0,1], X) [/math] modulo reparametrization?).
Then one forgets about the original space and tries to only work with paths. What information can be recovered about the original space?
Can one find axioms that define an abstract path space, and then topological spaces induce such path spaces?
I think we can also give paths a topology by setting the subbasis as [math] U_x = \{paths that contain x\}[/math] for x in X.

I feel like there must be some interesting structure there, because if I have a "map" with areas I can and areas I can't walk on, knowing all the paths lets me recover pretty much the whole map (like shipping lines outline the continents).

>>11587301
Sounds like some [math]\\infty-[/math]groupoids stuff.

Good morning!

>>11587301
Since you have the path concatenation operation, you could indeed modulo out the reparametrisation by taking the homotopy classes of the paths instead? That would still detect holes inside the path component as two paths going around it from different sides would not be homotopic to one another, and path components are pretty much what you would get out of it. For sure, you can recover the set of path components by doing this trick. Your claim about the subbasis is correct (since every path goes through at least one point and so the union of all your [math]U_x[/math]-sets is the whole path space. It could be simplified, though. If you instead set [math]V_x = \{ \gamma\colon I\to X\ |\ \gamma(0) = x\}[/math], you will also get a subbasis by the same argument, but these topologies need not coincide with the usual one (maybe worth checking, but I doubt it). Would they generate the same topology? If you have free time, please check it out.

Just a few quick observations. Have fun, anon!

>>11586075
university rankings are retarded anyway. beyond maybe the top 5 schools, the rest have a very comparable education in most cases.

>>11586215
>(you do want to live there, right? It's the best country in the world after all)

>>11587156
great choices. I do get genuinely angry when people think functional analysis is about the study of "functions" though, it has about as much to with functions as it does with anal

>>11586215
>you do want to live there, right?
Any sane person should realize that they aren't Japanese and will never be.
Obviously Japan is a better country then the shithole I am living in, but that will never make me Japanese...

>>11587387
>it has about as much to with functions as it does with anal
Does it really teach you so much about fucking women/men in their asses?
Never came up in my courses to be completely honest with you.

>>11587409
>they aren't Japanese and will never be
Senator Tsurunen is uncertain about this.

>>11587417
>Senator Tsurunen
If you put white people into Japan it will stop being Japan.
Especially if you give white people political power, that is an awful idea.

>>11587370
Don't know about the latter part yet, but I really don't want to consider paths under homotopy because then I just end up with basic topology again!
I want to have all the paths with all their details and swirls.
Pic related is the idea here: If you know all the paths you can recover information about the space.

>>11587409
>Any sane person should realize that they aren't Japanese and will never be.
I never understood this argument. for countries other than Japan, do you expect to emigrate there and suddenly be treated by everyone like one of their own? this might happen in America, not anywhere else in the world

>>11587419
https://www.youtube.com/watch?v=iZjGEje6hHw

>>11587425
Sorry. I don't speak moon runes.

>>11587430
Tsurunen-sama does.

>>11587420
I see, I see. Sadly I can't give you any ideas for such purposes out of the blue. The subbasis thing may still be worth checking out, homotopy classes or not.

>>11586215
>>Are there good papers that didn't get translated?
>You're kidding, right?
recommend untranslated japanese papers

>>11587422
>treated by everyone like one of their own
What the fuck does that even mean? I seriously couldn't tell you what it means to be "treated like one of their own".

>>11586937
here you go

>>11587434
>Tsurunen-sama does.
Yes, I highly suspected that.
It didn't refute any of my arguments though, namely that white politicians are all terrible and that Japan won't be Japan anymore when it is full of white people.

>>11587444
Does that seem like an attempt to refute it? For me, Japan merely produces entertainment and some maths.

>>11587450
>For me, Japan merely produces entertainment and some maths.
Good for you, but you can appreciate that without moving there...

>>11587461
I'm not interested in moving there.

>>11587463
>I'm not interested in moving there.
So why did you argue with me?
What was your point?

>>11587470
Where did I do that? I only used an opportunity to Tsurunen shitpost.

>>11587474
>Where did I do that?
>>11587417
Claiming that there is a person who would disagree me with me, at least on the surface, seems to me as you arguing against what I am saying.

