/sci/ - Science & Math

Math is gay

Math is gay

after a month of procrastinating, finally starting to read "categorical homotopy theory" by emily riehl

enjoying it so far, might read the HoTT book next.

after that, back to research i guess.

>>15946263
You're a smelly nigger

Off topic question:
If there was a book titled
>Everything the human race knows about polynomials in N, Q, R, C and their subsets
how big would it be, roughly? My study group said 15,000-20,000 pages but an prof who specialises in analysis said only 5,000-6,000 pages.

bump

>>15946236

Is there an algebraic normal field extension of Q whose Galois group (over Q) is isomorphic to a?

>>15946932
Not sure why it didn't render my unicode math symbols:

Is there an algebraic normal field extension of [math]\mathbb{Q}[/math] whose Galois group (over [math]\mathbb{Q}[/math]) is isomorphic to [math]\mathbb{Z}[/math]?

>open up intro to math book
>first lesson is about sets instead of natural numbers

Into the trash it goes.

>>15946989
So many years later and I still don't get the set theory hate meme.

>>15946992
Mathematicians hate it because it implies that problems related to infinity can be solved or even speculated about. It's essentially philosophy, not math, and will most likely eventually get outed for the pseudoscience that it is.
On a biological and anthropological level, it is a completely unintuitive way to introduce someone to mathematics. When humans first figured out about abstract quantity and value, they weren't thinking in terms of sets, they were thinking in terms of "how much of this stuff do I have."

Looking for some advice here, as a former NEET (currently 24) and eventually planning my return to school. I'm trying to relearn math, mostly hovering towards topics that will help me learn data structures and algorithms for CS.
Going through khan academy feels way to fucking slow. I spent a good two weeks just doing basic middle school stuff like learning the basics so I can deal with any fractions/arithmetic. now that i want to move on I was going through algebra basics part and spent the day on simplifying square roots. now its on to things that i feel like are completely useless or if they are useful it could literally be explained in a 5 minute video. literally thats what i did. spent a few days going through each problem then decided its way to easy. so i went. watched a video on it on youtube that was around 10 min, then finished the unit test.

im looking for a road map. and im tired of reddit responses they're all botted. like dont just tell me watch professor Leonard. i dont need to be reminded on how to use the order of operations or how to do long division.

and in highschool. I remember I was doing quadratic functions/geometry ,algebra and remember a few basic things like if a number is beside x and you know what x is. then multiply. and basic quadratic graphing formulas.
its all so blurry that i can't remember how i did it but i remember doing it.

>>15946263
this poster is sure to be a literal troon

>>15947001
eh. well disagree with you on every single point there but I don't think it matters.
>mathematicians hate it
might want to not equivocate your personal (bizarre) hot takes with mathematicians in general.

>>15947025
What does that have to do with anything?
They are smarter than you, which is what counts

>>15947004

Pick a calculus book and a linear algebra book and read the intro chapters. Whenever a new topic gets introduced that you haven't seen before, note it down. Then google that topic and so on and so forth, until you reach a topic you understand.

The shorter way of doing it would be to find a curiculum of every high school and college year leading up to what you want to learn.

For highschool, I would definitely say basics of 1 dimensional functions and how to do things like intersects and whatnot, sin cos tan basic trig and triangle trig, exponents and exponent operations, vectors. Basics of calculus and linear algebra.

For college, abstract algebra is a good basis for all math. Cal 2 and multivariable calculus are also very good. Then move onto analysis 1 and 2, and linear algebra (the advanced one). Lastly, ODEs and some PDEs would be nice for you to know. With this you should have a basis to approach most math things, should take half a year to a year to learn depending on how motivated you are.

Take a step back and also take exercice breaks and do sports. Try every couple days doing reviews of what you learnt that week and do more complicated exercices, purposefully look into the very hard stuff, or research open ended questions about the material to push further thinking

>>15947034
>might want to not equivocate your personal (bizarre) hot takes with mathematicians in general.
English protip: that's not what "equivocate" means.

>>15947056
meant "equate" just had a brain fart

>>15947051
Thanks for the advice

>>15946263
Let’s go Yume Nikki. You ain’t crap, anon; I’ll go find a pdf of that book myself and check it out.

I myself have been reading Godel Escher Bach: An Eternal Golden Braid.

>>15946236
I'm new to this board is OP baiting with picrel or does that kind of shit actually fly here

>>15947025
>>15946265
brainrot.

>>15947111
yes

Can /sci/ solve a Reddit problem?

>>15947233
Letting [math] \alpha = \pi-x[/math], using complex algebra we get [math] \frac{1-\cos((n-1)\alpha)}{1-\cos(\alpha)} = \left(\frac{L}{d}\right)^2 [/math]; I'm not sure how to solve further than this

>>15946263
>after that, back to research i guess.
what's your research anon? is it categorical-homotopy-theoretic related or are you just reading that for fun?

How do you prove intuitively that cos(y) = cos(x) results in that checker board pattern?

>>15947373
You plot it by hand

>>15947373
The inequality sin(pi*x)*sin(pi*y) < 0 results in a literal checker board.

>>15947111
what do you mean

>>15947233
Is L something like 179.8°

have you ever heard of Differential and Integral Calculus by Piskunov?
i'm tempted to choose that insteaof of Spivak's because it also covers advanced calculus in a style that i really like.

>>15947373
cos(y)=cos(x) just means either y-x is an I refer multiple of 2pi, or both x and y are pi/2 plus an integer multiple of pi.

>>15946992
set theory considering a collection of objects (set) and how its related to other sets is fine
set theory the supposed foundations of mathematics is a slapped together contraption with duct tape and handwaving that makes anyone interest in learning about the foundations of modern mathematics want to kill themselves over the sheer amount of rationalising over something as simple as natural numbers.
it goes so far that anyone bothering to teach mathematics and work in mathematics does not go anywhere near nor challenge the current foundations of mathematics because its so obtuse.

>>15947736
Wrong
cos(pi/3) = cos(5 pi/3)
for example.

>>15947742
Assuming for sake of argument my earlier post is improperly dismissive, can you give me some relevant literature pertaining to your viewpoint and difficulties you believe exist? Always open to changing my mind so long as there's good reason to do so.

