/mg/ - Math General

[Anonymous No.14960838]

Discuss math.
Last thread: >>14951840

[Anonymous No.14960842]

If study information could be represented by an equation, what would it be?

[Anonymous No.14960957]

>https://en.wikipedia.org/wiki/Sexy_prime
Do mathematicians really?

[Anonymous No.14960991]

>>14960957
https://en.wikipedia.org/wiki/Cox%E2%80%93Zucker_machine
https://en.wikipedia.org/wiki/Clopen_set

[Anonymous No.14961015]

>>14960991
>Clopen_set
we understand nothing

[Anonymous No.14961016]

>>14960957
>>14960991
https://encyclopediaofmath.org/wiki/Tits_building

[Anonymous No.14961017]

>>14960991
Already know about those

[Anonymous No.14961021]

>>14961017
>>14961015
>>14961016
https://en.wikipedia.org/wiki/Associated_prime
>associated primes of M are written as Ass(M)

[Anonymous No.14961022]

https://www.youtube.com/watch?v=X5iaZf21R8w

[Anonymous No.14961031]

>>14961021

[Anonymous No.14961049]

>>14960957
>Uohhhhhh! prime sexy! numbers erotic!
>Sextuple with sexy primes! uuoohhhhh!

[Anonymous No.14961072]

>>14961031
why is idempotent / nilpotent dirty? because it sounds like impotent?

[Anonymous No.14961157]

>/mg/ - Math General: 15yo humor and homework

[Anonymous No.14961159]

>>14960957
>The term "sexy prime" is a pun stemming from the Latin word for six: sex.

[Anonymous No.14961160]

>>14961157
Cox is 74

[Anonymous No.14961164]

>>14961157
>nerds are immature
doing a big think right now

[Anonymous No.14961169]

>>14961159
>>14961049
>>14960957
The video was taken off YT, but here's Terry Tao on Colbert talking about sexy primes:
https://www.cc.com/video/6wtwlg/the-colbert-report-terence-tao

May not be available outside the US. Someone reupload it elsewhere.

[Anonymous No.14961173]

Sometimes I look up to moon in jealously knowing that there's daylight there while I'm in the dark. Winter sucks.

[Anonymous No.14961180]

>>14961173
Imagine living in a place where it's dark at 4:30 AND it's hot.
Our 4 seasons are: summer, fall, summer, simmer.

[Anonymous No.14961390]

When did the term "computation" and doing mathematics in a classical pre cantor/Hilbert way, become a lesser/disparaging thing?
Is it just an American thing? People online calling things "computational" to belittle it and the such. Obviously calling university calculus a computational course is a true definition and make sense, but jm saying people who say "oh, abstract algebra is pretty much computational". Its almost synonymous with the word "trivial" in use.
Seems like a new way of academia mathematicians to harass industry mathematicians and their work.

[Anonymous No.14961453]

>>14961390
>"When we do physics, the traditional approach has been to start from our basic sensory experience of the physical world, and of concepts like space, time and motion—and then to try to formalize our descriptions of these things, and build on these formalizations. And in its early development—for example byEuclid—mathematics took the same basic approach. But beginning a little more than a century ago there emerged the idea that one could build mathematics purely from formal axioms, without necessarily any reference to what is accessible to sensory experiece..."

You were born too late. You will never practice non-autismic mathematics.

[Anonymous No.14961493]

>>14961390
Because it's grunt work that requires no intelligent thought.
You just pattern match and use the right formula or whatever. It's not fun at all. Math is about fun.

[Anonymous No.14961514]

>localization
>tensor product
>gcd
>lcm
>product
>coproduct
>pushout
>pullback
>quotient
>kernel
>cokernel
>completion
>literally any object with a universal property

[Anonymous No.14961617]

what do u guys use for notes a specific program or just pen/paper

[Anonymous No.14961649]

this is a dodecahedron, right?

[Anonymous No.14961718]

>>14960842
Entropy

[Anonymous No.14961825]

prof was doing some category theory. lost control of a morphism and it flew away and hit a student right in the eye. damn those things are sharp.

