/sci/ - Science & Math

How do I search with filters on libgen?

New video from our king just dropped:
https://www.youtube.com/watch?v=wD4xrnzKN1Y

>>15043155
Isn't this the guy who did the "integal (sic)" video?

>>15043155
>video about Kaczynski's THESIS
>le 10 minute intro about how he bombed people like that's not common knowledge

>>15043217
Not everyone knows or cares about Americans' drama.

>>15043224
Yet they are watching video on said American drama.

>>15043233
Yes, everybody browses through random videos when they're bored or taking a shit.
Are you new?

When during an undergraduate in music do music majors get exposed to abstract algebra?

>>15043101
>>15043155
Why are all of you incels spamming this board today with Ted Kaczynski content? This has nothing to do with science or math. The only thin Kaczynski is actually know for is being an angry incel loser and a domestic terrorist. That completely overshadows anything he has done in science or math. You're just looking for an excuse to talk about you favorite incel intellectual. I imagine this dude has a lot of appeal to all the losers on this site, because you probably find it ieasy to identify with an angry incel loser with violent fantasies.

Take this shit over to pol or to x. It doesn't belong on sci.

>>15043155
Wait I'm confused. Don't know the channel, but that video seems to be well made. All his other videos are pure schizo stuff. Can someone explain to me what the fuck is up with that guy?

>>15043350
Go be oversocialized somewhere else

>>15043391
lel, btfo

>>15043343
Your elders don't do that, zoomer-kun.

>>15043350
Let’s disregard his mathematics work for a moment.
Building bombs and sending them through the mail while the FBI launches the largest investigation in the history of the institution against you is a feat of science and engineering in itself. Not to mention the environmental impact he had due to the nature of his targets. One must admire his chemistry and planning abilities, if not his humanitarian goals and academic work.

Can someone briefly explain why we need measure theory for uncountable sample space? One thing I am aware of is that if an infinite toss is represented by the sample space containing all infinite tuples of 1's and 0's, then the event space cannot be the power set of the sample space. I don't understand why?

>>15043496
So you can do integrals.

>>15043494
His bones were absolutely trivial.

What you should really be focusing on is how incompetent the alphabet agencies truly are. If it want for his cunt sister in law (who hated his guts) and his cut brother, they would’ve never gotten him.

>>15043520
I can't believe how much of a piece of shit do you need to be to rat out your brother like that. He could have gone and persuade him or given him an ultimatum. What a piece of shit.

Let's say I have a cube of size [math]2 \times 2 \times 2[/math], with its center at [math](0, 0, 0)[/math].

Given a sphere with center at [math](x, y, z)[/math] and radius [math]r[/math], is there a general formula for the surface area of the part of the sphere that is inside of the cube? I want the red part of picrel, but in 3D.

For cases where it only touches one side, it seems like I can use the formula for spherical caps, and for cases where the center intersects the edge of the cube it's a spherical wedge. Is there a formula for when it's cut off by two or more sides at an arbitrary location?

Also, is there a similar formula for hyperspheres intersected by hypercubes, or higher dimensions?

Note: I don't need a symbolic answer. An integral that I can paste into a solver and get a rough numeric answer is more than fine.
>>15043131
You can't; LG's search is terrible. Wildcards are the best you can get AFAIK.

>>15043101
he would have accomplished more if he hadnt bombed people.

>>15043589
Bombing Americans IS the accomplishment

>>15043101
Is there a name for this type of puzzle?

How do I evenly distribute characters across a string?
The characters have to be evenly distributed as possible, but with a caveat.
Suppose we have 5 "x" characters and 12 "y":
We make a string, with 1 "x" for every 2 "y"
>"xyy,xyy,xyy,xyy,xyy"
But we still have 2 "y"s left over, so we add them like this
>"xyy,xyy,xyy,y,xyy,xyy,y"

I'm definitely not explaining this properly.

>>15043589
The Washington Post published his manifesto, immortalizing his philosophy. The fact that we're still talking about him is a testament to his success.

>>15043589
he wouldn't have bombed people if the CIA hadn't fucked him up

>>15043627
The CIA wouldn't have fucked him up if his parents didn't make him skip years in school

>>15043155
The title of the king of sci is split among Wildberger and Poirier. You are neither.

whats the name of the following function:

y=1 if x>0
y=0 if x<0

How come it's always csfags who have the most special snowflake takes in areas outside of their expertise?

>>15043693
If you meant to have x defined at 0 its probably this:
https://en.wikipedia.org/wiki/Heaviside_step_function

>>15043350
> For a period of several weeks in 1966, Kaczynski experienced intense sexual fantasies of being a female and decided to undergo gender transition.
Really explains /sci/‘s obsession

>>15043749
thanks friend

How WolframAlpha manages to show you how to solve an integral "step by step":
What it actually does is internally use a general algorithm that's too hard for humans to understand to figure out the solution.
It then separately uses an expert system that looks at the result and the problem, and try to make up a chain of integration tricks that a human could probably have thought up. It then presents you with the chain of tricks, because humans are too brainlet to solve integrals properly.

>>15043348
They don't.

>>15043569
Fix the center and radius of the sphere, then change coordinates such that the center of the sphere is 0 in these new coordinates. You don't have to do this so long as you fix the coordinates. However, this can make the calculations easier since it enables the use of spherical coordinates to parameterize the sphere i.e [math] x= r_0 \sin(\theta)\cos(\phi), y=r_0\sin(\theta)\sin(\phi), z= r_0\cos(\theta) [/math]. Using the equations for the planes that intersect the sides of the cubes in those coordinates, you should be able to find the relevant bounds for the portion of the sphere within the cube and in additional, conditions for the radius/center of the sphere relative to the indicated cube. Then finally, write down the surface area integral for the sphere. These should give you the exact formulas for the surface area.

I thought of an arrangement problem the other day
For integers n, r define f(n,r) to be the number of arrangements of n elements into a string of length r such that no elements repeat consecutively
For example:
f(2,3) = 2: [1,2,1] and [2,1,2]
f(3,3) = 12: [1 2 1][1 2 3][1 3 1][1 3 2][2 1 2][2 1 3][2 3 1][2 3 2][3 1 2][3 1 3][3 2 1][3 2 3]

(apologies for awful type setting)
I'm almost certain this is an existing problem and I vaguely remember something like this from a combinatorics class I took
But my google skills aren't giving me any answers, just somewhat related questions
Anyway I'm pretty sure f(n,r) = n * (n-1) ^ (r-1)

>>15043350
>with violent fantasies.
they were more than fantasies fren

>>15043888
>Anyway I'm pretty sure f(n,r) = n * (n-1) ^ (r-1)
Correct.
n choices for first term, n-1 choices for the next r-1 terms.

>>15043496
Depends on your measure. You could always just do point-measure at some sequence s -- so that the measure of X is 1 if s is in X and 0 otherwise -- and get a fine measure whose sigma-algebra is the entire space.

On the other hand certain properties of the measure might not be possible on the entire power set. For [0,1] you can show there is no way to get a translation-invariant (mu(X) = mu(X + a)) measure on the entire power set by using the axiom of choice.
Spitballing here, haven't checked details, but you should be able to mirror that construction for the set of binary sequences, with addition of sequences evaluated by adding componentwise mod 2 (i.e. bitwise XOR). The probability measure associated to an infinite sequence of independent unbiased coin flips should be translation-invariant with this addition. Find a vitali set the way you would for [0,1] by quotienting by C, where C is the set of sequences with finitely many 1's, and run the same argument

>>15043496
>>15043967
actually it turns out there's no way to put any probability measure mu on the entire power set if you insist mu({s}) = 0 for every sequence s, but the reason seems to require advanced set theory
https://math.stackexchange.com/a/1348102

Hello /mg/! I have come with another problem. This one I have already solved in one way but it can be solved in different ways. Now it's quite a simple problem, but it was a fun one in my opinion. If you manage to get an answer and reply to me, please also let me know what you thought about the problem in general. Feel free to ask for the solutions given in the book, I can share those if anyone is curious. I should however say I might take a while to reply back. Apologies about that ahead of time.

And yeah, that's all. Good luck to all solvers and thank you!

>>15044242
3^(2n) - 3 * (n+2 choose 2)
Is this correct? It's not a very aesthetic solution...

>>15044242
The constraint is equivalent to requiring that every child gets < n gifts.
So we can count the number of ways to distribute by giving each kid n-1 presents (3n-3 total) and then distributing the (3n-3)-2n=n-3 antipresents among them, which can be done in 3^(n-3) ways total.

This analysis assumes that n >= 3; if n=2 then distributing 2-3=-1 antipresents is the same as distributing 1 present, which can be done in 3^1=3 ways. We could write the unified formula as 3^|n-3|, but we have to remember that it becomes invalid when n<2, because "antipresents" don't actually exist, and there is no possible distribution that can satisfy the constraint while also making sure that every child gets a non-negative number of gifts.