>>15947747
If anyone doesnt think the current foundations of mathematics isnt stupid they are welcome to prove 5 x 5 = 25 from those foundations.

>>15947373
[eqn]\cos(y) = \cos(x) [/eqn]
is equivalent to
[eqn] \sin\left( \frac{x+y}{2} \right) \sin\left( \frac{x-y}{2} \right) = 0 [/eqn]

>>15947755
Welp I tried. Seems I was right to be dismissive.

>>15947746
Oops you're right, I'm retarded lol

>>15947762
This is a good way to do it. Using a similar approach, for example,
[math] \sin(y) = \sin(x) [/math] should be equivalent to
[math] \cos\left( \frac{x+y}{2} \right) \sin\left( \frac{x-y}{2} \right) = 0 [/math], correct?

>>15947742
>rationalising over something as simple as natural numbers
Formalization of the natural numbers is a core part of the machinery used in set theory to solve decidability problems, that ultimately DO have an effect in all areas of mathematics.

How do I become a tutor?
I asked my professor how can I tutor the freshmen and 2nd years and he said it's not possible that usually TAs do it.

>>15948098
this is not something that can be answered in general, it (obviously) depends wholly on your school.
(As an example of how it varies: my undergrad had a great tutoring center with standards, interviews, decent pay, both scheduled free appointments and general walk-in hours; my current grad school, on the other hand, offers the undergrads at least two different places to get walkin help only, both of which are seemingly staffed by dumbfucks who didn't pass the classes in question.)
-- that is, if by 'tutor' you mean something school-sponsored. Nobody can stop you from putting up posters if you want to run an independent business (well, okay, maybe they can depending on where you hang the posters). But keep in mind the school probably offers a similar service for free, so you need to compete with that. Best chance is to offer more flexible hours, make it seem like you offer a better service, and try to milk the rich kids whose parents will pay for tutoring so the little shits don't fail Business Calc again

>>15948552
yeah I want into the private tutor thing

>>15947675
bumping

>>15947233
these are just points on a circle radius L/2
piss easy problem

>>15949062
it's probably fine

>>15949539

>>15949100
No dummy, x does not necessarily equal y. (Or are you joking?)

>>15949100
Wrong. Even if they are on a circle, the circle need not have diameter L

>>15946236
yeahs

>>15949743
alpha = 20°
Use the fact that the sum of angles in a triangle is 180°.

>>15946236

Is there a polynomial [math] f(z,t) \in \mathbb{C}[z,t] [/math], irreducible, and monic in t,
such that [math] f[/math] and its "formal partial derivative" [math] \partial f / \partial t [/math] together generate the unit ideal of [math] \mathbb{C}[z,t] [/math]?

>>15946236

Is there a polynomial [math] f(z,t) \in \mathbb{C}[z,t] [/math], irreducible, monic in t, and with f having degree ≥2 in t,
such that f and its "formal partial derivative" [math] \partial f / \partial t [/math] together generate the unit ideal of [math] \mathbb{C}[z,t] [/math]?

>>15949567

>>15950041

>>15947742
what's your preferred alternative? for me it's weyl-style predicative foundations taking the natural numbers as the most basic object and constructing everything from there

>>15949739
they are definitely on a circle
the diagram made me think L was a diameter

>>15949743
i am stuck here i don't know how to solve this, can anyone help me please?

>>15950571
thats about here I got stuck.
fairly simpleup to that point.
then i dont know what to do.
simultaneous eqns?

>>15949835 is correct.
but i havent been able to solve it myself.

>>15950626
>simultaneous eqns?
i tried using them but i end up with the same equation , and when i try to make more equations i end up with more unknowns

>>15949835
can you please tell me how you got the answer?

>>15946263
imagine reading a book by a woman

should set theory be the foundation of maths?
should arithmetic with real numbers be the foundation of maths?
should something else be the foundation of maths?
if you have insights on this, they would be welcomed

>>15946989
it's bad when they define natural numbers in terms of sets. that is really unnerving.

>>15950712
predicative arithmetic with natural numbers

For some reason when studying math I thought I would eventually learn something that would be really useful and help people. I thought this because why else would there be so many math departments in the world teaching advanced math if it wasn't useful somehow? Now that I realize that it doesn't really go anywhere useful in the end I wish that I had studied medicine instead. I find biology boring but at least I could actually help people in a meaningful way.

>>15950734

>>15949122
why would you say that?

>>15950640
Imagine being less intelligent than a woman

>>15950743
It seems like a traditional textbook on the differential and integral calculus, there are many such books and they are fine. In general calculus books are good unless they are modern American "calculus (for engineers)" books with "updated pedagogical approaches" (i.e. they break the tradition with old differential and integral calculus books like Courant or this Russian book). Like Stewart for example.

>going through math textbook pdfs
>no solutions to the exercises to be found.

do I really have to spend real money on textbooks? the fuck is this

>>15950758
that's why i chose but since it's old it does things a little bit differently, for example it does not use the epsilon-delta definiton for limits and it tretas dy/dx as an actual ratio. moreover when explaining advanced stuff it doesn't even mention the hessian matrix.

i know there's not a best all-in-one book for calculus but i don't want to waste time.
Anyway i chose to study from it anyway and integreate a chapsters from other books.

>>15950765
https://quizlet.com/

>>15947233
X is 150 degrees, y is 75 degrees. Proof is I'm not a incel neet.

>>15950756
damn you make a good point

>>15950734
developing the future is useful in a meaningful way

>>15950494
categories > sets

>>15950871
Categories are great but they're not a replacement for sets. I don't know of any foundations that are more naturally stated in terms of categories than sets, unless you count HoTT, but infinity-groupoids aren't the same thing as categories.

>>15949743
>>15949835
>>15950571
>>15950626
i think i got it , alpha = 70°
because EDC and BAC are similar triangles
correct me if iam wrong

>>15951122
no wait i was wrong , BA and DE are not parallel

>>15951139

>>15951199
thanks but i still don't get it , i will be thankful if you explained how you solved it
those are 2 equations and 3 unknowns

>>15951223
sorry anon
i didn't get it.
got stuck about here. >>15950571

i used >>15949835 answer to solve the last part and check the rest of it.