[Anonymous No.14961855]

Are there any papers relevant to analytical ways of dealing with the integral of [math]x^{x}[/math]+f, for ordinary polynomial f? I'm sick of approaching the thing I'm doing numerically.

[Anonymous No.14961868]

>>14961855
Shit, fucked that up. I meant [math]log(x^{x} +f)[/math].

[Anonymous No.14962408]

>>14960957
>Prime too sexy for this...
https://vimeo.com/537469728

[Anonymous No.14962857]

In an "if and only if", which direction is "necessary" direction, and which is the "sufficient" direction?

[Anonymous No.14962859]

>>14962857
p is necessary for q iff q implies p.
p is sufficient for q iff p implies q.

[Anonymous No.14963602]

Is it normal to take a long time to solve questions like these? These questions took me 2 days to solve, but the solutions are very short and simple.

[Anonymous No.14963632]

Why is the answer 55 square feet instead of 55 square inches?

[Anonymous No.14963659]

[math]2^{32582657}-1[/math]

[Anonymous No.14963674]

>>14963632
Because it's a typo

[Anonymous No.14963681]

>>14963674
I was thinking that but there was another question on the test that went from inches to feet too, it threw me off.

[Anonymous No.14963734]

>>14960838
Thought this was an energy band diagram at first, lol

[Anonymous No.14963764]

>>14963681
Your professor probably edited an old exam and didn't change everything correctly. Don't overthink it.

The answer is just h*(a+b)/2 = 5*(4+18)/2 = 55. The length units were inches, so the area unit is square inches.

[Anonymous No.14963772]

>>14963764
I appreciate it

[Anonymous No.14963823]

>>14961493
Is physics grunt work? What I think of when I hear some math is computational, "oh, it some physics numerical methods shit" just like when I hear applied its "oh its some engineering shit"

>>14961390
Yeah so maybe, people are making fun of things computational the same way they make fun of applied fields like physics and engineering.

[Anonymous No.14963869]

>>14961390
>doing mathematics in a classical pre cantor/Hilbert way,
Suck it up nerd, math isn't allowed anymore. You HAVE to live in Hilbert's Nu-Math universe or be ostracized, called names, kicked out of journals, and harassed at every turn.

Modern day mathematicians are all Hilbert goons.

[Anonymous No.14963883]

Do girls think your love of mathematics is “cute”? Multiple of my girlfriends and women I’ve spoken to have said it’s cute that I love maths

[Anonymous No.14963912]

>>14963883
My wife does, but she idolized her grandfather, who was a very influential physicist, which leaves me feeling perpetually inadequate.

[Anonymous No.14963925]

>>14963869
>rightoid persecution fetishist

[Anonymous No.14963930]

>>14963883
I enjoy talking to people who passionate about something. Other people feel similarly, I think.

[Anonymous No.14964075]

pic related is technically incorrect since the sum on the right hand side must be conditioned on
>(1) k_i=0 for all I, or
>(2) k_r>0
to make sure that 1 is counted and duplicate "prime factorizations" such as 2=2*3^0 aren't

[Anonymous No.14964104]

1.9954559575000368

[Anonymous No.14964116]

>>14964075
This exercise is confusing. I'll skip it. Thank you!

[Anonymous No.14964129]

>>14964104
x

[Anonymous No.14964131]

>>14964129
go on..

[Anonymous No.14964133]

>>14964131
2x

[Anonymous No.14964179]

>>14964133
2.5x

[Anonymous No.14964192]

[Anonymous No.14964211]

>>14963883
>DO YOU THINK YOU'RE SPECIAL?
>WELL, I THINK YOU'RE CUTE!
https://vimeo.com/532705433

[Anonymous No.14964237]

>>14964211
>YOU'RE TRUE AND YOU'RE FALSE
>YOU'RE SET AND YOU'RE CLEAR
https://vimeo.com/516418493

[Anonymous No.14964259]

>>14964179
0

[Anonymous No.14964268]

>type of types over the category of contexts
I should have stuck to number theoty

[Anonymous No.14964279]

>>14960838
That's beautiful. What is it?

