Set theory solely exists to facilitate the creation of contrived logic puzzles of no more mathematical merit than a game of sudoku.

Previously >>16899914

Bose was a crank

what math do I need to write cool looking shaders

>>16922249
Define shader

>>16922268
the things that run on your gfx card

What are some cool concepts in the intersection of numerical analysis and linear algebra?

>>16922249
Basic geometry and some linear algebra - the latter is true for most coding though.

>>16921941
fuck miggers

Do you think there exists a polynomial-time integer factorization algorithm? If so, what do you think such an algorithm would look like?

>>16922249
topology

>>16922249
>>16922269
Just learn how to do basic calculations (+, -, x, /) with 3x3 to 4x4 matrices in binary, octa, hexa and decimals.

Is Matt Parker smart enough to do motivic cohomology? Is he smart enough to compute Ext functors? Can he describe what a bialgebra is off the top of his head? Or.... Is he a midwit grifter who can only regurgitate funny math facts and write jeet-tier Python code?

it's crazy how 99.99999% of math was useless until the invention of electricity

>>16922564
It's crazy how you're fucking retarded.

>>16921941
Is there something akin to orientation that has 3 states instead of 2?

your mother is so fat that the axioms of set theory are unable to either prove or disprove that there exists a set b such that it can contain her

>>16922600
Maybe triality?

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>>16922645
The word fat was against the TOS so I had to tell it to say hamburger instead.

so I heard if your elementary algebra sucks you're basically fucked trying to move on to higher math

are there any good algebra problem sets or whatever so I can figure out if I actually know algebra and not just some fucked up version of it from the book I followed?

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What if 1/0 is just another type of imaginary number like sqrt(-1)? Ever think of that, huh?

>>16922700
There are two ways your algebra could suck. The first is you don't even get the point of algebra, you don't understand solving for x, and how x is a representative from an entire class of numbers. Algebra gives you tools for abstraction and speaking in generality. Yes, this is crucial for higher math.

The second is just not memorizing the basic facts (theorems) in algebra like the quadratic formula and the difference of two squares.

If you took algebra in grade school you probably get the point of algebra but you don't remember the important facts. Better yet, you should understand how Algebra give you the tools to *verify* the difference of two squares is as it is

[eqn] a^2 - b^2 = a^2-b^2 +0 [/eqn]
[eqn] = a^2-b^2+ab-ab = a^2+ab-ab-b^2 [/eqn]
[eqn] = a(a+b)-b(a+b) = (a+b) \cdot (a-b) [/eqn]

>>16922709
use case?

>>16922700
>so I heard if your elementary algebra sucks you're basically fucked trying to move on to higher math
Actually, the best way to assess this would be to actually try to move on to higher math. Start reading elementary linear algebra right now:
https://understandinglinearalgebra.org/home.html
Maybe try these interactive challenges, but they include trigonometry and precalculus:
https://www.khanacademy.org/math/get-ready-for-algebra-i/test/x127ac35e11aba30e:course-challenge
https://www.khanacademy.org/math/get-ready-for-algebra-ii/test/x6e4201668896ef07:course-challenge
Try this problem book for the basics:
https://books.openbookpublishers.com/10.11647/obp.0168.pdf
More resources at:
https://textbooks.aimath.org/
https://realnotcomplex.com/
https://github.com/rossant/awesome-math

>>16922700
Ask the AI to test your knowledge

>>16922747
>muh ai
kys

>>16922700
Personally I think solving word problems until you can see how to express them algebraically with minimal effort is the best skill you can develop at that level. Actually performing the baby algebra should be trivial, you can probably fit all the non-obvious rules on a single notecard.

>>16922559
Eh, I used to watch him a lot in high school; many of his older videos are quite nostalgic to me. I don't mind his combinatorics or prime number videos. As for his topology videos, I have no idea - I almost never watch them.
Though the Kellogg's video he released a few days may be the worst video he's ever uploaded. I was about to unsubscribe, but then I remembered he's one of the OG math YouTubers, so I let it slide.

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>x^2 - 3x = -1
>x(x - 3) = -1
>x - 3 = -1/x
>1/x + x = 3

i give up

>>16923010
You should be able to immediately recognize what number plus its reciprocal equals 3.

>>16923010
You're almost there, just multiply both sides by X, then subtract X^2 from both sides, then factor out an X

They cause permanent harm to school children by even teaching them the concept of "degrees" in regards to angles. Any teacher that does so should be imprisoned alongside pedophiles and child murderers.