>>11587477
Read >>11587474. Though I do understand why you would think that is an argument, as the quality of most of the serious online discussions is so low nowadays. For the next time you see his face or name pop up, Tsurunen is a meme.

>>11587481
>Read >>11587474.
I did. And I now am able to accept that you were just meming around, although previously I didn't think so.

>>11587482
Let us depart as friends.

>>11587484
Yes!

What's the next step after linear algebra?

>>11587486
non linear algebra

>>11587486
graduate middle school

>>11587486
What do you want to do?

>>11587488
>>11587489
>>11587490
Actually are there any good books on applied mathematics?
I want to get used to applying these differentials, and I'm very curious how matrices can be used.

>>11587498
if you want to study more about matrices, do matrix analysis (Bhatia, Horn & Johnson), it's pretty fun. if you just want to see how they're used, idk study engineering or machine learning or something. if you want to do more of the abstract linear algebra, progress towards functional analysis (you'll most likely need real analysis and topology first)

>>11587498
>and I'm very curious how matrices can be used.
Applied mathematics doesn't deal with "how this thing is used", it is the study of things that are used in other fields.
Matrices are basically everywhere you can bother looking, from mechanical engineering to machine learning.

Does anyone know what textbook this is from ?

>>11587498
yes my notes on applied mathematics

>>11587539
protip, google exists

>>11587565
thanks, didn't realise I could do that with books

a few months ago there was this mathematician who announced his own death on the discussion page of his wikipedia article. does anyone remember his name?

why figures with the same perimeter can have different areas?

i know they can, but it doesn't make sense

>>11587747
>why figures with the same perimeter can have different areas?
Seems obvious why. Can you not imagine a rectangle?

>but it doesn't make sense
All intuition I have about space tells me that this should be the case.

>>11587781
that doesn't answer my question at all

same perimeter different areas

DOESNT MAKE SENSE AT ALL

>>11584605
If this was now, they would all be glued to their phones & not interacting.

>>11587792
Your question doesn't make any sense.
There are very obvious examples of it not being true, do you want to hear them?

>>11587810
i know there are examples, but what's the underlying reason

>>11587815
>but what's the underlying reason
That question doesn't make any sense at all.
It's like asking "why are Maxwells laws true", there is no answer, except that is just how reality is.

>>11587819
are there metrics/spaces where perimeter defines the area size? what is it about the euclidean space that makes it work it that way?

>>11587831
>are there metrics/spaces where perimeter defines the area size?
It absolutely isn't clear how you would define the perimeter in an arbitrary metric space, neither a definition for volume seems totally obvious.
At least not to me.

But if you chose the right measure you can obviously do it. Look at the definition below and replace lambda with the zero measure, for example.

I mean, it isn't even trivial how you would define the perimeter for an arbitrary set in euclidean space, but you can do, at least for every Borel set E, via
[eqn] \sup \{ \int_E div \ g \ d \lambda : g \in C_{cpt}^1(\mathbb R^n, \mathbb R^n), \sup |g| \leq 1 \}[/eqn]
that formula should make it really obvious that there is no chance for the perimeter of sets to be defined solely through their volume.

>what is it about the euclidean space that makes it work it that way?
Why is 1+1=2? That question is totally meaningless, there is no possible answer.

>>11587156
I've seen bad lists before, but that one looks like it was made by a literal high schooler who just got into /mg/ and thinks he can recommend stuff without knowing anything about them other than the shitposts here
>>11587387
No, it's beyond terrible, I don't even know where to start:
>Serre's book before Aluffi
>Trigonometry book
>Graphs as precalc
>Functional analysis as precalc
>Grauert's book as precalc
>EGA as precalc (you can't read it with only english)
>Adult Rudin as the main calculus book (wtf)
>Jech as the main set theory book (not even researchers in set theory use this book as a textbook, it's a reference)
>Unironically recommending to study IUT
>Awodey for CT instead of MacLane
Holy shit, please never post that list here again, it physically hurt me and some clueless people might think it's actually serious

>>11587895
I'm genuinely serious right now: you might have autism, buddy

>>11587443
That one is a little better but it also has some red flags

>>11587885
>It absolutely isn't clear how you would define the perimeter in an arbitrary metric space
Best I can give you is Hausdorff measure of the boundary.