>>15950494
can you get to topology & sheaves from there?

>>15951002
That's why I am still uncertain about whether this "set hate" stuff stems from a meme I'm somehow still not appreciating after 10+ years or genuine narcissism driven schizobabble. Sometimes it's presented as a meme, other times it seems people genuinely believe wacky shit but when asked why they never give a sensible reason and make shit up about "real mathematicians bla bla bla".

maybe I'm getting too old for this.

>>15949743
alpha cannot be determined uniquely from the given information. It depends on the length of the segment AB.

>>15946236
Please anons how the fuck do I solve this? I dont know how to get rid of that 7
Rta means answer

>>15951480
Go to the stupid questions thread: >>15951180

>>15951480
Start by ignoring the (1/7). Can you see that everything else equals x^14?

>>15951495
>Can you see that everything else equals x^14?
No, I got (x6/x-8) because (x2)-4 = 2.-4 = -8?
Help me man, please

>>15951480
[math] \left[ \frac{x^6}{(x^2)^{-4}} \right]^{1/7} = \left[ \frac{x^6}{x^{-8}} \right]^{1/7} = \left[ x^6 \cdot x^8 \right]^{1/7} = \left[ x^{14} \right]^{1/7} = x^{(14)\cdot(1/7)} = x^2 [/math]

>>15951509
Thanks!
What happened that changed the -8 to 8 and the : to a .? They didnt teach me that

>>15951506
That's right. And what happens when you multiply or divide the same number with exponents?

When you multiply, you add the exponents. (x^2)*(x^2) = (x^4). (x^6)*(x^3) = (x^9).

When you divide, you subtract the exponents. (x^12) / (x^4) = (x^8). (x^3) / (x^2) = x.

That doesn't stop being true because the exponent is negative. So what is (x^6) / (x^-8)?

>>15951514
>So what is (x^6) / (x^-8)?
(x^-2)?

>>15951511
[math] \frac{1}{x^{-8}} [/math] is the same as [math] x^8 [/math]

>and the : to a .
There was no ":"

>>15951522
But then why did the x6/x-8 change to x6.x8? Why not x6/x8?

>>15951521
(-8). Not 8. The bottom is (x^-8). What's 6 - (-8)?

>>15951530
Because [math] \frac{1}{x^{-8}} [/math] is not the same as [math] \frac{1}{x^8} [/math]

>>15950712
Probably not, Type Theory makes for a better foundation in many ways (though it's a lot more boring).

>>15951537
14? I think I got it. I was fucking up.
-(-) = +, now I see!
Math may not be my thing...

>>15951544
Everybody makes algebra mistakes, all the time. Everybody. Don't worry about it.

/sci/ bros, where do i start with math? ive discovered an endless passion for humble learning for myself after 23 years of being an idiot.

Im embarrassed for my own sake, i barely passed trig in highschool and i dont think ive gotten much better since. I want to learn calculus but i dont even know where to begin! Anybody know what the course to follow is? Ill dedicate several hours a day to math study if i can find the path. Ive started in a small way already..

>>15951610
Read Calculus Made Easy by Silvanus Thompson and M. Gardner. Its a really good book and small compared to other calculus books.

It'll teach you calculus 1, calculus 2, and part of calculus 3 in one semester of daily study.

>>15951617
thank you

>>15950734
you're not going to help anyone by studying medicine

>>15951686
Well I suppose if I didn't become a doctor then someone else would, but by "helping people" I mean "be a person in the community that people appreciate what I do" instead of "someone working on things most people despise and only really benefit well connected institutions with the resources to fund and productize mathematical research for either profit or power motives"

>>15947375
Now that's based

"Not In The Database... I Don't Know Why" - Tucker Carlson Exposes Epstein Brother's Battle For 'Basic' Records
https://www.zerohedge.com/political/tucker-carlson-exposes-jeffrey-epsteins-brothers-battle-basic-records

Is it not in the database because no one ever did they stuff they're saying I'm obviously stupid for doing right now? While they have their position, my position is to know that I don't the stuff that they think they know but actually don't.

>>15952542
>my position is to know
my position is **that I'm smart enough** to know

>>15952542
I think the amount of typos in this post reflects not electronic intrusion via a man-in-the-middle attack, but rather it reflects a jew using the rape hatch in the wall of my hotel room to enter while he has my brain turned off with the rape ray and then use my keyboard to mechanically insert the typos.

Anyone in SF kicking it with the shadow government?

Idk if this is a stupid question, but:

Do there exist connected boundaryless topological manifolds X,Y such that each contains a subspace homeomorphic to the other, but X is not homeomorphic to Y ?

>>15951610
Try Basic Math by serge lang

I don't "get" rudin, you assholes lied
what do I do now?

>>15953369
Read Éléments d'analyse by Jean Dieudonné

It's better since it's more autistic.

>>15953384
This shit is in fucking french

>>15953399
And? Just learn French.

The recent Prject Euler problem is interesting, but so hard:
https://projecteuler.net/problem=870

Here's what I got:
>for each r, the sequence of L(r) EVENTUALLY follows a linear recurrence
>each term equals the last term, plus some previous element in the sequence (how far back is fixed)
So for L(1), you get {1,2,4,8,...} the powers of 2, which has the recurrence a(n) = a(n-1) + a(n-1), so you have to go 1 element back.
For L(2), you get {1,2,3,5,...} the Fibonacci numbers, which has the recurrence a(n) = a(n-1) + a(n-2), so you have to go 2 elements back.
Again: The recurrence might not hold immediately. You could have 20 terms not following the pattern (even if you need to go like 6 elements back), and then after that it starts following it.

These are the first 22 values of T (or q):
>1, 2, 5/2, 3, 7/2, 11/3, 43/11, 4, 13/3, 31/7, 9/2, 14/3, 33/7, 5, 51/10, 41/8, 27/5, 11/2, 45/8, 65/11, 6, 145/23

>>15953437
How do I learn french fast enough to read this book?

>>15953447
NTA, but I've been learning French from Duolingo for 5 years so far just to read French math papers.
I can barely understand what that screenshot says.

>>15953306
Think about what it would mean for X to be homeomorphic to a proper submanifold of itself.

