/sci/ - Science & Math

I just trained my body to think about math, instead of sleeping, when I'm on my bed.
Since a few weeks ago, I have been stuck with this problem (for my research) and I always thought about its details before I started to sleep on my bed.
Sometimes I got new ideas, sometimes I was wrong (duh). But generally it's not very efficient.
I didn't realize it at first. Then in the past 2 days, I can't put myself to sleep and all I think about are fucking math.
I needed to take melatonin to sleep.
Don't be like me.

>>11761654
How do we know Cauchy sequence for [math]\pi[/math] if we don't know every digit and therefore we don't know every term of the sequence?

>>11761684
we don't - in fact it's one of the greatest unsolved problems in mathematics

>>11761684
Please give an example of a digit that we do not know. Protip: they do not exist.

What do I need to learn if I want to DESTROY the putnam?

>>11761687
But [math]\pi[/math] is proven to exist, in fact every irrational number is proven, using this Cauchy sequences although we don't know every digit from every irrational number. We only know that the cauchy sequence for that number starts something like (3,3.1,3.14,3.141,...) But that is only how it begins, we don't really know what is this sequance really is? We are assuming that it is not (3,3.1,3.14,3.141,3.141,3.141,...) the sequence for the rational number 3.141, then how are we so confident that [math]\pi[/math] exists and belongs to the system of real numbers?

>>11761701
the first thing you must learn is how to use google instead of whining to be spoonfed every thread

How can Graham be such a chad?
Is he the ultimate /fit/ + /sci/ dream?

>>11761718
a pretty substantial proportion of the real top-level mathematicians are also chads
positive traits tend to pile up in people. trading one for the other instead of having it all is what the alphas one tier beneath the true chads do

>>11761700
Only 3-4% of digits of pi are known to mankind. In fact the mathematicians suspect the rest of the number pi is made up of so called "dark digits" and "dark numbers", which were first introduced by Terence Tao.

>>11761684
what do you mean we don't know every digit ? we absolutely do know every digit

>>11761726
I feel like top mathematicians are either chads or autists. There's no inbetween.

>>11761659
I already am. Thinking about stuff till 1-2 o'clock, waking up at 6-7 hoping not all the ideas I have written down are completely stupid. At least it beats thinking about life in general.

>>11761729
You speak of dark numbers, but do you know the darkest of them all? It is the black dot on white in the Yin-Yang symbol, an anti-sun in the middle of light.

>>11761709
Not that anon but you're wrong.
>We only know that the cauchy sequence for that number starts something like (3,3.1,3.14,3.141,...)
There is no one Cauchy sequence for pi, there are infinitely many. One starts like (3,3.1,3.14,3.141,...), another like (1,0,99129391,-2312323,222,...), another like (0,0,0,0,....).What you said is mathematically meaningless/trivial.
>>11761684
>How do we know Cauchy sequence for π
We know many many equivalent Cauchy sequences for π. Two of them are:
1) a_n= sqrt(6 sum_k=1 ^n of (1/k^2))
2) a_n = 4 sum_k=0^n of (-1)^k/(2k+1)
We know them completely: given any position we can algorithmically compute the n'th term in the sequence.
There are even spigot formulas that let you explicitly find the n'th digit base 16 of pi without reference to previous digits.
Your premise is invalid.

Don't you hate it when you spend 6 hours thinking about a problem, stuck in tunnel vision, writing the same thing over and over again, expecting your mind to notice something new, when finally you realize all it took was a simple change of perspective that renders the whole problem trivial?

>>11761770
>don't you hate it when you solve a problem
no.

bros... i have been doing maths today... for the seventh day in a row

I'll study algebra now and I won't give up until I fucking master it!

I feel like the biggest thing I lack right now in maths is the sense of rhythm. I have the tendency to bite more than I can chew, not just in maths but with everything in life. What inevitably happens is that I go far enough into a book where the whole structure of the concepts just starts to fall apart because I haven't spend enough time on it. Everything starts to look stupid, I burn out and not read for a long period of time.

>>11760764
"We named it College Algebra because we couldn't have named it The Algebra You Should Have Learned in High School"

>>11761654
>>11761358
diffeq poster from previous thread. Ive skimmed through the rest of the book and the notational frickery with differentials seems to only occupy the first chapter of the book, rest of the material is fine. seems weird to introduce it in the beginning, it makes things confusing if you are beyond any analysis I, especially that they drop it in further chapters.
It also accompanies examples related to physics so maybe thats their thing.
Thanks for reading my blog, I decided to type this for no substantial reason other than satisfying the urge to talk about it to someone who understands this.

Is applied math good? Would I be able to get a field medal?

>>11761770
I know the feel, but some say it's part of learning.

>>11761783
After a week you are no longer weak!

>>11761789
Show us what you are made of!

>>11761824
I sometimes binge read and then return to the chapter from which I started. Then I re-read it properly, proceed to the next one which I will read somewhat properly, and then return again to the starting chapter. After a sense of confidence, justified or false, has been obtained, I move to the next one and do the same kind of back and forth movement and so on. Have you tried this? And exercises should be solved/tried if the book has them.

>>11761684
We know several predicate definitions characterizing an effectively computable sequence of digits. That's what a computable real number is.
(Although note that not all numbers are definable and of the definable ones, not all are computable like pi is.)

And if we say "a number that's not definable", one must of course recall that we're just talking about symbols on a paper, and concepts of sets of individuals is a notion independent of those individuals being accessible, i.e. it's a game.

>>11761777
based and checked

>>11761912

Applied math is solved. You may use it to get a medal in other fields tho.

>>11761938
>And if we say "a number that's not definable", one must of course recall that we're just talking about symbols on a paper, and concepts of sets of individuals is a notion independent of those individuals being accessible, i.e. it's a game.
i've been trying to read this sentence for a while. i am very confused. some word association vagueness is telling me you probably think about math in terms of dialogical games https://plato.stanford.edu/entries/logic-dialogical/
this is as far as i got

>>11761729
>3-4% of infinite
hurr durr

>>11762005
In the second half of that sentence I was more giving a framing of math akin to
https://plato.stanford.edu/entries/formalism-mathematics/

Incidentally, this also refers to the word game right in the first sentence.
But I mostly said it to trigger Platonists.

The first half can be informally be made more concrete as in..

Fix a finite language (say ascii characters that we can use on 4chan, which translate to some byte code) and enumerate all sentences in that language. Let [math] \Delta(r) [/math] express when the expression [math] r [/math] in the language defines a unique real number.
Such as you get when you break down [math] 2 \int_{-1}^1 \sqrt{1-x^2}\,dx [/math] (e.g. defining [math] \pi [/math]) to expressions in our language.
Let [math] D = \{ x \mid \Delta(x) \} [/math] by all definable numbers.
The set [math] U = {\mathbb R}\ D [/math] has the cardinality of [math] \mathbb R [/math] but no elements of this "set" can be stated. Or arguably, none of the elements of U can individually be conceived.

(Caveat, [math] \Delta [/math] is not definable by Tarski, at least not on the first/immediate logical level of anaylsis.)

A collection is conceptually always a collection of individuals. But here the individuals of [math] \mathbb R [/math] need a theory of collections to be defined, which a would find not pretty. If you care about such consideration but aren't a wild Burger, you can back up and say well it's just symbols moving, I never meant "set" to mean "set" in some ontological sense. Math is a game of moving characters around on a table here.

[math] U = {\mathbb R}\setminus D [/math], all of the reals except the definable reals.

[math]\mathbb{C}^2[/math], the simplest area of several complex variables

>>11762159
Sounds extremely likely.

|- E. y ( x e. y /\ A. z ( ( z e. y -> E. v ( v e. y /\ A. w (
A. u ( u e. w -> u e. z ) -> ( w e. y /\ w e. v ) ) ) ) /\ E. w ( (
w e. z -> w e. y ) -> ( A. v ( ( v e. z -> E. t A. u ( E. g ( g
e. w /\ A. h ( h e. g <-> ( h = v \/ h = u ) ) ) -> u = t ) ) /\
( v e. y -> ( v e. z \/ E. u ( u e. z /\ E. g ( g e. w /\ A. h ( h e.
g <-> ( h = u \/ h = v ) ) ) ) ) ) ) \/ z e. y ) ) ) )

>>11762243

>gauss's perfect proof

>>11762243
This is the sound my dog makes when she throws up

mathlet here
for what values of [math]n[/math] is [math]2np+n^2[/math] a square for some prime [math]p[/math]?

>>11762327

2np + n^2 = (n + p)^2 - p^2

>>11762327
n = 0

>>11762336
are you trying to helpfully guide me towards the answer because i warn you im too stupid for that
>>11762337
ty this was what i wanted thanks

>>11762341

it's a factorization trick to get a notable product:

You notice 2np + n^2 just lacks the p^2 term to be the (n+p)^2 expansion. So you then add p^2 - p^2 to the expresion and then factor it to (n + p)^2 - p^2.

>>11762350
but i still dont see which values of n make it a perfect square

>>11762354
Hint: D********* o* s******

>>11762350
>>11762359
This is a very dumbass convoluted way of saying "factor the n out"

>>11762359
(n+p)^2-p^2=(n+p+p)(n+p-p)
n(n+2p)
>>11762366
please dont be rude i just want help

>>11762366
this is why there is something more teaching that merely being too stupid for research.

>>11762370

you got the answer senpai

So when is n(n+2p) a perfect square?

>>11762150
i get what you meant now, this would certainly trigger platonists.
>I never meant "set" to mean "set" in some ontological sense. Math is a game of moving characters around on a table here.
i think this is probably close to my actual opinion.
i sympathize with the desire for simplicity that drives people to systematically define all of the mathematical terms, and then define all the terms used in the definitions(and so on recursively); but i think the people who are by temperament most compelled to engage in that sort of work are often the people who do it unreflectively, and the most extreme cases are the ontologists. they're just chasing dopamine highs.