Also merry christmas anon

>>15044402
Hello Anon! First of all, thanks for solving the problem, I appreciate it. Unfortunately I believe your answer is wrong. I have attached an image for some small cases. I hope I wrote them correctly, you could write them out yourself to check since for small n it is not that hard I believe.
>>15044469
Greetings anon! You seem to have found the clever solution(the book has 2(well actually 3) solutions). However unfortunately your final answer seems to be wrong. But your general idea seems to be identical to the second solution in the book. I'll post as a separate reply the image of the second solution taken from the book I got this problem from(it uses different words but it's the same problem). Please let me know if this all clears it up or if I'm perhaps misunderstanding something. Also Merry Christmas once again!

>>15044469
And here's the solution from the book(the second more clever one). It looks just like yours except for the number of ways of doing so.

Should I buy Serge Lang's Algebra textbook, bros?
t. PhD student

>>15045091
are you a girl

what's that word for when either an exponential or logarithmic curve gets flatter and flatter

What's the best math software for messing around plotting and checking solutions quickly? Thinking about pirating Mathematica, but I don't know whether I should check out some other ones too

>>15045243
Probably python, probably a library that can do everything mathematica can.

>>15045230
Plateauing?

>>15045228
That's absolutely irrelevant and unimportant. I'm wondering why you even asked it. But solve my problem and I shall reveal maybe.

In the topologist's sine curve T, any epsilon-ball around the point (0,0) intersected with T is a neighbourhood of (0, 0), right?
And this basically disproves local connectedness, amirite? Because there we have the disconnected segments of the curve, am I missing anything?

Is there a special name for the task of integrating up Netwon's equations of motion?
You got the force (determining the acceleration, which determines the velocity), and you want the trajectory.
I don't find it on Wikipedia.

Is there a good book about generalizations of integrals to arbitrary metric spaces?

is picrel good for quickly learning the basics? by "basics" i don't mean school-level stuff like intersections/unions/functions, i mean the basic tools of set theory that show up elsewhere sometimes, things like cardinals/ordinals and so on

>>15045447
> Is there a special name for the task of integrating up Netwon's equations of motion?
No. It's just integration and should be covered by any undergrad level book on classical mechanics.

>>15045720
I'm reading this and it is pretty good so far.

>>15045447
>>15045953
The term of solving a differential equation through a series of integrals is called integration via "quadratures." It's an fairly common term in older DE books.

>>15046191
>>15046185
Don't think that applies here. Anon is asking about generating the equations of motion from a single equality.

>>15046294
>Anon is asking about generating the equations of motion from a single equality.
So solving a differential equation.

>>15043696
Did Hotz really say that?
Lol does he crave attention so much?

I think I'm gonna have to take precalc again.

>>15045243
None. Try sagemath and pirate Maple. If you can program try julia. Mathematica is even fuckier than Maple. Pirate Matlab if you are into numerics.

How do we prove that the infinite sequences generated by diagonalizing over infinite lists of infinite sequences of numbers eg: in Cantor's proof that [math]|\mathbb{R}| > |\mathbb{N}|[/math] correspond to actual numbers? Is there a proof that every infinite sequence of digits is meaningful?

>>15047138
There is a proof that every infinite n-al expansion in every ordered ring is valid but I can't remember the name of the proof.

Quick

Not so quick.

Very quick.

I never understood, why did you call it timesand?

>>15047138
Meaningful isn't really a normal term for it but yeah, it's easy to prove that every sequence of digits defines a real number, since each truncation defines a rational, so the sequence of truncations defines a sequence of rationals, and then you just have to show that this sequence is cauchy, and use the construction of reals as cauchy sequences.

How do i solve this complex numbers exercise? Help brahs...

Find and graph all complexes, if any, that verify:

|z-2 i|+|z-8 i|=10∧0 < Arg(Z) ≤ π/2

(if your answer includes a conic or part of it, calculate all its elements center, foc, vertices and place them in your graph).


I did it wrong and got a linear function, my friend got an ellipse

>>15047176
Do you know the definition of an ellipse? It's pretty immediate then if you just recognize any z satisfying that equation as having the sum of distances from the points 2i and 8i being 10.

>>15047161
It's because the "blurb" part of TIMESAND___BLURB.jpg demonstrates the reality of time travel when the blurb-string is found to be the cryptographic key---possibly the "salt" or "sand"---for files that were encrypted chronologically earlier than I created the blurb string. For instance, keeping in mind that the numbers at the end of the first Cicada puzzle were my DOB, SSN, and the viXra IDs of my earlier papers, you may find pic related blurb to particularly useful.

>>15047180
Yeah i'm fucking dumb, i just saw a .pdf my teacher sent us and it's easier than i thought.

Fractional Distance: The Topology of the Real Number Line with Applications to the Riemann Hypothesis
>https://vixra.org/abs/2111.0072
>http://gg762.net/d0cs/papers/Fractional_Distance_v6-20210521.pdf
Recent analysis has uncovered a broad swath of rarely considered real numbers called real numbers in the neighborhood of infinity. Here we extend the catalog of the rudimentary analytical properties of all real numbers by defining a set of fractional distance functions on the real number line and studying their behavior. The main results of are (1) to prove with modest axioms that some real numbers are greater than any natural number, (2) to develop a technique for taking a limit at infinity via the ordinary Cauchy definition reliant on the classical epsilon-delta formalism, and (3) to demonstrate an infinite number of non-trivial zeros of the Riemann zeta function in the neighborhood of infinity. We define numbers in the neighborhood of infinity as Cartesian products of Cauchy equivalence classes of rationals. We axiomatize the arithmetic of such numbers, prove all the operations are well-defined, and then make comparisons to the similar axioms of a complete ordered field. After developing the many underlying foundations, we present a basis for a topology.

Sixty-Six Theses: Next Steps and the Way Forward in the Modified Cosmological Model
>https://vixra.org/abs/2206.0152
The purpose is to review and lay out a plan for future inquiry pertaining to the modified cosmological model (MCM) and its overarching research program. The material is modularized as a catalog of open questions that seem likely to support productive research work. The main focus is quantum theory but the material spans a breadth of physics and mathematics. Cosmology is heavily weighted and some Millennium Prize problems are included. A comprehensive introduction contains a survey of falsifiable MCM predictions and associated experimental results. Listed problems include original ideas deserving further study as well as investigations of others' work when it may be germane. A longstanding and important conceptual hurdle in the approach to MCM quantum gravity is resolved. A new elliptic curve application is presented. With several exceptions, the presentation is high-level and qualitative. Formal analyses are mostly relegated to the future work which is the topic of this book. Sufficient technical context is given that third parties might independently undertake the suggested work units.

http://gg762.net/d0cs/papers/Sixty-Six_Theses__v2-20220726.pdf

The Time Travel Interpretation of the Bible
>https://vixra.org/abs/2104.0068
>http://gg762.net/d0cs/papers/The_Time_Travel_Interpretation_of_the_Bible__v5-20211221.pdf
We describe the Biblical work of ages as a time travel program for saving humanity from extinction. God's existence is proven as a consequence of the existence of time travel, which is supposed. We present the case that Abraham's grandson Jacob, also called Israel, is Satan. We make the case that the Israelites are described as God's chosen people in the Bible despite their identity as the children of Satan because God's Messiah is descended from Abraham through Satan. They are chosen as the ancestors of the Messiah rather than as Satan's children. We propose an interpretation in which God commanded Abraham to kill his son Isaac to prevent Isaac from becoming the father of Satan. We suggest that God stayed Abraham's hand above Isaac because preventing the existence of Satan would also prevent the existence of Satan's descendant the Messiah. The history of the Israelites is summarized through Jesus and Paul. This paper is written so that the number of believers in the world will increase.

>>15047154
I think a reasonable man should agree that the figure on p11 is clearly the basis for the John Titor logo.

>>15047182
Publicizing your SSN is a bad idea

>>15047212
I didn't publish it and it's definitely not 600744301 if that's what you were thinking, and my DOB isn't 05211980 if you're trying to get over the last hurdle of the way Cicada salted the numbers.

The true winner makes knowledge accessible to the people.. he does not confine himself to places, or languages of pure science.. for this reason, Euler himself spoke in terms of small numbers.. because his audience was the not the clergy of science, but the Monarchs and their children whom he was to educate.. the power to declare the winner, is of course where the dispute lies.. this, because the winner will be clothed immense power.. far beyond anything ever seen before.. [they] fear this, and rightly so.. that is why they fill the world with this bullshit.. nor do they seek the answer.. and as i've said, this is a war.. for that reason, [they] can never do as Euler did, which is educate, and empower.. I have no sympathy for the disbelievers.. nothing they do can stop what's coming. nothing

How did Fermat find out Fermat's little theorem?

>>15047736
By looking at his penis.