>>15953471
In the smooth case at least, X cannot be a compact boundaryless smooth manifold and diffeomorphic to a proper submanifold of itself.

What else can be said?

>>15953453
>>15953399
Translation:
>Chapter 1: Elements of Set Theory
>We will not attempt, in this chapter, to base set theory
>on axiomatic information; it is, however, possible to do so,
>and we refer the interested reader to Kelley and Bourbaki for
>a complete axiomatic study. The results that appear in this
>chapter without being accompanied by a proof or a definition could
>be considered as axioms connecting undefined terms.

>>15953306
Just realized an obvious counter-example: [math]X = \mathbb{R}^2 \,,\, Y = \mathbb{R}^2\setminus \{(0,0)\} [/math]

>>15953524
* example, not counter-example

is there a special word for a group whose set has finite measure? like the points on a unit circle, for example.

>>15953399
lrn2use mtl

>>15953536
actually, i meant to ask about groups whose identity element can be expressed as a multiple of a non-identity element. like [math]2 \cdot \pi = 2pi = 0[/math].

>>15953540
Torsion

>>15953602
ah ive heard that before, tyty

>>15953540
There's no specific term for this. An element of a group is called a torsion element if it has finite order. What you're describing is just a group admitting a non-identity torsion element.

A *group* is called torsion if *every* element has finite order.

>>15953633
thanks for the clarification. torsion was the term i was looking for.

from raymond smullyan's beginners guide to mathematical logic.i don'treally know what's going on lol

>>15953749
bump. plshelp.

>>15953749
>>15953832
What's indexing?

Stuck on a problem, and I don't see what's the pattern.

Can anyone notice any patterns in these numbers?
https://pastebin.com/tWufdMhJ

Leftmost column is just the row number.

Next three columns are the same values written in different ways.
First one is as a rational number.
Then that rational number written as a "mixed fraction".
Then in decimal form.

Obvious out of the way: Yes, they are increasing, becoming more frequent, and the gaps between integers are getting bigger.
But is there a way to calculate the next, knowing all the previous entries?

Lean 4 theorem prover.

Baby Rudin fails because he doesn't discuss equivalences and relations, he does it briefly and it's fucking useless. He should have just double down on axiomatic assumptions about R and numbers.

>>15953975
If you want to learn more about the foundations than why don't you read a book about the foundations rather than an Analysis book?

>defining numbers as sets for no reason
REEEEEEEEEE
constructing counting numbers with sets is nonsense because you're still counting, any set with a cardinality of a counting number presupposes a counting number.
I didn't define the number two by holding two sticks I merely represented its platonic ideal.
>Bbb-b-b-b-but I invented to naturals with empty sets
NOOOOOOO YOU DIDN'T
you merely represented that 0 => 1, something true with or without set theory.
I HATE SET AUTISTS SO MUCH
>now look at how I construct rationals cause I says so
No you're again just representing rationals to match a presupposed idea of rationals.
>no you don't get it 1/2 is (1,2) because uhhhh well uhhhhhhhhhhhhhh IT JUST IS OK CHUD!!!
DILATE!!!!! REEEEEEE

Why do some normies claim to be good at math despite the fact that they struggle with basic arithmetic? These individuals sometimes cite remedial courses taken in high school and college as evidence of their "aptitude". These individuals also have typically never even taken Calc (I-II), Linear Algebra, Discrete Math which are all common first year courses. They also aren't even familiar with competitions like the AMC, AIME, USAMO, IMO, or Putnam. Do these people suffer from Dunning-Kruger? Why are they like this?

>>15953984
I'm merely demanding sufficient rigor, which clearly Rudin lacks. So I'm just saying that you should stop recommending Baby Rudin to people because it'a a bad book.

>>15953995
First of all math competitions are fucking stupid, the only thing that matters is research.
I'm saying that because when I was studying for the putnam it literally distracted me from my research and gave me nothing meaningful in return and it also impeded on my studying for finals, so I basically did no research during that time.
But yes not just normies have a serious misunderstanding of mathematics but most stem tards don't even realize they're still in elementary school in terms of mathematics.
A lot of people cope by saying "well it's more than the greeks knew" well the greeks were raped to death by turks so clearly they didn't know too much.

Anons I ran across something I thought was a little hard to explain, I wondered if you might be able to explain what's going on.

I ran into this indian "mathstrick" which really pissed me off because of how diningenuous it is since it only applies to 6 numbers
>>>/wsg/5397501
But it made me curious how common the phenomena was so I thought I'd see how many other exponents it applied to, I compared all exponents below 99.
Raise a number to a certain power, sum the values of each individual digit, then subtract the exponent from this sum and see whether the value is the same as the starting number.
>>>/wsg/5400336

So what is the cause of every multiple of three having at least one valid result while 2, 20, 38, 56, 74, and 92 are the only other valid exponents?

>>15954015
That's a well thought out response. What do you do now, fren?

>>15954038
finance because they gave a sick signing bonus

>>15946236
Scientifically, why do Fields Medalists have such low fertility?

>>15954079
if they're competent enough to win the Fields, chances are they're competent enough to know that the numbers say that having children is a massive money and resource sink and not worth the time or effort

>>15953993
meds

>>15954079
They are extreme autists.

3blue1BROWN is flooding my feed with youtube shorts snippets of his old ass videos. fuck that guy unsubscribed

>>15954120
>i'm the one that needs meds
lol lmao

>>15953993
>cause I says so
>presupposed idea
>IT JUST IS OK
That's what definitions are, retard.

>>15954324
oh yeah? prove that that's how definitions are defined

>>15954328
Why prove?
It is because I say so.

define definition haha

>>15953993
defining natural numbers as sets is probably one of the dumbest things to be done in maths.

based take. Math comps are for giga autists who can only memorize shit and spit out answers.

>>15951610
>/sci/ bros, where do i start with math?

>>15954796
I mean defining natural numbers as classes.

>>15954801
they should be doing research instead

>>15954079
it's the current culture

>>15954079
Being dead.
Ask Maryam.

Do you truly, in your heart, look at this and say "Yes, this is a good definition of the cardinal number 1"? The same cardinal number 1 which is present in natural language?