>>16923010
x^2 -3x + 1 = 0
x^2 -3x + (1+c) = c
x^2 -3x +(1+c) = (x-r)^2 = x^2 -2r*x + r^2

r = 3/2 => (1+c) = 9/4
c = 9/4 -4/4 = 5/4
x^2 -3x +1 + 5/4 = 5/4
x^2 -3x + 9/4 = 5/4
(x-3/2)^2 = 5/4
x-3/2 = +-sqrt(5)/2
x = (3 +-sqrt(5))/2

>>16923010
anon, you're supposed to try to recognize patterns, not just mindlessly apply rules in an infinite loop

>>16923189
Actually, he just needs to mindlessly apply the quadratic equation formula.

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What if you have a square inside of a regular hexagon with unit sides so that three of the vertices of the square are on the perimeter of the hexagon and the fourth one is on the line drawn between two of the vertices of the hexagon like in picrelated.

What is the side length of the square?

>>16922709
Say 1/0 = x, try to prove 2/0 != x. Else x * 0 = 1 and 2. Also does 0 * 1/0 = 1?

>>16923244
let i = 1/0, then 2/0 = 2(1/0) = 2i

OK, I'm studying Group Theory at uni and I love it. I'm a month in and have made a separate sheet with around 40 definitions and theorems that I've come across so far. I'm drowning in them. I can prove only some of them. Do I need to make sure I can prove them all on my own? How do I remember them? I don't want to rely on a sheet of paper laying next to me while I study. I want to be able to do things from memory. Should I memorise them with flashcards? This is my first serious subject. I coasted through Calculus without memorising or doing much work at all, so this is new for me.

if you have to flip the inequality sign doesn't that mean the inequality was wrong from the start?

>>16923544
In what context?
If you're doing something like taking the reciprocal or negative, no

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>>16923544
If negative X is less than 0 then clearly X is greater than 0.

>>16923546
>it is self-evident
fuck off euler I know that's you fucking frog

>>16923560
Euler would never give a proof by "it is trivial".
That's Fermat posting

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>>16923570

>>16923543
Do exercises. Lots of them. You'll remember the ones worth remembered.

>>16922700
There was a book called something like The Huge Book of Algebra Problems that I remember being pretty decent

Math bros, do you have a special place you do math? I'm small brain but also brain hacking and I get most "stuff" done when I've walked to a special location and have some peace and quiet away from a computer. Has to be outside the house. I think I'm gunna start reading some math books for the fun of it. I am a NEET and taking the "learn everything" pill. Math isn't the only thing I'm doing. Please wish me luck. In both finding a quiet well lit place and not being pwned by phd physicists while trying to learn algebra and trig. My 4 books I'll have on hand are elements of set theory by enderton, how to solve, how to prove it, and basic mathmatics. Gunna do some math studying for the hell of it. On top of everything else I do. For what purpose? I don't know. Why try? I don't know. I have yet to master my own life and am like a man stranded at ocean swimming in any direction looking for dry land or a boat to take me to one.

just read math books and stared at the stars. Reading about induction in how to solve it was really interesting. So was learning about heuristics. Endermans set theory is really cool, I just don't know how I could commit something like that to memory. But I do read it from time to time. Reminds me of my old algebra notebook where I wrote down a bunch of rules, which is now missing. Any book specifically about calculating in algebra after you've mastered basic PEMDAS would be great, I still have to practice my basic PEMDAS abilities, specifically long division on paper, practicing long multiplication, etc, calculating exponents, even beginning with rules of exponents. I also like stuff like associative and communicative properties. I would go to my school online curriculum but I would rather just buy a book.

I really enjoyed reading the math books /mg/ recommended. They're dry and boring sometimes but other times they're just as interesting as a novel or videogame. My favorite writing style wise is how to solve it (reads more like a book) and my favorite for actually learning "difficult" concepts is basic mathematics, but it's not perfect. I will go back out later tonight and do more math and report back if anyone is interested.

Another math topic that greatly interests me is mental math, there is a great book on the subject I'll dig up if anyone is interested by an author in my locale. I also have a second hand "the Great Courses" dvd with only disk 2 of mental math to watch. I will report back if I ever.