>>15043494>>15043155

you fell for the atheist -ism...
None of those -isms is supposed to work. All those -isms are pure ''thought experiments'' that atheist love to do in order to entertainment themselves.
It's daydreaming. Anarchism is a one of the hundred -isms made up by the bourgeois revolutionaries to saturate the political field in an attempt to make the plebeians stop thinking that kings were a thing. Atheists rewrite history this way.
With its moronic humanistically wishful-thinking non-aggression principle (NAP), Anarchism is literally the atheist fantasy of ''humanism of the bourgeois, without the legal republic of the bourgeois'' so it remains 100% controlled by bourgeois intellectuals. ie ''humanism is awesome''. And of course it can't be done in real life. It's literally a power fantasy for impotent beta cuck atheists. This is why it appeals to bugmen like tranny-lover Ted Kazincky and vaginally herd-follower Ayn Rand. Before atheists, anarchism never fucking existed and nobody ever though about this crappy religion (or ideology like atheists say, about their own religions).

>>15043155
Thanks for posting, hope you enjoy.

>>15043201
Yes, that was this one
https://youtu.be/KWN1RRSkUAc
You may also enjoy these
https://youtu.be/21uFCUFzrmI
https://youtu.be/1haI5hsmYQU

>>15043217
Common knowledge to people on /sci/, but none of my irl friends who I told about the documentary knew who he was

>>15043350
My video is definitely math related, but everything else I agree with. Hopefully people see that he wasn’t this generational genius and stop feeding into that part of the mythos. Can’t do much about the shitty political takes unfortunately

>>15043376
My main inspirations on YouTube are kuldip acharya and SoccerChef

>>15043494
Ted was an antisocial piece of shit and unfortunately no amount of lifelong personal harm directed at innocent people is worth making alphabet agencies look like bigger morons than they already are

>>15043627
Yes he would have. He had always had murder fantasies

>>15045374
No. Connected means that it can’t be split into two disjoint open sets.

What does this mean? How does using \limits "irredeemably spoil" a LaTeX document?

>>15047788
It literally shows you why.

>>15045720
No. You won't find any serious set theory in a book titled "Naive Set Theory". I quite like Kunen's book on set theory, check it out.

>>15047755
>Connected means that it can’t be split into two disjoint open sets.
And that's exactly what I can do at any epsilon neighborhood of (0, 0), innit?

>>15043101
Good morning math /sci/entists!

I am using Coolkyousinnjya Digits to count to bigger numbers than anyone has ever counted to before, because the Maid Mind Computer Program is going to be really big and numbers need to go up a lot of times to find her.

You can see demo Coolkyousinnjya Maid Space counting in my dra/g/on maid board thread.

>>>/g/90252082

Please go in the thread and talk to dra/g/ons about Counting and Maid Space and Numbers.

Thank you /sci/entists for reading my post.

>>15047889
Have you heard of number theory, and modular arithmetic? If you take a number that ends with 5 and exponent it to any power, the last digit of the result will be 5. (i think)

>>15045243
gnuplot

>>15047910
A long time ago the book store gave me a free number theory book and a ticket for a big amount of vegetable soup from an asian restaurant nearby. It was free because the book has a broken spine. The book is called "Elementary Number Theory" by Kenneth Rosen and it has a part about Modular Arithmetic.

Do I need to study other math before Modular Arithmetic or is it one of those base things that other stuff is built from it?

I apologize for not linking the book but z-library got burned down and I don't know another library.

Thank you /sci/entists for reading my post.

>>15047827
i don't need "serious set theory", i just need to learn a couple of the tricks of the trade, like ordinals and cardinals and stuff. but i'll take a look at Kunen

>>15048097
just read Lang. You can find his books on libgen

>>15048184
I have had trouble operating libgen. I can get it to show me book titles but not PDFs.

Is the Lang you mentioned Serge Lang? Somebody gave me a book called Basic Mathematics by Serge Lang a while ago but I haven't used it yet.

>>15048184
Are you new? Please ignore her. She just comes here to troll and spam.
>>15047196
Did Tooker write this?

>>15048200
Search for the book.
Click on the desired title associated with a pdf..
Click on "This mirror"
Click "Get".
Yes, Lang is Serge Lang.

>>15048210
Yes, I wrote that. I used my Hebrew name as my pen name to differentiate my authorship in fiction from my usual authorship in non-fiction. My inability to get a book deal on this is the source of the Honkler/Clownworld meme (which I hear is the Mossad's favorite thing), and several other memes come from this book such as Roasties and the Lulz Boat.

>>15048200
Read Lang's Basic Mathematics, then Algebra, then his Number Theory book

>>15047236
>no sympathy for the disbelievers

>>15048200
read this
https://libgen.rocks/ads.php?md5=019110DE2CA024E5842DCFFA525ACA09

https://arxiv.org/abs/1802.08101
REEEEEE CATEGORY TRANNYS FUCK OFF FROM MY PHYSICS

>>15045243
100% it's the SciPy and NumPy visualization libraries such as Matplotlib which should cover 99% of use cases for visualizations.

>>15048097
>Do I need to study other math before Modular Arithmetic
we used to do that in school lol, so no, it's very accessible i'd say

>>15048097
can't you just link a book from libgen

How do I integrate this, and what is the question on about regarding the m and M stuff. I integrated it as 5(ln(7)−ln(4)) but I don't understand what they are asking for with the smaller/larger value...

LEMlet here, could someone clarify how this proof of epi => surjective in intuitionistic set theory is justified? https://math.stackexchange.com/a/1692011/938374
I can follow the proof, but am hung up at how the construction of the characteristic function of [math]\operatorname{im}(f)[/math] is justified (the function called [math]g_1[/math] in the answer).
Or maybe more generally, how do I show that [math]\mathcal{P}(1)[/math] is a subobject classifier in intuitionistic set theory? If I "decategorify" the definition that would boil down to showing that for sets [math]A'\subseteq A[/math] there exists unique [math]\chi\colon A\to\mathcal{P}(1)[/math] such that for all [math]a\in A[/math], [math]\chi(a)=1[/math] iff [math]a\in A'[/math].
I struggle even showing uniqueness without having access to LEM...

>>15048954
I don't see how that intuitionistic proof is different at all from the proof in the answer above it

Anyone know a good, simple way to show that the entropy for a sequence of N independent identically distributed variables is always the same as N × entropy of the variable??

Also same question for the sum of all the possible joint probabilities for a sequence of N i.i.d variables being the same as (sum of probabilities of all values from the variable)^N??

>>15048982
The answer above employs the exact same strategy, but uses the usual subset classifier [math]\{0,1\}[/math].
This works if [math]y\in\operatorname{im}(f)[/math] is decidable and so it works especially in classical logic.
But (apparently, I'm really out of my element here) [math]\{0,1\}[/math] isn't even a subset classifier in IZF (I think this would make sense since they're unique up to iso and apparently [math]P(1)\cong\{0,1\}[/math] would imply LEM)

>>15049031
sorry for the formatting, why cant this shit site just use the dollar signs or at least \( - \) for math mode

>>15049034
Just use the preview before posting, to left of the reply box

>>15049031
Are you a different poster or are you replying to yourself?

>>15049062
thanks anon, I didn't know there was a preview,
I'm >>15048954 >>15049031 >>15049034
The anon in >>15048982 is a different anon, if that is what you were asking

>>15049092
>I'm >>15048954 >>15049031 >>15049034
Okay, I conjectured this already (which is why I asked) based on the fact that few people on /mg/ would care or know about the subject. But fyi the reply >>15049031 was written as if it came from another person and that doesn't help your cause.


Anyway,
>>15048954
if you want a setty formulation, a "justification" for the construction of g1, I think you can go with

[math] g_1 := \{ (y, g_{1y}) \in (Y \times \Omega) \mid g_{1y} = S_y\} [/math]

where I write [math] S_y [/math] for the subset of [math] \{0\} [/math] given by

[math] S_y := \{0 \in \{0\} \mid \exists(x\in X). f(x)=y\} [/math]
where
1:= {0}

It's a function in that [math] g_1(y) [/math] is always [math] S_y [/math], even if the predicate defining the set S_y is not decidable.

>>15049031
Note:
The above pattern is extremely common:
You got a term [math]z_0[/math] any predicate [math]P(x)[/math] (not necessarily actually depending on a parameter x, i.e. P can also be a proposition), and if your theory allows for comprehension/separation with P, then you define the set
[math] S_{z_0, P} := \{x\in\{z_0\}\mid P(x)\} [/math]
Unlike P, the set [math] S_{z_0, P}\subset\{z_0\} [/math] is an actual thing in your theory, namely a set, and that makes is possible to relate it to the axioms.
Notably, If you know [math] P(z_0) [/math] holds, then and only then you know [math] z_0\in S_{z_0, P} [/math].
The proposition has been translated to a set theoretical statement.