[Anonymous No.14964308]

>>14964259
axiom of choice

[Anonymous No.14964324]

>>14964308
Acceptance of this axiom is required in the Mathematics community, because rejecting it means that a large portion of this edifice of "proofs" built upon prior "proofs", under construction since Cantor, would have to be torn down and cast into the waste bin. This is unthinkable to those who grew up thinking that the Axiom of Choice wasn't rotten timber, but that doesn't mean it's not the correct thing to do. And refusal to face the unthinkable, is a psychological barrier, not a mathematical one.

Unthinkable, because it would mean your dissertation was was... worthless. Unthinkable because it would mean your whole career has been wasted mining iron pyrite (fool's gold). Unthinkable by those at the top of the pyramid of academic reputation. But again, these are all psychological barriers, NOT mathematical ones. Belief doesn't transmute iron sulfide into gold. Belief can certainly DELAY the collapse of a fiat currency, or a Ponzi scheme, but only temporarily.

Properly understood, the Banach-Tarski Paradox isn't a paradox at all, it is a simple case of Reductio ad Absurdum, or proof by contradiction. In this view, it demonstrates that Cantor was WRONG.

If you think that belief doesn't create a powerful fake reality that can vanish into thin air, when doubt begins to infect the community of believers, then you don't understand hyperinflation of fiat currency, you don't remember the "dot-com" bust, or the financial crisis of 2007-2008. Mathematicians, unlike physicists, don't have a Mother Nature to lay waste to their theories with "inconvenient" experimental results. Mathematicians, unlike theorists in physics, rely ENTIRELY on reputation and consensus. This consensus-only system, unique to Mathematics, works well MOST of the time ...until it fails. And then there is no mechanism to correct it.

Unless, of course, we are visited by advanced aliens from space with crania so gigantic that even the most insufferable professor emeritus will stand down his ego.

[Anonymous No.14964374]

>>14964324
Are you quite certain that you don't know how to reason about sets in ZF+!C?
I mean, aside from the obvious lack of a way to build certain sets (boo hoo my favorite gadget broke) you should be happy that Santa arrived early and brought a young alien into our midst, a
>NONEMPTY SET WITH NO CHOICE FUNCTION
unimaginably vast by the standards of ZFC
rarer than the rarest pepe
obviously the only thing to do is to find explicit examples of sets in ZF+!C that illustrate the equivalence of AC, well-ordering theorem, trichotomy, and a grab bag of other equivalents, in essence using constructions of "poorly behaved" sets in ZF+!C order to establish equivalents of AC rather than working in ZFC

[Anonymous No.14964396]

>>14964279
your gif was a puzzle in the game Shivers and it was fuckin' hard as a ten year old

[Anonymous No.14964479]

https://www.youtube.com/watch?v=YxZL-rIYG8k
great advice from a great math communicator

[Anonymous No.14964579]

Can an algebraist help? Is this the latest classification of rings of order [math]p^3[/math]?
>https://zbmath.org/?q=an%3A0507.16016
>Antipkin & Elizarov, Rings of order p^3, Sib. Math. J. 23, 457-464 (1983).
I've searched on Zentralblatt and Google and can't find a more recent paper discussing the classification of finite rings of order [math]p^3[/math].

[Anonymous No.14964612]

What's your opinion on calculators?

[Anonymous No.14964629]

>>14963883
Cute means they don't consider you manly

[Anonymous No.14964631]

>>14964612
They're mental training wheels for babbies who can't calculate like men

[Anonymous No.14964636]

Do I need to be quick to be considered good?

[Anonymous No.14964638]

>>14964636
Try asking that on your next date.
Serious answer: No, I don't think so.

[Anonymous No.14964641]

Now that z-lib is dead, where do I get my books from?

[Anonymous No.14964642]

>>14964638
I need a lot of catching up to do.

[Anonymous No.14964716]

>subtracting a negative from a negative.
>accidentally add it to the negative instead.
>get the problem wrong and it's khan academy so to get a perfect score I have to redo the whole quiz.
I hurt myself really bad after that. I punched myself in the forehead really hard a lot until it hurt too much to keep going. I fucking hate myself.