I'm thankful there is a math general on 4chan, no matter how much I may not like it sometimes. For topics like computer science and game design there is no general at all, and discussion is even worse. Physics discussion is literally non existent. /lit/ is its own beast but similarly grim. The question remains. Can a 4chan user increase his or her IQ to be genius level and beyond through force of will or will fate take them silently into the brainlet night like many. I like to think IQ tests are just a game that can be trained for. Regardless, I have an autistic obsession with learning stupid things for no reason.

Also, I learned the words heuristics and pedagogy. Is there a word for the studies and practices of independent learning? Any schools of thought on the subject? I would like to learn from someone who has mastered learning, if at all possible. Not just any one thing either, but broadly. In so much as the limitations of depth vs breadth and the achieving "mastery" and what that even means.... As well as preserving knowledge, personal biblification techniques, with a auxiliary section on pedagogy and heuristics, or at least references. I would like to understand the forefront knowledge at the most auxiliary and bite sized atomic factoids level, "cosmological" concepts, grand theories, as well as new developments in minute understanding. I am wondering if it's humanly possible to be educated on art, science, technology, world events, etc, be a "well educated person" in todays society, or if it's too much for any one person to know.

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1st year undergrad in math in EU
our uni basically closes off theoretical math for only the best students since day 1 like literally day 1 hour 0 but you _technically_ can sign up for required courses during 2nd and 3rd year it's just that the versions of calculus and linear algebra they make you take are very computation heavy and dont have a lot of proofs.
I'm not the most hardworking person but how would I go about catching up? Besides theoretical specialization we also have data analysis, applied maths and some finance jewery i dont think i'm interested in any of those particularly much

>>16924465
It's all about the holy grail of learning calculus. Which you're supposed to do in high school. Basically PEMDAS -> Algebra -> Trig -> Calculus

Geometry is the fabric being woven. If you're a brainlet you can learn PEMDAS, in like a month. Algebra is where you're supposed to give up. If you can make it past algebra to trig you can actually learn calculus, and be a big boy math literate gentleman. It's not as hard as people make you think. You too can go to grad school. And get the PHD. And be the post doc researcher. Your own lab, out of reach? Some say this is a myth. Many such cases.

>>16924473
not sure if youre replying to the right guy

>>16924465
if you can't do calculus by hand you're not ready. I'd work on this if you're not there yet. 4 years of uni undergrad should just be showing up to class and networking after class. The real study is being proficient at calculus by hand, being able to prove theorems, basic understanding of philosophy etc, if you're already at this level I would pick up chemistry and physics. Or do some wacko courses that may inspire you in the future for your undergrad. Or just make friends at school.

>>16924478
Well I seriously doubt he can do calculus by hand and basic proofs, being a first year math major. It's the bare minimum but there's lots of frauds who haven't even met that bar.

>>16924479
>>16924480
ok just so we're on the same page here, what do you mean by calculus? since i'm in the EU and it might not be 1:1
also i have made ZERO friends and i wont make a single one one because i'm mentally ill

>>16924479
>calculus by hand
that's the only way to do calculus, computers literally can't perform it

>>16924481
Finish the book issac newton wrote on calculus, order a copy of the original text and study it. Supplementary texts may also help, but that's what I'd go with https://en.wikipedia.org/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica

There are other books by newton, i'm not sure, but calculating motions in the universe and a firm grasp on mythology and astronomy helps. Get a telescope.

>>16924487
calculus by micheal spivock is also very good, /mg/ talked about it historically and everything they recommend is great. I would generally start looking into the bibliography of Issac newton, for calculus. If you want to really learn...

>>16924437
>I just don't know how I could commit something like that to memory
If you've got a lot of time and paper to burn, copy the book down verbatim into a notebook and add your own commentary.

>>16924490
That's probably a good idea

>>16924487
ok but how do i learn how to prove things and learn from reading proofs and find proofs etc

>>16924496
if then therefore, do I believe it? The biggest proof is that there is no proof.

>>16924491
It works great with dry/dense textbooks

>>16924496
But really it's more about making mathematical arguments, and learning logic is probably where I would start.

>>16924500
we had logic during 1st semester and it was the only course i enjoyed. i really, really enjoyed it and did well

>>16924496
If you're really looking into learning proofs, how to solve it/how to prove it are really great. With basic mathmatics and the ocassional math trainer/khan academy/notebook work I'd imagine you could get really far.

>>16924501
schizophrenia pilled

This conversation is getting old but it's been productive. I go now. China numba wan.