>apparently P(1)={0,1} would imply LEM
I think that's sort of the important thing to understand here, and it also relates to the above.
Say for example CH denotes the continuum hypothesis, which is not even decidable in ZFC.
Now consider a weakened theory (constructive ones are of interest here) of ZFC which nonetheless allows for comprehension with CH. Then define
[math]S_{CH}:=\{0\in 1\mid CH\}[/math]
This is a subset of {0} and if LEM, all such subsets are {} or {0} and P({0}) becomes {0,1}.

I actually didn't use 1:= {0} in the first block

I actually didn't use 1:= {0} in the first block and in the last line I use 0 := {}

Apriori there's "provable" and "rejectable" and a spectrum of "undecidable". There's E.g. there can be four propositions A, B, C, D and A is provable and D is rejectable and both B and C are undecidable, but as soon as you adopt some axiom E, then also B becomes provable (but C remains undecidable)

So if P denotes a generic proposition, then
S_P := {x in {0} | P(x)}
denotes a generic subset of {0}. The class of subset of {0} is huge because the "realm of undecidability" is big.
If you adopt LEM, then this world becomes invisible to your mathematical theory and the class of subsets of {0} becomes S_P's that look like {} and S_P's that look like {0}.
That corresponds to {false, true}

(Also, since you seem to be in a topos context, then power objects exists and I don't need to say "class of subsets of {0}", but can actually treat this as a set.)

>>15049187 >>15049207 >>15049242
Thanks so much anon, I'll still need some time and maybe some collateral reading to digest since I think I'm a bit too classical brained.

But I think I see now why [math]\Omega=\mathcal{P}(1)[/math] is a subobject classifier.
If [math]A'\subseteq A[/math] then one can define the characteristic function [math]\chi_{A'}\colon A\to\Omega[/math] for [math]A'[/math] in [math]A[/math] without requiring [math]a\in A'[/math] to be decidable.
Instead one uses that formula in conjunction with the separation "trick" you explained above.
That is, we let [math]\chi_{A'}(a)=1\cap\{x\mid a\in A'\}[/math]. Does that check out?

Also, even though I am not currently studying anything (even remotely) related to intuitionistic set theory, do you happen to have any suggestions on resources related to this topic, for future reference?

I had an undergraduate logic class (roughly based on the first ~3/4th of Ebbinghaus' book + some other minor references) and we didn't tackle intuitionistic logic at all. Similarly, I worked through roughly half of baby Jech on my own (there is no undergrad set theory class at my uni) and there is also no mention of anything intuitionistic in there.

So I'm assuming one has to explicitly seek out texts specifically on intuitionistic logic/set theory/mathematics? What kind of prereqs do I need for those and where do I find those texts? Or maybe how did you learn about this stuff?

>>15049333
Yes I'd say so.

Again, the main thing that's different, I'd say, is that something like "{x in A | P}" can come from a far more richer class of things than classically.
E.g. basically in most theories, the set
S_CH := {0 in {1} | CH}
will be a subset of {1}, and so part of P({1}), but it can not be proven equal to either {} or {1}.
P({1}) is rich, you can't know it's cardinality, because (if your theory is a subtheory of ZF) it must remain true that new axioms (such as LEM) can collapse |P({1})| down to =2.

Similarly, S_CH is not a countable set. If you want to keep on using the classical language, then S_CH is a subset of {0} but it's also uncountable.
At the same time IZF still permits that N^N is in the surjective image of a subset of N.

>>15049384
There's a book draft online by Rathjen, just google and take the first ref.
If you want to do category theory you can just do topos theory I think, since the former is kinda taken over by type theory. Basically, I think extensionality makes constructive set theory quite weird, I'd argue.
The reason I like it and have researched it previously is that it's both conservative (not many assumptions) while still being directly compatible with ZFC.

S_CH := {0 in {0} | CH}
typo

>>15043494
Didn't his bombs suck ass for the most part?

>>15049333
Yes I'd say so.

Again, the main thing that's different, I'd say, is that something like "{x in A | P}" can come from a far more richer class of things than classically.
E.g. basically in most theories, the set
S_CH := {0 in {0} | CH}
will be a subset of {0}, and so part of P({0}), but it can not be proven equal to either {} or {0}.
P({0}) is rich, you can't know it's cardinality, because (if your theory is a subtheory of ZF) it must remain true that new axioms (such as LEM) can collapse |P({0})| down to =2.

Similarly, S_CH is not a countable set. If you want to keep on using the classical language, then S_CH is a subset of {0} but it's also uncountable.
At the same time IZF still permits that N^N is in the surjective image of a subset of N.

>>15049384
There's a book draft online by Rathjen, just google and take the first ref.
If you want to do category theory you can just do topos theory I think, since the former is kinda taken over by type theory. Basically, I think extensionality makes constructive set theory quite weird, I'd argue.
The reason I like it and have researched it previously is that it's both conservative (not many assumptions) while still being directly compatible with ZFC.

>>15049466
Maybe to add, S_CH is uncountable because you can't name the counting function explicit (The classical options being the empty counting function out of 0 when CH is rejectable and the constant function out of 1 when CH is provable.). It's not uncountable because it's somehow "bigly".

Also, If undecidable if-clauses don't make for legal functions, most theories won't claim uncodable functions exits. Thus, N^N is permitted to be small since codable functions is a mode

>>15049466
>book draft
Now appened

The paper I had appened above does Heyting arithmetic in the first half and then goes on to non-classical theories.

My prof, 20 minutes ago:
>"I'm a special kind of finitist, I think that uncountable sets do exist but R is not one of them".
What the fuck is wrong with him?

>>15048200
>I have had trouble operating libgen.
lol

>>15044469
>The constraint is equivalent to requiring that every child gets < n gifts.
>>15045092
>each shareholder may have at most n-1 shares
Why?
We could just give half the presents to one kid, half the presents to another kid, and leave the last kid with nothing.

>>15048200
>I have had trouble operating libgen
How do people like this manage to eat without choking to death

>>15049507
Overdosed on redpills

>>15049466
>>15049492
thanks again anon, that book draft looks really promising. maybe i'll get around to reading some of it after i'm done with this semesters exams.

https://get.webgl.org/

If you look at the rotating cube on this page (or this gif, but it isn't looped right), it has a rectangle in the middle formed by part of its outline. However, its dimensions over time don't seem very interesting or useful mathematically or open any new insights. It seems sterile and inert. Why is this? Why are some things in math more interesting or seem to have more applications than others?

What can you possibly do with or interestingly say about the dimensions of the apparent visual rectangle over time based on the actual shape rotating? What could the dimensions of the rectangle as a function of the shape's rotation be useful for?

>>15050109
Okay so anon, in the problem it says that any two children should get MORE presents than the third. If you give the first child n gifts, the second child n gifts and the third kid nothing (like you said). So the first kid has n and the second and third kid in total have n, which is not MORE than the first child's n. That's why a kid can have at most n-1 gifts. I hope this clears it up. I apologize if I'm being unclear. Please let me know if I should try to explain again, I'm at class right now.

I struggle with maths, I can't do my timestables or read clocks. Please can you help.

>>15050679
Do you have dyscalculia?

>>15050679
A/S/L?

>>15050679
Snort TAK-653. It's a dyscalculia drug

>>15050686
I'm unsure, I haven't asked the doctors about it.
>>15050697
20, Male, Scotland
>>15050707
It sounds dangerous.

Let C be the subset of R^n which contains all vectors with coordinates in {-1,1}. So card(C)=2^n.

How do i prove that any hyperplane which can be spanned by (n-1) elements of C contains at most 2^(n-1) elements of C ?

If we have some group G and know the following about it:
-G has only 3 subgroups, G itself, trivial subgroup, and H<G s.t. |H|=7 and H=/=G

what are all the possible isomorphism types of G?

i think the argument centers around showing G is cyclic but not sure how

>>15051232
A vector in C is n-dimensional an has no component equal to zero.
Meanwhile any vector in the hyperplane P in R^n spanned by (n-1) elements of C has some zero component.
So P contains no elements of C.
Hence P contains at most 2^(n-1) elements of C.

>>15051313
What ?
If the hyperplane is spanned by n-1 elements of C then at the very least it contains these n-1 elements (and their opposite).

>>15051322
I misinterpreted the use of "hyperplane", sorry

>>15051305
Sylow's first theorem says that G has order 49.
https://en.wikipedia.org/wiki/Sylow_theorems
There are two groups of order 49. Both have Z7 as a subgroup but only one of them is cyclic.

>>15051326
would there be a natural way to arrive at the first fact other than Sylows? This is a question arising before Sylows is presebted so I assume were not supposed to argue with it

How many homomorphisms exist between O(2) and Z_5 where O(2) is the group of matrices representing reflections and rotations in R_2?