[Anonymous No.14964719]

>>14964641
Buy them or go to the library.

[Anonymous No.14964736]

I confused it

[Anonymous No.14964756]

-112/4 - 9/4

somehow my dumb fucking brain comes up with -221/4. What the fuck is wrong with me? I do this kind of shit all the time. Is there a term for math dyslexia? It's like, I understand what I'm doing, but I keep making these weird mistakes. Maybe I should go to bed.

[Anonymous No.14964801]

>>14964279
It shows you the primes of Z, Z[x], and (Z/pZ)[x] (and some of their elements).

For example, you see that sqrt(-1) on the right? There's a curve coming out of it, going left, touching the leftmost vertical line, then coming back. This entire curve represents the polynomial x^2 + 1, which has sqrt(-1) (and -sqrt(-1)) as a solution, and is a prime in Z[x].

The places where this curve crosses means they already have sqrt(-1). For example, in the vertical line for (5), you see two crossings, marked with black dots, labelled 2 and 3. If you plug 2 and 3 into the polynomial x^2 + 1 mod 5, you get 2^2+1 = 4+1 = 5 = 0 mod 5, and 3^2+1 = 10 = 0 mod 5. So there are already solutions to x^2+1 in Z/5Z (i.e. Z/5Z already has sqrt(-1) and -sqrt(-1)). Here, the polynomial x^2+1 "splits" into (x-2)(x-3), and is no longer a prime of (Z/5Z)[x] (it factored).

But then at the vertical line for (3), there are no solutions, and that's what the dotted circle means. (try plugging 0,1,2 into x^2+1 and reduce mod 3, and you'll get 1 or 2. but not 0) In these places, there is no sqrt(-1), so x^2+1 remains a prime in (Z/3Z)[x] (it doesn't factor), and we say it's "inert".

For the vertical line at (2), there is a solution to x^2+1, which is just 1: 1^2+1 = 2 = 0 mod 2. But instead of having two solutions, there is only one repeated solution. So x^2 + 1 factors into (x-1)^2. Instead of saying it "splits", we say it's "ramified", because there's a repeated solution.

The curve for 1/5 crosses every line: 1/5 is 1 mod 2, 2 mod 3, 3 mod 7, but if you look at the line for (5), it crosses at infinity, and that's because 5 = 0 mod 5, hence 1/5 would be 1/0.

[Anonymous No.14964803]

>>14964756
>I keep making these weird mistakes
We all do. It never stops. Don't pay it much thought.

>>14964641
Libgen still works.

[Anonymous No.14964805]

>>14964756
Arithmetic visualization trick for all a-b, -a+b and -a-b. Use the a or -a as the starting point on the number line, the middle symbol as the instruction on whether to move left or right and b as how much to move by.
Don't worry, you'll get it eventually.

[Anonymous No.14964916]

I want to write a list of equalities in LaTeX, and each equality with its own justification next to it, and have the equalities be aligned and justifications aligned.
How do I do that?

Something like pic related.

[Anonymous No.14964936]

>>14964916
Do you want the justifications flushed to the right? Then you can use \tag*{}.
Otherwise, if you want them aligned left but not flushed to the right, you can use even & in align equation. In align equations, the odd & aligns symbols, while even & separates the equation into a different column. So you can use a second & before the justification to separate them into another column. Using a third & right after the second, would align them to the left.
If you want them aligned to the left as well as flushed to the right, you can use flalign equations, which are equations with three columns, the first (third) is flushed to the left (right), and the second in the centre. Put your equation after the second &, and justification after the fifth &.

[Anonymous No.14964940]

>>14964374
"!C" would also be a strong axiom with many consequences.
Better to just use ZF than ZF+C or ZF+!C
(I assume you mean the negation of choice by !C and not unique choice. But if you use "!" for negation you make yourself a laughing stock among mathematicians, so I'd avoid that. It's shit notation anyway)

[Anonymous No.14964982]

Can you figure out this sequence:
1, 2, 11, 3, 101, 21, 1001, ...