>>11762337
[math]\sqrt{0}[/math] is the best prime.

>>11762370
Now that you [math]n(n+2p) = q^2[/math] for some prime [math]q[/math], you have either [math]n=1[/math] or [math]q[/math] dividing both [math]n, n+2p[/math] (try to figure out why). If we assume that [math]q[/math] divides them both, then [math]n=aq, n+2p = bq \Rightarrow q^2 = n(n+2p) = abq^2 \Leftrightarrow a=b = \pm 1[/math], but then [math]n = n+2p \Leftrightarrow p = 0[/math], not nice. Thus, [math]n=1[/math], and so you should now try to check if [math]q^2 = 2p+1[/math] makes any sense. (I hope I didn't make any dumb mistakes)

>>11762407
>ontologists
?

>>11762428
so the only possible (nontrivial) value is 1? tyvm anon, that helps a lot

>>11761654
when did math get hard in school?
what was the thing that actually kinda substantiated people's claim that it was a hard subject?
I basically breezed through math all of school so I don't really get it.

>>11762327
>>11762444
No.

There is exactly one even solution [math]n = 2\frac{(p-1)^2}{4}[/math] for every p (odd p, at least). For example, if p = 7 then n = 18 gives you 2np+n^2 = 24^2

Pretty sure there are no odd solutions.

also n = 0 works.

>>11762444
There's a reason why I suggested you'd try seeing if that makes any sense. Namely, if you try that with [math]p=[/math] some small prime like 2, 3, 5, 7, 11, 13, 17 or 19, you don't get anything reasonable out of that (reasonable in our context, that is). Let's for example try 13. We would get 27, but that is not the square of any integer, and in particular not the square of any prime. Maybe it could work for some bigger prime, but I am feeling too lazy to find out. I could very well be wrong, though. I'm bad with numbers. n=0 doesn't work because 0 is not a prime.

>>11762452
For me it was when equations were introduced. It took me months to understand that multiplying both sides by 0 is not a valid method to solve them. I guess that is an example of how violence doesn't solve problems but removes them.

>>11762327
>>11762400
Let's say [math]n^2 + 2np = k^2[/math] for some k, then
[math](n+p)^2 = k^2 + p^2[/math]. So we have a pythagorean triple [math](n+p, k, p)[/math], if p|k or p|n then there are no solutions, so it suffices to think about the case when this is a primitive pythagorean triple.
In fact, if you have any pythagorean triple involving p, let's say [math]x^2 + p^2 = y^2[/math], this gives you a solution of the original equation, just take k=x and n=y-p. So it is enough to ask yourself "what are primitive solutions to a^2 + b^2 = c^2 where a or b is a prime".
Now if you look up "primitive solutions to the pythagorean diophantine equation" you will get the answer quickly.

>>11762456
>>11762463
>>11762468
good thing im an engineer or i'd feel pretty discouraged right about now
thanks for the help guys, im gonna go back to playing vidya

>>11762470
Have fun!

Is [math]SO(n)[/math] sufficient to generate the full [math]n-1[/math] sphere, or do I need the full orthogonal group?

In symbols, I suppose this could be restated as, for any fixed [math]x \in S^{n-1}[/math], is it true that the orbit [math]SO(n)(x)[/math] equals [math]S^{n-1}[/math]? If so, how do I understand the fact that I don't need reflections to hit every point on the sphere?

I ask this because the wiki page on spherical measures demonstrates the relation because measures on [math]S^{n-1}[/math] and [math]O(n)[/math], but it seems equally valid to relate the spherical measure with the Haar measure on [math]SO(n)[/math] in exactly the same way.

>>11762336
>>11762444
You want
(n+p)^2 - p^2 = m^2 for some n,m
Rearranging,
m^2 + p^2 = (n+p)^2.
Then we either have (by the theorem on pythagorean triples: LOOK IT UP ON WIKIPEDIA)
(CASE 1)
m=a^2 - b^2
p= 2ab
hence
a=b=+- 1 in which case the solution is trivial or (CASE 2)
m=2ab
p=a^2 - b^2=(a-b)(a+b)
n+p= a^2 + b^2
a-b=1 and 2b+1=p
n+p = a^2 + b^2 = b^2 + (b+1)^2 = 2b^2 + 2b + 1
so the answer is: express p as p=2b+1 for some integer b, then get
n=2b^2 + 2b + 1 - p
m=2(b+1)b

Example:
p=7=2*3 + 1, so b=3.
n= 2*9 + 6 + 1 - 7 = 18
m=2*3*4=24
indeed
(n+p)^2 - p^2 = 25^2 - 7^2=24^2
>pic related is me after typing this out

>>11762452
I thought calc 3 and differential equations and stuff was hard, but everything after that was easy again.

>>11762456
Can I ask how you found n?

>>11762366
that's what they're trying to do in america

>>11762485
Assume WLOG your x is (1,0,0,...,0) in coordinates. Now write down a determinant 1 matrix that takes it to the point you want.

>>11762532
cant tell if joke about american education or getting rid of niggers

>>11762434
ontologists are philosophers that specialize in questions of ontology. the basic questions of ontologys are "what exists?", "what is existence?", "are there objective answers to those questions?"
there is a selection effect where only people who answer yes to the last question end up specializing in ontology, because they think it's deep and meaningful and worth studying. unfortunately this is the wrong answer, so ontology selects for retards. they're like UFO experts only instead of aliens they look up at the sky searching for numbers.

>>11762601
I know what ontology is, but thanks.
I just can't think of a philospher trying to map out mathematics - at least not after Russel.

>>11762533
I suppose you just set the first column to any unit vector [math]y[/math] and the other [math]n-1[/math] columns to the orthogonal complement of the subspace spanned by [math]y[/math]. What I am unsure of is whether we can always choose those [math]n-1[/math] columns such that the whole matrix remains +1 det. I suppose the idea is that there is always enough freedom there to do so (2 reflections is 1 rotation), but I don't know a formal way to show this.

>>11762544
Whatever makes you happier anon

>>11762643
dude the matrix is orthogonal so det is +1 or -1. if it's -1 just switch one column for its negative lol

https://youtu.be/x-6Ebx1LA5g

>mfw anon points out an error in my reply

>>11762452
Kid school: basic trig in grade 10
Currently: Real analysis

>>11762676
Oh, right. I forgot how determinants work.

>>11762452
For most people I think they just never learn basic geometry or algebra properly so the trig rapes their minds when they get to highschool and they never recover from the trauma. In college I think its the number of moving parts in calculus and linear algebra that fucks normies.

>>11762619
oh, i didn't understand what you meant. i don't think philosophers are trying to map out mathematics either. the people who map out mathematics are mathematicians proper.

but there is a characteristically philosophical tendency to want to map out the concepts which are used to define mathematical concepts. have you ever caught yourself pacing around the house while daydreaming about explaining a particular concept to an imaginary audience? i do it, and in particular when i'm on adderall. i find myself starting to explain concept A, but i end up thinking that the best way to explain A is to first explain B and C, which are part of the explanation of A but are not clear enough to my liking. so i get to explaining B and C, but then i end up thinking that in order to best explain B and C i must first explain D and E and F and G, and F and so on. eventually i get carried away and forget what i was trying to do in the first place. i'm doing it right now.

i think this behavior is characteristic of analysis, and i think this tendency to want to go from the concrete to the abstract is how people start out trying to map out mathematics, and end up doing ontology. also, on my account of the intellectual efforts involved in inquiry or analysis or however you wish to call it, the work of mathematicians and the work of ontologists is the same kind of work basically, and the main psychological motive that drives it is wanting to explain, and not to understand. understanding is only a side effect of explaining to yourself, and is in general experienced passively as an involuntary moment of insight, but explaining is work that you can do. given that the goal of the work is to explain, by my lights theories are best evaluated by practical and pedagogical criteria, and it seems this is already being done in mathematics. ontological theories however are generally evaluated according to some criteria for truth.

>>11762869
>have you ever caught yourself pacing around the house while daydreaming about explaining a particular concept to an imaginary audience?
I have a big (and cute) stuffed dog to which I explain my newest insights. I think it's really helpful to actually have to say or write it, as that makes the shapeless blob of thought take the concrete verbal form much easier approached by not only others but also the original thinker.
>eventually i get carried away and forget what i was trying to do in the first place
Same. Nice to see someone else do this, too.
t. not the one you were talking to

>>11762869
>have you ever caught yourself pacing around the house while daydreaming about explaining a particular concept to an imaginary audience?
thats literally how i learn, after watching a lecture or reading a chapter in a book i imagine myself as a lecturer giving a lecture to imaginary audience and sometimes they ask me questions sometimes i crack some jokes
its pretty fun
sometimes if a topic really strikes my attention i also imagine myself explaining it to a girl that is really dear to my heart

>>11762931
Based until the last part

>>11762931
whoa wtf me too

>>11762485
The result is clear for n = 2: SO(2) acts transitively on the circle.
In dimensions higher than 2, given two points x and y on the unit sphere, you know that there exists a rotation in a plane containing x and y that maps x to y. Extending this by the identity on the orthogonal gives you an element of SO(n) that maps x to y.

>>11762931
>thats literally how i learn
yes what you said is very important. i think many people are suffering a great loss because they are unable to enjoy learning in this way, so they don't pick up the habit. it's the same way that physical exercise feels like a chore when you don't have a fun way to do it.

and i like what you said about explaining to a girl that is dear to your heart. although i don't think about it in romantic terms, i have great admiration to some of my teachers because i felt from them this kind of love and care, they really only wanted to help me understand with all they had. there is something about explaining to another person that makes you become closer to them. it is like you helping them rise to your level so you could see eye to eye. you explain because you want to be together with them, so you won't be alone with your knowledge. when i think about it in this way i become sentimental and wish we could all live this way in together.