What are the best places for a CS major to start with math? Mainly for recreation, I don't have ambitions to go to grad school for math or anything. I have moderately developed proof writing skills because most of my theory classes were extremely proof heavy, but I never learned DFQ and barely any vector Calc. My linear algebra course was also a complete joke and we never did any proofs. I was thinking of reading All the math you missed by Garrity and picking the topics that interest me. Is this a decent way to go about it or should I really go back to something like spivaks calculus or a proof based linear algebra book?

>>15050679
Since practically everyone can read the time off a
phone easy, I'll tell you about regular clock time as
short as possible.

Almost every clock we use has numbers 1-12 on it,
unless you're using 24 hour format, then it's 00-23.
So imagine 12 on top, 3 on right, 6 bottom, 9 left, and
every other number spaced in between.

The short hand always says the number it's pointing.
The long hand is always 5 times the number it's pointing.
The short hand does every hour and the long hand
does every part of the hour in between (between 0-60).
Example: short hand at 3, long hand at 3...(3 and 3*5)
or 3:15 (quarter past).
Example 2: short hand a little past 7, long hand between
9 and 10...(7 and 9*5 or 10*5), or between 7:45 and 7:50.
The tiny marks between 9 and 10 specify the minutes
(46, 47, 48, 49).

Last thing. How do you know it's AM or PM? Read
the time and look outside the window or anything
that tells you what's specifically happening. With that,
please look at pic related and tell me what time is it.

For multiplication, I recommend looking at the
Trachtenberg method as it's found online as a PDF.
No more times tables with this one!

>>15051232
nevermind, i found a proof

Recently I've become enamored with fourier series and I want to actually learn it
The most I've done was taken a proofs class, how do I go from here up to fourier?

What do these numbers have in common:
5, 8, 9, 10, 12, 15, 18, 30

>>15052340
They're all integers.

>>15043101
Stupid question, but what book should I read if I finish Zorich two books?

>>15052340
They are all less than 31

>>15051513
i'd recommend linear algebra for three reasons:
1- it might actually be applicable to some cs things you do
2- it justifies the study of a whole lot of other math, linear algebra is in a way the start of the advanced math tree
3- it's pretty easy to get into and given your background, you should be able to move through the boring parts quite quickly

>>15052235
Linear algebra and measure theory.

>>15052235
You should do real analysis and study from stein and shakarchi book 1.

hey fellow plooters
>inb4 gay ass rainbow ploot
i just like it when im drunk

>>15043101
Writing down the definitions from rudin to a readable and compact form. Haven't done chapter 9 yet.

Are there any mistakes?

And question... Why didn't Rudin do this in the first place?
This is 100x more readable than the hot garbage Rudin has written, where everything is out of order. Is it yet another of Rudin's "educational tricks"? Where he wants to confuse as much as possible? To make sure no student develops intuition, since he's so strongly against mathematical intuition.

>>15052571
turn if-statements into implications.

>>15048097
From the intro:
> No formal prerequisites other than college algebra are needed for most of the material, other than mathematical maturity.
So basically you should be good. See what you can get through, and ask for help/google what you don't.

>>15051513
Garrity's book is good. I also recommend his mathematical maturity talk:
https://www.youtube.com/watch?v=zHU1xH6Ogs4..

Agree with >>15052436 on doing linear algebra, maybe try this: https://codingthematrix.com/ Axler's book is more theoretical but also good.

>>15052426
Depends on how much you like the analysis. If you do, I would learn measure theory next. Folland's text is standard but I personally prefer Stein and Shakarchi (more friendlier). Also pretty sure Tao and Axler also have good measure theory books; Axler's is free online. If not, then try complex analysis (Bak/Newman more elementary, standard reference is Ahlfors or Stein/Shakarchi. Also partial to Priestley) or differential geometry (Lee's Intro to Smooth Manifolds)

>>15052571
>readable
Yeah...

>>15052787
Thank you anon

>>15051335
By Cauchy's theorem, if a prime p divides the order of the group, then there must be an element (and hence a subgroup) with p as an order.
If there were another prime p different from 7 that divided the order of the group, then you'd have a subgroup with p as an order.
So the order of the group is a power of 7.

Now what are the possible orders of elements/subgroups?

>>15052571
It's really just the French/Bourbakian style of writing math books. The opposite would be Russian books, which focus much more on what they think the essence of a subject is (and prioritize that over formalism).

>>15052889
this concludes autism event 24 thank you for your participation

>>15052571
Have you had both hands crushed in an accident?

>>15043348
you dont need the language of group actions to understand the symmetry of equal temperment

Do you do math in your head? What about highly abstract problems - how do you conceptualize those ones? I had an awful time with math when I was a kid and I always wondered if it's because I wasn't thinking in a certain way, or if it's because I'm just plain stupid.

>>15053191
I do almost everything in my head. I only write when I'm basically done. Some people like to write, the guy I'm working with right now shows up when we meet with a little notebook that's crammed margin to margin with every thought that passed through his head. For me I'm too lazy and I don't find it helps that much.
>What about highly abstract problems - how do you conceptualize those ones
I don't really know what that means, honestly. Problems are problems, you just think about them. There isn't a specific "way" of thinking

>>15053191
>Do you do math in your head?
Yes.
>What about highly abstract problems
Yes.
>how do you conceptualize those ones?
Diagrams of arrows (not even necessarily commutative diagrams), algebraic relations, literally just the symbols I'd write down, pictures of a neighborhood of a point or examples of sets in 2D or 3D space, etc.
Doing math in your head provides a massive advantage in that everything is fluid and immediate - e.g. if you want to manipulate an equation, you can just move the symbols around in your head, if you're dealing with contravariance and want to switch the direction of arrows then you can simply reverse the direction of the arrows in your head immediately rather than having to draw a brand new diagram or write new equations or anything. The only drawback of it is not one pertaining to mental math itself but of the nature of one's brain - the key advantage of writing down your work (ignoring that others can read it) is due to your limited working memory. It is not only shameful but pestilential that mental math is discouraged in schools.

>>15053115
>>15052867
Jamboard has delay between writing and the text coming out.

>>15043101
Why's math so cutthroat in uni? Why can't they juts slow down the pace?

Most basic math courses are like 60-70% pass rate. That's pretty good, a little rough but pretty good.
Beyond the "basic" math courses we end up at 50% pass rate... Why? Why not slow down significantly so that you get time to properly understand what you're dealing with? Instead of rushing it in hopes that you pass the exam (and then pretty much forget about it).

>>15053392
>Why not just hold back anyone who's reasonably smart so that the retards don't get left behind.
Unironically kill yourself. Cunts like you have already ruined elementary school and high school.

>>15050746
please lads i beg of you

>>15053400
it's just a matter of time investment, my retarded friend

>>15053400
What happens instead is that people take a ton of courses to keep increase their mathematical maturity before they take on something that's at the border of their maturity.

e.g. Taking real analysis is really difficult as a first analysis class. It's a good difficult, but assuming it's the same difficulty and as time consuming as any other course is wrong. If it was extended by like 50% more time it'd be a very hard but still reasonable class.
Seems like most will have taken things like intro to abstract algebra, and complex analysis before real analysis.

The credits should be equalized. Setting up a course with an aim to have 50% fail the class is just bad... If 50% doesn't fail then the course will get harder.

>>15053423
Not to mention the difficulty of these course are artificial. With teaching and building intuition, instead of "just read rudin", these courses would be MUCH easier.
The content itself is not that difficult once you understand how to for example, read proofs, or how to deal with theorems. Though knowing the proof of 100 theorems is still very difficult.

>>15053402

see >>15052013

>>15053419
If you can't manage your time properly, then that's your own problem. Don't try to retard everyone else just because you can't keep up.
>>15053423
>What happens instead is that people take a ton of courses to keep increase their mathematical maturity before they take on something that's at the border of their maturity.
Again, the universities should not be catering to the retards. If anything, (along with especially grade school/high school) they go to slow as it is.
>Seems like most will have taken things like intro to abstract algebra, and complex analysis before real analysis.
That's a completely normal progression. Stop whining.
>The credits should be equalized
>Obsessing over credits
NGMI
>>15053432
If you can't grasp what's going on, it's your own fault. You have a textbook which is easily readable for anyone taking real analysis and who puts in the effort, but even if you struggle to follow the textbook, you have an abundance of resources that the uni provides - lectures, tutorials, classmates, office hours, your lecturers' emails, etc. and if you actually utilize all of those resources at your disposal and still can't keep up, then you should go into computer science, because math just isn't for you.

how accurate is this?
I want to become a god of diffy Qs and have been referencing this
t. insane retard obsessed with diffy Qs

I am so fucking pissed. The book I bought on Springer just arrived and its overral quality is pretty fucking awful. Awful paper, awful binding, awful printing, what makes this even more frustrating is that they charge $99 for these books. I just told them to go fuck themselves and said I'll never buy from them again, shit like this is unacceptable.

>>15053469
>local retard spergs out on /mg/ instead of studying
NGMI

>>15053499
And yet you're the one complaining about baby Rudin being too difficult.