>>11587444
Oi, fucking retard, immigrants in Japan are less than 1% of the population and if we take out chinese and korean it's even less, Japan will never be 'full of white people', but there will always be some who'll want to live there and their numbers will never amount to anything significant that could change the face of the country, your post is retarded alarmism and you're a dumb piece of shit

>>11587486
Kolmogorov or Roman then AlgGeo

>>11587932
I am just pointing out the contradiction.
You wanting to live in Japan inherently makes Japan less Japanese.

Also, again, white people make terrible politicians.

>your post is retarded alarmism and you're a dumb piece of shit
Without a doubt they said the same about my country, but evidently the alarmists were right.

I just started doing the chartrand proof book.
Are you supposed to do every exercise for every sub chapter?

>>11587947
How could a group that amount to less than 1% of the population make Japan less Japan? Dude, it's less than fucking 1%, and this number isn't growing because immigration laws are strict, and even though their population is shrinking they're not making immigration any less difficult, again that very small group will always exist and will change absolutely nothing in how Japan is

>>11587947
>Also, again, white people make terrible politicians.
It's more the fact that liberal, capitalistic democracies foster awful politicians — they're backed by the corporate world and have no real reason to listen to the people. Latin America is just as much as a joke in that sense, and the more conservative East seems like it has some exceptions at least.

>>11587955
I'm doing every exercises for every section of Velleman's How to Prove It

>>11587904
I suspect I do have asperger but never did any tests

>>11587966
>Dude, it's less than fucking 1%
in 10 years:
>Dude, it's under 5%, relax
in 20 years:
>Dude, it's 10%, nothing's gonna change
and in half a century you have another Europe. fuck off, everywhere's full.

>>11587966
>>11587966
>How could a group that amount to less than 1% of the population make Japan less Japan?
You are missing the point entirely.
There is an inherent contradiction between the things you want.

You obviously want to become assimilated into Japanese culture, but the more tolerant Japanese become of foreigners, the more foreigners will come.
OBVIOUSLY your own individual actions make no difference at all, there is just an inherent internal contradiction among emigrants and people who want to emigrate.
Simultaneously they want to do something which at the same time is nullifying what they wanted to begin with.

>less than 1%
The point is that you want that number to grow.

>>11587970
>liberal, capitalistic democracies
That's a white people thing.

>>11587993
Except Japan and japanese people are too conservative to allow that number to grow to 10%. Also, even though Europe faced waves of immigrants they still amount to less than 10% in almost all countries, even in Sweden their number is not that big

>>11584605
Did my professor miss any steps or am I just retarded?

>>11587991
Good, nothing will change after getting the diagnosis anyway. Everyone including yourself already knows your weird.

>>11588008
Yeah, maybe that's why people bully me on college

>>11587895
Out of curiosity, did you not notice those toxic women's studies and queer theory sections? They should make it obvious that this list is a joke, and thus makes one immediately question whether the other books are serious picks either.

>>11588021
>toxic

>>11588018
Actively bullying or just getting left out? I think im wrong about the no reason to get tested thing. Maybe it helps you cope and come to therms with your own personality.

>>11588005
>Except Japan and japanese people are too conservative to allow that number to grow to 10%
The exact same thing could be said about the Germans in the 50s...

>Also, even though Europe faced waves of immigrants they still amount to less than 10% in almost all countries
You are missing an important thing here. That in Europe you have already generations of immigrants and those second generation immigrants aren't technically immigrants at all.

>less than 10%
Firstly in Germany there are 8% of *foreign nationals* that means people who have no German citizenship. But that obviously does not include people who already became German nationals.
In fact if you look at the major cities roughly 30% of the population have a "migration background".
(source https://de.wikipedia.org/wiki/Migrationshintergrund#Statistik))

If you want to tell me that the place where I live can still be considered "German" in any way except that it is geographically inside the region that is administered by the German government you are deluded.