>>11761915
I enjoy your writing style

>>11763155
You don't think it's forced? It is literally what one gets when they forget stupid little stuff like which preposition to use if trying to say this or that, and then quickly constructing a detour to go around the problem. Also, growing up with all sorts of fantasy stuff going as low as reading Runescape fanfic (not my proudest moment) leads to some strange word choices sometimes. I don't know, maybe I'm too self conscious about stuff. But if that is really your opinion, it made me smile. Thanks.

/gnmg/

>>11763216
>which preposition to use
On arriving in Chicago, he was met at the station by his friends.

>>11762468
>>11762486

Yeah pretty clever unless you read anon's question correctly. It asks for what n does [math]2np + n^2 = p^2[/math].


[eqn]
n^2 + 2np = p^2 \\
n^2 + 2np + p^2 - p^2 = p^2 \\
(n + p)^2 = 2p^2 \\
(n+p)^2 = (\sqrt2p)^2 \\
n+p =\sqrt2p \\
n = p(\sqrt2 - 1)
[/eqn]

>>11763392

>>11763398

"for what values of n is 2np+n2 a square for some prime p"

>>11763409

>>11761654
How am I supposed to use the empiric distribution or the histogram function to estimate the probability that the variable excedes a certain value?
In the empirical distribution i would asume that the estimation would be tha number of elements greater than that value dividede by the ammount of elements in the sample but i have no clue with the histogram function.

Does anyone IIT know where I can find a proof of the Jordan Curve/Jordan-Brouwer theorem that isn't three pages long?

Also what's a good book to start functional analysis if I know undergrad level analysis?

>>11763411

someone is mad I btfoed his fancy pythagorean triple solutuion with simple text interpretation

>>11761834
It's literally just always a condensed notation of the chain rule.

>>11763424
I know of a proof that's 5 pages long.
Proofs of the Jordan Curve Theorem are long. That's how it works. It's not an easy proof.
To start functional analysis, I recommend the latter parts of the Stein and Shakarchi Real Analysis book and their Functional Analysis book. PDFs online.

I don't know where else to ask. Please someone tell me why I'm wrong:

It is well known that the general halting problem is undecidable.
An arbitrary program P has a set of inputs I with alphabet A and a set of terminating outputs O with an arbitrary alphabet
G is the grammar with alphabet A such that consists of all recursively enumerable syntaxes of I that result in terminating output of O when input into P.
By Gold 1967, this grammar is learnable at the limit. Therefore a paradox is formed as this provides an algorithm to solve the halting problem.
https://raw.githubusercontent.com/townie/Landmark-CS-Papers/master/gold67limit.pdf

>>11763689
Thanks anon. Is it any better for Jordan-Brouwer? Or worse?

>>11763424
>>11763689
The proof in Hatcher is quite short, like a bit over half a page IIRC, but it's short because it nukes the problem with homology. There's many pages of machinery going into making the proof simple.

>>11763694
>By Gold 1967, this grammar is learnable at the limit
are you sure about that? according to table 1, the only class of languages that is learnable in the limit without access to an "informant" is the class of finite languages. In your example, an informant would be an oracle to solve the halting problem.

>>11763769
Oh you're right. For some reason I was thinking the program itself could act as informant. But it can't, at least not in any naive way.

I would be curious though if a statistical approach based on observed runtime would yield any interesting information.

>>11763787
yeah it probably would. if you really wanted to go nuts you could even try to train a neural network to predict whether a program would halt or not (e.g. represent it as a parse tree and run it through a DAG-LSTM). main difficulty with this kind of approach is getting enough annotated training data (i.e. a big database of programs where you know whether or not they halt)

>>11762516

Not the OP, but desired to carve an intuitive path as to how one would arrive at this result.

We are concerned with the transformation of :

n^2 + 2np

For prime p and natural n.

Into a form (g(p))^2, where g(p) is a rational polynomial of prime natural variables.

One may see immediately that supposing n is even yields :

n = 2k

Leading to :

(2k)^2 + 2p (2k) = 4 ( k^2 + pk )

Further factoring delivers :

4k (k + p)

Now the question is how may we define k in terms of p such that it delivers the desired form.

Note that because k is external to (k+p) and we desire a square, k itself must be a square of some p polynomial.

Also (k+p) must be processed via k's form such that it is also a square.

Simplicity dictates the further steps.

Recall the Pascal Triangle and it's relations to polynomials of the form (x+1)^m or (x-1)^m for natural m.

1 is chosen because it identitively maintains the magnitude of binomial coefficients which emerge. Again, think simply.

Look upon the Triangle and see where one may alter between (x-1)^m and (x+1)^m with just a multiple of 'x'.

This is only possible between (x-1)^2 and (x+1)^2 as :

(x+1)^2 - (x-1)^2 = (x^2 - x^2) + (2x + 2x) + (1-1) = 4x

Clearly establishing that :

(x+1)^2 = 4x + (x-1)^2

But note the 4. Divide both sides by 4 to eliminate approriately, and you end up with the desired form in terms of 'x'. Translate back to in terms of 'p' and you have your result :

k = (p-1)^2 /4

Which produces :

4 (1/4) (1/4) (p-1)^2 (p+1)^2 = (1/2)^2 ( (p-1)(p+1) )^2

Which cascades back to prior definition, delivering :

n = 2 ( (1/2) (p-1) (p+1) )^2


Again, at least for me, the series of steps to arrive at this are majority-based on intuition. To think of the evens is to notice the symmetry presented by the 2's. To think of k being the square of some p polynomial is a combination of algebraic position and desired form. The rest is a practice in simplicity and translation by looking at the coefficients.

>>11763828
The last line is wrong.

Once you have k, n is trivially delivered by prior def. Outlining explicitly what the prior anon reported.

Ignore the final def of n.

>>11763814
Interesting idea.
I would think that there are algorithms to synthesize some subset of programs that are known to halt on certain classes of inputs. Definitely gives me some more to look into, thanks!

>>11761659
I just saw a sleeping pill ads. Anyone who thinks they are safe on 4chan should think twice.

>>11763891
Use AdNauseam

bros... I didn't do maths today... for the seventh day...
bros... is it over...

What is an area of math you've reviewed recently that you really like? For me, it's abstract algebra and specifically vector spaces. It covers such a useful/practical application of algebra (specifically linear algebra).

>>11763964
I decided to research "imaginary time" on whim and it got me into the operator algebra rabbit hole.

/gmmg/

>>11763241
My version would be something similar to "upon arriving to Chicago" but the ending would be the same.

>>11763964
I've been playing a lot with different cofibre sequences while trying to construct spaces with desired cohomology.

>>11763952
Yes it is.

>Soulless

>>11764150
[math]e^{i \frac{\pi}{2}}[/math] makes my pp hard

>>11764090
How old are you

I think somebody was asking about Fuchsian groups a few threads ago. Not that I would know anything about what this paper is about, it could still provide examples of their use: https://arxiv.org/abs/2006.02817
And this one is a nice alternative proof for finite group stuff (not related to Fuchsian groups!): https://arxiv.org/abs/2006.02265

>>11764150
Maybe, but so are we.

>>11764209
Assuming quickly fertile offspring, old enough to be someone's grandparent. 27.

>>11764244
>27
How does it feel to be one of the few people with a PhD posting in these threads?

>>11764261
I don't know. Assuming the doctor version of me would coexist with me-me. I would say this alternative me would probably suffer intensely from cringe levels beyond human description while reading my posts and follow the seductive whispers of the kingdom of death. However, that is just me self-inserting myself inside the mind of a fictional character, so I suggest you ask someone else.

>>11764270
>Assuming the doctor version of me would coexist with me-me
Wait... what? Are you trying to say that you're over the age of 24 and still don't have a PhD?

>>11764273
Well deduced.

>>11762060
Imagine being so hurr durr you don't get obvious satire

>inb4 this is also satire
Then my post is also satire

>>11764287
Bully not those who have not yet found out what dark numbers are.

anime is fucking gay

>>11764390
Tell me about it.

are there any cute putnam problems?

>>11763216
Well I'm not a native speaker so I'm probably not the best judge, but I find it pleasant. The posts usually being kind helps as well.

i just ordered apostol ii for multivariable calc
did i fuck up

>>11763952
Please kill yourself

>>11764634
that depends on whether or not you actually read it

>>11764571
At least they aren't too broken, then. That's good to hear. Sometimes I feel like a potato when I look at my text. Have you found out anything interesting today?

What kind of porn do I need to fap to to enhance my math skill?

>>11764711
blacked

guys I think my advisor wants to fuck (we're both men)

>>11764746
you forgot to attach your blushing kawaii anime girl

>>11761654
I have an analysis exam on diferentiation today.
Lend me some of your power bros.

Coq users
Coq users: you have a mature system which has been around for decades and is tried and tested. You have formalised several very difficult proofs about undergraduate-level mathematical objects such as planar graphs and finite groups. You have done lots of computer science things which I do not understand too. But where are the MSc level mathematical objects? Where are the schemes? Coq is French! Schemes are French too! It’s a match made in heaven! Where are the statements of local and global class field theory? Assia Mahboubi is someone who is actually doing mathematics in Coq which “proper mathematicians” are interested in. She cannot do it alone! Where is the manual which tells mathematicians who have no idea what a type is but know what a Noetherian ring is, where to start? What if an undergraduate wants to try formalising the Hilbert basis theorem? What do they do? Ask on the mailing list? You know that undergraduates don’t actually use email any more, right? I am told by my teenage children that email is for old people. Where is the way in for us? [Note added 14th Feb: thanks to Théo Zimmermann for pointing out to me on Twitter that Coq has a Discourse forum. Young people wanting to learn Coq — try asking some beginner questions there. Ask how to make class groups of number fields! Let’s get more serious mathematics done in Coq! It’s an extremely powerful system! ]

>>11764487
Why are autistic virgins so obsessed with asuka? Shes just annoying and fucking 14yo

>>11764746
Never have any relationship with your advisor, nor choose your future based on it.
t. choose a field because I crushed my advisor.
Turn out he's a dickhead.