It's not in OEIS

[Anonymous No.14964984]

>>14960957
this proves without the shadow of a doubt that all mathematicians are incels

[Anonymous No.14965011]

>>14964982
Number of bitches I fucked by year

[Anonymous No.14965013]

>>14964984
How am I an INcel when I voluntarily pay for sex?

[Anonymous No.14965014]

>>14964396
>Shivers
It looks beautiful. Was it fun?
The puzzle of that >>14964279 GIF is a board game called "Peg solitaire"[1]. Did you know that?
>>14964801
>Z, Z[x], and (Z/pZ)[x]
What are those, anon?
Thank you so very much for you explanation. It's beautiful. I'll read your post again.

[1] https://en.wikipedia.org/wiki/Peg_solitaire

[Anonymous No.14965020]

>>14964982
looking at every second term i can see a pattern
1, 11, 101, 1001,... (https://oeis.org/A000533))
Other than that the sequence looks random, you need to give more terms.
Is this a sequence you discovered in a problem or one you cam up with just to test us?

[Anonymous No.14965022]

>>14965011
What happened in the 4th year?

[Anonymous No.14965023]

http://math.fau.edu/Richman/docs/venice.pdf

[Anonymous No.14965027]

>>14965014
>What are those, anon?
Z is just the set of integers {..., -2, -1, 0, 1, 2, ...}

Z[x] is the set of polynomials in x with coefficients in Z, like x^2 + 1 and 16x^3+7x-10.

Z/pZ is harder to explain. Think of it as the set of numbers 0, 1, 2, ..., (p-1) (so there are p of them), and then you can add/multiply/subtract them as usual, but after you do any of these operations, you add/subtract multiples of p until you end up with a number from 0 to p-1. The typical example is with a 12-hour clock: What time would it be if I add 7 hours to 9 o'clock? Should be 7+9 = 16, but 16 is the same as 4 o'clock, because we can add/subtract multiples of 12.
If p is prime, you can even "divide" (not gonna get into that).

Then finally (Z/pZ)[x] is just polynomials in x with coefficients in Z/pZ.

[Anonymous No.14965029]

>>14965020
Next terms are 4, 12, 201, 10001,
It's concatenated prime signatures, in order of the least integer in each signature. Weird that some autist hasn't already put it on OEIS.

[Anonymous No.14965032]

>>14965023
negation of countable choice is just dumb

[Anonymous No.14965044]

>>14965029
>concatenated prime signatures
Huh?

[Anonymous No.14965079]

>>14965032
Not accepting countable choice does not mean t negate it.

Anyway, the paper is exactly an argument for why not to accept it. Instead of "is just dumb" I think it's better to refute the arguments in it.

[Anonymous No.14965080]

>>14965044
Prime signatures: [math]p, \; p^2, \; pq, ...[/math]
[math]2^{1}, \; 2^{2}, \; 2^{1}3^{1}, \; 2^{3}, \; 2^{1}3^{0}5^{1}, \; 2^{2}3^{1}, \; ...[/math]
Only autists do number theory, so if you see a sequence, expect autism.

[Anonymous No.14965097]

>>14964324
Can you explain what determines whether an axiom should be accepted or should not be accepted? Your feelings?

[Anonymous No.14965226]

>>14964324
>yeah dude a product of nonempty sets CAN be empty

[Anonymous No.14965280]

>>14964940
>But if you use "!" for negation you make yourself a laughing stock among mathematicians

[Anonymous No.14965285]

>>14964940
>a laughingstock among mathematicians
ftfy

[Anonymous No.14965309]

>>14965226
if you're using ZF to prove that existence of a set without a choice function implies existence of a set that can't be well-ordered
outside a proof of an equivalent of AC, you get a severe thwacking from your average Hilbert-Cantor goon when you carry on that way
>brutal darkness engulfs the dusk sky and thunder claps can be heard in the distance while a light drizzle begins to fall...
>you see a young man in tattered clothes scrawling arcane runes in the gutter...
>strangely, the agate he is using as writing implement causes the surface to glow ethereally and opalescently
>as you look at his marks, you begin to feel comfortable and warm...
>sometimes when you read a bible or gnostic text you would feel the same way...

