/sci/ - Science & Math

>>14856127
Kripke was not a mathematician, but a mediocre philosopher.
>>>/lit/

>>14856127
a good multivariable calculus book for self-study? I know real analysis and i want to get into differential geometry and manifolds but first i need multivariable claclus. I know abstract algebra and general topology.

>>14856229
I have seen people recommanding Spivak's Calculus on Manifolds but I haven't read it myself.

>>14856127
Kripke has credible accusations of sexual misconduct and sexual harassment. Rumors have been circulating for years.

>>14856241
He's a jew, what do you expect.

>>14856221
Yep, look at few of his publications, there's not much mathematical notation and rather poor rigour

>>14855965
Not quite, but you've got the right idea.
Try again. You're almost there.

>>14856229
I’m confused. If you know real analysis doesn’t that include multivariable calculus?

>>14856269
Maybe he means Linear Algebra?

>>14856241
he was autistic

>>14856241
based

>>14856229
>real analysis, topology
If you already know so much what you're looking for is a book on Analysis on Manifolds, like Munkres'.

>>14856241
>Kripke has credible accusations of sexual misconduct and sexual harassment.
At this point who doesn't

>>14856495
Newton?

>>14856492
agreed just read an analysis book

How the fuck are you even supposed to think of an example to this man what the fuck?

>>14856544
The obvious way would be to construct a function with
f(1) = 1/2
that keeps oscilliating more strongly as you reduce f(x) until [math]\limsup_{x \to 0} f(x) = 1[/math] and [math]\liminf_{x \to 0} f(x) = 0[/math].
So something like
[math]f(x) = \frac{1}{2} + \frac{1}{2} \cos \left( \frac{\pi}{2x} \right)[/math]
but you could of course find different solutions.

>>14856570
Sorry this doesn't work. You also need some scaling factor before the cos that goes to 1 as x goes to 0.
So add an factor of 1/(1+x) before the cos.

>>14856495
Kripke is also a practicing Jew, and other's in his circle, such as Marvin Minsky and Steven Pinker, are incidentally also Jewish, and they also have close ties to Jeffery Epstein. It's all circumstantial evidence, admittedly, but it's very interesting how there are so many Jews working in fields like mathematics, logic, computer science, cognitive science, etc. who have faced accusations of sexual abuse or sexual misconduct. Furthermore, it is especially puzzling given outpouring of censorship and firings of academics in recent years for stuff like criticizing the iraq war and zionism (Finkelstein is the best example, but there have been many others), confusing the names of black students (pic related), misgendering trans students, and even simply for investigating the lab leak hypothesis and criticizing COVID lockdowns. Certainly accusations of sexual misconduct can be exaggerated or even fabricated, and of course everyone deserves fair treatment and the right to defend themselves, but it's interesting how there's no interest or concern whatsoever in academia about someone like Kripke or Pinker, but when academics start criticizing big tech, or the military industrial complex, or COVID narratives and policies, all of a sudden that is a very serious concern and we must have a zero tolerance policy for professors engaging with these topics. We effectively have a zero tolerance policy when academics are accused of spreading "disinformation", but when academics are accused of rape or molestation or even possible engagement with international sex trafficking rings, in that case we just let things slide.

>>14856577
>Kripke is also a practicing Jew
he's dead mate

Rate his set theory, [math]n[/math] out of [math]\omega_1[/math].

https://en.wikipedia.org/wiki/Kripke%E2%80%93Platek_set_theory

>>14856573
Thanks.

Hilbert's 9th Problem Solved! Check my paper out /b/ros. I went to Harvard, did my Ph.D etc. l8r

>>14856570
Is the pi necessary?

>>14856635
No, really the only thing that matters is the behaviour near 0 as long as all other values of f(x) are between 0 and 1.

You should know that continuous functions map connected sets to connected sets and compact sets to compact sets so if
f((0,1]) = (0,1)
you must have that for every 0<epsilon<1
f((0,epsilon)) = (0,1)

>>14856653
>f((0,1]) = (0,1)
>you must have that for every 0<epsilon<1
>f((0,epsilon)) = (0,1)
I don't understand how that follows.

>compact sets to compact
None of the sets are compact, so how is that relevant?

I did it...

>>14856692
[eqn]f((0,1]) = f((0,\varepsilon)) \cup f([\varepsilon , 1])[/eqn]

[math]f([\varepsilon , 1])[/math] is a compact and connected subset of [math](0,1)[/math] of it's of the form [math][a,b][/math]. Therefore [math]f((0,\varepsilon))[/math] has to cover at least [math](0,1) \setminus [a,b] = (0,a) \cup (b,1)[/math] but since the image of [math](0,\varepsilon)[/math] must be connected it must also cover the rest too. This implies that the part [math]f([\varepsilon , 1])[/math] is pretty much useless for the problem.

>>14856704
Pretty nice calculator and the only brand that
uses RPN now, other than HP. As much as I want
to take it for a spin, it's worth $230 USD.

I'll do RPN on paper and pen for much less
unless I'm missing out on something cool the
calculator does.

Reposting again from >>14855733

Here's a fun exercise:

This function I've written in Python creates a list of the inverses mod a prime p (inv[0] = 0 to keep the list at length p); e.g. when p = 7, then inv[3] = 5.
See if you can understand how it works.
It's a cool application of the division algorithm.

The point of code like >>14856942 is that solutions to "cumulative" problems can often be solved much more efficiently than the naive "iterate over individuals" solutions.

Here, instead of calculating each inverse from scratch (the naive approach), we use the inverses previously calculated to cut down on computations.

A simpler example is when you want to sum the first n cubes. You could just calculate the cubes in constant time separately, then add them up in linear time. Or you could use the formula (n*(n+1)/2)^2 in constant time.

The nature of the problem isn't simply "instead of doing the thing once, you do it n times", but rather that the nature is completely changed from the single instance, because the cumulative problem has its own structure.

>>14856714
Thanks for the explanation, anon.

Let A be a set of 14 different integers {a_1 , a_2 ... a_14} all between 1 and 21.
You don't know the values of these integers.

You need to build a list of triplets of integers such that at least one of the triplets is a subset of A. You want this list to be of minimal size.

What will be the size of the list ?
I was able to build a list of only 13 triplets but i don't know if a better result can be obtained.

Also, i would like to know the answer for the general case (so "A is a set of k integers in the interval [1,n] and you want to build a set of j-uplets of minimal size such that blablabla")

>>14856913
Modification is pretty extensive and it has an active community. Can run RPL + infinite stack if you're willing to adapt programs yourself, or keep RPN at 4 and 8 level stacks now. Interested to see how it keeps being expanded, but the forums around it are pretty great. I've been using a casio CFX-9850G for a while now, and the DM42 in the long term is a better alternative to the HP prime. Too many calculators are ruined by being forced to adapt to high school requirements.
Ideally, I'd like to see wolfram alpha in a handheld calculator.