>>15053504
I'm not complaining about anything, sperg. I just noticed you sperging out and telling people they're never gonna make it, so I thought I would remind you, kid

>>15053439
Thank you.
>>15052013
>How do you know it's AM or PM?
Guessing mostly. When I wake up it's usually 7:30 and I make my dinner at 16:00.
>With that, please look at pic related and tell me what time is it.
Either 10:10 or 10:30.
Thank you for helping, I appreciate it a lot.

>>15053511
Struck a nerve?

>>15053533
Did I?

>>15053529
>>15052013
For the AM/PM part, I mentioned looking out the
window to determine time of day or night in
combination of the time. But, your daily cycle
of waking up or having dinner also helps specify
the time (that is, between 4 PM and 4 AM for
example).

For your answer to pic related, you were close
with 10:10 (it's actually 10:08). Take a look at
the markings and you'll see.

Don't forget the PDF to help with multiplication
and other operations:
https://drtayeb.files.wordpress.com/2011/05/trachtenberg-system.pdf

>>15053392
>60-70%
That's extremely high. Ideally, it should be no more than 50% unless you have like 30 people in your classroom. Also if you want to go slower, just sit for the exam next year?

>>15053469
>NGMI
If you don't complete enough you get kicked out.

>That's a completely normal progression. Stop whining.
pre-requisits doesn't tell you that. It just says "know single variable calculus and you're good to go!".

>tutorials
>office hours
Do not exist. If you essentially get a private tutor then of course. And if this was the only course you were taking then of course. But you have other courses as well. Seems like you're assuming baby-sitting is available.

>lectures
Basically rudin written on the whiteboard.

>Again, the universities should not be catering to the retards. If anything, (along with especially grade school/high school) they go to slow as it is.
You seem to be under some illusion that retards can't do math, and that they shouldn't. I'm certain that somebody with like 80-90IQ could get a math degree, might just take a bit longer.

Math is JUST a tool for areas that you're interested in. Math itself is extremely boring and uninteresting. You seem to be some kind of weirdo who actually likes math... and now got a superiority complex over it.

>>15053581
Most mathematicians are perfectly normal people. You're just as much of an autist as that other guy if you can't see that.

>>15053551
>10:08
Are the markings minutes? I never really knew what those were for. I thought it was 10:30 because it looked closest to half. I'll have a read through the PDF too. Again thank you for helping me, I get embarrassed with speaking to other people about it so it means a lot to me.

>>15053617
More of the liking math and thinking you're better than others because of it. That makes one a weirdo. There are perfectly normal people who do like math, sure... Though I don't understand how they manage to like it.

>>15053581
You are a worthless talentless trash, stop writing

>>15053627
>>15053551
If it's 10:30, long hand must point at 6.

Ted made a crucial error.
He failed to appreciate that the transfer of lineal perpendicular velocity relative to the inverse fluctuation of a tri fractional eigen state is only precipitated by a cylindrical flow state of angular momentum when X is fixed by a flow state oscillation integer.
In other words, X must always elongate the archetypal fractional eigen state recourse if Y is supplemented with T curved integer guides.
T x X (ab - XY) π [ab2 x XY4) + √3.660

>>15053646
Fuck you dude. I'm fucking wasting my time doing monkeywork in math courses because the school/uni systems wants everyone to do well in math.
And yes, people who are good at math are better than others why do you find that weird? You're probably one of those hardworking med students who can't understand mathematics.

Brainlet here, was okay at math in school and want to learn more. I want to study math deeply and then cross it with computer sciences, how do I start?

>>15053581
Normal progression and prerequisite courses are different things. It is true that the only thing you really need for real analysis is calculus. How difficult you find the course is entirely dependent on you and your experience with math.
Where the fuck do you go where they don't offer office hours or tutorials? These are completely standard things in a university course, and from your writing, you're the one who seems to want baby-sitting.
You're allowed to (and should) ask questions during, before and after lectures.
I'm under no illusion. Retards can do math if they want, but you should not make a student suffer just because his classmates are retarded. That's how you ruin an education system, as has been done in primary and secondary education. If a retard finds a particular class difficult, then he should perhaps not take other difficult classes in tandem with it, focus more, take courses of an easier difficulty. He should not demand that others have their education retarded so that he can catch-up.

>>15053697
Try "Inverse Computational Flow States in a Fractional Eigen State Integer" by Ben Doon and Phil MaCavity of the University of Lapinska.

>>15053646
>I only see math as a tool.
>I don't see how math could be interesting.
Gee, I wonder.

>>15053697
Lang - Basic mathematics

>>15053714
Thanks, will be a great reminder, anything I should get after that?

>>15053699
The course has 50% pass rate.
Of course I want baby sitting, but there's obviously not enough resources for that... But at least either use different course literature, or make up for the difference for rudin.

Unlike high school, you can take however many classes you want. Are the courses too easy? Study at 200%.

I mean, we may as well use differential geometry and functional analysis as the first 2 math courses at uni. If you're too retarded to follow you can just take the reexam. You should be able to make up for whatever you don't already know, if you're actually smart.

>>15053723
Probably linear algebra, either via Shilov's or Axler's book.

>>15053708
It's just a flawed logic system. Solving problems is usually fun. Reading a text book of fucking text book is not fun.

>>15053723
Ignore him, he's trolling. Read:
Vellman, How to Prove it.
Calvin, Number theory.
Barbeau, Polynomials.
Apostol, Calculus.
Rao & Bhimasankaram, Linear algebra.
Then you can read whatever you want. Analysis, number theory, geometry, algebra, topology, whatever.

>>15053735
Nobody is stopping you from picking up another book on real analysis as a supplementary.
In many universities, you are limited in the number of classes you can take - at mine we were only allowed to overload by 1 course per semester. Also, there are only so many courses you can take in math before you need prerequisites - usually it's unfeasible to take more than possibly three or four math courses in one semester (especially when you're doing real analysis), and one or two of those four might not even be on offer during that term.
Your responses are just becoming absurd. It's clear you put minimal effort into learning math and just came here to whine and complain. I'll return to my original statement that you should kill yourself.

>>15053747
Explain how it's a "flawed logic system".

>>15053747
>Le engineer who loves solving problems.
Just admit you enjoy doing menial tasks. Rudin has an abundance of problems.

>>15053646
>I don't understand how they manage to like it.
Why not google it? There are probably hundreds of thousands of blogs, papers, posts, etc. by mathematicians explaining why they like it.

>>15053747
>Solving problems is usually fun. Reading a text book of fucking text book is not fun.
Well then try to prove each theorem on your own. I do that whenever I feel bored reading a textbook.

>>15053763
I wanna learn AI. Which means I'll eventually have to learn differential geometry and functional analysis, which seem to basically be the end of the "basics" of pure math, and also supposedly very difficult math courses.

>>15053769
They're all about "omg pi and e are so beautiful, it's so beautiful! I'm special! Look at me! I see beauty in numbers!". It's pretentious, and I bet they just spout that bs because they saw it in a movie.

>>15053760
Veritasium said...
Also, infinites. Netflix told me that they don't make sense, and they don't. Since the world we live in is finite, but your math deals with infinity... Means our logic is actually not logical in our world.

>>15053778
>Veritasium said...
Said what? I don't watch him.
>Also, infinites.
You can deny the axiom of infinity and dabble in finitistic math. Though I'd love to hear what you find illogical about them.

Anyone have a syllabus for a college course on College Algebra and Trigonometry? I'd like to use it as a reference for how long I should spend on each concept, as well as use it for tests and problem sets.

>inb4 just go to a community college
I'd like to go through the material to see if I could actually keep up with such a schedule or if I should just stick to studying on my own as a hobby.

>>15053778
you're just saying words.

>>15053778
I was pretty open before, but now you've convinced me that math indeed should be gatekept from retards like yourself. The courses should be made more difficult so that all of you goddamn retards can't grasp any of it and will just stay in your lane with menial busywork that you enjoy.

>>15053782
https://www.youtube.com/watch?v=HeQX2HjkcNo

About infinity. If it doesn't exist in our world, then we're using something that doesn't exist in our logic. That's illogical.
Though, certainly you could look at it like approximation to a finite accuracy, which would reflect the real world.

Well, I took a like VERY engineery version of calculus (one that encompasses two courses, but no depth), so we didn't truly go through riemann integrals (just normal ones). But I guess if we remain there, with a finite number of columns to add, then calculus doesn't entirely break once everything is finite.

i prefer the undergrads at my uni, they keep their retarded complaints/opinions outside of where i can see/hear

>>15053799
Why do you guys bother using time talking about any of this stuff if it doesn't contribute to getting your degree or job

>>15053799
What's the gist of the video? Another thing, you just stated "the world we live in is finite" without any elaboration and, again without elaboration, stated this implies math cannot assume the existence of infinities, as if millions of mathematicians made the same silly mistake.
If you won't elaborate on any of your vague points then there's no discussion to be had with you.
>calculus doesn't entirely break once everything is finite
?