>>16924503
i may or may not have schizophrenia symptoms and be schizoid too
i'm interested in systems and determinism and formalizing concepts
i thought when i'd do a math degree we would stop with gay faggotry that are numbers after 2 semesters but apparently thats not how it works here

>>16924505
You should be able to play doom with pen and paper

>>16924487
ive just checked
its in latin
i wanted to learn latin but im not ready yet

>>16924437
>Another math topic that greatly interests me is mental math, there is a great book on the subject I'll dig up if anyone is interested by an author in my locale.
I'm working through "Secrets of Mental Math" by Benjamin and Shermer. It's pretty good. It made me realize there were mental math things I was doing incorrectly my whole life and it's because the methods taught in schools are not good. One of the authors, Benjamin, also has a good book on combinatorics if you're into that.
>>16924465
Don't listen to the trolls telling you to "do calculus by hand" (whatever that even means).

Work through these books:
Calculus by Thomas
How to Prove it by Velleman
Linear Algebra by Friedberg
Abstract Algebra by Judson
Understanding Analysis by Abbott

You can skip the Calculus book if you've already done the material. If you don't like Velleman's proof writing book then try Book of Proof by Hammack. Don't focus on trying to do every question in these proof writing books. Just make sure you understand the material and get to the Linear Algebra, Abstract Algebra and Analysis books as soon as you can. I went full retard and did ALL the questions in Velleman's book and it didn't help me too much. What worked was actually banging my head against actual Linear Algebra, Abstract Algebra and Analysis proofs. You'll probably want to throw in an elementary number theory book too. I've heard good things about Elementary Number Theory by Jones and Jones.

>>16924729
I'll pitch Elementary Methods in Number Theory by Nathanson for a good and accessible number theory book

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What is his life strategy, exactly?

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>2011+15
>not doing your calculus by hand
ISHYGDDT

>>16924729
ill definitely (not) check it out after i come home (i'm a lazy fucking loser)
thanks for sharing though, how to prove it seems to be a common recommendation

I exclusively perform mental calculus.

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>>16924905

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Does this problem have a closed form solution?

Two circles are inside a regular pentagon, the blue one twice the area of the yellow one. A line is drawn across the pentagon being tangent to both circles at the point in which they intersect.

The length of the segment AB is one unit. The problem is to find the length of BC.

How many of you actually have a pure math doctorate or are at least a PhD student?

>>16924729
I hate these lists because they're always some crazy ancient books.
If I don't see Stewart Calculus in these I just ignore. I'm in grad school at a T10 now and I used Stewart for Calc 1-3. For analysis just use Ruin. Its a well worn path and its been done like a million times.

>>16925274
I'm an APPLIED math MASTERS student. How pathetic am I in your eyes from a not-worthy-of-life to degrading-manual-labor-only tier?

>>16925300
>complaints about crazy ancient books
>uses rudin

>>16925204
Idk. Played around with it for a bit. I thought of collapsing the pentagon into a rectangle with an open top, doesn't do much though. You've got more unknowns than equations so it's hard. There's probably a relationship between the diameter of the circle and the side length.

>>16925300
Thomas' Calculus is direct, contemporary competition of Stewart's

>>16925300
Which ones are ancient? Thomas is used as a Stewart alternative in North America. As for the analysis book: I recommended Understanding Analysis to that guy specifically because it's gentle and he said that he has no experience with higher mathematics. Advising him to work through Rudin would be torturous. I used Understanding Analysis as my first analysis book and I found it to be very good. Rudin and the rest of the BORE-baki group suck all the fun and creativity out of mathematics. To me, Rudin is ancient.

Besides, why are ``ancient'' books bad? For undergrad mathematics, you can pick up a book from, say, the 1970s and be just fine. Not much has changed at the undergrad level. Why would it matter? The guy I replied to isn't doing cutting edge research mathematics.

Now let's go through the authors I recommended:
Thomas <- Dead
Velleman <- Alive
Friedberg <- Not sure
Judson <- Alive
Abbott <- Alive

The majority of the authors I recommended are alive and are willing to accept errata for new editions.

Now let's do you:
Stewart <- Dead
Rudin <- Dead (good riddance)

Are there any modern books (say, from the last 200 years or so, and very must have pdfs somewhere online) that teach geometry mainly with straight edge and compass? Or is Euclid still the gold standard for this stuff?
>why
I do math for fun and drawing is fun.