>>11587998
>You obviously want to become assimilated into Japanese culture
Who says so? A westerner will never be assimilated to japanese culture, only retarded weebs believe that, there will always be lots of people who'll give you bad stares, but so what?
>but the more tolerant Japanese become of foreigners, the more foreigners will come.
That's not happening in a bigger scale, in fact, even the majority of those who live daily with foreigners probably have some pretty bad opinions on immigration in general, they just 'accepted' (as long as he's useful) very few.
>Simultaneously they want to do something which at the same time is nullifying what they wanted to begin with.
Where's the contradiction? Foreigners want to start a better life in a new place most of the time, how does this contradicts anything? Unless you're implying foreigners somehow 'destroy' the places they immigrate to.
>The point is that you want that number to grow.
Never said that, I want it to stay the same and I want to be part of it someday. Anyway, the reality is that Japan is extremely conservative and anti-immigration and that won't change in the next decades, but there'll still be immigrants that will amount to nearly nothing in the demographics of the country.

>>11588021
>toxic women's studies
Are there non-toxic women's studies?

>>11588021
I did, but somehow my autism made me believe it was serious
>>11588033
All kinds. Where can I do a test?

>>11588043
Im not a burger, but id say visit a psychiatrist that specialises in (adult) autism. Maybe your uni offers some counselling.

>>11588038
>Who says so?
I thought that was the premise of the discussion?
And you say the same thing a few lines down? " I want it to stay the same and I want to be part of it someday"

>That's not happening in a bigger scale, in fact, even the majority of those who live daily with foreigners probably have some pretty bad opinions on immigration in general, they just 'accepted' (as long as he's useful) very few.
Great!

>Unless you're implying foreigners somehow 'destroy' the places they immigrate to.
No, they just turn the place they are living in into the same thing they had at home, just with higher standards of living.

>I want it to stay the same and I want to be part of it someday.
But you being part of it, inevitably changes it.

>>11588043
In that case I would definitely suggest getting the diagnosis. For example this first: https://www.clinical-partners.co.uk/for-adults/autism-and-aspergers/adult-autism-test and then you can go talk to someone with some pre-existing data to cite.

>>11588035
Germany is still Germany bro, you're out of your mind, go outside and count how many white people and how many immigrants are on the street, /pol/ os rotting your brain man. Also, that's life man, cultures die, nothing lasts forever.

"The Wheel of Time turns, and ages come and pass, leaving memories that become legend. Legend fades to myth, and even myth is long forgotten when the Age that gave it birth comes again."

>posts anime
>has autism
Yep i think that checks out

>>11588061
Oopsie, 28/30 for me...

>>11588063
>go outside and count how many white people and how many immigrants are on the street
40% people with migration background 60% Germans, I would guess, a bit further down the street it's reversed.

Again, for the whole city it's 30%, but I live in a poorer area.

>Germany is still Germany bro
In what way except that it is being administered by the same institution.

> cultures die
Yes. But that doesn't mean I should be fine with seeing everything I could ever love dying around me.

>"The Wheel of Time turns, and ages come and pass, leaving memories that become legend. Legend fades to myth, and even myth is long forgotten when the Age that gave it birth comes again."
Can you PLEASE not cite very shitty fantasy books as an argument.

>>11588047
>>11588061
Would it change anything in my life though? I don't really feel anything about it, just curiosity.

>>11588095
Depending on where you are an autism diagnosis makes you elegible for extra gibs and a free accountant to handle taxes for you

>>11585258
same boat man, jesus. If you know grad students or can still rope a prof in, ask them about something remote and get a local job too? That was my move at least, I'm collaborating with a grad student bud on something instead and just tryina work at a record store or something in the rest of my time once the world opens up again.

>Let [math]C[/math] be a closed set in a normed space, and let [math]\mu[/math] be a probability measure supported on [math]C[/math]. Show that [math]\int_{C} x \,d\mu(x)[/math] is in the closure of the convex hull of [math]C[/math].
How can I show this? I can definitely see this if [math]\mu[/math] is a discrete probability measure like [math]\sum_{i=1}^\infty p_i x_i[/math], but don't know how to proceed in the general case.

>>11588085
I'm not there but I dount it's that much, not even Sweden is like that.
>In what way except that it is being administered by the same institution.
C'mon, what's really changed?
>Yes. But that doesn't mean I should be fine with seeing everything I could ever love dying around me.
You should love people, not abstract concepts like 'culture'
>Can you PLEASE not cite very shitty fantasy books as an argument.
>Calling the Wheel of Time shitty
Now, I'm convinced you're retarded, I'll stop derailing the thread, so this is the last post directed at you.