[Anonymous No.14965440]

>>14965285
what did you fix?

[Anonymous No.14965505]

oh my gauss what did I just ploot

[Anonymous No.14965507]

In this definition of a regular sequence, do I understand that a regular sequence can, for any two index value n1 and n2, at most differ by 2?

[Anonymous No.14965567]

>>14965226
>yeah dude a product of nonempty sets CAN be empty
A finite product is an iterated binary product and a binary product has simple models, e.g. (x,y)={{x},{x,y}}. Under the assumption that a finite amount of set x,y,...u,v,w is non-empty, the claim that their finite product is non-empty is another finite chain of existence claims.

But an infinite product is a generalize function space, the elements of which are not finite supples but maps from an infinite domain into the sets the products are taken of. The claim that all factors are non-empty is a universally quantified claim, ranging over an infinite domain. You can't prove it without further axioms because you can't unpack infinitely many logical statements and recompose them into a new statement.

An infinite product assumes you already have an infinite index set, but it's not "obvious" that a space of other infinite objects (the mappings) are there.
Especially if you go at it from a constructive angle. But you don't need to go that far to see the issue of finite description and that it needs some justification.

You can have ZF+dependent choice and adopt the similarly nice but similarly elusive claim
>all sets of real numbers are Lebesgue measurable
and this rejected Choice, for example

https://en.wikipedia.org/wiki/Solovay_model

[Anonymous No.14965568]

>>14965505
Probably a sum of cosines with increasing frequencies, some shit like cos(x) + cos(5x) + cos(25x).

[Anonymous No.14965575]

>>14965507
Yeah, sure, but that's not the point.
The point is that is you go farther and farther into the sequence, the terms get closer and closer.

[Anonymous No.14965751]

>>14965568
Yes, it's the continuous, yet nowhere differentiable Weierstrass function
>https://en.wikipedia.org/wiki/Weierstrass_function

[Anonymous No.14965753]

I have a question: Is there an algorithm to determine the minimum polynomial of a given algebraic number?

[Anonymous No.14965763]

>>14964940
>But if you use "!" for negation you make yourself a laughing stock among mathematicians
It's fine on the internet but you're 100% retarded if you do it in handwriting.

[Anonymous No.14965771]

>>14965763
I'd just use [math]\neg[/math], instead

[Anonymous No.14965805]

>>14965753
You'll get more out of it if you pin down more in which way you're given the number. If you're given an algorithm to compute the stream of digits, then you won't be able to decide whether it's the solution of any equation, since deciding whether a real equals zero requires [math]\Sigma_1[/math]-LEM

https://en.wikipedia.org/wiki/Limited_principle_of_omniscience

Assuming you can decide, for any polynomial, whether your number is a solution of it or not, then the set of equations that fulfill it is at least a semi-decidable set.

This is because I can give you an explicit enumeration of all finite sets of natural numbers, i.e. it's a few lines of code to get a surjection [math]\omega\twoheadrightarrow \omega^\omega[/math], and you can map any set of integers to one of the polynomials.

So if you further are willing to limit the size of the coefficients, then its's certainly possible.

[Anonymous No.14965809]

>>14960838
where can i find the solutions to wendell fleming's book on multivariable calculus??

[Anonymous No.14965811]

positively decide whether it's the zero of any polynomial equation*

[Anonymous No.14965856]

>>14965805
Can all algebraic numbers be written as

[math]x^{\frac{a}{b}} + (yi)^{\frac{c}{d}}[/math]

with [math]x, y, a, c \in Z[/math] and [math]b, d \in \mathbb{N}[/math]? If so, I'd pass them to the algorithm in this form. I won't use decimal fractions.

[Anonymous No.14965863]

mathbros can you help >>14965724 ?

[Anonymous No.14965873]

>>14965856
No.
The expression you wrote is made up of "radicals", and by the insolvability of the quintic, there are algebraic numbers that AREN'T made of radicals.