>>11764746
it depends on if he's more intelligent than you. i wouldn't let my advisor fuck me unless i could call him daddy and really mean it

>>11764772
kevin pls go

Isabelle/HOL users
Isabelle/HOL: Manuel Eberl is tirelessly generating 20th century analysis and analytic number theory. This is a highly respectable thing to do — he is planting the seeds. He is doing the basics. He cannot do it alone! Furthermore, HOL has no dependent types. Does this mean that there are entire areas of mathematics which are off limits to his system? I conjecture yes. Prove me wrong. Can you define the Picard group of a scheme in Isabelle/HOL? I am not sure that it is even possible to write this code in Isabelle/HOL in such a way that it will run in finite time, because you have to take a tensor product of sheaves of modules to define the multiplication, and a sheaf is a dependent type, and your clever HOL workarounds will not let you use typeclasses to define module structures on the modules which are values of the sheaves. So how will you do the tensor product? I don’t know. Does anyone know? Is this actually an interesting open research problem? Picard groups of schemes are used all over the place in the proof of Fermat’s Last Theorem. They are basic objects for a “proper mathematician”. What can Isabelle/HOL actually do before it breaks? Nobody knows. But what frustrates me is that nobody in the Isabelle/HOL community seems to care. Larry Paulson says that it’s easy to understand: different kinds of maths work best in different systems, and so you might want to choose the system depending on the maths you want to do. But do you people want to attract “working mathematicians”? Then where are the schemes? Can your system even do schemes? I don’t know. Does anyone know? If it cannot then this would be very valuable to know because it will help mathematician early adopters to make an informed decision about which system to use. [Notes added Feb 14th: Josh Chen told me on Twitter that Isabelle has a Zulip chat like Lean!

Mathematician beginners — go there and ask some questions about how to do basic maths in Isabelle! Furthermore, Manual Eberl has sent me what he claims is a formalisation of sheaves in Isabelle. But he does not profess to know anything about sheaves — mathematicians who want to learn about sheaves could try using it! Ask him about it in the chat! Let’s get some 21st century mathematics formalised in Isabelle/HOL! ]

Here's a question I've always been curious about related to the current pasta dump:
Has formalization of mathematics in a proof assistant ever actually lead to the discovery of a nontrivial error in something? Somebody tried to punch in a published proof and the computer said "nope, that doesn't work"?

One of the common talking points of type theory people and others trying to push computerized proofs seems to be "math is getting so complicated we can't reliably check it" but I've never heard of a computer actually finding an error missed by human readers.

>>11764773
Eye penetration guro obviously

>>11764795
>but I've never heard of a computer actually finding an error missed by human readers.
a human reader finding errors by doing calculations with a piece of paper is called a computer ;^)

>>11764795
Your common math paper prove doesn't list its assumptions nor most of its steps, so you're just asking if, for a claimed proof, actually the opposite has been formally proven.
I don't know, but most proofs (inside the papers uploaded to arxiv every 10 minutes) ever see the eye of another mathematican anyway. The proof is what makes the obsticle indigestible in the first place, if we want to assume a statement that's not by a popular mathematican or circle of interest, we must just believe the claim.

>>11764795
Your common math paper proof doesn't list its assumptions nor most of its steps, so you're just asking if, for a claimed proof, actually the opposite has been formally proven.

I don't know, but most proofs (inside the papers uploaded to arXiv every 10 minutes) ever see the eye of another mathematician anyway. The proof is what makes the obstacle indigestible in the first place, if we want to assume a statement that's not by a popular mathematician or circle of interest, we must just believe the claim.

>>11764806
>so you're just asking if, for a claimed proof, actually the opposite has been formally proven
Not really. A proof can be wrong without the theorem itself being wrong.

>>11764810
I don't think what you express is anything else that a lemma during the proof being false

than

go to bed anon
you're breaking out in hives
SLEEP

>>11764812
This is only true if you interpret every logical microstep of a proof as a "lemma", including the "lemma" that my given proof actually implies the theorem. This seems like a ridiculous abuse of the word.

... really?

>>11764824
Mhm, no I think it's technically the case no?

Yes, most proofs are "full of errors", starting with stuff like rings R being secretly identified with the equivalence class formed with the trivial ideal R/(0), a set of vastly different rank, etc. Or sets {a,b,c} secretly being mapped to {{a},{b},{c}}.
I'm personally not aware whether there's a result or lemma that was claimed to be true but actually it was independent or false w.r.t. Zermelo-Freankel with Choice and large cardinal axioms. Lots of statements are stated because they are "easy be seen to be true" but the PhD student who goes through the labour of formalizing schemes in Lean will not be known because he's just working through 50 year old math and x'es out the details
https://www.imperial.ac.uk/media/imperial-college/faculty-of-engineering/computing/public/1819-ug-projects/Fernandez-I-MirR-Schemes-in-Lean.pdf

But few theorems get formalized these days -only interesting well studied ones- and few papers get read.

>>11764838
At least he's not one of those fuckers who calls objects with the property he wants "good".

Lads... Every time I post on /a/, thread ends almost without fail after 0-2 other posts... There is no way, mathematically speaking, that I am not cursed, right?

>>11764843
>Mhm, no I think it's technically the case no?
Again, it's only "technically the case" if you're going to be a smug pedantic autist who claims that every single sentence of a proof is a lemma.

I understand that proof formalization is the domain of smug pedantic autists, but it's completely asinine to say that if I somewhere use the fact that 2+3 = 5 then my proof says
>lemma: 2+3 = 5

>>11764746
>we're both men
Then you go be a man and ask if that is what he wants.

>>11764769
Good luck!

>>11764838
What's wrong? Clean actually makes sense if you think about it. You are trying to filter something out, and then you end up getting rid of the extra mess. Did you know that pure submodules of absolutely pure modules are absolutely pure?

>>11764845
>There is no way, mathematically speaking, that I am not cursed, right?
I don't know about that, but you will now be cursed at! Fuck shit hell piss dick

>>11764849
I don't claim all statements have the same emotional impact to the reader.

Otherwise, sure, they are lemmas in the same sense as every expression in a sentence is a "world". A statement that maybe proven or disproven, or neither.

>but it's completely asinine to say that if I somewhere use the fact that 2+3 = 5 then my proof says >lemma: 2+3 = 5
Why tho? It's just a formalization. If you want it being structured and searchable, then you'll have to come up with some indexing and labeling.

If it would be easy, it would arguably be nice.
You open a paper, read a statement, parse the associated proof and your interpreter validates that indeed what you read is not up for discussion, as far as the formal system goes.

>>11764857
>What's wrong? Clean actually makes sense if you think about it.
i know it makes sense, its just that... you know... lol

What is the simplest proof that a composition of two rotations about an axis through the center is another rotation about an axis through the center in R^3?

>>11764849
I don't claim all statements have the same emotional impact on the reader.

Otherwise, sure, they are lemmas in the same sense as every expression in a sentence is a "word". A statement that maybe proven or disproven, or neither

>but it's completely asinine to say that if I somewhere use the fact that 2+3 = 5 then my proof says >lemma: 2+3 = 5
Why tho? It's just a formalization. If you want it being structured and searchable, then you'll have to come up with some indexing and labeling.

If it would be easy, it would arguably be nice.
You open a paper, read a statement, parse the associated proof and your interpreter validates that indeed what you read is not up for discussion, as far as the formal system goes.

>>11764860
No, really I don't.

>>11764838

>>11764863
Product preserves determinants and the logs their matrix multiplications are multiples of each other.
A weaker but less computationally intensive way to say this is that vectors along some axis (the rotation axis) of all three is the same

Let [math]0 < m < M[/math], and let [math]\mu[/math] be a probabilistic measure on the interval [m, M].
Prove that:
[eqn]\int_m^M t^2 d\mu(t) \leq \frac{(m+M)^2}{4mM} \left( \int_m^M t d\mu(t) \right)^2 [/eqn]

>>11764863
Product preserves determinants and the logs their linear representations are multiples of each other.

A maybe weaker but less computationally intensive way to say this is that vectors along some axis (the rotation axis) of all three is the same

>>11764863
every orientation preserving orthogonal transformation is a rotation by analysis of the eigenspaces
a composition of orientation preserving orthogonal transformations is an orientation preserving orthogonal transformation

>>11764879
>that vectors
(those vectors are the eivenvectors)

>>11764886
>>11764879
>>11764878
>>11764876
Shut up retard
This is now an ELEVEN thread
Like bedroom pop?
Like indie rock?
Like cuco/clairo/joji/billie eilish and all them niggas?
Then you'll definitely enjoy this song!
https://soundcloud.com/elevenshxt/sets/blue-skies

>>11764857

>Then you go be a man and ask if that is what he wants.