>>14857051
>>14856913
I've worked with TI-BASIC language for a bit before
I lost my TI-89 for some reason. Also, given high
school requirements as what they are, why not
have a choice to use RPN calculators in the
sciences and elevate the students' skill and
usefulness a bit?

>...I'd like to see wolfram alpha in a handheld calculator.
No one man can handle all that power...

Meet my husband: Topology...by Munkres.

>>14857136
your husband is gay as fuck, algebraic by allan hatcher is beter

>>14856269
I didnt read about strokes theorem and multiple integrals while studying real analysis

>>14857179
Try Zorich Mathematical Analysis Volume II. Do you know which differential geometry book you'll be studying?

>>14857176
That's ignorant. Munkres covers general topology and hatcher doesn't

>>14857176
>your husband is gay as fuck
Well yes, I am male.

>>14856544
f(x)=1/x maps (0,1] to (0,1), continuously (with the caveat that it technically maps to (0,1], but if it maps to (0,1] then it also maps to (0,1), necessarily). If you restrict the domain to (0,1], then 1/x is obviously continuous on its domain, and will map only to your desired range.

If your professor is that much of a stickler about it, then I will point out my own frustrations with being an applied mathematician trying to talk to pure mathematicians or take theory courses under purists.

Really hating this retarded internet meme of "If you truly understand something you can teach it thoroughly and so a child can understand it!"

No, I think having a PhD in math means I have a pretty strong fucking grasp over Calculus II content, and just because I'm not babysitting you so you don't have to read the book and handhold you through 10000 problems in a lecture, doesn't mean I don't understand it or "you didn't teach us this in the lecture!". I'm at a top 50 University, how the fuck is this pathetic fuck mentality still around? I thought these little fucks had to get fairly high scores and grades to even get in through the door.
Lower level courses shouldn't even have an instructor. Just read a fucking book and stop being such a god damned moron.

>>14856544
(f(x))^0.5
Where f(x) is a quadratic function with roots at 0 and 1 with a positive x^2 coefficient

>>14857346
and if the y value has to be between 0 and 1 then you can also make it so that the maximun of f(x) is 1

>>14857327
memeversity

>>14856513
he is accused of being a closeted homosexual

>>14857327
>"If you truly understand something you can teach it thoroughly and so a child can understand it!"
Why does this quote become more contrived every time I read it?
Soon enough people are going to be saying "You only have the barest hint of an understanding of a subject if you can pick up a meth addict from the street and turn him into the subject's number two expert."

>>14857327
I was in a calc 1 course recently with a professor that was highly rated on rmp.
That actually just translated to they'll hold your hand (annotated lecture notes which was just the textbook but chewed up) and have a lot of free points/forgiving grading structure.
I honestly kind of wish there were some courses where the grade was just exams and you just have to show up on exam day.

Is there any lucrative career I can get with a plain old BSc mathematics major

>>14857509
Pretty much anything CS related.

>>14856544
[math]1-|\frac{3x(x-2/3)^2}{2x(x-2/3)}|[/math]

How do you avoid winding up like people that think they've solved the Collatz conjecture? Is there any way to know you aren't like them than being told?

>>14857660
Wait I didn’t make it continuous

>>14857666
Even Atiyah tried publishing a Riemann hypothesis proof, nobody is safe. Just look at mochizuki

F

>>14856613
metaphysics boards are /lit/ and /his/

>>14856127
>After graduating from high school in 1958, Kripke attended Harvard University and graduated summa cum laude in 1962 with a bachelor's degree in mathematics. During his sophomore year at Harvard, he taught a graduate-level logic course at nearby MIT.[10] Upon graduation he received a Fulbright Fellowship, and in 1963 was appointed to the Society of Fellows. Kripke later said, "I wish I could have skipped college. I got to know some interesting people but I can't say I learned anything. I probably would have learned it all anyway just reading on my own."

Incredibly based.

>>14857666
Just don't be a schizo. It's not hard unless you're a 90 year dementia patient

>>14857179
what did you read about?

Is f : x -> x the only bijective function that maps from the natural numbers to the natural numbers?

>>14857327
>courses shouldn't even have an instructor. Just read a fucking book and stop being such a god damned moron.
Then where would you have to get money to do your PhD level research work from?

>>14857327
>just because I'm not babysitting you so you don't have to read the book and handhold you through 10000 problems in a lecture, doesn't mean I don't understand it or "you didn't teach us this in the lecture!"
Just had one coming to me last week asking if the calc 2 quizzes will "have questions from outside the material like calc 1".
I taught calc 1 as well. There's no such thing as questions from outside the material you cocksucker, you're just fucking stupid because you're a teenager. To you, all the questions will be from outside the material when you're on the phone and not paying attention in class.

>I thought these little fucks had to get fairly high scores and grades to even get in through the door.
Same here. Mine is one of the best in my country. The entry requirement is a weighted percentage based on high school grades and some standardized national exams, with so little weight given to the high school grades and most of the weight to the national exams.
We still get morons. Literally airheaded idiots that don't know what's going on at all. Idiots that think we don't see them when they're cheating from their phones.

>>14856544
Here are my thoughts on the replies you got so far:

>>14857274 schizo and wrong answer because he's applied
>>14857346 >>14857351 just straight up wrong
>>14857660 >>14857667 wrong and doesn't know what simplification is

>>14856570 Closest thing to a correct answer, but 1 is in the range, so fails
But the solutions was saved by this guy >>14856573
Final answer (with no pi) is 1/2+(1/2)*(1/(x+1))*cos(1/x)

This general is shit because morons roam

>>14857707
*celebrates digits*
https://www.youtube.com/watch?v=FmCmN5q1x_0

>>14857872
Think it depends on the question. I've got good responses for slightly higher level math.

>>14857274
>your professor
Who said anything about having a professor? Dumb applied schizo.

>>14857872
The first anon helped very nicely so it's fine. If anything the morons are very comforting because I was thinking I am very bad at Real Analysis.

>>14856942
i hope you're not invoking that in a class initialization because the small time save might be pointless if only a few inverses end up being used

>>14856942
This is a math general.

>>14858290
>"modular arithmetic"? Huh? Is that some architecture gobbledygook?

>>14858283
>small time save
>few inverses
This is for Project Euler problems. That suffices as a response for both of these.

>>14858293
Cool but this a math general. So get your fucking C""""S"""" retardation out of my general.

>>14857047
i get 12
(1,2,3)... (19,20,21) as the first seven cases where only one of each triplet is bad
then (1,4,6) (1 and either 4 OR 6 can be bad)
(2,3,6), (2,3,4) (ONLY 2 OR 3 can be bad)
(1,4,5) (ONLY 4 can be bad)
(1,5,6)

>>14858320
for (k-1)d integers in between 1 and kd you can pigeonhole the first d into the case where each has exactly one, then construct tuplets out of (1... d), (d+1... 2d) until there always exists a tuplet not containing either element of any bipartite pair
the general case is probably NP complete or very close

>>14856942
I think some newer versions of python let you just say pow(3,-1,7) to get 5.