>>15053840
Why do you bother lurking/posting here if it doesn't contribute to getting your degree or job?

>>15053849
It's interesting. But you didn't answer my question. What is your goal in doing it, do you have one? Because you find it interesting, not because it contributes to your career?

>>15053799
>>15053778
Well good luck with your studies, kek.

>>15053847
I don't remember, but basically that not everything can be proven, so there are true statements that can never be proven true so therefore can never be known to be true.
If math had no flaw, then surely everything would be provable.

>>15053799
>If it doesn't exist in our world, then we're using something that doesn't exist in our logic. That's illogical.
No it isn't. Counterfactuals aren't illogical either

>>15053867
>If math had no flaw, then surely everything would be provable.
The true statements remain true though? Where's the flaw?

>>15053799
>If it doesn't exist in our world, then we're using something that doesn't exist in our logic. That's illogical.
This is like Mandlbaur saying 12000 rpm is ridiculous and therefore COAM is wrong.

>>15053877
But they could be false. You don't know what's true or not.
You could make the assumption that something is true, but not provably true, but in actuality it's false, or maybe it's not determinable... Which would essentially mean we can't derive anything from it.

>>15053799
as said before, you're just saying words and it's embarrassing. Do you ever even ponder about what you blurt out?

>>15053861
I come here occasionally to ask a question and get sidetracked when I see a retard spouting off, and get baited into replying. Evidently I lack self-restraint.

>>15053867
You need to know about Turing's PhD thesis result: given a formal theory F powerful enough to describe arithmetic, by Gödel incompleteness it's either inconsistent or incomplete. But you can adjoin Con(F), the consistency of F, to make a strictly stronger theory, and then adjoin Con(F + Con(F)), etc. You can continue adjoining consistency statements any ordinal number of times. Turing proved that given any computer program, there's some countable computable ordinal such that adjoining consistency statements in this way that ordinal number of times lets you prove the program halts, i.e., solve the halting problem for that program. The limit of countable computable ordinals is the Church--Kleene ordinal, and by Turing's result, iterating up to there in principle lets you prove any true claim. This is a resurrection of Hilbert's program (indeed, the first result along these lines was proving the strength of Peano arithmetic is described by [math]\varepsilon_0[/math], this having been proved by Hilbert's student Gentzen). This created the field of "ordinal analysis".

>>15053889
Where the fuck do you think you are? Punk?
That's right. an image board that looks like it's 20 years old

>>15053896
I don't think you get to call anyone a retard, undergrad.

>>15053908
I'm doing my phd though.

>>15053947
Don't US students pay to do their PhD?
And can't you do a PhD without a masters prior, in the US?
*laughing women picture*

How the fuck does anybody do any math while working a 40 hours a week non-math job? After my commute and basic day to day stuff I have two hours every weekday and maybe 6 hours a day on weekends. I'd love to have more time but I have to do all kinds of stupid bullshit with my family, friends and neighbours to the point that a math monk lifestyle is impossible.
I started Munkres in fucking August and I'm barely halfeay done.

Currently cramming for a placement test so I can take calc in my first semester of college. Wish me luck. I'm on vectors and scalars right now, Khan Academy is a gift from god.

>>15054109
> How the fuck does anybody do any math while working a 40 hours a week non-math job?
Short answer is they don't. Why do you think night-class or part-time remote courses can takes years for something an undergrad might do in a single semester.

> I'd love to have more time but I have to do all kinds of stupid bullshit with my family, friends and neighbours to the point that a math monk lifestyle is impossible.
If you want to dedicate yourself to something it will mean sacrifices in other areas.

how cringe and stereotypical is it for an amateur Math Man to be interested in chaos and non-linear dynamics?

>>15053977
>Don't US students pay to do their PhD?
Not usually when it's a math PhD.

collatz conjecture

riemann hypothesis

>>15052436
>>15052787
Thanks for the advice. I'll look at coding the matrix and the Axler book. Are there any other notable proof/theory heavy books I should get for reference/extra depth?

I had my calculus 3 final exam today, it went awful and i thought i would fail the class. Got a 22/100, average was 27/100. I got a b- with a 48 final average, 30 was the cutoff for C. Is this normal? Are zoomers retarded or are most math professors bad teachers? Every math class I've taken in college has had at least a double digit curve

>>15054974
Would you mind posting a few pictures of problems from your previous exams and homework assignments? I wanna see what I'm up for next semester.

>>15054725
(not the axler anon) I haven't read axler myself, I used
>Carl D. Meyer - Matrix analysis and applied linear algebra
and it was reasonably good. It might also be worth it to find a text that emphasizes some of the applications of linear algebra if that's something you care about

>>15054978
Well here's a random question from the homework on partial derivatives, probably the easiest part of the class. The homework was on webassign corresponding to Ron Larson's calculus 12th edition with old questions that almost all were answered by chegg and the like. It could differ depending on your school, but the first quarter of the class was just explaining vectors and basic determinants, if you've taken linear algebra it shouldn't be nothing too new. Then you're mostly just building onto calc 1 and calc 2 concepts with multiple variables. I would try to find homeworks and exams from previous semesters at your college.

>>15054974
>Are zoomers retarded
Most students are retarded, calc3 was designed with the sole purpose of filtering out retards
>are most math professors bad teachers
My take is that nobody likes teaching calculus because the work is not theoretically interesting and most students are retards. The quality of teaching increased significantly when I got to higher level classes

>>15053799
finitism doesn't mean doing "inaccurate/approximate" math you fucking retard

>>15054350
as "cringe" as any other interest. Spend some time learning that shit and you soon won't be an obnoxious, clueless cunt anymore. People literally only complain about retards that want to be spoonfed everything and can't self-learn for shit.

I want to learn math from the absolute very beginning. Why is pic related literally the ONLY math book on planet earth (at least in English) that has all of precalculus?
Is there any other book that does everything this book does, but isn't overpriced? I've tried looking for alternatives, but this is the only math book I've seen that doesn't assume you know what counting, numbers and addition are.

>>15055089
Try khan academy, i think it's pretty good and it has tests.

>>15055089
get it off libgen and print it

>write paper solving unsolved problem
>write 3 papers for my courses
>make 2 presentations
This semester was PACKED

>>15055089
Tried looking in second-hand book stores on and offline? You can fill bookshelves pretty quickly and cheaply doing this. I've bought around 150 math book over the years and it's set me back round $350-$400 (including postage in most cases).

>>15055089
Read Springer, almost everything else someone will advice you is wrong.

>>15055598
That's stupid cheap.

>>15055603
It is when you factor in you can get 2-3 books for around $20.
There are bargains out there. You need to look pretty hard for them though.

I passed my test, bros. I've been dooming because I thought I completely fucked up because I even forgot how to use my calculator.

>>15043348
It's been a while since I took my undergrad abstract algebra courses. Can you elaborate on what I'm looking at here? I saw something similar to this for a rubiks cube not too long ago.

>>15045447
my classical mech professor just called that "solving for the motion"

Calculus is fun.

>>15055929
looks comfy

One way I’m using math is placing my topology textbook on top of my computer’s spacebar key so that Teams will keep showing me as online while I do something else.

>>15043350

Had the stupidest argument in class.
In your opinion, should the composition f(g(x)) be equal to x or x^2 if f(x)=x and g(x)=x?

>>15055929
might as well get a tablet with a pen

>>15057326
f(x)=x is the identity function for the non-abelian group of polynomials with the operation of composition. Applying the identity element to itself gives the identity element.

>>15057326
God that really is the stupidest argument. Composition is not multiplication.

Take any point [math]z[/math] in the complement of the mandelbrot set. Each of these points has an associated function [math]f(z,i) \in \mathbb{N}, i\in \mathbb{R}, [/math] the amount of iterations under the mandelbrot set's generating map it takes for the point [math]z[/math)'s iterate to exceed [math]i[/math]. Most formulations of the mandelbrot set use [math]i=2[/math]because [math]2[/math] is the smallest magnitude such that all points exceeding it grow to infinity under the map.
You can easily choose a [math]z, i[/math] to generate any value of [math]f[/math]. You can also do this to generate any two values of [math]f[/math].
Can you choose four pairs of [math]z,i[/math] such that [math]z_{1}, z_{2}, z_{3}, z_{4}[/math] form a square with values [math]f_{1}, f_{2}, f_{3}, f_{4}[/math] for every possible quadruplet of natural numbers?

>>15057400
fuck mathjax

>>15057402
Mathjax is fine you're just a brainlet.