I'm a complete virgin, never had a gf or a bf

>>11764889
Shut up faggot xD
This is now an ELEVEN thread
Like bedroom pop?
Like indie rock?
Like cuco/clairo/joji/billie eilish and all them niggas?
Then you'll definitely enjoy this song!
https://soundcloud.com/elevenshxt/sets/blue-skies

>>11761654
dead general

>>11764894
Kill yourself fag
This is now an ELEVEN thread
Like bedroom pop?
Like indie rock?
Like cuco/clairo/joji/billie eilish and all them niggas?
Then you'll definitely enjoy this song!
https://soundcloud.com/elevenshxt/sets/blue-skies

>>11764878
I could prove that, but I don't want to sabotage your learning. T-trust me. Could Hölder help for example? If you set [math]t = s^{\frac{1}{2}}[/math], then maybe... Have you tried that?

>>11764889
Well, I'm a capricorn but this isn't about horoscopes. This is about you either being a man.

AND BEFORE YOU ASK: I haven't listened to those artists.

>>11764907
Shut up faggot weeb
This is now an ELEVEN thread
Like bedroom pop?
Like indie rock?
Like cuco/clairo/joji/billie eilish and all them niggas?
Then you'll definitely enjoy this song!
https://soundcloud.com/elevenshxt/sets/blue-skies

>>11764896

>bedroom pop?

aka out of tune singing and bad guitar playing with a lot sliding through chords

what kind of IQ is required to think spamming a mathematics thread is a good way to advertise your band

>>11764916
But it isn't out of tune?
Or are you saying bedroom pop in general?
This is now an ELEVEN thread
Like bedroom pop?
Like indie rock?
Like cuco/clairo/joji/billie eilish and all them niggas?
Then you'll definitely enjoy this song!
https://soundcloud.com/elevenshxt/sets/blue-skies

>>11764921
I'm not a band faggot I'm one person. And a higher one than yours cavenigger.
This is now an ELEVEN thread
Like bedroom pop?
Like indie rock?
Like cuco/clairo/joji/billie eilish and all them niggas?
Then you'll definitely enjoy this song!
https://soundcloud.com/elevenshxt/sets/blue-skies

>>11764916
90's Polish BM like Graveland is probably bathroom pop, at least the vocals' echo sounds like me singing in the shower (sorry neighbours).

>>11764929
Shut up fag nobody cares.
This is now an ELEVEN thread
Like bedroom pop?
Like indie rock?
Like cuco/clairo/joji/billie eilish and all them niggas?
Then you'll definitely enjoy this song!
https://soundcloud.com/elevenshxt/sets/blue-skies

/mg/ Thoughts on Pauls Online Math Notes?

>>11764935
Thoughts on stfu?
This is now an ELEVEN thread
Like bedroom pop?
Like indie rock?
Like cuco/clairo/joji/billie eilish and all them niggas?
Then you'll definitely enjoy this song!
https://soundcloud.com/elevenshxt/sets/blue-skies

Can there be two finite simple groups of the same order?

>>11764921
People like him are usually unironically mentally ill (likely having a manic episode right now).

>>11764907
I tried all kinds of Cauchy-Schwarz, I gave up already and I hope someone will give me a solution...

>>11764945
Yes. [math]A_2(4) \neq A_3(2)[/math] but the order is the same. https://en.wikipedia.org/wiki/Group_of_Lie_type#Chevalley_groups

>>11764946
>>11764945
I don't have any mental illness diagnoses but you are posting on one of the most mentally ill websites on the internet that school shooters and incel losers have posted on for decades not to mention it's reddit tier now. tl;dr is you lack self awareness and should off yourself.
This is now an ELEVEN thread
Like bedroom pop?
Like indie rock?
Like cuco/clairo/joji/billie eilish and all them niggas?
Then you'll definitely enjoy this song!
https://soundcloud.com/elevenshxt/sets/blue-skies

Keep boosting my plays brainlets.

>>11764773
yes that's why

>>11764981
>>11764963
For the record I'm spamming all boards because it's easy to bait redditchanners into playing my shit. Which boosts my songs into soundclouds related tracks algorithim and gains me more fans/followers.
For a mathematics board you people sure are fucking stupid
This is now an ELEVEN thread
Like bedroom pop?
Like indie rock?
Like cuco/clairo/joji/billie eilish and all them niggas?
Then you'll definitely enjoy this song!
https://soundcloud.com/eleveniscool/sets/blue-skies

>>11764949
https://en.wikipedia.org/wiki/H%C3%B6lder%27s_inequality#Probability_measure This is pretty much the only idea I have. I'm just a bit unsure about the coefficient in the front of the squared integral. The s-substitution would allow you to use Hölder, and then maybe give you what you want (ish), but I can't promise you anything.

>>11764945
>>11764959
related

http://oeis.org/A119648

>>11761770
Einstein knew this feel so

>>11764996
Yep. 20160 is the example I gave.

>>11764949
>>11764994
How would the measure actually react to such a change of variable? Do you have any cold hard facts about that?

If [math]X[/math] is an algebraic variety, then the local rings [math]\mathcal O_{X,p}[/math] for [math]p\in X[/math] holds a lot of local information, and the variety is said to be [math]S[/math] if the condition [math]S[/math] holds at every such point.

For example, if the local rings [math]\mathcal O_{X,p}[/math] are regular, then the variety is smooth. If they are normal, then the variety is normal, and apparently, this is equivalent to the fact that [math]X[/math] hasn't had a subvariety glued to another variety finite over the latter.

What other properties of rings translate to a readily visualizable geometric property of varieties? For example, what does it mean for the local rings (or maybe, if [math]X=\text{Spec}(A)[/math], then the whole ring) to be a UFD? Or a PID? Or flat? Or Euclidean?

I'm still baffled by the fact that animefag is old and doesn't even have a PHD
Can we really trust the things that he posts?

>>11764865
>lemmas
lemmatia is the plural
important word for showing off

>>11765050
>Can we really trust the things that he posts?
No, but the good thing is that my stuff can be checked and my mistakes can be pointed out. A healthy dose of skepticism instead of blind trust.

>>11765079
Why aren't you a doctor anon?
Don't you want the proper title to post the daily dose of math?

>>11765087
I'm a hobbyist seeing how far I can get.

>>11765091
how pure

>>11765098
I'll probably drop out after I get my PhD, though. The researcher life doesn't look too tempting.

>>11765091
does it become more difficult as you proceed through grad/postgrad maths? that's what I'm concerned about, there's a lot of resources for undergrad and even early grad maths, but I'd expect it to become progressively more difficult the further you go. the fear is at some point there's a glass ceiling of things u can self teach, I suppose there's only one way to find out.

i do find it strange there is so much free information available when it comes to technical knowledge

>>11765106
I think it's pretty much the same all the time. There are things you know and there are things you don't know. The things you know help you build the bridge between the stuff the same way as you would on lower levels, but that could depend on the individual. Finding the material is the actual challenge.

I have the following recursive formula, do you think I could write an explicit function out of it?
[math]
f(1) = 1
f(2) = \sqrt(f(1)^2 + 1^2) = \sqrt(2)
f(3) = \sqrt( (f(1) + f(2)) ^ 2 +1^2)
f(n) = \sqrt((\sum_i f(i))^2 + 1^2)
[/math]

I have this recursive formula, do you think I can write an explicit formula for f(n)?
[math]
f(1) = 1 \\
f(2) = \sqrt{f(1)^2 + 1^2} = \sqrt{2} \\
f(3) = \sqrt{ (f(1) + f(2)) ^ 2 +1^2} \\
f(n) = \sqrt{(\sum_{i=1}^{n-1} f(i))^2 + 1^2}
[/math]

>>11764772
Lean is doing better at that outreach.
https://www.youtube.com/watch?v=Dp-mQ3HxgDE

>>11765414
Let a_i:=f(i)^2
Then we have
a_1=1
a_i = sum_j<i a_j + 1
Let b_i = sum_j<=i a_j
Then b_i - b_(i-1) = b_(i-1)+1
So b_i = 2b_(i-1)+ 1
So b_i= 2^i - 1
So a_i = b_i - b_(i-1) = 2^i - 2^(i-1) = 2^(i-1)
So f(i) = 2^((i-1)/2)

>>11765461
It was
[math]
f(n) = \sqrt{(\sum_{i=1}^{n-1} f(i))^2 + 1^2}
[/math]
Not
[math]
f(n) = \sqrt{\sum_{i=1}^{n-1} f(i)^2 + 1^2}
[/math]

>>11765473
Consider it a lower bound then.

Third edition of the book.
Based Springer.

>>11765507
Wait, have you not used [math]\subset \text{Idxaaak@} \subset[/math] to denote being a subset? You must be American.

>>11765507
>Not using [math] \subset Idxaaak@ \subset [/math]
Look at this scrub.

bros... i have been doing maths today... for the eighth day in a row

>>11765733
Kill yourself please. You contribute nothing to the thread by blogposting.

God I love this book so much
That is all

>>11765733
Save yourself please. You contribute everything to the thread by motivationposting.

Half a year ago known hacker guy (known from opening the iPhone and PlayStation), who today has an open source self-driving car project, did several twitch coding streams trying to write parsers, compilers and interpreters for proof checkers and assistents from scratch. The guy is literally sitting there, several times, for 7 hours, without real proof assistent experience I think and tries to put together, I think, and interpreter
https://youtu.be/OAXjsUZoOgo
Admirable durability.
Also looks at coq here
https://youtu.be/VTFaWOPspEo
Spoiler: Lots of googling is involved

Currently watching his reflection and hot take on the self-driving car industry
https://youtu.be/Nnh5TQ60hek

>>11765055
Yeah, I had already written that but then reworded it because I didn't want to open a google tab to make sure I use the right amount of m's, not make a fool of myself

>>11764945
https://en.wikipedia.org/wiki/List_of_finite_simple_groups

>>11765733
please leave some theorems for us mortals

>>11765047
how come nobody has responded to this guy yet, aren't you all AG fags?

>>11765733
based
>>11765759
cringe

>>11764773
If your not an autistic virgin GTFO.