>>14857732
That's easy for people to say from within the system. But when you're out on your own it's harder to find people to discuss your work with, to present your findings and be taken seriously, etc. His position in academia allowed him to succeed.

>>14858467
RT >>14856987

>>14858467
STOP ENTERTAINING THE CS FAG.

>>14858472
Why have people not yet realised that whole point of colleges is to network not muh learn.

>>14856544
A function that goes up and down really fast close to x=0, with upper and lower bounds getting closer and closer to 1. Here is an example:

[math] (1-x) \sin(1/x)[/math].

Nothing more complicated than that.

>>14858467
>>14856987
Just as a comparison:
For p = 10^8 + 7, the naive approach took 104 seconds, while this approach took 20.

>>14858499
>goes negative
Moron

>>14858499
Doesn't work. If you plug in x = 4/pi into your function and you get (1 - 4/pi)/sqrt(2) which is clearly negative.

>>14858499
[math]0.5 + 0.5(1-x) \sin(1/x)[/math] is an obvious transformation. But my main question was how the fuck am I supposed to come up with a solution, not what the solution is. This >>14856653 is the closest answer I have gotten so far

>>14856987
>solutions to "cumulative" problems can often be solved much more efficiently than the naive "iterate over individuals" solutions.
The traditional names for this are 'dynamic programming' or 'memoization'. Both names are stoopid but they're quicker than explaining the whole idea every time.
>>14858467
>>14858501
>pow(3,-1,7)
It's good to know about tools like this, and when to use them. Often the "naive approach" is to waste a lot of time rolling your own implementation when it's already here at your fingertips :p

>>14858507
>x = 4/pi
>domain is (0,1]
All of you are morons.

>>14858509
I used the word "cumulative" because it's more general. The other example I gave (summing cubes) has nothing to do with memoization/dynamic programming.

>>14858499
>>14858511
How are you fags so confident that you all give answers without at least checking it on Desmos.
https://www.desmos.com/calculator/yrbdw2i9e8

>>14858303
grow up and stop taking /sci/ memes seriously you pathetic cringey retard

>>14858522
Make you own fucking CS general tranny.

>>14858526
>babby first time learning that subjects aren't separate like in high school

What the fuck is even this?

This is in a functional analysis book. I searched the whole book and found nothing about these highlighted classes. What do they even mean?

>>14858516
yeah ok, I don't know a standard term that encompasses all possible things like that. Like say your program solves a combinatorics problem by making a generating function and pumping it through a theorem of complex analysis. Just "there's a faster way" I guess.

Projecteuler is full of shit like that

>>14858532
https://en.wikipedia.org/wiki/Von_Neumann_algebra#Factors

>>14858528
No matter how much of math there is in Physics, Physichads have their own thread >>14809934, but you troons always have to invade math threads.

>>14858532
MAYBE:
>https://en.wikipedia.org/wiki/Von_Neumann_algebra#Factors
?

>>14858535
>>14858541
Thanks, though I don't get it.
Could you explain it?

>>14858533
>Projecteuler is full of shit like that
I know. I'm on the Eulerians list.

>>14858532
>I searched the whole book and found nothing about these highlighted classes.
this is why reading books by ESLs can be frustrating

What is [math] C[0,1] ?[/math]

>>14858605
Without further context it's probably the set of continuous functions from [0,1] to R.

>>14858555
Thanks

>get birthday card from friend/math classmate
>she wrote "thank you for existing"
Resisting deep urge to ask about uniqueness.
Send your thoughts and prayers.

>>14858728
>female
>friend

>>14857198
Nah, Im self-studying so I will probably be choosing when I get there

>>14856127
How do you all think of the books I have planned to read for self-studying algebraic topology??

>>14858753
None of those books cover algebraic topology.

>>14858759
Sorry, I wanted to say Manifolds, topology, homology... My bad

Are there any made continuous magic squares? Instead of the sum of integers in a row, the integral of a line being the same? Differing, maybe procedural methods for generating them? Pictures?

>>14858770
Is there any chance that all possible continuous magic squares would be "continuous" to each other without any "gaps" by changing one variable in some kind of equation

V-volume?

>>14858784
Volume as in the 2-dimensional Lebesgue measure. Where is the problem?

>>14858736
It's mostly one-sided from her side, but yes, friend.

>>14858796
If you don't give a shit about the ""friendship"", then just say you want for the keks

>text uses "ssi"
>no fucking clue what that is
>Google it
>French for "if and only if" ("si et seulement si")
Why

>>14857829
>There's no such thing as questions from outside the material you cocksucker, you're just fucking stupid because you're a teenager
> airheaded idiots that don't know what's going on at all.
I'm glad I didn't have a pseud like you teach me math in college.

I’m currently learning linear algebra. It’s not too difficult, but what on earth do we use it for besides balancing chemical reactions and finding currents in circuits?

>>14858753
bump?

>>14858994
Pretty much anything useful done with computers uses matrices. There wouldn't be machine learning or AI without it.

>>14857136
Willard is the GOAT general topology book that's affordable. Munkres is still a good book though. The only more comprehensive book is Dugundi but it's pretty hard to get a hold of.

>>14859113
also, yes I know libgen exists, but I'm still talking physical copies here.

>>14858808
*celebrates digits*
https://www.youtube.com/watch?v=rvsYWYyrlQ4

>>14858994
>he doesn't live in a world where the answer to everything is literally Bolshevism
look into Wassily Leontief
watch Blade Runner (1982)
watch The Matrix (1999)
'The Matrix' is a reference to input/output economics...
...when you combine this with Kolmogorov's probability theory, the stuff you read about in, say, pic related...
...just don't open your fuckin' wallet when you cross Wall St.

>>14858994
A better question to ask would be what math applications do not use linear algebra. For one, anything with coordinates (think of rotating your view in some video game) use them. So any spatial motion, e.g. in vehicles.
Almost all equation solving in praxis is linearized equation solving.

>>14858904
>>14858910
So what does /mg/ think?

>>14858994
>>14859095
>>14859209
I guess he's asking what's the point of theoretical linear algebra. The matrix stuff has obvious uses, but why care about muh vector spaces, especially the weird ones like power set with symmetric difference over F_2.

>>14859113
I have heard from r*ddit it is hand wavy sometimes.

>>14859113
In what world are there books currently in print that are not affordable? How does someone studying topology and enjoying math as a hobby make under 100k salary? Mi first job out of college 15 years ago was 90k starting.

>2022
>Neither wolfram alpha or symbolab can solve the most basic implicit partial derivative of functions of greater than 3 variables

>>14859375
In a world where people pursue PhD

>>14859420
Most decent programs offer accelerated masters, and if you attend during summers, you can finish a BS and an MS in mathematics in only 4 years. If you want a PhD and actually are capable of doing something that matters, your employer will fund you.

>>14858954
AI is so cool, it can almost write cohesive posts
Hello bot!

>>14858808
If you're a horny teen that can't think of the opposite sex in a normal way, then I recommend you cut off your balls.