>>11586075
Fuck that dude, anyone who's tryina turn mathematics into flexion is a fucking idiot and you're living a healthier and more enjoyable mathematical life for not being that asshole. Plus, what he's saying makes no sense anyway lol, so fuck it. Shit sucks, but you're killin it man.

>>11588100
Holy fuck, that's true, thanks.

>>11588105
Did you try approximating with simple functions?

>>11588084
Can also be social anxiety, being shizoid or whatever. Get it tested to know "for sure" and generally dont associate yourself with "being aspie" too much imo.

>>11588095
Depends on the case. Some thing a diagnosis might give you:
1. government gibs
2. clarity
3. feel better about yourself. There is a reason for past failures, maybe helps with bullying when you tell them that youre aspie
4. access to a therapist where you can discuss things and coping strategies
5. Under circumstances comes in handy when applying for a job if they want to meet a quota

>>11586075
Seems retarded since the factors these rankings are based on might not even affect you or the quality of your teaching directly.
A better comparison if you want to compare dick size is comparing what you are doing vs the classes he is taking.

>>11588095
It could help you understand yourself a bit better, and provide you help with difficulty in social situations. Not necessarily a salvation of any sort, but perhaps helpful.

>>11588105
finitely supported probability measures are dense in all probability measures

>>11588112
math is so boring that flexing is the only enjoyable thing you can do with it
having said that, I agree that there isn't much difference between schools and the rankings mean jack shit

>>11588084
24/30 here, strong likelyhood

>>11586944
AG Probably like Hartshorne, but I like Vakil more for self study. Functional Rudin? Haven't read tho people just hype it up.

>>11588108
>but I dount it's that much
What?
I literally showed you the Wikipedia like where it says that it is around 30% in the whole city (in 2011!!): https://de.wikipedia.org/wiki/Migrationshintergrund#Statistik
How hard to believe can it be that it is 40% in a poorer are, where I live? And even more in some other areas?

>C'mon, what's really changed?
Have you ever been abroad in a country where everybody is totally different from you, they look different, speak a different language and in general aren't really tolerant of outsiders?
That is how I feel going outside far too often.
Also having to deal with the Somalis trying to sell me drugs on the way to University, and the one time some Albanian gang committed a drive by shooting on the way to my University aren#t exactly "fun".

>You should love people, not abstract concepts like 'culture'
A culture is just a way the people around you express themselves. Also there is no culture here, at least you won't find any unless you try really hard.

>Now, I'm convinced you're retarded
I read the first 100 pages of the first book and dropped it hard.

>>11588116
>>11588122
shit of course. thanks

>>11588131
Hartshorne is too hard as an intro to AG, one should start with Shafarevich or Ueno. For functional analysis Folland is the gold standard.

>>11588130
Either get a real Diagnosis or fuck off, these questions fit any introverted shy shizo young male. Yes im gatekeeping autism, but especially in online Communities like 4chan where its cool to be "autistic" so many people self diagnose with these bullshit questionaires.

>>11588108
>You should love people, not abstract concepts like 'culture'
not him, but oof
Honestly, you don't get how much a difference a close knit culture (and I don't mean an artificial suburbia culture or something of the like) can make unless you're a part of one. I've met people who I never knew from anywhere that treated me like a son because I shared some culture with them. It's a very warm feeling. Once you've felt it you'll feel empty every second without it.
I genuinely feel bad for all the american mutts I'm surrounded by. they really won't arrive at such a feeling with any ease

>>11588158
Oh, how very sad, the white man won't have his 'warm feeling' anymore, maybe we should let those immigrants die in war or starve, at least that way we might preserve this 'warm feeling', am I right?

>>11588184
what the fuck are you on about m8

>>11588150
It's not cool to ne autist here, in fact one of the reasons Resetera hates 4chan is because of the autismphobia here

>>11588184
Jealous minority, please get out.

>>11588120
>Can also be social anxiety, being shizoid or whatever
this
I tested high on one of those autism self tests and high for shizoid on another self test
frankly I don't care to find out which it is, but it's fairly intuitive why they test false positive for each-other

>>11588141
>For functional analysis Folland is the gold standard.
reading Folland is masochistic. I really don't know why people like it.