>>11765825
Shut up faggot stop encouraging him to shit up this thread.

>>11765507
The latest Linear Algebra Done Right has something somewhat similar on the first few pages

>>11765823
I watched his SLAM and chess engine videos. They are fun to watch, but yeah lots of googling, copy pasting, and then figuring out what to do.

>>11765846
My gf literally sucked my dick less than ten minutes ago, what are you gonna do about it faget

>>11765846
This.
>>11765885
Leave.

>>11765885
you are not welcome here i will ddos you now

Why are you here at this hour? t's friday night.

>>11765908
why are YOU here?

>>11765912
I can't sleep.

>>11765908
Can't go clubbing or drinking with friends in these times sadly

>>11765919
Just get wasted at home. Cheaper, easy and makes nights easier. Post your newest insight.

>>11761654
Which one is the best text editor for [math]\LaTeX[/math], Vim or Notepad++?

>>11765929
Do you need anything beyond syntax highlighting?
I'd not use the general syntax and keys for anything but papers, if you have to.

>>11765932
I don't even know what those things mean, I'm a complete noob when it comes to PCs, all I know is a little Python and learning [math]\LaTeX[/math] right now, someone recommended Vim here awhile ago, that's why I'm asking.

>>11765759
we don't bully people for trying if they don't disturb anyone with their incompetence, anon. its only the posters that ask for help without having made any effort of their own that are unwelcome.

>>11765929
I use TeXworks, it's decent and it gets the packages for you. It also keeps track of brackets, so you need to want to have a different number of (s and )s.

/gnmg/

Is there a database of acoustic attenuation properties of materials between 1 kHz-1MHz? Having trouble finding some sort of attenuation coefficient for materials at all.

sorry if this is off-topic I don't see an engineering general here anymore

>>11766114

we don't apply math here, kid

>>11765934
I would recommend you overleaf or some online latex editor for start. That way you don't have to worry about installing LaTex and getting packages.
But for programming and writing text files in general I would recommend Vim.

Okay so I've been working through baby rudin a little (on stieltjes integrals), and I was wondering if there exists anything on sequences of them i.e. let [math] \alpha_k(x) \text{ be a sequence of increasing functions on }[a,b]\ \forall k \text{ such that } \alpha_k(x)\rightarrow x,\text{ and let } f \in \mathcal{R}(\alpha_k(x)) \text{ for all }k[/math] . Would it then follow that [math]f\in\mathcal{R}[/math]? Maybe they'd have to converge uniformly? Or perhaps [math] f [/math] would have to be bounded?

>>11766202
sigh...
figured as much

what the fuck does algebra have to do with algebra? it's just groups and rings. has fuck all to do with what I learned in high school

>>11766679
High school algebra was using a specific ring.

>>11761729
This. The existence of these dark numbers are highly controversial but have recently been accepted by a wider professional audience in the past couple of years after Terrence Tao showed their likely existence after finding certain patterns after calculating over 5 trillion digits of pi.

>>11766680
Which one?

>>11766690
The polynomial ring over the complex field, typically.

>>11766226
>writing text files in general
Wouldn't word or libreoffice better in that case?

>>11761729
Include me in the screencap.

>>11761729
PHYSISHITODDLERS BTFO

>>11765929
>>11765934
Vim's got a bit of a learning curve but you might like it.
Luke Smith on youtube is a weirdo but has a lot of videos on vim + latex usage

>>11766742
I use spacemacs, evil mode. LaTeX layer. Best of vim and emacs. If you like vim, spacemacs has a lot to offer.

>>11763891
>not using an ad blocker in [current year]
>>11765908
>>11765923
drunkposting in 4chan is a thing too
>>11766679
HS algebra is "applied" algebra in some sense: use field axioms in a particular field to deduce new identities from known ones, and maybe some facts about polynomial rings (euclidean algorithm, root/factor theorem, etc.). Research-level algebra is about finding similar structural properties in a given set.
>>11761729
>>11766711
no

>>11765934
vim is for LARPers, please don't torture yourself and get a 21st century text editor. Sublime Text is good; it's technically not free but it doesn't force you to buy it to get the full featured program (kind of like WinRAR). For LaTeX you can start in Overleaf so you don't worry too much about getting it to work, and once you can typeset documents fluently you can install TeX Live or a similar distribution in your computer along with a text editor, or an IDE like TeXMaker.
>>11766701
Not for LaTeX. MSWord is it's own proprietary format for typesetting (even though recent versions "support" LaTeX as a way to include formulae in your document) and libreoffice is a FOSS copycat. TeX is essentially an engine that renders a well typeset document from text, and LaTeX is a set of macros for TeX that most working scientists and mathematicians use in practice.

Bois, idk if this is the thread but
Basically i started reading Concrete Mathematics by Patashnik and I feel like im a fucking degenerate of some sort
Not that i was good at math to begin with, but here im stuck at the first two chapters for a week and i still cant understand it all
Are there any anons who went through the same shit or do i just need to get gud at math and if so whats would /sci/ recommend as a good way to do so(books, courses, etc)

/gmmg/

>>11766834
>drunkposting in 4chan is a thing too
Indeed it is. Not necessrily the best hobby, but it helps you to fall asleep.

>>11766857
Maybe you could be a bit more specific.

>>11766865
I could try

I kinda can understand the problems and the solutions given, after reading through them few times, but as soon as i touch the exercises about the same problem i feel like ive never read the book what so ever
So idk whether im competent enough for this book or its just a common thing

>>11766458
Neither condition is sufficient, I think.
One of the autistic children of rigorous analysis is the Volterra function v; it is bounded on [0,1] and discontinuous exactly on a nowhere dense set of measure 1/2. The "discontinuous on measure 1/2" implies it's not Riemann integrable.

But you can make a sequence a_k -> x uniformly where v is always a_k-integrable. Choose a_k to be a step function such that x-a_k(x) < 1/k, and such that it only jumps at points where v is continuous. You can do this because v's discontinuities are nowhere dense.
Then the integral of v against any of the step functions a_k exists and is just a finite sum, but the integral of v against x doesn't exist, even though v is bounded and a_k -> x uniformly.

>>11766901
There are examples in the book, I would assume. Can you follow their reasoning? I used to skip examples as useless filler at first, but they show you how to apply the theory. You could also ask in the stupid questions' thread (or here) and maybe get help, but remember: >>11765935

>>11766927
> Can you follow their reasoning?
Not always thats the problem. And if i do it takes me way more then usual, so im trying to deduce whether im a brainlet, or thats the norm for this book

>>11766857
I've found that autistic math people try to make their books as confusing as possible on purpose. This makes them feel superior to "laypeople" who don't understand "their" language. It's all basically a circle jerk over who can say the most mundane thing in the most confusing way possible using autist symbols, so that they can jerk each other off and high five over being able to understand each others nonsense while turning their noses at anyone who can't digest their autistic vomit.

instead of actually, you know, explaining things in a way that is simple and easy to understand in plain english

>>11766952
brainlet cope

>>11766954
yes, call everyone who doesn't speak autism a brainlet because you think talking in retarded symbols makes you smart.

>>11766957
brainlet cope

>>11766941
I suggest you try asking for someone to explain what is going on in an example. Take a screenshot and post it in the /sqt/, wait, receive enlightenment.

>>11766952
Abstract nonsense is the best genre.

>>11766971
Well ill try, thank you
Also a follow up question
How good is the /sci guide on math?

>>11767026
>How good is the /sci guide on math?
it's awful
use this instead

>>11767026
don't read proof books or books on set theory for any reason. don't read discrete math books. otherwise its fine

>>11767032
> don't read discrete math
Im trying to learn math to apply it to problem solving (so cs in a way), is it really that useless in this case?

>>11767031
> it's awful
How come?
Also does this imply that courses arent even an option?

>>11767057
>Im trying to learn math to apply it to problem solving (so cs in a way), is it really that useless in this case?
Then you might enjoy >>>/g/ and >>>/r/eddit

>>11767061
> >>>/g/
Ive heard enough arguments about linux distros to last me a lifetime

Thanks nevertheless, /mg

>>11766952
That is not how this works.
And you reductionism applies to anything, chemists and physicists use complex symbols too and their books are just as inaccessible to a layperson.

>instead of actually, you know, explaining things in a way that is simple and easy to understand in plain english
Mathematics can not be explained in words. The expression of mathematical ideas has to be in a language of its own. It is literally impossible to describe a reasonably mathematical subject in plain English.

>>11766842
>vim is for LARPers
The editor itself probably, yes. But the meta editor of how you interact with text is absolutely awesome.
And basically any editor supports vim keybindings.

>get a 21st century text editor. Sublime Text is good
Sublime is a very shitty VSCode.

>TeX is essentially an engine that renders a well typeset document from text
No. You have no clue what you are talking about. TeX is a programming language.
To compile LaTeX you use a "compiler" e.g. pdflatex, lualatex, xelatex together with preprocessor programs like biber, etc.

>>11765929
Vim is full of technical legacies. Basically nobody actually uses vim itself, they use a decent text editor which can use vim keys.
Good text editors are:
- emacs (specifically doomemacs or spacemacs)
- VSCode (or VSCodium)
- neovim
- etc.

Notepad++ is horrible.

>>11765939
Any not totally retarded Texteditor has those features.
All the TeX IDEs are also pretty horrible and way worse then what VSCode with a Plug-in has to offer.