[Anonymous No.14965879]

>>14965856
Is the i inside the bracket on purpose?
Does your conjecture here imply that every real algebraic number is the b'th root of some natural number?

[Anonymous No.14965885]

>>14965873
Oh, you're right.

>>14965879
I wanted to include all of the roots of the imaginary unit i. It's wrong, anyway. I think, I would have had to use a separate pair e, f as exponentials for y, too.

[Anonymous No.14965937]

Question to non-Americans:
My advisor said that (1) the purpose of an MS in Math is to learn how to write Math, and (2) the contents of the thesis don't actually matter when applying to a PhD program.

How much do you (dis)agree with these statements?

[Anonymous No.14966015]

I have dyscalculia and don't have much education since I grew up in a bad city. How do I become smart like you?

[Anonymous No.14966123]

>>14966015
don't be yourself

[Anonymous No.14966189]

if i do enough truth tables will implications and equivalences etc eventually just make sense or am i fucked

[Anonymous No.14966197]

>>14966189
>if i do enough truth tables will implications and equivalences etc eventually just make sense
yes
>or am i fucked
if you're lazy, then yes

[Anonymous No.14966200]

>>14965873
Is there anything more powerful than radicals but less powerful than infinite series that can extract the decimal expansion of such algebraics?

[Anonymous No.14966225]

>>14966200
You can have an algebraic number being implicitly given by a polynomial equation, say
[math]\tau x.\, x^3 + x = 7[/math]
and you have continued fractions, although those are also infinite series in numbers.

You also have explicit numbers like the golden ratio [math]\frac{1}{2}+\frac{1}{2}\sqrt{5}[/math].

[Anonymous No.14966236]

>>14963602
you should just aim to do a dense subset of the exercises at a time

[Anonymous No.14966277]

>>14966225
Sure, but what about, for example, the real root of x^5 = x+2? Is there anything between the polynomial definition and an infinite series that can represent it?

[Anonymous No.14966287]

Can define two distinct, but subsequent Dedekind cuts such that one describes 1 and the other the number 0,999..? How can can you reconcile these distinct cuts to describe the same value (namely, 1)?

[Anonymous No.14966385]

>>14966287
>subsequent dedekind cuts
how

[Anonymous No.14966453]

>>14966385
using supremum or infimum of the two cut sets

[Anonymous No.14966461]

how can you non-numerically solve

[math]x + ln(x) = 0[/math].

[Anonymous No.14966468]

>>14966461
You don't. It's easy to see that it has no algebraic solution.

[Anonymous No.14966490]

>>14966461
x^x * ln(x) + x^x = 0

This equation has a non-algebraic solution, but can be non-numerically solved..

[Anonymous No.14966494]

>>14966468
this >>14966490 was meant for you

[Anonymous No.14966504]

>>14966490
Go write the solution down then.

[Anonymous No.14966509]

>>14966504
x^x * ln(x) + x^x = 0 <=>
x = 1/e

[Anonymous No.14966511]

>>14966509
Continue
I want to see how you non-numerically calculate 1/e.

[Anonymous No.14966526]

>>14966511
I see what you mean. But it's not satisfying. The solution involving e is more expressive than a solution calculated numerically and represented with a approximated decimal. My question is, whether or not such an expressive solution exists for the equation in >>14966461

[Anonymous No.14966529]

>>14966526
The solution is [math]f[/math] where [math]f[/math] is defined as the solution of
[eqn]x + \ln(x) = 0[/eqn]

[Anonymous No.14966752]

Bumping question: >>14965937

[Anonymous No.14966821]

>>14966453
Supremum/infimum only works if you’re already in the reals. Give me an explicit definition of two distinct dedekind cuts, one being 0.999…, and the other being 1

[Anonymous No.14966908]

Guys, how good is the book "Calculus Early Transcendentals" by Howard Anton? I was trying to follow the Calculus book by Ron Larson to learn calculus but my lecturer is following the Howard Anton book. I also tried to check out Calculus Made Easy and Calculus The Easy Way books because I'm quite the brainlet while it comes to calculus. But, unfortunately I can't keep up with so many books. I need help on which one to follow.