>>11588184
>maybe we should let those immigrants die in war or starve
Not a single Immigrant from the Middle east came to Germany because he fled from war or starvation and that should be obvious from just looking at a map.
They already went through multiple totally safe countries with no food shortages, but instead of staying there and waiting till their countries would become safe once again they choose to move on.

And in fact most immigration into Germany was exclusively the result of economic Immigration, which Turkey, with support from the US, forced upon West Germany.

>>11588184
honestly, modern whites are the group most lacking in this sort of culture except a few groups
if you're indian or some shit you immediately pick eachother out from a crowd and associate with eachother. that level of culture exists so casualy
for them like water to a fish
I think that's why modern whites dive into sub-cultures. they don't feel comfortable identifying themselves as white (which makes sense, "european identity" on a broad level doesn't exist and is a /pol/ meme)

>>11587156
local fields made me kek the most

>>11588188
>>11588196
How utterly fun to see europeans desperate because their 'culture' is dying, guess what, you've destroyed all all countries you've been into, stole their riches, waged war in their lands and now you're trying to pose as the innocents here hahaha, it's too funny man, I can't help but laugh at the hypocrisy of the white men.
>Warm feeling
Let me guess, you're desperate for affection, so when someone shows you a little bit of it you cling to them and justify it under the guise of 'close knit culture', what a joke, if you ever gave a fuck about that 'warm feeling' you'd want this to be felt and expressed by all people, not only the ones in your dying culture.

>>11588217
you don't pick out white people from a crowd because you live in a white country... there absolutely is a sense of "european identity" among, say, expat groups in foreign countries. it's so much easier to get along with people with a similar culture.

>>11588006
they changed to cylindrical polar coordinates

>>11588220
>if you ever gave a fuck about that 'warm feeling' you'd want this to be felt and expressed by all people, not only the ones in your dying culture.
except that just doesn't work
if people identify themselves as an other they're automatically another culture. if you're trying to connect to everyone and they're not you'll just end up feeling rejected socially. Culture must be mutual.
If you want that human culture you'd essentially need to get people to stop identifying with anything, which isn't going to happen

>>11588220
no one's trying to pose as innocents, we just want you to fuck off.

>>11588217
>I think that's why modern whites dive into sub-cultures. they don't feel comfortable identifying themselves as white (which makes sense, "european identity" on a broad level doesn't exist and is a /pol/ meme)
But you don't have to identify as "white" (which indeed is mostly a meme) to identify with a regional culture and the point is that whites usually identify either with (totally banal) "sub cultures" or even with foreign/"exotic" cultures.
To me the "I wan't to live in Japan weeb" and the "wannabe gangster" (which in the US is an association with African American culture and in Europe with Arab culture) are both the result of that exact phenomenon.

>>11588220
>not only the ones in your dying culture.
Exactly, I believe in homelands for all people's. I would be the last person to deny Arabs to live out their culture in Arab countries and I wish nothing more then for white people to leave the rest of the world alone, *especially* Africa.

>you've destroyed all all countries you've been into
That is just false.
Whites came to Africa and Japan with the exact same intentions, but somehow one of them ended up differently for miraculous reasons.

>>11588222
fair enough, but that's why i said in a broad sense. something like "being french" is better defined (except perhaps in france as i'll mention in a bit)
european identity can only become apparent when compared with some other culture. when being european is the standard it isn't a carrier of culture.
just like in a homogeneous nation regionalism dominates nationalism in domestic contexts because national culture is just the water you swim in.

>>11588225
You're advocating for racial segregation under the guise that people will build a 'close knit community' in that way or will make them feel more connected, you're no better than a nazi if you think that. Anyone who actually cares about people would be trying to show love to anyone no matter which race or culture.

Also, you're on /sci/, so unless you post actual scientific studies about shit like
>Culture must be mutual.
If you want that human culture you'd essentially need to get people to stop identifying with anything, which isn't going to happen
I won't simply be convinced
>>11588227
And I wanted you to gtfo my country during the 1500s, but you didn't, so you reap what you sow I guess.