>>11764878
bumping

>>11767155
>All the TeX IDEs are also pretty horrible and way worse then what VSCode with a Plug-in has to offer.
I haven't used VSCode and I currently use TeXstudio (a fork of TeXmaker with more features), so let's have a look if I can find the TeXstudio features I like in VScode plugins here https://marketplace.visualstudio.com/search?term=latex&target=VSCode&category=All%20categories&sortBy=Relevance

>Inline pdf viewer
It seems there is one ( https://marketplace.visualstudio.com/items?itemName=ajshort.latex-preview ) which supports basic backlinking features between the document and source. However, I'm missing a magnifier, which is the only reason I use the inline viewer over my external pdf reader. Also, the latest reviews claim the plugin doesn't work anymore (no idea whether this is true or not)

>One button compilation (running multiple passes of pdflatex and bibtex to get all references right with one command)
Couldn't find a plugin that supports this. I guess it wouldn't be too hard to write a script yourselves and integrate and call that from the editor, but that again is a bit of work.

>Document structure overview (basically a directory tree of your sections, related files and other parts relevant for your document(s))
Couldn't find it. There may be a plugin intended as a document tree for function/class declarations that may be adapted to get similar results, but this would probably be quite some work.

So, my impression is that VSCode cannot offer the full feature set I have now, only a subset with some work and potentially unmaintained plugins, while TeXstudio just werks. If you know of any useful features VSCode that TeXstudio lacks, I'd like to hear them. Of course, many basic features are available in both, and if you like VSCode you will probably like writing TeX with it. But that goes for every half decent text editor.

Also, I do admit that there are many terrible TeX IDE's, for example TeXworks and WinEdt are pretty bad.

Is Bayesian stat based?

>>11766952
The lay person is not supposed to understand advance mathematical notation and it's not really for the purpose of impressing them or shutting them out from understanding. It's to communicate with other mathematicians in a convenient way (imagine having to write everything in English like the Greeks). This is also not unique to mathematics (for example music pic related) or chemistry have the same "problem". There's a point where you advance in a subject were you need to be able to communicate with each other with brevity and most mathematical notation is "pregnant" and contains a lot of information in a few "symbols" so we can quickly communicate our ideas.

What is the canonical bundle of a variety? How do I think of it?

>>11761729
Actually, we know 100% of the digits of pi.

Is this a meme

>>11767427
Yes, mathematics is a meme

>>11767290
Literall the first extension "Latex Workshop" has:
>"Inline" Pdf viewer
The plugin is totally PDF viewer agnostic. If your PDF viewer supports synctex and magnifier then you can use these features with that Plugin.

>Compilation
Literally supported by the Plugin, you can invoke whatever commands you want in whatever order on whatever key combination you want.
But this is moreso a property of the extremely flexible VSCode editor itself around which the plugin wraps itself, which allows you to do this.

>Document structure
Can be a function of the PDF viewer, but the plugin also shows a file overview

>my impression is that VSCode cannot offer the full feature set
Literally just fucking try the first extension. You are going of vague description looking for very basic features barely worth mentioning...

>If you know of any useful features VSCode that TeXstudio lacks, I'd like to hear them.
- Decent syntax highlighting and customization, I think TeXstudio just looks really horrible
- Plugins for different keybindiong, e.g. vim
- Integration with all the other VSCode extensions, bracket highlighting, bracket matching, snippets, auto formating, spell checking- Works for basically every other programming language just as well
- Git Integration
- Can preview equations *inside* the Text editor, although that feature isn't quite developed
- In general I think it is a bad idea to develop an editor *for a programming language*, instead you should develop a modular platform on which you can implement different programming language. Making a good text editor is extremely hard, making a good tex editor aware of a certain programming language is usually relatively simple. And it seems pretty clear to me that history supports that claim.

>>11767389
What is digit number 32434535462456243565436425624356245645654678845753458736457863487563487563847165873465873614856134875634187561384756132598314765834658763458734657384657834651837^3453248957398425798342759834275983475983457983465873465763487658734657634257348658734265324786534287658732465831460238757823465086348546206548732456807324580263845683247568032465320548

>>11767441
>32434535462456243565436425624356245645654678845753458736457863487563487563847165873465873614856134875634187561384756132598314765834658763458734657384657834651837^3453248957398425798342759834275983475983457983465873465763487658734657634257348658734265324786534287658732465831460238757823465086348546206548732456807324580263845683247568032465320548
What's the fifth digit of your "number"?

>>11767441
7

>>11767445
2

>>11767459
Wrong, it's 6.

>>11767471
Proofs?

>>11767472
It's your number, how can you not know that the fifth digit is 6?

>>11767474
But I know that it is 2?

>>11767477
You're confused

>>11767439

>>Document structure
>Can be a function of the PDF viewer, but the plugin also shows a file overview
No, I meant the structure of the source files and sections, bib entries, references etc. in them. So this is something the editor has to do, not the PDF viewer.

>Literally just fucking try the first extension. You are going of vague description looking for very basic features barely worth mentioning...
Ah, I see, I didn't see the full overview at first. I'm not going to bother installing VSCode if I don't see any advantages though, I'm not going to spend more time than a first impression to see if it's worth it, sorry.

>Decent syntax highlighting and customization, I think TeXstudio just looks really horrible
I think the default is fine, but it can be completely customized.

>Plugins for different keybindiong, e.g. vim
Granted, but not useful for me

>Integration with all the other VSCode extensions, bracket highlighting, bracket matching, snippets, auto formating, spell checking- Works for basically every other programming language just as well
Yes of course, and all of that is in TeXstudio as well, perhaps slightly different.

>Git Integration
I never really bothered with git integrations in editors. I do all my git interactions in the terminal, which works well enough. But yes, TeXstudio lacks this.

>Can preview equations *inside* the Text editor, although that feature isn't quite developed
Seems neat.

>In general (...)

Perhaps. I care more about what specific program helps me write better than design philosophies, I don't have to build this editor, just show me what it can do.

Anyway, far too much non-math for /mg/ , I'm out.

>>11767553
>No, I meant the structure of the source files and sections, bib entries, references etc. in them.
Something pretty similar is available in the VSCode explorer.

>I think the default is fine, but it can be completely customized.
No, it can't. Or can you finally get rid of the shitty buttons everywhere? Get some non atrocious colorschemes without literally having to punch them in yourself? And have they finally jumped away from qt to something which isn't just atrocious to look at (or styled it in any reasonable way)?

>Yes of course, and all of that is in TeXstudio as well
I can guarantee you that it is not.

>I do all my git interactions in the terminal
Why would you do that?
What if you want to figure out where another person has changed a particular file? Are you gonna open the diff in TeXstudio and manually search through it?

>Granted, but not useful for me
You say that and then you go "I care more about what specific program helps me write better".
Vim keys literally make everything better. It is just so much easier to write things.

>I'm not going to spend more time than a first impression to see if it's worth it
Your "first impression" was failing to click on the first search result for "LaTeX".
I mean, if you just do not give a shit about how good/bad the things you use are, that is completley fine, but otherwise it is just dumb.

>>11764711
tranny

>>11766923
hmmm, interesting, thanks! I guess my only other question is if the sequence [math] \int_a^bf\ d\alpha_k [/math] would converge under similar conditions, or if not Riemann integrable implies that the sequence wouldn't converge

>>11767747
https://www.amazon.com/Counterexamples-Analysis-Dover-Books-Mathematics/dp/0486428753
https://www.amazon.com/Counterexamples-Topology-Dover-Books-Mathematics/dp/048668735X
Perhaps these would be of interest to you, the first one in particular.

>>11763891
Any site that uses Google's captcha is not safe.

>>11767786
thx very much!

>>11767796
No problemo. Those are pretty handy (at least the topology version) if you want to, for example, use some actual counter-example instead of just knowing/guessing that one exists. Alternatively, you could just google things, but when there is a book full of stuff like that, you may end up learning more examples than the one you were actually after (which is possible but less likely while googling).

>>11767793
It would be interesting to know how many Turing cops have become traumatised by observing these threads. Do not fear the predator, make the predator fear you.

>>11766754
Never could figure out Spacemacs, but it does seem neat.

>>11768021
Not him, but if you want an alternative doomemacs is pretty cool. Does a lot of similar things, but is much "lighter".

bros... supervisor told me to read paper, cant even understand the first sentence...

>>11767793
thats why you shouldnt fill them with 1 simple trick

>>11768044
I know the feel. Some names are such tongue twisters that you just get stuck thinking about how that person introduces themself.

>>11768045
THE ADVERTISERS HATE HIM! With 1 simple trick this anon bypasses captcha CLICK HERE TO LEARN MORE

>>11761744
>You speak of dark numbers, but do you know the darkest of them all? It is the black dot on white in the Yin-Yang symbol, an anti-sun in the middle of light.
0

>>11768073
That is a good guess, but we must remember that 0 and 100 are the holy numbers God gave us as the freezing and boiling point of water. The correct answer is 24, as that is the length of the rebirth cycle of the Sun. For humans, it is also the threshold between the bright and dark age.

>Doing a complete rerun of calc
>Trapezoidal integral estimation
Skipped all the estimating the last time around, might as well check it.
>Solve problems without issue
>Except for the time I get some number error from rushing the quick maffs
>Look at how they solved the problem because I can't be bothered to go through my own solution

"Huh"
"What is this shit?"
>Suddenly it dawns on me
>The triangle can be flattened
>I was doing the pillar and the triangle at the top separately

I feel like such a retard, and I'm not even 24!
Should I just end it right now?

>>11768060
>tfw you mispronounce names while talking to your supervisor
it's not my fault, who the fuck anglicizes "tz" as "c"

I'll bite. What's so good about SCV?

>>11768128
You have my permission to end it the way you wish, but not before you turn 24.

>>11768129
It's OK, anon. Just remember all the Serbia memes and Karadzic the next time.

>>11768173
>several
The more the merrier.
>complex
Not for the feeble minded.