>>14859490
>t. """friends""" with a girl he likes

>>14859490
the contradiction is quite laughable in this post and clearly the autistic thoughtchild of a seething brainlet

This might be an odd question but, is Math community as retarded as Chess community?

>>14859554
yes

>>14859562
A shame, really.

>>14859539
>"It's contradictory!!!!"
>why?
>"because!!!!!!!!"

>>14859404
*celebrates digits*
https://www.youtube.com/watch?v=PUGKI17RJbU

>>14856544
Constant functions are continuous.

>>14857666
You WILL go insane if you study math for long enough.

>its another episode of self grade exam and estimate grade as failing but close to 70%
>professor belittles me by giving me good job partial credit points and an A

>>14859719
and?

>>14859719
>>14859874
Sometimes authors use range to mean image, sometimes they use it to mean codomain.
In this case, it’s supposed to mean image. A constant function would only work if they meant codomain but that’s too easy

>>14859926
>sometimes they use it to mean codomain
Literally never happens.
Unless by "some authors" you mean one mathematician from 1932 Slovenia.

My professor said: If a DFA is rejecting a string, it has to reject a string shorter than the number of states. I'm confused by this. Can't a DFA have some input that causes a transition to a previous state, in that case the string would be longer than the number of states.

>>14859255
Almost everything in math that describes the real world involves vector spaces, and a substantial number of them are not the standard Euclidean ones. Studying a generalized or unusual vector space has obvious appeal, for instance in the realm of Fourier transforms

>>14860124
okay, so think of it this way: you have the string and you know the DFA rejects it
problem: the string is long
however, you know this means that the string must be causing the automation to return to a previous state
so just split the string, remove the substring 'detour' that caused transition to all of the states seen in between visits to the previously visited state
keep doing this until there are no transitions to previous states
by construction the string never causes the automaton to visit a previously visited state, and one state must be the reject state, so the length of the string is strictly less than the number of states
note that in this case arbitrarily long strings will be rejected, but nevertheless there is at least one string with a number of symbols less than the number of DFA states
check out the pumping lemma
pic related is where I learned about it
https://en.wikipedia.org/wiki/Pumping_lemma_for_regular_languages
one line proof: 'unpump' the long string to get a string with the desired property

>expensive ivy
>high department ranking
>webasssign unproctored exams or take home exams
>everyone fails them, they all get curved
>real grades seem determined on some hand wavy value generated by class participation in small classes of 5 to 9 students, research assistance, and how often you go to spend extra time talking about math during office hours, making office hours pretty much mandatory

This has been my entire undergraduate math experience, as I'm graduating at the end of this semester.

>>14860151
So basically: Delete all inputs that cause a transition to a previously visited state -> the string is shorter than the # of states?

I can understand why the two strings are technically the same, but it's still a little hand wavy for me.

>>14859375
By affordable I mean "reasonably priced". If a book is out of print remaining copies are scalped and sold online for stupid amounts like $250+. There's a book on set theoretic topology that only has a single listing on eBay I think and the guy wants like $600 for it or something.

>>14858427
Thanks for the answer !
I made a mistake when i explained my question, so the problem might not be NP.
You're not actually building a set of triplets.
What you do is that you choose any specific triplet and you ask me "is this triplet a subset of your set ?" and you keep going on as long as i answer "no !".
This should make the problem easier, right ?

>>14860124
example: three state DFA
state one: initial state S_0
state two: intermediate state S_1
state three: reject state S_2
there are no accept states; any string that leaves the DFA in S_0 or S_1 is neither rejected nor accepted
there are two symbols: a,b
there are four transitions:
while in state S_0 and reading symbol 'a' transition to state S_1
while in state S_0 and reading symbol 'b' stay in state S_0
while in state S_1 and reading symbol 'a' stay in state S_1
while in state S_1 and reading symbol 'b' transition to state S_2
so to 'unpump' the string 'baab' we first delete the initial 'b' since it corresponds to a transition to a previous state (or in this case staying in the same state...clearly the remarks above should be modified slightly to obtain the formally correct solution) leaving us with 'aab', and now the middle 'a' should be deleted since it is another 'pumped character' meaning 'aab' is derived from 'ab' by applying the pumping lemma to insert an 'a' between the 'a' and the 'b' in 'ab'
...leaving us with the rejected string 'ab' with a number of symbols (2) less than the number of states (3)

>>14860170
Thats insane lol. I've purchased signed copies of books for less.

>>14860124
If the DFA rejects a string w=w_1, ..., w_n that has a transition to a prior state, then there exist substring
w1,...,w_i
and
w_1,...,w_i,...,w_j
such that the DFA ends up in the same state S on both input strings w_1,...,w_i
and w_1,...,w_i,...,w_j.
If this is the case, then we can simply construct a new string
w_1,...,w_i,w_{j+1},...,w_n
which skips over all the intermediate states between w_i and w_j.

>>14860215
By the way, this is closely related to a property of graphs which states that every walk over a set of edges contains a path on the same set of edges.

>>14860177
>, ..., w_n that has a transition to a prior state, then there exist substring
>w1,...,w_i
>and
>w_1,...,w_i,...,w_j
>such that the DFA ends up in the same state S on both input strings w_1,...,w_i
>and w_1,...,w_i,...,w_j.
>If this is the case, then we can simply co
>>14860215
This makes more sense now, thank you

>>14860168
you have to understand how the pumping lemma creates a 'lineage' (not really, it's a directed acyclic graph) of rejected strings where the 'parent' of a rejected string a x^{n+1} b is a x^n b where a,x, and b satisfy the premises of the pumping lemma...essentially once you transition into the state obtained by reading 'a' you then go in circles by reading 'x' an arbitrary number of times until transitioning to reject state obtained by reading 'b'
I think there's an episode from pic related on this topic

>>14856241
Well, he was from the cunny institute so...

>>14859554
You don't see mathemagicians throwing a tantrum when someone scoops them

How many practice problems do you guys typically do per topic for a typical course? Should I focus on deep understanding and fundamentals through long proofs and such before applying them? I wish I had the time to slowly read through multiple texts and work through every exercise but the pace is just going way too quickly for that now. I don't know if I'm truly learning anything with how fast things are going.

can anyone post that infograph of the mathematics books with the anime girl saying I should be able to solve this

>>14860384
it was this one actually

>>14860296
Sadly in my undergrad, I've been rushing through 8 week courses to finish within a personal deadline. So I do just about 340 to 480 problems a course? I think that is a fair estimate of 40 to 60 a week. That seems to be enough to maintain As and Bs. In the few full term courses I've taken, its closer to 1000 problems.
Note, this applies almost entirely to courses in the calculus series and linear algebra, discrete math, combinatorics, etc. For stuff like abstract algebra or intro to proofs I've done significant less, and I have not tracked it. I track my study hours in a calendar, of ~25hrs a week of math. Would do more but I have a full time job.
I am the "28 year old doing a math undergrad" if you've been in these threads long enough. I started with precalc, and am 29 now, turning 30 soon. Projected finish date is end of next year.

>>14860384
Oh wow, I already did all of these, save for analytic number theory.