>>11588257
>Anyone who actually cares about people would be trying to show love to anyone no matter which race or culture.
by that standard most people do not care about people

>>11588242
right, I never felt European when I lived in Europe (where nationalism/regionalism overtakes pan-Europeanism, with the latter pushed only for political purposes by various groups), and I used to dislike the concept of a European identity. but since I moved to Asia a few years ago I've absolutely started to feel how similar I am to, say, a random French person on the street compared to most other people around me. it really changed my perception of a European identity, even though I still won't hang out with fucking Frenchies

Hey I'm trying to find the basis of the intersection of two subspaces.

I found the basis of each vector space. Combined them by setting them equal to zero and row reduced that. Now I have a matrix with 3 free variables and I'm not sure what to do. I know the dim of the basis is 3 from finding dim U+V. Is the free variable columns just my basis vectors? How do I proceed.

>>11588260
No shit, Sherlock, most people don't give a fuck about anything or anyone other than themselves and their children. But this is especially true with white people, they're by far the most individualistic, hypocrit, petty of all races.

>>11588257
>Anyone who actually cares about people would be trying to show love to anyone no matter which race or culture.
But this is just absurd.

You do not care more about a random stranger then about your mother, or the rest of your family and it is the same for the rest of the world.
Nobody cares about everybody the same and "if you love people" you should care about the ones closest to you.

>1500s
Which country?

>>11588257
>You're advocating for racial segregation
where?
>under the guise that people will build a 'close knit community'
those cultures already exist

people can associate with whoever they like, it's just that people like to associate with people of similar interests, background, and of mutual care. ie a people that share their culture

>>11588269
>Now I have a matrix with 3 free variables and I'm not sure what to do.
You solve the system and the solution should tell you the basis.

>>11588271
people care about things at different levels, that's hardly particular to whites, like >>11588275
said. it's natural that one cares for ones family, then for oneself, then for one's associates, etc
people are going to care more for people they feel close to, people they share a culture with
find me a single person on earth that genuinely loves everyone equally

>>11588275
>You do not care more about a random stranger then about your mother
I might care more about my mother, but I do care about that random stranger, I'll always show love to anyone no matter which race, taste, culture etc. You're just trying to justify your egocentrism.
>Which country?
Brazil
>>11588276
>it's just that people like to associate with people of similar interests, background, and of mutual care. ie a people that share their culture
And why can't a black man have the same interests, background and mutual care than an european?

>>11588257
"your race invaded my country 500 years ago, therefore I have a right to live in a white country" is one of the stupidest arguments that I have heard in my life

>>11588269
If you orthonormalize the base for U or V you can compute the projections of U onto the span of V or vice versa.
Then, the span of the projections is the intersection.
>>11588287
WAAAAAA WAAAAAAAAA MUH EUROPEANS
Vai se fuder maluco.

>>11588288
It's not that I have a right to live in a white country, it's just that you can't complain, bunch of hypocrites.

>>11588287
>And why can't a black man have the same interests, background and mutual care than an european?
save for background, they very well could have all of that
not all forms of culture exists on racial lines
that fact was in my first post in this reply chain "[the american mutts] won't arrive at such a feeling with any ease" ie they aren't born into a culture, it's implicit in that statement that they could make effort to adopt or form one

>>11588290
>WAAAAAA WAAAAAAAAA MUH EUROPEANS
>Vai se fuder maluco.
Vira-lata achando que é gente.
Stray dog syndrome

>>11588293
shoulda fought harder 500 years ago, now watch while we make you live in ghettos and eventually force you out of our countries back to your shithole

>>11588293
eye for an eye, eh?

>>11588299
Heh, go tell that to Merkel, Macron, Johnson. You're deluded. Also I can say the same to you then stop complaining on the web and 'fight harder'

>>11588287
>I'll always show love to anyone no matter which race, taste, culture etc.
I think you are confusing respect with love.

>You're just trying to justify your egocentrism.
Yes. Caring for the people I love is without a doubt egocentrism, why wouldn't it be?

>And why can't a black man have the same interests, background and mutual care than an european?
The answer to that question is that obviously he could, but just as obvious 99% of Africans do not.

And the point isn't that there can never be a well integrated Arab or African who fits perfectly fine into a European society, the issue is that *as a matter of fact* almost none of the blacks and Arab who live in Europe do.