>>15954324
that's not what definitions of already used terms are. you can't write whatever definitions you want in a dictionary. you have to see the way people use those words.

>>15954079
Because they spend their time on math instead of on getting married and having kids

>>15954830
What is a "unit class"

>>15954015
Did the Turks know more math than the Greeks?

>>15954898
a class with only one member

>>15947233
If im not mistaken the following identity holds(at least for odd values of [math]n[/math])

Setting [math]\omega=\frac{\pi}{2}-\frac{\alpha}{2}[/math] we get
[math]\frac{L}{2d}=cos(\omega)+cos(2\omega)+cos(3\omega)+...+cos((2k-1)\omega)[/math], where [math]k[/math] is just some number that depends on [math]n[/math].

We can express this equation as a polynomial in terms of [math]cos(\omega)[/math], thus there isn't actually a straightforward way to solve this for large values of [math]n[/math], because the degree of the polynomial would get too huge to solve analytically.

[math] \frac{L}{2d} [/math]

>>15954993
ignore that L/2d at the bottom idk wtf happened there

help a noob out, chatgpt was no help, I know the correct way to prove it but where did I go wrong in my reasoning

>>15955000
short answer: [math] 1^{1/2} [/math] could mean either -1 or +1, since both -1 and +1 are square roots of 1

>>15955017
that makes sense, but doesn't that also imply that that the answer could either be -1 or 1 regardless of whatever manipulation you do to the formula?

I don't understand the notion of a "equivalence class modulo equivalence relation"

For example a tangent vector at a point of a manifold is defined by any equivalence class of [math]C^1[/math] curve [math]\gamma[/math] modulo the equivalence relation where two such curves [math]\gamma_1, \gamma_2[/math] and some chart [math](U, \phi)[/math] are equivalent iff [math](\phi\circ\gamma_1)'(0)=(\phi\circ\gamma_2)'(0)[/math]

>>15955030
>>15955000
Open up your textbook, and see where "a^(bc) = (a^b)^c" applies.
You'll see it says 'a' has to be non-negative.

>>15949100
L just needs to be a chord of a regular polygon.

>>15955030
No, as is apparent if you try it out yourself with any n.
Trying to "factor the square", so to speak, is a bit of a dangerous game because the square root (exponentiating to 1/2) is a multivalued function. If you manipulate your way into using it, you can effectively destroy any knowledge of which value you were using prior, even if it was obvious from the original question

>>15954906
No but they had less gay sex

>>15954796
>>15954804
Set Theory and its delusions have been a disaster for Mathmat-kind

>>15955038
>If you manipulate your way into using it, you can effectively destroy any knowledge of which value you were using prior
that's weird, so certain algebraic steps actually change the value(?) of the formula even if they're valid steps

>>15955038
doesn't say anything like that, Basic Mathematics by Lange

>>15955043
>>15955065

>Want to learn German
>Ought to learn French (to read math)
>Demanded to learn Spanish (I'm hispanic)
>Barely know English (native language)
FUARRRRK!!!!
Any of you mathbros learn languages? It is so American to be a monolingual, I can't even speak to my dying grandparents.
Learning languages just does not click with my math brein.
I see words in math and I translate it to mental pictures.
Maybe it is just the pedagogy that is bad for a guy like me, but in general I'm not the most lingustical.
Any of you guys know da secrets?
I figure reading math in a new language might kill two rats with one glock.
Know any good math books in spanish, german, and french?
What is the most languages I should learn so I don't waste too much space in my brain? I think 3 new ones sounds like enough.

>>15955065
>doesn't say anything like that, Basic Mathematics by Lange
Nigga

>>15955077
>MUH REAL SOLUTIONS!!!
fuck you lang

>>15955077
he introduces the rule a^mn = (a^m)^n before that and doesn't specify a needs to be positive but he also hasn't introduced fractional powers yet so that's on me

>>15955060
its actually kinda based tho

Bump >>15953921

>>15955122
Give n+1 reasons why

>I HATE SET THEORY BECAUSE I CAN'T INTO RECURSION
every single time

>>15953919

>>15955031
Look up "equivalence relations", and "quotients by equivalence relations". This concept shows up everywhere: in set theory, abstract algebra, geometry and topology. You can try studying it in each of those contexts

>>15955058
Manly gay sex is based. The Greeks were manly about their gay sex, not effeminate.

bump

I hate set theory because it doesn't apply to the natural world. Neither the physical world, nor the mental world of humans is divided into sets (the exact concept of set used in set theory).

>>15955042
no it doesnt
even if it did there would be infinitely many solutions (a smaller infinity tbf :^) )

>>15956709
Okay, what is your preferred alternative?

>>15955584
bump

>>15956945
If I think an alternative, I'd publish it. Anyone else should do the same.

>Passed with a 7.0 in honors linear algebra
With a score like this, I'm bound to stay in my shit university in this shithole for all eternity.
It's over.

>>15956709
>>15956945
>>15957444
There are a number of more physically natural alternatives, function realizability (realizability over kleene's second algebra) is one, ZF+Determinacy is another.

>>15956709
Naive set theory?

>>15957969
what is not mentioned here is that in the previous "static, print-oriented mathematical culture" a lot happened in (((private correspondence)))

Sum of interior angles = 5pi = 5x+2y

For some positive reals m, n let x=m*pi, y=n*pi.

Then 5pi=5m*pi+2n*pi and n=5/2-5m/2. Since n is a positive real, m is within the interval (0,1).

So x=m*pi, y=(5/2-5m/2)pi for m in (0,1).

Another user gave the solution x=150, y=75 which is one possible solution.

No I didn't use latex.

>>15947233
Sum of interior angles = 5pi = 5x+2y

For some positive reals m, n let x=m*pi, y=n*pi.

Then 5pi=5m*pi+2n*pi and n=5/2-5m/2. Since n is a positive real, m is within the interval (0,1).

So x=m*pi, y=(5/2-5m/2)pi for m in (0,1).

Another user gave the solution x=150, y=75 which is one possible solution.

No I didn't use latex.