Did undergrad in CS, self-studied quantum computing and commutative algebra (with some basic algebraic geometry), and currently doing grad school in math and taking functional analysis.

>>14860384
why study euclidean geometry before linear algebra?

>>14860440
Euclidean geometry is 2000 years old while Linear Algebra was invented in the mid 19th century by people like Grassmann and Cayley.

How do you catch up on lectures if you've missed classes? I had to sort out my schedule so I'm about a week to 2 weeks behind in most courses. Do I go through their notes or through the textbook?

>>14860446
Just read the books. I have never had a lecture that could compare to a textbook.

>>14860446
excerpt from pic related

A related problem is faced by students who get behind in a course. Being behind presents you with a choice: do you try to catch up by going back to where you last understood it and working forwards, or by trying to understand the new material as it appears, and going back to fill in the gaps according to what is currently needed? I would favor the latter option, for the following reasons.

First, the working-forwards option is emotionally unpleasant because you will probably always be behind. It is also practically wasteful because it means that you'll spend a lot of time sitting in lectures you don't understand. Second, the start-from-here-and-go-back-to-fill-gap option fits in better with the strategies for learning from lecture notes discussed in Chapter 7. Making it work requires a bit of thought, though, and I suggest the following. If the course has lecture notes that are given out in advance, look at what's coming up in the next lecture. If it doesn't, look at the notes from the most recent lecture instead. Either way, identify any key concepts or theorems that are used, and go back to study those: look up the relevant definitions, examples, and proofs, study them using the strategies from Part i, and try any associated problems.

>>14860448
>>14860463
Thanks for the advice, I'll try the forward backward approach recommended in that excerpt

>>14860129
>not the standard Euclidean ones
example?
>muh complex numbers
Doesn't count, that's practically the same thing.

Do US PhD programmes typically have mandatory attendance for lectures? I don't want to waste my time sitting in lectures.

What are some easy applications of basic spectral theory from functional analysis?

Hi /mg/. Here is a simple combinatorics problem.You should be able to solve this, I believe.

>>14860220
Every walk between two vertices.

>>14860639
Why are you using such large numbers?
I guess the first step would be to use a calculate to calculate the mod 3 of those numbers.

>>14860639
Might as well reduce them mod 3 to get:
0,1,2,0,1,2,0

Suppose you have the substring (not just subsequence) a,b,c,d,e.
Then a+b+c+d = 0 and b+c+d+e = 0, both mod 3. Subtracting gives a = e mod 3.
This tells us that every 4th number is the same residue.
So for the 0's, they can only be in the ends and exactly in the middle.
This tells us that between the 0's, you should have a 1 and 2.
If the 1 comes before the 2 (in between two 0's), then that should also be the case in the other pair. So there are two choices for this.

So we have 2 "templates", then each has 6 options to arrange the 0's, 2 for 1, and 2 for 2, giving 2*6*2*2 = 48.
Done another way (reading left to right and counting options): 3*4*2*2*1*1*1 = 48.

EZPZ git gud at problem setting.

>>14860667
that is the first step, yes. I'm not using such large numbers, that's just how it is.
>>14860670
BZZZZT. Wrong I'm afraid. You were on the right track, but 48 is not the answer. Try again.

>>14860873
My mistake was jumping to "0's can only be in the ends and exactly in the middle".
Anyways, from "every 4th number is the same residue", the sequence goes:
a, b, c, d, a, b, c
a, b, and c all distinct (since if they're equal, then we have 4 equal residues, when we at most have 3), and d = 0 (same reasoning of only 0 having 3).
3 choices for d, 6 for a, 4 for b, 2 for c, giving 144.
3 times my initial answer because I can move the zero in any of the 3 places (a, b, c, not just a).

SUCK ME

>>14860173
no, there was no mistake, you were clear in what you wrote
the pigeonhole method is probably minimal for small cases, but there are probably smaller solutions for more general problems using some graph theory methods that are likely NP complete

>>14860935
Yes that's correct. However I don't understand why you say I should suck you. I won't be doing that. I think it'd be nice if you acted a bit more kind.

>>14860973
THEN FUCK ME
IN MY ASS

>>14860935
You are a worthless talentless trash

>>14861018
Worthless talentless college kiddie

>>14861022
luv u 2 bb

Newfag here, does /mg/ approve of the /sci/ guide for math, provided in the pinned thread? I'm not seeing anything provided in the /mg/ OPs.

>>14861095
I agree.

>>14861035
You are worthless

>question asks to construct a polynomial with a root at some particular complex value.
>I write [math] f : \mathbb C \to \{0 \} [/math]
>NOOOOOOO that does not count because... because... it just doesn't okay!

>>14860639
we’re talking about 7 numbers a1…a7 of which three are 0 mod 3, two are 1 mod 3 and two are 2 mod 3. If it is a solution then we also know [math]a_n\equiv a_{n+4}[/math] for n=1,2,3. So a_4 has to be 0 mod 3. Now the other three in any run of four have to be one 0, one 1, and one 2. In other words the whole sequence mod 3 is uniquely determined by a1,a2,a3 mod 3 and you can see any such arrangement will give rise to a solution. Therefore the answer is

( # of those a1 a2 a3 arrangements mod 3) x ( # of arrangements of the 0s) x (# arrangements of the 1s) x (# arrangements of the 2s)
[math]= 3!3!2!2! = 144[/math]

>>14860384
Logic before set theory? What sort of books? Enderton 'Mathematical Introduction to Logic' followed by Enderton 'Elements of Set Theory'?

Does my DFA work for this problem?

>>14861218
Yup, works perfectly.
It's pretty obvious. Have a little more self-confidence and trust yourself.

>>14861252
Thanks

Does anyone know any book with a good scan, on polynomial algebra and trigonometry stuff that is very difficult? The sort of questions that you would find in Olympiad exams.

What are some tools to plot functions like Thomae's?

>>14856127
If I'm gonna simplify (x-5)^2 do I write it as (x-5)(x+5) or as (x-5)(x-5)?

>>14861624
[math] \text{Let } z = x - 5 [/math].

>>14861624
the latter. (x-5)(x+5) would be x^2-5^2.

>>14861632
Handholding faggot, kill yourself.

>>14861624
you're multiplying it by itself so (x-5) * (x-5)

>>14861637
Huh?

>>14861557
Do you want to learn how to use python to plot math?

>>14861252
>Have a little more self-confidence and trust yourself.
except when you made a mistake :^)

>Have sex
Yes but how?

>>14861632
>>14861641
Thanks lads

>>14861637
I got back to school for a technician program and they have some math in it, I haven't studied any math for more than a decade and I'm rusty. I was also embarrassed to ask the teacher because he's younger than me.

>>14861156
Yes sir, that's absolutely correct. Good job. Thank you very much for solving my problem, I hope you enjoyed it although it may have been a bit elementary. What did you think of it?

>>14858856
Pourquoi non?