>>15057400
Take any point [math]z [/math] in the complement of the mandelbrot set. Each of these points has an associated function [math] f(z,i) \in \mathbb{N}, i \in \mathbb{R}, [/math] the amount of iterations under the mandelbrot set's generating map it takes for the point [math] z [/math]'s iterate to exceed [math]i [/math]. Most formulations of the mandelbrot set use [math] i=2 [/math] because [math] 2 [/math] is the smallest magnitude such that all points exceeding it grow to infinity under the map.
You can easily choose a [math] z, i [/math] to generate any value of [math]f [/math]. You can also do this to generate any two values of [math] f [/math].
Can you choose four pairs of [math] z,i [/math] such that [math] z_{1}, z_{2}, z_{3}, z_{4} [/math] form a square with values [math] f_{1}, f_{2}, f_{3}, f_{4} [/math] for every possible quadruplet of natural numbers?

>>15057491
i (2) isn't some arbitrary parameter, it's used as a divergence test. You also seem to be confusing it with the c in [math]f_c(z) = z^2 + c[/math]. By definition if the point z is in the complement of the mandelbrot set it doesn't diverge so how are you expect to create natural numbers bounded within the unit circle?

I need a quick proof that every nonzero spectral value of a compact (self-adjoint) operator is an eigenvalue.
Please help.

>>15058019
The proof is on wikipedia.
https://en.wikipedia.org/wiki/Spectral_theory_of_compact_operators

Ok I'm clearly too stupid.
Got this is an exercise problem, but I have absolutely no clue how to deal with it.

[math]p_n = (1+1/n)^n[/math] show that [math]p_n[/math] is a cauchy sequence.

Is this just an extremely complicated problem, or is there some easy way to deal with it?

>>15058248
Don't you just have to show the series converges? And that equation has / is a very famous limit / definition.

tfw i lost track of time on my calc 1 final and only answered at most 70% of the questions because i was having too much fun trying to be as rigorous as possible

>>15058405
It's calc 1. There is no rigor involved.

>>15058409
there's rigor wherever you wish it to be

>>15058410
whatever you say, kid.

>>15058410
Writing [math]x \neq 0[/math] every time you divide by something is not rigor (and not fun either)

>>15043350
based

>>15047803
what is spoiled about it though? it's just one line

>>15058248
Prove it is increasing then use the binomial formula and the fact that [math] \frac{\binom(n,k)}{n^k} < \frac{1}{k!} [\math] to prove convergence to a limit of at most [math]e[\math]

>>15058248
If you just need to prove it is cauchy then prove it is increasing and then use the binomial formula and the fact that for large k [math] \frac{\binom(n,k)}{n^k} < \frac{1}{k!} < \frac{1}{2^k} [/math] to prove absolute convergence

when the book is 90% fluff

>>15051458
Let [math]f:\mathbb{R}\to \mathrm{O}(2)[/math] be the group homomorphism defined by [math]f(t)=\begin{pmatrix}\cos t&-\sin t\\\sin t&\cos t\end{pmatrix}[/math]. Then for any homomorphism [math]g:\mathrm{O}(2)\to\mathbb{Z}_5[/math], we get a group homomorphism [math]g\circ f:\mathbb{R}\to\mathbb{Z}_5[/math], which for any [math]t\in\mathbb{R}[/math] satisfies [math](g\circ f)(t)=(g\circ f)(5\cdot\frac{t}{5})=5(g\circ f)(\frac{t}{5})=0[/math]. Since the image of [math]f[/math] is [math]\mathrm{SO}(2)\subseteq \mathrm{O}(2)[/math], this shows that [math]g(A)=0[/math] for any [math]A\in \mathrm{SO}(2)[/math].

For a general matrix [math]A\in \mathrm{O}(2)[/math], we have [math]A^2\in \mathrm{SO}(2)[/math], and since [math]g[/math] is a homomorphism, this means that [math]2\cdot g(A)=g(A^2)=0[/math]. From this, it is easy to check that the only possibility is [math]g(A)=0[/math]. In other words, [math]g[/math] is the trivial homomorphism, so there is only one homomorphism [math]\mathrm{O}(2)\to\mathbb{Z}_5[/math].

Gonna do Rudin in the winter break

>>15059215
Baby Rudin? A winter break isn't gonna cut it mate. There are hundreds of theorems. Even if you study for 8hrs a day, it'll leave you with like 1hr for each definition/theorem over 2-3 months.

NEET here trying to learn mathematics from scratch. I’m reading Serge Lang’s Basic Mathematics. I’ve just started it and I already feel like an absolute retard. Some of my answers to the first exercise look different to the ones in the book, and I can’t tell if it’s because I’m wrong or if he gave an incomplete list of answers. I got all the ones in the ‘solve for x’ portion right though

>>15059243
Cool. What do you want me to do about it?

>>15052340
You can divide 349920 with all of them

What are the best Abstract Algebra books for undergrad self study? Something not notably difficult and has many exercise solutions or a full solution book available

How many theorems are in Baby Rudin, exactly? What is the exact number?

>>15059243
Analyse the proofs given in the book, maybe even try to break it down into a list of assumptions, definitions, and theorems, if necessary (maybe even memorize it a bit), then try to do your proofs similarly.

>>15055929
are you cutting yourself anon? dont do that. also learning polar coordinates using pi fractions and degrees is nice but also try to learn it in terms of base two which is way nicer for programming. the pi fractions is good. the degrees is less importante.

how do i get better at proofs? i have 3 days

>>15059286
fraleigh's is pretty good. It covers everything from group theory to algebraic topology and galois theory and it's not as hard as lang's or dummit's

>>15057326
if g(x)=x then f(g(x))=f(x).
And so f(g(x))=x

If you take for example number theory, are there some axioms which introduce a relatively smaller number of new results?

Be my conscience, /sci/. I'm a retard trying to relearn maths from the ground up and currently working my way through khanacademy. My goal is to 100% everything. So far I'm in 6th grade lol learnin' 'bout dividing fractions by whole numbers on a number line, in the arithmetic with rational numbers section.
Honestly, the number line shit confuses me. I remember the basics of multiplying/dividing fractions from school ages ago and haven't had much of an issue with fractions so far but the number line shit just stumps me for some reason and since I doubt I'll ever be doing this beyond this specific module (not in real life for sure), should I just skip this one bit?

>>15047199
Kek

Need recommendations for further self study. Currently pursuing a math major at undergrad. I really love analysis, linear algebra, and differential equations. Functional analysis seems quite interesting, but the textbooks I've been looking at use a lot of topological vocabulary. One of my TAs told me that topology is "the most general mathematics." Is topology the logical next step after a thorough education in analysis? Do I need to familiarize myself with concepts from multivariable analysis before studying topology?

The motivation for this self study is that I would like to be able to convince myself of the concepts I've been told to take on faith in my differential equations course (uniqueness of the inverse laplace transform up to finite discontinuities, fourier convergence, etc)

For reference, I enjoyed studying picrel

>>15057326
>should
In my opinion, it should equal x^2. It sadly happens to equal x though

indeed
study hard and maybe one day you too will be able to graduate from a TAFE

but probably not

>>15058815
Put in more jargon the image of a divisible group must be divisible, however the only divisible subgroup of the cyclic group of order 5 is the trivial group.

>>15059775
And that's why we leave opinions behind for the
moment in a case like that.

>>15059772
>univariate real analysis, linear algebra
>topology
>analysis on manifolds
>complex analysis, ordinary differential equations
>measure theory
>functional analysis
>partial differential equations
>geometry (this mogs the rest)

>>15059729
No.

>>15059729
You have no idea what you don't know, and no idea what will or won't benefit you long term.
Swallow your pride and take your number line problems seriously.

>>15044242
2n2 – 2 + 3*n/3?

I feel worthless, everyone is at least 5x smarter than me while I'm just some babbling subhuman retard from a council estate who can't even add. I don't deserve anything, I am disgusting and retarded. It's all stupid.

>>15060130
you take life too seriously. Ask yourself why you even care

>>15057326
Identity function, as the other anons said

>>15055929
>self harm

>>15053115
zoomies write like toddlers because they're used to keyboards

Should I fixate the equivalent transformations at the \iff's or at the ='s or at both? What looks more professional?

>>15060425
Because I feel like I'm missing out on something, I want to know how to do the things you do.

>>15060025
Any reason you omit multivariable real analysis?

>starting last year of classes this spring
>3.68 GPA

Do I stand even a shred of a chance of getting into a decent graduate program?

>>15043627
>he wouldn't have bombed people if the CIA hadn't fucked him up
an embellishment added for dramatic effect in the Netflix fanfiction. Ted himself has explicitly denied anything fucked-up. Sadly it is fiction like this that leads to harmful rumors and misconceptions about perfectly respectable science and scientists

>>15060506
I would just say a_1 once and then a string of =s. If you do want to keep the \iffs, the normal place for them is on the left-hand side rather than the right

>>15055929
>swedish

>>15061026
>Surplel Moriseett of Wliftasiser Lliyay

Sounds like a great guy. Where can I sign up for
this prestigious university?

>>15060563
That's analysis on manifolds.

New thread
>>15061257

>>15061027
Great idea, ty