>>15947233
>to simplify and breakdown the problem:
>Sum of interior angles = 1080°
>bisect the figure with Line from midpoint of base line to Center angle at top of figure
>results in two identical mirrored figures
>for each of the two resultant figures, sum of interior angle = 540
>for each of the two resultant figures angle at L = 90°
>continue from there

>>15947233
>>15958556

>>15958568

>>15946236
Why are so many theologians mathematicians?

>>15947233
assumption 1. this is not a self intersecting polygon
0<x<pi/2, y=f(x,n) = (pi-2x)*(n-2)/4
there are infinitely many solutions
proof: play with some sticks and a piece of string

>>15958588
What are you trying to do with this?
You do realize that the red lines are of different lengths and do not bisect the angles x unless you're in the trivial special case where x = 2y, right?

>>15958568
This gives one equation for two unknowns x and y

Why is a (G, *) a group if it's finite and cancellative?
I'm fine with doing problems where it's already assumed that something's a group but I'm bad at showing why something is or isn't a group.

>>15958719
yes i noticed. it was an exercise.
points 'x' may lie on the arc of an ellipse, but not a circular curve.

>>15958568

>>15958568
>>15958588
>>15958785
wrong
wrong
wrong

Sum of interior angles for original polygon = 900°

[ interior angle sum = (n - 2) x 180°, where n is the number of sides. ]


recompute

>>15958748
I assume G is a monoid.

Given x in G; then 1,x,x^2,… cannot all be distinct since G is finite. Hence x^m=x^n for some m<n nonnegative integers, hence (using cancellation) 1=x^(n-m) , thus x has a (two-sided) inverse, which is in fact a power of x.

>>15958819
I had to look up the definition of monoid but I don't know if that's what it is. This exercise is pretty early on. I'm given that G is a nonempty finite set under some associative binary operation, and it's left and right cancelable. From that I have to show that it's a group, and there's a follow-up question about why it doesn't have to be a group if the assumption that it's finite is removed

>>15958748
>show something is a group
usually its show its a subgroup or just run through the group axioms

>>15958829
>associative binary operation
If it also has a (two-sided) identity element for the operation, then it’s a monoid.

I guess since your exercise didn’t say there is an identity element, you may need to first show there is an identity element, before doing the trick in >>15958819 which shows every element has an inverse (assuming already that there is an identity element).

Tbh I’m not sure yet how to do that, and I’m busy rn, but I’ll let you know if I figure out something

>>15958829
>>15958863
Actually I think the following shows there is an identity element:

First pick any g in G. Then g,g^2,g^3,… cannot all be distinct as G is finite. So we can find integers 0<m<n such that g^m=g^n .

Let u=g^(n-m) .

We claim xu = x for any x in G. Indeed, g^m=g^n , so xg^m = xg^n , and after canceling out g^m on the right this gives x=xg^(n-m)=xu, proving the claim.

A similar argument shows also ux=x for any x in G.

Therefore u is a two-sided identity element.

Can I do this as a way do denote indexing?

>>15959261
We'd rather you didn't.

Has anyone ever fucked with categorification of any specific algebraic structures? I am looking at a few constructions relating to the Heisenberg algebra

>>15951264
couldn't draw clear lines.
>>15959261
kill yourself

>>15959261
Just say [math] \exists (c_i \in \mathbb{C})_{i \in \mathbb{N}} [/math]

>>15951617
This book is 120 years old and teaches calc without limits lmao, you're better off on Kahn Academy

>>15958873
by g^n do you mean g * g * g *... *g for n times?

>>15960151
Duh

>>15960367
:(

>>15960476
R u d e

>>15960367
R u d e

I just created a useless and neat method for solving a very specific type of ODE, but of course I'm not gonna share with you guys because someone may steal my idea

>>15960563
go ahead and show us, Senpai. we wont tell anyone.

>>15960577
No.
This method is mine and mine alone, I won't let people use it, or claim that they created it.

>>15960581
science doesnt work in a vacumm. we can only move human knowledge forward if we corroborate and share ideas and discoveries.
this is like a science lab we should share our notes.

>>15960600
Don't care, I created it and it is mine.
I won't share it.

>>15960563
>>15960581
>>15960603
Okay then why bother saying anything in the first place

>>15960603
this is exactly why we cant get to Mars

>>15960581
You can't just pull a Fermat and die with the solution now. In a way, you've built something for that particular
class of ODE's that is built off of your knowledge and work which could possibly stand to be recognized and
attributed to you always. If you could, you can state the class of ODE you were focused on and one
observation you have noted about it. This doesn't give much away of what you have done, but you can garner my interest.

>>15947043
transexual = mental illness = discounted credibility
Really not that hard to understand

>>15960640
John Nash had schizophrenia lol. But he was not retarded. Unlike you

>>15960631
>>15960636
>>15960638
I'll only say this: This method only works for ODEs
[eqn]
\sum_{i =0}^np_i(t)x^{(i)} = q(t)
[/eqn]
where [math]q(t)[/math] and each [math]p_i(t)[/math] are polynomials. It's not that useful if you consider the wide range of different types of ODEs you can find, but it's still a fun method nonetheless.

>>15960649
Can't you just use the method of undetermined coefficients or something for this?

Also I assume x is the unknown function of t here, and x^(i) means the ith derivative of x w.r.t. t? You need to be more precise

The derivative is defined as the limit as c goes to zero

f(x+c)-f(x)/c

How is it defined in implicit differentiation. Like when finding dy/dx in x^4 + 2y^2 = 8

>>15960649
>>15960638
It does look fun, though...I'll be thinking about this guy

>>15960650
>Can't you just use the method of undetermined coefficients or something for this?
I forgot how to do undetermined coefficients and I didn't want to look it up, so I created my own method.
And after testing it a little bit, I found it to be quite efficient.
>x is the unknown function of t here
Yes.
>and x^(i) means the ith derivative of x w.r.t. t?
Yes.

>>15959261
is it i in N or c_i in N?

>>15960654
It's still [math]\frac{dy}{dx} = \lim_{c\to 0} \frac{y(x+c)-y(x)}{c}[/math] , but it may depend on which part of the curve you're looking at.