>>14861714
Faggots who needs to handheld for the smallest of obstacles don't belong in any muh technician programme. Did you even bother trying to figure it out yourself, testing with random numbers? Of course not, you retarded niggers need to be told everything.

>>14856127
Guys, what is this shit?
Is this some informal extension of regular expressions?

I'm having trouble with a characterisation of normal extensions: let [math]L/K[/math] be algebraic, [math]\overline{L}[/math] alg. closure of [math]L[/math], if [math]L[/math] is a splitting field of some set [math]A\subset K[x][/math], then every embedding [math]\phi:L\to\overline{L}[/math] satisfies [math]\phi(L)=L[/math]. The proof shows that if [math]S[/math] is the set of roots of elements of [math]A[/math], then [math]\phi(S)\subset S[/math] (this is clear), from there it concludes that [math]\phi(L)=L[/math] must hold because by assumption [math]L=K(S)[/math]. The last part is what's not clear to me. I realise that from [math]\phi(S)\subset S[/math] follows [math]\phi(L)\subset L[/math] (because [math]L=K(S)[/math]), but I can't see the reverse inclusion. What am I missing?

What do you guys think of polynomials? Do you like them?

>>14861843
forgot to mention [math]\phi[/math] is a [math]K[/math]-embedding
i've found a way of completing this, namely if [math]\phi(L)\subset L[/math], then [math]\phi[/math] is a [math]K[/math]-embedding of [math]L[/math] into [math]L[/math] and these are known to be automorphisms when [math]L/K[/math] is algebraic, so [math]\phi(L)=L[/math]. however i do feel that this is overkill and there must be something simple i'm missing

>>14861871
Very much so

>>14861751
tg fdp

>>14861843
any individual p in A has only finitely many roots. Since phi maps roots to roots and it is injective, it can only permute them. So phi(S)=S. It seems like maybe this is what you were missing?

>>14857660
??????????????????????????

What is wrong with you??????????

[math] \frac{(x-2/3)^2}{(x-2/3)} = (x-2/3)[/math]

>>14862081
you're right. i was trying to show phi is bijective on S, but i had no direct way of showing its surjective, what you're saying makes sense. what i said here >>14861890 is pretty much the same, because to show embeddings are automorphisms you use the same root-permuting argument
thanks

>>14861752
Don't be a cunt, newfag.

>>14862100
But with a discontinuity

Is this a valid proof that a^3 divides b^2 implies a divides b?
Me and my classmates keep discussing if you can assume sqrt(a*c) is an integer or not?

>>14862389
It is not.
So the lemma you want is:
>Let a and b be positive integers, and suppose a^2 divides b^2. Then a divides b.
The proof is by looking at the exponents of the prime factors in the prime factorization of a^2 and b^2. Hint: the difference of two even numbers is also an even number. Use this to prove that the exponent of each prime factor in c = b^2 / a^2 is even, hence c is a square number.
Now you can use a^2 | a^3 and transitivity of the binary divides relation to demonstrate a^3|b^2=>a|b.
https://archive.org/details/introductiontoth0000nive

>>14862389
A rational n/d written in lowest terms cannot square to an integer if d > 1. If n and d didn't share a prime factor before, they're not gonna share one after squaring and you cannot simplify, so you're left with a denominator that isn't 1.
Sqrt(ac) is obviously rational, but since it squares to an integer, it must be integer.

Alternative method:
For each prime p, look at the exponent of p.
k is exponent in b, r in c, m in a.
2k = r+3m >= 2m
k >= m for every prime factor of a
So a must divide b

"left/right-exact" is confusing for contravariant functors.

E.g. is Hom(-, N) right exact because the right part in the original short exact sequence stayed exact, or is it left exact because in the resulting SES that's where the exactness is?

Brainlet here. Why are complex numbers so important in electrical engineering?

>>14862471
I can't speak for electrical engineering in particular, but complex numbers are important in general. (Though I know they may describe waves compactly using exponentials with complex entries, and using them for Fourier transforms maybe)

Just like how real numbers describe shifting and scaling/rotation on a line via addition and multiplication (respectively), so do complex numbers but with a plane instead.

(Note: "rotation" in the real line means flipping the axis using multiplication by -1, which is clearer once you go to the complex numbers and you see it's rotation by 180 degrees)

These are basic building blocks, so of course they're important.
You may ask "why not just use 2x2 matrices for that", but they're really the same thing, just renamed.

How many different surjections are there from two finite sets, A and B?

>>14856127
How do i do rule of inference Simplification without using it?

I am trying to prove the conclusion p -> q and i have worked down the hypothesis to:
~r & (~p v q)

I know i have (~p v q) becomes (p -> q) but i want to get rid of r on my own without invoking the rule of inference.

would i do something like this where i introduce my own axiom thing?

~r & (~p v q) & T

i've never introduced anything before like this so im not sure what to do from T.

would i do something like using T like T = (~r v r)?

>>14862863
Check the answer by user78715
https://math.stackexchange.com/questions/216360/counting-the-number-of-surjections

>>14862877
There is no way to get rid of of ~r.
Show us the full problem, you may be leaving something out.

How do you derive the covariance of x and y are 0 if x and y are independent. Here's what I have so far:

cov(x,y) = E[(X-E[X])(Y-E[Y])]
= E[XY -XE[Y]-YE[X] + E[X]E[Y]

are XE[Y] and YE[X] supposed to cancel out? why?

>>14862935
>are XE[Y] and YE[X] supposed to cancel out?
No.

You're missing a bracket at the end for the expectation outside:
E[XY -XE[Y]-YE[X] + E[X]E[Y]] (this last one)
= E[XY] -E[XE[Y]]-E[YE[X]] + E[E[X]E[Y]] (linearity of expectation)
= E[XY] -E[X]E[Y]-E[Y]E[X] + E[X]E[Y] (E[X] and E[Y] are just constants that can be taken out)
= E[XY] - E[X]E[Y] (last two terms cancel out, no the middle terms)

The equality Cov(X,Y) = E[XY] - E[X]E[Y] is always true for any two random variables. What's different in the case of independent variables is that E[XY] = E[X]E[Y], and so the covariance is 0.

>>14862925
(r v ~(p -> (r v q))) v (p->q)

which i turned into ~(r v ~(p -> (r v q))) -> (p->q)
so i could use ~(r v ~(p -> (r v q))) as my assumption

then ~r & (p -> (r v q))
~r & (~p v (r v q))
(~r&~p) v (~r&(r v q))
(~r&~p) v ((~r&r) v (~r&q))
(~r&~p) v (~r&q)
~r & (~p v q)
is where i got to, then i need to use the rule of inference to get (~p v q) which then gives (p -> q) which is the conclusion

i thought maybe there was some way to isolate (~p v q) on my own without using the rule of inference

>>14856127
>Kripke
So tired of e-celeb mathematicians

>>14862947
Thanks

Is there a guide to bases? In particular oddities when using high bases, like 60, 120, 360, or larger?
I try googling it and get chemistry.