>>11588293
>it's just that you can't complain
Why not?
Why can't I complain, because the grandfather of my grandfather of my grandfather of my grandfather of my grandfather of my grandfather of my grandfather shared a continent with someone who invaded "your" country.

>>11588317
You know nothing about love. I feel sorry for you.
>>11588322
You're a hypocrite if you complain, that's all, not that it matters, complaining or not your country will eventually become more and more miscigenated

>>11588340
>You know nothing about love.
I know nothing about love because I care about the people who care close to me?

>You're a hypocrite if you complain
Why?
What makes me a hypocrite? I seriously don't get it...

>>11588342
>I know nothing about love because I care about the people who care close to me?
Because you somehow think that one can't have love for others who aren't close. There was a man called Christ who proved you wrong 2000 years ago.
>Why? What makes me a hypocrite? I seriously don't get it...
You're fine with your country destroying other countries but you're not fine with other countries doing the same the yours. That's hypocrisy son, who do you think finance the wars in the middle east? Who 'enforces' democracy in asian and latin american countries? Who steals all the riches from Africa? Pro tip, starts with white and ends with people.

I know some one here has done the chartrand proof book because it was recommended here to me so im asking: Why are their only answers to the uneven numbered questions?

jesus what a fucking dumpster fire of a thread

>>11588353
Most books are like that, actually most books don't even have answers at all. If you want an equally good book with all answers available, read Velleman.

https://www.inchmeal.io/htpi/

>>11588353
This is fairly common practice in lower-level textbooks (in any field, not just math). It's an attempt to have a balance between having solutions to check your work and not having solutions so the prof can assign homework questions from the book.
It also has the minor benefit of making the books less fat. Solution sections would be all 100+ pages if they had answers to every single problem.

>>11588351
>You're fine with your country destroying other countries
I distinctly remember saying the exact opposite? See >>11588241
What did I say that made you believe that I advocated for foreign involvement of my country?

>Because you somehow think that one can't have love for others who aren't close.
My grand mother died a few moths ago. How much did you cry for her?

>There was a man called Christ who proved you wrong 2000 years ago.
Even supposing your Christian basis, clearly Jesus Christ wasn't just "a man", he was literally god and while it is certainly imaginable that god loves all people, claiming that you do (without having anything to show for it) reeks to me of blasphemy. As you are literally placing yourself next to Jesus Christ.

NEW THREAD >>11588370

>>11588373
>279 replies
>:(

>>11584605
Those are some peak jawlines

>>11588676
>>11588699

>>11588711
yeah, well, y'know, people have starting new threads earlier and earlier recently and...

>>11586863
just pick an element at random and see if it's outside of the span of the basis
dont ask me how to pick an element

>>11586147
No GF. Ever.

Who's got an Erdos number? I trying to get me one of those. Don't be shy, I know you're reading this.

>>11589744
Mine is 4, AFAIK.
You're going to get one automatically as soon as you coauthor your first paper with your advisor. Anything higher than 2 is basically just your "welcome to math" ribbon.

Seriously, guys, pay attention
NEW THREAD >>11588370 #

>>11589799
nah

>>11589811
NEW THREAD >>11588370 #

>>11586414
no lines - pinch it in the middle, joining A and F together, the rest is already connected by the frame

>>11589849
so you say, but is this true?

>>11587229
Just use Julia lmao

https://www.youtube.com/watch?v=BipvGD-LCjU

/mg/ anthem?

>>11589893
>>11589886
>>11589875
>>11589871
NEW THREAD >>11588370 #

>>11590966
nah das lame

Is anyone having issues studying mathematics outside of uni environment/without peer pressure? If so, how do you approach this?

>>11592407
Wake up at a good time, shower and get dressed. It helps to put you in the mindset of work.

>>11590966
nigger

>bump

>>11593170
Three /mg/ threads at the front page, based

>>11593182
absolutely based

well boys, we did it, we lasted longer than the /mg/ which came after, proud of you

>>11594843
realest coo/mg/uzzlers in this thread, report in

>>11594851
yuh

>>11595131
/mg/ never dies

>>11584807
There are lots of countries which are not soulless mutt colonies that have stupendous english, faggot.

>>11585138
Not him, but integrate 1/x^2 from 1 to n.

>>11584798
I'm going to start using this analogy