For example x^4 + 2y^2 = 8 can be described as two pieces, one is [math] y = +\sqrt{(8-x^4)/2} [/math] and the other is [math] y = -\sqrt{(8-x^4)/2} [/math]

>>15960660
Since everything is a polynomial here, you can convert this entirely into linear algebra. If you haven't done this before, figure it out as an exercise.

It's possible you've figured out a more efficient method though. I'm not an expert on Diff Eqs so idk what that might be

>>15960649
Looks neat anon.
its well beyond my math level.
i wouldnt know what to do with it. im just a tourist here.

>>15960666
Diiiiiiiigits

I understand the formula but not the theory

>>15960649
It looks like a linear ODE though

>>15947233
i might be a retard but i don't think the problem gives enough info
see my shitty freehand for possible polygons that fit the criteria in the problem

I want to calculate the various minutes in one day(=1440min) or a 5-day period (5x1440min) which are exactly a power of 2 of microseconds.

so i go to wolfgram and input this https://www.wolframalpha.com/input?i=(2^n)%2F(6x10^7)

but I do not know how to restrict the input ''n'' to integer values and make wolfgram output the minutes which can be expressed as 2^(some microseconds)

>>15961380
if really there's no minute expressible exactly as 2^(some microseconds), then I want the floor of (2^n)/(6x10^7)

>>15961295
But L is different in all of those

I think if d and L are fixed then x and y are determined

Say I have this linear equation I want to graph

[math]
y=-\frac{1}{2}x-\frac{7}{2}
[/math]

For the y-intersect, do i need to convert 7/2 to mixed number? and for the slope, is the Run always a positive number? -1/2 means go down from the Y intersect 1 unit, then move 2 units forward on X to find the other point on the line, right?

>>15961404
depends on the program you use to ploot. but that is just a line so quite trivial

>>15961392
2d diagrams are notorious for not being drawn accurately, so there is no real indication for the scale of d or L
L could be anywhere between 0 and (n-1)d long

>>15961380
Make a python script, gpt it if dont know how

>calculus
>algebra
>model
dumb question, but what do these words precisely mean in mathematics?
why would something be an "X calculus" instead of an "X algebra" or "X model" and vice versa?
I know that in first order logic a 'model' is just the interpretation of a first order formal language and obviously i know thee calculus and algebra

>>15962062
What I mean is you can calculate it for yourself. Even with d fixed, L will vary depending on x and y

Greetings bros, I need help figuring out what's the best way to teach my little 8 y.o nephew arithmetic math, I struggle in making him understand, and I think a reason of that is because all of it is second nature to me now. Would appreciate of if you got any books/channels that I can use to give him a solid foundation and thought process.

>>15962843
well yeah, unless its some funky self intersecting polygon

Some people like mystery novels, I like math

>>15964337
Some people like mystery novels, I like having sex with your mom (and math)

>>15962843
But the question is how do you calculate it? What's the formula?

>>15951617
>>15953315
>>15954802
Any infographics with cute anime girls telling me what to do? Already got fluent in jap, looking to get into math (so if there are any good math texts in japanese, please recommend).

in latex are you supposed to use the in-line/smaller sum when it's inside a radical e.g
[math] \sqrt{\sum_{x}^{y}}[/math]
vs
[eqn] \sqrt{\sum_{x}^{y}}[/eqn]

How does this have 30k views in 3 minutes

>>15965777
indians

>>15947001
What is the largest number? Infinity is what you have to do because you'll never give a proper answer to this question.
>muh huh these questions are meaningless
Cope.

>>15965339
Use complex numbers

Is there a term for the elementwise difference of two arbitrary vectors?

Say a is m elements and b is n elements, a . b would be an m x n matrix of each difference

>>15966169
i've never heard of one. what would that be useful forrrrgn

>>15966189
>what would that be useful forrrrgn
Probably nothing, I'm falling down a rabbit hole of frustrated math schizophrenia

>>15946989
Based.
>>15946992
Set theory is a fake. What is a set? You don't know. QED
>>15947001
>Mathematicians hate it because it implies that problems related to infinity can be solved or even speculated about
Can't? Did you make a typo here?
>>15950713
Defining natural numbers is like defining presents in terms of santa claus.

>>15950734
>For some reason when studying math I thought I would eventually learn something that would be really useful and help people
It is.
> . I thought this because why else would there be so many math departments in the world teaching advanced math if it wasn't useful somehow?
It is.
> Now that I realize that it doesn't really go anywhere useful
But it does.

>>15966169
>elementwise difference of two arbitrary vectors?

Maths is easier when you stop saying things that don't make sense

>>15966210
The difference of each element in both vectors
Math is easier when you know what the fuck you're talking about

>>15966191
typically we don't consider sums/differences of vectors in different vector spaces/of different dimensions.

if you have an actual application in mind that might change, but the first thought that comes to mind is to take the smaller dimension vector and embed it in the higher dimension space by zero padding, then taking the normal difference between two vectors of same dimension

>>15966215
well, in my specific application, m and n would be equal. I was generalizing just to be as broad as possible

>>15966219
>well, in my specific application, m and n would be equal
then what the fuck are you talking about

you give me two vectors of dimension m and want all of the pairwise differences between every element?

>>15966220
>you give me two vectors of dimension m and want all of the pairwise differences between every element?
Yes, and I want the result as a matrix

>>15966223
i see. in programming languages/linear algebra this is going to be related to an outer product. in python use this
https://numpy.org/doc/stable/reference/generated/numpy.ufunc.outer.html

>>15966231
Interesting. I actually figured out a way to accomplish this right before you replied
Given u and v of dimension m, what I'm looking for can be expressed as:
u . i - i . v
where i is a vector with all elements being one and . is the outer product

This is actually turning out to be kinda neat

Baby rudin filtered me... please help me it's so fucking over.

>>15966457
are you actually filtered, or is this the first time youve had to work hard at math and so you gave up?

baby rudin was difficult for me in undergrad but i'm almost done with my phd now. work through it

Ahhhh shit here we go again

>>15966468
I just can't imagine in my mind what the fuck he's talking about

>>15966575
Ditch Rudin and read a book with pictures.