>>14857666
checked
the answer to the collatz conjecture is probably related to the sum of (1)(-1)(1)(-1) to infinity. collatz relies on an odd number being multiplied by itself 3x +1 to guarantee an even which is kind of cheating IMO, and that you can map even/odd numbers as (1) and (-1). i have a feeling his trees and their reverse are also connected to the step nature of squares where the Nth square can be defined as previous , in N=(n-1)^2+2(n-1)+1

>>14857666
>>14857669
I have something going that looks big that I can't find anything about.
It's really tricky with mathematics. Things that people have already tried don't have a reference dustbin you can look at. Thing that people have already tried and are interesting but not terribly useful can't be looked up unless you already know about it because the names of things are so arbitrary.
There should be a hotline where you can call a mathematician and ask if you're schizo or not.

>>14862997
they do, it's called /mg/

>>14862987
Use the division algorithm

>>14856127
i swear that was a picture of godel when i first looked at it

am i ascending?

>>14863155
Godel mogged every attempted logician since Boole, or perhaps since Leibniz, or even Aristotle. And that’s not even counting the incompleteness theorem

I am going through the strauss book for pdes: https://s2pnd-matematika.fkip.unpatti.ac.id/wp-content/uploads/2019/03/Walter-A-Strauss-Partial-differential-equations-_-an-introduction-Wiley-2009.pdf, currently on section 1.2 First-Order Linear Equations.

Question 9 states Solve the equation ux + uy = 1. How are you supposed to derive the knowledge to solve this problem from 1.2, the only types of equations this section talks about has the right hand side = 0.

What the fuck is actuarial math. Im aware of what an actuary is, but why do they have their own degree and don't just fall into applied math? Aren't they just a glorified accountant?

>>14863224
has a bit more finance in it like time value of money/etc, but even accountants have to learn that shit

>>14863217
It's a linear equation. You take the general solution for the homogeneous problem and add one solution for the inhomogeneous problem like u=x.

>>14861648
No.

>>14861793
It's variations to Chomsky Normal Form Grammar, used to describe rules of automata.

>Homework is worth 30% of the grade
>Quizzes are randomly given without notice

Why do professors do this. Homework no longer becomes practice.

Really stupid question. Let's say I have a square labeled 1234 like pic related.
p1 is counterclockwise rotation of 90 degrees, which can be written as
1234
4123
μ2 is flipping along the horizontal bisector of the square, i.e.
1234
2143
I want to rotate and then flip the square.
The thing is, when I apply the rotation first, the indices of the vertices of the square would change, which makes the horizontal flipping bijective incorrect (not horizontal flipping anymore?)
Is this supposed to happen?

>>14863467
The dihedral group is not abelian so the order of the group actions matters.

>>14863467
Yes, the dihedral groups are not abelian so their elements dont commute.

>>14863224
>Aren't they just a glorified accountant?
In a way, but the exact set of skills/knowledge required is not the same, and they have to pass a completely different test to get certified and licensed

>>14863467
>The thing is, when I apply the rotation first, the indices of the vertices of the square would change,
Yes, unfortunately the numbers 1234 are being used in two different ways at the same time
>labels on the square that move around as it gets rotated and flipped
>absolute positions that don’t move, used for defining my and rho
There are ways of rationalizing it or rewriting to avoid it, but in the end like a lot of notation it’s something you just have to be aware of, and get used to

I'm an amateur who'll have study math next semester. I have a question. Is Latex something you have to know to do math professionally, or is "only" an addition that you don't necessarily have to be able to use?

>>14863703
>professionally
as important as breathing

>>14863722
Thanks

>>14863703
>do math professionally
A professor must know latex because thats the format they have to submit their papers to the journal in. A student normally doesnt have to because they submit their stuff in pencil.
> "only" an addition that you don't necessarily have to be able to use?
This. However the core functionality - leaving out all the bells and whistle - is just two modes, text mode which lets you type normal writing, and $math mode$ which lets you type math symbols in a nice format. Its not hard at all, and worth trying out if you havent yet. Like every tool it deserves neither fear nor worship

>>14862949
>>14862877
You can avoid rule of inference Simplification using only rule of inference Modus Ponens, together with a tautology like [math]\neg r \land (\neg p \lor q) \Rightarrow (\neg p \lor q)[/math]. Your last step is the antecedent of this implication.

>>14863805
Perfect, that's precisely what I needed to know. I'll give Latex a try. Thank you.

Is finite set always countable? I'm currently reading Abbott's Understanding Analysis and he doesn't seem to include it in his definition.

>>14863918
Countable sets are any set that can be put into a one to one correspondence with a subset of natural numbers. So countable definitely includes finite sets. However, Abbot uses 'countable' to mean 'countably infinite' sets, so finite sets are excluded.

>>14863231
>>14863550
I'm a math major but I've come across some guys specializing in actuarial mathematics, which looks like the exact same thing but with some variations of upper level classes aimed at financial applications. It doesn't seem you need to go through that kind of course to pass the exams either, and its a well paying job...
Is this a no-shit career field where you get to play with math all day?

is specifying the meanings of terms philosophy? is meaning philosophy?

>I've come across some guys specializing in actuarial mathematics, which looks like the exact same thing
kek

>>14863918
“Countable” has two common meanings: the one you are thinking, and the one in your book. The closest thing I can think of to a reason for it is that each of the two choices frequently requires a really annoying expression: “countably infinite” for the former, and “finite or countable” for the latter.

Yes, its literally that easy.

>>14863918
Abbott's definition makes the most sense in terms of efficiency. Countably infinite implies existence of countably finite, but the countably before finite is redundant, since all finite sets are countable. Therefore, it's more efficient to associate countable with only infinite sets.

The other definition make more sense conceptually since you can definitely count finite sets, but now you have to declare whether you mean finite or infinite whenever you say countable.

>>14864090
>finite or countable
This is not a very frequent expression in Real Analysis from my experience, besides you could say non-uncountable sets instead.

>>14864120
>This is not a very frequent expression in Real Analysis from my experience
it is a common expression in set theory for example, perhaps because finite sets are uncommon there, but more likely just that math keeps splitting into smaller subcultures with their own lingo
>you could say non-uncountable sets instead.
never ever heard that one before. might be worth using though

>>14864075
It is the same thing, I just looked at the course descriptions, and if anything its actually easier. Rather than the courses for math majors, they take applied versions just for actuaries.

I just took some practice exams online, 30 questions each and they're pretty fucking simple. Is this really a career that pays 100k out of the gate, or are the practice exams pulling my leg, like online IQ exams?

>>14864164
Applied math is always gonna be easy since it's all just plugging in algorithms. If you want a taste of what an actual Actuary would do in a real job, take a proof based math course, since that is the only subject in all academia where you have to develop strategies yourself to solve problems.

>>14863561
Thanks. This is what I want to confirm. So the actual indices of the vertices don't actually move, only the labels of the vertices move.

>>14864172
I'm not yet at the point where I can really choose what "branch" of math to major in as I've yet to take upper level courses. I am in my sophomore year honors track, completed calculus 1-3, intro to proofs, linear algebra, abstract algebra, and am at the moment enrolled in a statistical analysis course and an ODE course. The statistics course is just an elective and were I've met some other students that want to be actuaries.