>>16925435
Try:
Jacques Hadamard's Lessons in Plane Geometry (the new edition with Mark Saul's Reader's Companion)
Kiselev's Planimetry
Daniel Callahan's Euclid's Elements Redux

if group theory is real then why aren't there group theory cpus? checkmate atheists

>>16925535
Technically integers are a group, so...

>>16925460
Thank.

>>16925301
I think you'll make great middle-management.

Imperial Analysis

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>the limit of any function as the denominator approaches 0 behaves in consistent and predictable ways
>somehow division by 0 is undefined and unknowable

>>16925795
have you considered f(x)=1/x

>>16925807
basically any time you see me I am internally contemplating 1/x

>>16925814
any progress?

>>16925795
>>16925814
contemplate the following:
1. there are two directions from which the denominator of 1/x can approach 0
2. the behaviors of those two directions are not consistent with each other
3. the inconsistency grows as they approach zero
4. they don't even agree on which infinity they're asymptotically pointing to at 0

>>16925836
Protip: it's entirely consistent when you realize that it simply wraps around the numberline

A superhyperreal number b is said to be positive infinitesimalimal if b is positive but less than every positive hyperreal number

>>16925807
why don't we just say that
lim x-> 0 1/x = {-inf,inf}
it just produces two different numbers at the same time. Let it be a set man.

>>16922700
The book by Aluffi is good.

>>16925848
follow-up questions:
A: What is 1/0 + 1/0?
B: What is 1/0 - 1/0?

>>16925873
if hyperreal numbers sit "between" real numbers, then real numbers aren't continuous
if the hyperreal number system somehow creates gaps between real numbers, then in the context of the hyperreal number system real numbers are discrete

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>>16925882
All numbers are discrete because no number exists until you calculate it.

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>>16925885

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>read proof
>that makes sense
>immediately look away and try to do the proof myself
>uhhhh uhhh uhhhh
>stare blankly at the page for 10 minutes
>give up

Can anyone explain how to use spatial vectors in rigid body mechanics?

>>16925965
there used to be a guy but he died back in '76 so you're on your own

>>16925970
Who?

>>16925970
kek used to happen in biology all the time before gene sequencing

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Why is this wall-hitting man constantly called (on X and in magazines, that is) a "legend" and "the greatest living mathematician alive".
He won some championship, then proves half a dozen notable results in meme subfields, and then after winning some prices in 2010 people just kept calling him a legendary mathematician ... I assume because nobody else is known?
I mean yes, he is a super strong mathematician - but is that really all that exceptional? And is any of his work actually relevant?

>>16926115
everything major has already been discovered, even if the greatest mathematician to ever exist were born today the best he could hope to accomplish over his life would be a few proofs of things already taken for granted

So I just mastered my multiplication tables up to 5. Why are people always saying math is hard? This shit is easy.

>>16926259
just wait until you get to fractions

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I've speedran 6 different calculus books/courses and this is the first time I've seen this explicitly defined. I mean, it makes sense, just weird how most courses never distinguish them (probably because they're "infinitely close" or whatever).

honestly what they really need is just a new number system that allows for blurry numbers with overlap

>>16926239
actually ... good point

(ofc, this doesn't quite explain why people are so needy to call someone a legend. Or "Mozart of Math", as one article of some famous outlet put it)

>>16926264
I'm confident that all calculus texts you looked at - I mean at least Springer texts or whatever - were clear about this.
Basically, just from writing down the definition of f' in terms of limits, you have that \Delta is finite. And no math textbook uses \Delta in place of d if the limit has been taken. At worst, some thermodynamics books may do this.

>>16926323
nta but most calculus courses are pretty bad, they just start using d's instead of deltas because "that's the calculus notation lol" and then they give you a table of rules to memorize
luckily if you just memorize and keep going to higher courses eventually you pick up the skipped details (or you fail out)

>>16926331
>a table of rules to memorize
I like the Keisler book from the wiki, if you actually follow along with it you don't need to memorize shit because everything becomes dead obvious at a glance.

I saw I cool problem on the internet. The dimensions of the cracker are 60 mm by 120 mm. The dimensions of the cheese are 73 mm by 88 mm. It always sucks when some of the cheese is hanging outside of the cracker. So the problem becomes as follows. What is the maximum percentage of the cheese that can be in contact with the cracker when you put the cheese on top of the cracker?

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>>16926361
100%
you bite off the excess