>>15946236
what books would you recommend for someone attempting Calculus I a second time around?? CompSci student... I failed it this past fall semester
I thought I had a strong enough math background the first time around despite being a returning, older student. I'd passed Algebra and PreCalc in high school, and PreCalc again before dropping out at age 20. am now 24
I was just going to get Calculus I for Dummies, and the accompanying exercise workbook, at this point. the "for Dummies" series has never steered me wrong before. But I am open to any other suggestions or additions at this point, to be honest..
rly need help /sci/. figured I'd post here

>>15966761
oh yeah, I got filtered as soon as we hit "logarithmic differentiation" in Unit 3 of the curriculum, and a couple other points in that section as well. related rates. anti-derivatives. the definite integral and fund. theorem. that kind of stuff, if it helps to know where I started getting lost.
if maybe

>>15966761
my number one tip for getting through calculus is to do more problems. almost everytime ive seen a student say they dont understand a topic, they just havent dont enough problems

i know this sounds like shitty advice but 80% of calculus I/II/III is mechanical. get better at the mechanics and it will mostly fall into place.

stewart is an okay textbook to start with. if you want something more difficult get spivak. most other calc books are drivel

>>15966773
>my number one tip for getting through calculus is to do more problems. almost everytime ive seen a student say they dont understand a topic, they just havent dont enough problems
I get that at this point, cause I think that point hit home during fall semester. Hence why I wanna get a start now, just a bit ahead of the spring semester
I guess it wouldn't really matter, besides the textbook material itself, what book I get then. I will take a look at the books you're suggesting, but I guess your answer tells me that there's certainly no harm in ordering any old textbook, but maybe a couple to a few supplementary text/workbooks too. just for more problems to work through

>sister wants to transfer into a natural science degree from polsci
>just started a physics prereq course
>helping her with algebra and basic math stuff
>2nd day today
>she comes home and tells me she worked on some problems with her friends
>they redid everything we had done the 1st day
>ask her if she remembers any of it
>"uhhhh not really"
>we spent like 30 minutes on the quadratic formula alone
>"but we didn't write the answer this way!"
>we literally did

I'm in fucking disbelief
legit never felt this awful

>>15966789
stewart is an okay place to start because lots of the mechanical problems follow from the examples he works out and then increase in difficulty. also fully half of the questions have answers in the back and everything else can be looked up on wolfram alpha
logarithmic differentiation is just differentiation with an extra step. if you're solid at differentiation then logarithmic differentiation is trivial. related rates require a little more thinking but is just a straightforward application of problem solving (what rates/quantities do i have -> what do i want -> what formulas do i know -> differentiate appropriately). anti-derivatives, at the start, are just derivatives in reverse (at least for power rule, trig, exponential). after that it's about learning the little tricks and applying them

all of this to say that the "brute force" approach of doing more problems almost always works to learn these concepts. they're not very novel or complicated. if you learn the mechanics you can get through them

>>15946236
I proved goldbachs conjecture chatgpt is freaking out

I feel like our number system is broken. How can .999... = 1? Something just seems wrong, like we chose the wrong bases or something

>>15967055
(not saying this happened, but) if you 'explain' stuff by pretty much just showing the solution there's a good chance she just mentally checked out while you solved it.
When I teach kids elementary maths or science I have to really let go of the urge to explain, and let them struggle for themselves to make something stick.

Can /mg/ recommend a *short*, concise, grad level book on (basic) commutative algebra?

>>15967722
Atiyah-Macdonald

>>15967595
same thing as 0.333... = 1/3

>>15967976
I think you mean 0.333... ~ 1/3

>>15967981
no. as soon as you write the "..." after 0.333, you're smuggling in some concept of "an infinite number of digits", and in that limit, 0.333.... = 1/3 exactly.

F math

I finished an intro to topology class. It covered everything in pic related, as well as some graph theory.

I want to learn more topology.

Where do I go next?

>>15968235
How much calc did you use in topology? What are the most important prerequisites for it?

>>15968251
The prereq was two real analysis courses. It wasn't very calc heavy I think.

The textbook is available here, in case you want to see what the course covered: https://files.owenoertell.com/textbooks/math/metric-sutherland.pdf

>>15968235
>>15968263
The two next steps are algebraic topology and differential topology, though neither follows purely from point-set. You need to understand at least the basics of group theory for the former, and multivariate calculus for the latter

I made an algorithm that finds means given multiple overlaid normal distributions, and it's getting good results. The difficult I'm having now is figuring out how to determine how many means I should target. I've found that having the algorithm seek more than what is actually present produces multiple similar means, while still approximating the true values pretty well, but that's not an ideal approach

>>15968273
can I study differential topology without knowing anything about differential geometry?

>>15968491
If anything, I'd say diff topology is a prerequisite for diff geometry

>>15968499
Ok nice.
I think I'll start with algebraic topology.

>>15968504
its a good place to begin, then you can move on to algebra, topology, then maybe some euclidean geometry after

>>15946236
Somebody draw me a hexagon like one sees on graph paper on a square graph paper. I´ve been trying for hours and 4 out of the 6 sides do not mirror each other like they actually should.

>>15946236
Can someone guide me through how the summation and integral were interchanged in pic related? First time hearing of this and it fucked my ass

>>15967595
Let x = 0.9999... = 0.9 + 0.09 + 0.009 + ...
Then 10x = 9.999... = 9 + 0.9 + 0.09 + ...
So 10x-x = 9
So 9x=9
So x=1

>>15968534
I had this from /tg

>>15968534
Just have chat make you the graph of that and then print it out
Also you maybe could look for a way to use circle constructions to help make your grid out of triangulations of circles instead of just tilings

I'm just reading about determinants and cross products. For v, w in R^2, det[v, w] is the area of the parallelogram spanned by v and w. The definition of the cross product also says that |v x w| must be the area of that parallelogram. So det[v, w] = |v x w|. How should this connection be interpreted? Is it just defined this way for convenience in calculating that area?

>>15961404
if you are trying to graph this expression by hand, then for the sake of being intuitive I would convert your Y intercept to a mixed number.
In the function you gave here, yes the run part is positive and you will be increasing 2 units for every 1 y unit down. Run isn't always a positive number. For example, you could have y=-1/-2x-7/2, where 'run' is now a negative number. There's no real limit to what you can have as a slope as long as it is simplifiable down to be a function.

New >>15969522