How are their strategies any different than mathematicians working in engineering or software? I don't think anyone there is plugging and chugging.
I'm looking more into it as I've never considered it a valid career field, but if its as math heavy and intense as people describe, it looks like a much cushier and comfortable job than anything else math related. Are you an actuary? I'm only 20 and my dad works at a steel mill, so I have no perspective as to what a good career is. Sorry if this belongs in /SCG/, I think it 404'd.

>>14864186
Correct. In particular you can check: [math]\mu_2 \rho_1 = \rho_1 \rho_1\rho_1\mu_2[/math] by computing them both as a 2-by-4 table.

I know there are just two possible classes of number systems: there are those that use finite or rational numbers as the base and thus make common (or uncommon, doesn't matter) irrationals or transcendentals have an infinite/maximum-entropy (i.e. unpredictable) encoding or in more simple terms, it makes them, well, irrational; and then there are those with an irrational/transcendental base that turn every rational number into a max entropy encoding.

My question is: what would be the implication if there were found that two ordinary rational numbers in an irrational base differ in these two depictions? I.e. one rational would render as the equivalent of "7", the other as the equivalent of "pi" (purely conceptually, not referring to actual values).
Is this even possible? I assume not.

Do you pray to any gods to help you write your theorems?

>>14864228
If you are basing cushiness of a job by how much money it will fetch you, trust me it won't be cushy.

>>14864273
>irrational-base number renders as 7
Think about it. What does render even mean here? If it means
>a/b=7c/d
then you can probably answer your own question. If it means something different then describe it specifically.

Is Math a good way to numb your desires and emotions? I got betrayed recently and it hurts, I tried Stoicism and everything but noting worked. I heard about mathematicians who went crazy and all they could think about was math, is it possible to get to this state for everyone?

>>14864449
>I heard about mathematicians who went crazy and all they could think about was math
im positive that if you dont have prior mental issues, this wont happen. ive only seen this happen once in the movie Pi.
and if you want to pass the time and not think about your issues, i wouldnt recommend math. doing math is very static, not very distracting if youre going through something. try watching a movie or playing a video game.
also generally you cant just pick up math as a hobby just because. you either like math or not. if you dont, this 'math hobby' wont last a week.

>>14864449
>Is Math a good way to numb your desires and emotions?
After a while, sure. The certainty of it. Whenever I have troubles in life or uncomfortable situations I end up thinking to myself "Oh god I wish I were home doing math right now"

>>14864460
>>14864509
Thank you for your opinion. Is there a particular subfeild of Math that really grabs your attention?

Christopher Poole, 2022

>>14856127
Hi math /sci/entists.

In another thread someone was talking about using magic powers to influence random number generators.

I want to make an experiment where I generate a billion numbers while thinking about raising or lowering the numbers, or nothing as a control.

However, I am a mathlet and I don't know what math to use to check if the data is abnormal.

It someone helps me figure out that math part I will code it in SLAM and post results. I already know how to make a billion random numbers and put them in a stack.

>>14862319

>get told non-stop that CalcII is the hardest math class
>Get an A
>Think I'm in the clear for the rest of my undergrad until analsissy
>Calc III is harder

>>14864449
It does distract me from my oneitis, but only when I am actively doing math.

>>14864591
Depends. How experience are you with math right now?

>>14864659
Calculus II is only difficult if you can't pattern match, as series and sequences will kill you.
Calculus III is shape rotation and visualization.
Both require the same level of asspulls for integration, which is less pattern matching and more memorizing a variety of them.

>>14864449
Can say from experience, yes. I had some bad experiences and drowned my worries away with maths but the insanity isn't fun. Good mathematicians aren't mad men

>>14864460
>also generally you cant just pick up math as a hobby just because. you either like math or not. if you dont, this 'math hobby' wont last a week.
am i chosen by math?

I haven't solved an infinite series in several months, I'm depressed and might have thyroid cancer. Please post beautiful math illustrations, bros

Nothing like spending 40 minutes on a problem to get the wrong answer and start all over again.

>>14864659
>>14864758
Calc 2 was my worst personally, I'm good with series but fuck me, even though the prof was my best friend's dad I barely got a C

If you didn’t finish calc iii and linear algebra by high school you’re ngmi

>Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.

[math]2^\sqrt{2}[/math]
How do I prove the irrationality of this?

>>14865164
Use the Gelfond–Schneider theorem.

>>14865183
You're cheating..

>>14864314
Sometimes yes, but you'll be cursing the same
when you're recalling anything!

I just started to learn Algebraic Topology and why is it so fun?
Am I getting tricked into learning something useless? But it's so fun.

>Semester starts
>Swear will do better this semester and study
>Still get shit grades

I guess this isn't particularly the right place to talk about it but I don't want to make a new thread. Am I really just a brainlet who's getting filtered by math?

>>14865755
>swear will do better and study
well did you study? did you do the homework?

>>14865769
I did study and do the homework. Somehow I always think I do well on the homework only to get it back in the 50-70% range. I go to professors after class to get help/review homework and it still hasn't improved.

>>14865779
What topic are you learning?
There are some topics that didn't click with me until I'm done with the semester which isn't good for grades lol.
If I had a chance I wish I should have read and worked on the materials in the summer/winter breaks.

>>14865789
combinatorics, applications of math in finance, set theory, pdes, and a ml course

>>14864728
High school level.

>>14856942
>8 spaces tab
>aligning the equal signs
disgusting

>>14865755
Well shit, I get bad grades overall since there's a few tests I don't pass

>>14865852
getting bad grades since i do poor in both :)

>>14865846
Aligned equal signs are pretty, eat shit.

What do I do to prove this

What's the easiest way to publish a small paper?

Is this book actually good or just a meme?

What is the meaning of this?

What's meant by this definition?

>>14865779
>I did study and do the homework. Somehow I always think I do well on the homework only to get it back in the 50-70% range. I go to professors after class to get help/review homework and it still hasn't improved
Damn. I get straight 100% or very close to it for all my homework, 80s and 90s on quizzes, then exam time comes and I get 70s. Can't spend over an hour one one problem when taking exams, sadly.

>>14866310
Is the upper bound of the limits of series with coefficients a_m

>>14866299
Just category autism. Honestly, really getting tired of schizo nonsense. I guess its fun, which is why its the main topic in these threads, but real mathematics is stuff like applied PDE's and numerical analysis, which is too time consuming and "work" rather than fun math.

How do you pronounce Lipschitz?

>>14866931
lip...shits...

shit on a lip, man

>>14866931
I pronounce it like Laip-shais

Hypothetically speaking, if there were an algorithm that could get individual prime factors out of a composite using a greatest common denominator function, would that be impressive?
Asking for a monsieur Flammonde.

>>14858856
>texte utilise "iff"
>je n'ai pas idee quelque c'est
>je googlise
>Anglais pour "si et seulment si" ("if and only if")
Pourquoi?