Any help with these? It's converting regular expressions into state-transition tables, I just can't reduce the states as much as my professor wants, I think he's doing something non-standard (wouldn't be the first time).

https://imgur.com/a/13yX1PY

>>11768221
B
A
B
C
D

>>11768236
I mostly need help filling out the transition tables, I imagine if I can figure out the first one I can solve the rest, but thanks nonetheless!

>>11768045
I'll never pay for those fuckers who don't give a fuck about privacy unless people give them money.

>>11765047
A variety (or scheme) with UFD local rings is "locally factorial", which means that every prime divisor (irreducible subvariety of codim 1) is locally the vanishing locus of a function.

Flatness should be seen as a relative notion. If B is an A-algebra (and A is nice) then B is flat over A if the fibres of the induced map Spec B -> Spec A vary without jumping in dimension.

Other local properties are Cohen-Macaulay, which means that the singularities of X have no embedded components (weird bits of the wrong dimension sticking out) and is equivalent to having a well-defined canonical sheaf.

There's also the Gorenstein property, which means the canonical sheaf is a line bundle and can be interpreted as a type of local symmetry.

>they don't know
reddit.com/r/math/comments/gxtb6p/is_24_too_old_to_pursue_new_discovered/

>>11768296
Pretty interesting, thanks. Toughing my way through Hartshorne right now, but progress is slow

>>11768348
Poor r*dditor being lured into a trap. Universities have the walls of shame for failed PhD students where you can spit and urinate on their photos, and they are trying to add the OP to one of these. Brutal, not nice. I thought we were the bad guys and they were the good guys.

>>11768365
>Universities have the walls of shame for failed PhD students
You are not supposed to talk about this.

>>11768371
Sorry. I just got a bit sentimental. Rainy days tend to d that.

>>11768360
Yeah Hartshorne doesn't always motivate things clearly.
It might help to check out The Rising Sea by Vakil side-by-side with Hartshorne.

Is C really necessary for a mathematician?

>>11768458
mathematicians use [math]\Gamma[/math]

>>11768390
I think I can follow the proofs, but when it gets to the exercises....

>>11768348
>reddit.com/r/math/comments/gxtb6p/is_24_too_old_to_pursue_new_discovered/
>If you had asked me at 23 to solve the equation 3x = (34-0), I seriously wouldn't have been able to answer you. This week, at 31, I started my PhD position in computational neuroscience and AI research!
>It's not too late for you man!
that's pretty nice.

>>11768467

3x = (34-0)

why would he choose such a weird equation

>>11768467
why do non-mathematicians feel that they can give input to careers in math?

>>11768458
Unless you're working in number theory or combinatorics and need extremely efficient code for some reason, no. You can do with some Python and SageMath, or with a proprietary package like (((Mathematica)))

>>11768458
Probably not. I've never had to learn even the basics.

>>11768512
Well, if he made it into a PhD position in computational neuroscience and AI research, then he would probably make it in a math PhD as well if that was his area.

>>11768527
>number theory
I am, how is it useful in NT?
>Python and SageMath
I hear a lot of people hating on Python in /g/.
>proprietary package
Yikes!

>>11768536

>/g/.

why would you listen to them

>>11768548
Who else would I listen to when it comes to technology if not the technology board itself?

>>11768527
SageMath is very commonly used in combinatorics as well.
If you're trying to compute something SO hard that it really can't be done without going down to a low-level language, rebuilding all the routines you need by hand and optimizing the shit out of everything, you're either trying to do something stupid or you've essentially stepped into computational math where your paper is just going to be "here's my program, I ran it on the supercomputer for 2 weeks, here's the output".

>>11768564
Never go to a board and expect a correct opinion on the topic of that board.

>>11768583
>*Never go to a board and expect a correct opinion
FTFY

>>11768536
>I am, how is it useful in NT?
Only if you need extremely efficient code, as I noted. For most practical purposes (usually exploring conjectures by computing some sequence, or very specific stuff such as proving something for low [math]n[/math] when you have an upper bound on possible counterexamples) you can do with knowing a high-level language. You're free to learn C for fun, but otherwise leave it to the CS and computational maths people as >>11768572 points out.

>>11768548
>>11768564
/g/ is a consoomer board, not a board about actually using and developing technology.

>>11768583
And why's /g/ a bad board?

>>11768564

/g/entlemen aren't concerned with productivity, most of the board is dedicated to brand loyalty flame wars and nitpicking issues with software and programming languages. It's similar to /sci/ with the spam of IQ and racebait threads.

>>11768458
Do you plan on working in numerical analysis?
Or computational algebra?

C is honestly a pretty specialized language, at least it has become that. Knowing how to programm won't ever hurt, at this point it is just a basic skill everybody should learn. But there are other languages which might be more useful, Python is pretty good.

>>11768564
Nobody on /g/ knows anything.

>>11768536
>I hear a lot of people hating on Python in /g/.
It is a meme to hate on Python.

But you also have to realize that it is */g/* who does that. And nobody on /g/ has any clue about programming.
Python, just as a matter of fact, is a pretty decent language, which allows a wide variety of programming paradigms and has very good library support.
/g/ hates it because there is the perception that it is "babies first language" which might be sort of true, but really is not actually an argument against it.

>>11768723
>/g/ hates it because there is the perception that it is "babies first language" which might be sort of true, but really is not actually an argument against it.
Honestly it's argument _for_ it in the case of a lot of mathematicians.
Almost all mathematicians are very bad programmers, and many of them (especially older ones) are just clueless with computers in general.
But that's okay because it takes virtually no technically skill to get a crappy-but-functional script working in Python. It's easily the best "I don't care about programming, but I need to write a program" language.

>>11768605
It's not bad exactly, a good amount of cunny connoisseurs, but it's mostly just about consumerism, and you're less likely to get worthwhile info from someone on there.
It really all depends on what you value personally.

>>11768740
>It's easily the best "I don't care about programming, but I need to write a program" language.
Which might be exactly the reason the elitists on /g/ do not like it.

But python really can do both, it works as a scripting language where you can just let it solve a dumb problem without thinking too much, but it can also work perfectly for more complex tasks which require "real" programming.
Which, I think, is exactly the reason why learning it won't hurt.

>>11768755
Really learning a programming language is a meme.
If you can't solve it in Exapunks, then are you even really trying?

>>11768780
Good to see you animeposter. I enjoyed Exapunks, pretty cool game.

>>11768711
>specialized language
for what?

>tfw you ask your professor if [math]X \subset \mathbb{C}[/math] is ideal in [math]\mathbb{C}[/math] even though you pulled an all nighter to cram some introductory ring theory and catch up on other readings

>>11768790
>for what?
Usually things which requires low level manipualtion.
High performance computing, OS development and embeded systems.

>>11768780
>Exapunks
Hey, I see you're a man of culture as well

>>11768799
>>11768780

let me see you brainlets solve a 9x9 kenken before we talk about puzzle games

.

>>11768847
Interesting game, I'll check it out! Do you know any other cool puzzle games?

how does one study without caffeine?

>>11768937
meth

>>11768937
How does one study with caffeine? I tried it today and now I remember why I avoided it. No focus whatsoever.

>>11767427
>Calc 1 & 2
>Multivariable Calc
Wait, what's 2 for you guys then?
>>11768780
Zachtronics games are so fun man.

I know that by Cayleys formula there are 125 distinct, non-isomorphic labeled trees. I was able to show that there's 60 distinct labelings of the top left tree, 5 distinct labelings of the bottom tree, but I'm not yet satisfied why my explanation for why there's 60 in the top right, so here it goes:

The tree is 'T-like', and is non-distinct when it's symmetrical over the long axis of the T. So for each labeling in the number of total possible labelings (5!), we have a non-distinct duplicate, and must divide it out. So our total number of distinct labels for this graph is 5!/2=60.

How's that? I feel like it could phrased better to splash more combinatoric intuition.

>>11768980
>Wait, what's 2 for you guys then?
Calc I is limits+continuity+differentiation. Calc II is integration+sequences/series.

This seems like a long time to spend on calculus (and in some sense you can argue American schools do prioritize an endless calculus/analysis sequence too much) but you have to remember that American public high schools are ASS. A substantial group of the class each year will not have ever seen a limit before. It's absolutely not feasible to try and cram single-variable calc down into a single semester unless there's serious reform at the HS level. Literally half the class (or more) could not keep up with it.

>>11769003
Basically what you're trying to argue is that the tree has two automorphisms, and there are [math]n!/|Aut(T)|[/math] distinct labelings of a tree T on n vertices. Whatever you argued for the other two is essentially the same thing (the other top tree also has 2 automorphisms, since all you can do is flip it over, while the bottom one has 24 because you can permute the corners arbitrarily)

bros... i have been doing maths today... for the ninth day in a row

>>11769010
Gotcha. Sometimes Calc II here is what you said + multivariable, to varying degrees of rigour.
And oh man, if you knew what high schools over here are like. It's okay though, since a lot of people don't even finish it :^)

>>11769083
Kill yourself.

>>11769083

can you at least post your progress?

>>11769215
The only thing he should post is a livestream of him hanging from a noose.

>implicit

>>11768536
>listening to /g/
I shitpost on /g/ all the time and trust me everyone there is a braindead consoomer, all the faggots claiming to be CS majors complain about anything more advanced than linear algebra, if you actually want to do computing python is perfectly fine.

send help pls

>>11769296

>>11769298
ty

>>11768980
1 usually just includes calculation and derivative + integral, basically preclaulus + introductory calculus, but when the advanced stuff comes in like taylor they lable it as calc 2 i think

can anyone help explain inner products?

using formula pic related
take example (1 1 0)^T the norm is root 2,

but isn't it supposedly 2?

Am i tripping or did i get the dot product and inner product mixed up

>>11761738
they are both