[Anonymous No.14967017]

Why does the binomial coefficient create combinations but the multinomial coefficient create permutations?

[Anonymous No.14967037]

>>14967017
That's their definition.

[Anonymous No.14967330]

why do mathematicians hate talking about philosophy?

[Anonymous No.14967334]

>>14967330
same reason they hate programming.
They're brainlets.

[Anonymous No.14967340]

>>14967330
I don't like it, because it never yields any results. It's all speculation to me.

>>14967334
I like programming, but I dislike the "culture" surrounding it.

[Anonymous No.14967347]

>>14967340
>I don't like it, because it never yields any results.
That depends on what you mean by "philosophy".

Do you think that the "rules" of math and logic are essentially facts of the physical reality? They have to be since you use your brain to think, and your brain is a physical object right?

Are there any questions of math that you would think of as "just philosophy"?

[Anonymous No.14967355]

>>14967347
>That depends on what you mean by "philosophy".
True. For me, philosophical questions are such questions of which you can't know if they can be answered or not. For example: "What happens after you die?".

[Anonymous No.14967367]

>>14967330
Because /lit/ards come here making philosophy threads in the veil of maths.

[Anonymous No.14967368]

>>14967347
>Do you think that the "rules" of math and logic are essentially facts of the physical reality?
No, I'm not a Platonist.
>Are there any questions of math that you would think of as "just philosophy"?
No, I believe there's a principle of evolution in Math. Those concepts are being researched that yield (material) results.

[Anonymous No.14967398]

[math]
e + e/1 * (x - 1)^{1} + e/2 * (x - 1)^{2} + e/6 * (x - 1)^{3} + e/24 * (x - 1)^{4}
[/math]

[Anonymous No.14967438]

How long does /mg/ take to solve exercises?

[Anonymous No.14967527]

>>14961390
dude i fucking love odd taxi

[Anonymous No.14967539]

what is the "start with the greeks" of mathematics?
euclid, archimedes, apollonious and nichomachus?
anything else?
Also what classic, foundational works of mathematics would you put in a timeline from scratch up until newton?

[Anonymous No.14967663]

>>14961390
engineers and IT people are STEM kings, this "computational" thing is an underhanded insult by pure-math virgins

[Anonymous No.14967668]

>>14967539
>analysis
>linear algebra
Next question

[Anonymous No.14967684]

>>14967539
If you want to start with the Greeks for mathematics, you don't want to learn mathematics, you want to learn history. Not the same thing, so fuck out of here and go to >>>/his/

>>14967668
Retard.

[Anonymous No.14967691]

>>14967539
Euclid's Elements is very nice but everything else is basically a meme.

[Anonymous No.14967732]

How long will it take to learn quantum mechanics starting from algebra 1?

[Anonymous No.14967734]

I have a topics in topology exam in 2 hours.
I spent all weekend with my textbook and notes open, but watching trombone champ videos while drinking energy drinks instead.

I am going to lose my fucking mind, and drop below 3.0 GPA because of this.

Its so fucking pathetic. Just imagine a near 30 year old man watching this shit at 2am while chugging down sugary drinks
https://www.youtube.com/watch?v=W-59sWasI98

[Anonymous No.14967747]

>>14967734
Your problem isn't not studying in the weekend.
Your problem is not paying attention in class.

[Anonymous No.14967762]

>>14967747
I am socially anxious and just go to lectures for the sake of going. I talk to my advisor almost exclusively via email.

[Anonymous No.14967768]

>>14967747
>Your problem is not paying attention in class.
Kek. These are the people who post in /mg/.

[Anonymous No.14967769]

>>14967734
Your post perfectly encapsulates how I already pictured every autist that majors in math.

[Anonymous No.14967794]

>>14967732
About 3 years

[Anonymous No.14967800]

https://youtu.be/v5LF6pFpmZA
https://taipeiteentribune.com/math-is-useless/
https://medium.com/scribe/when-numbers-dont-make-sense-79e4f66f0fd3

Reasons not to do math
1. Teachers teach math just to release their pressure on students
2. Useless in daily life
3. Too complicated to understand
4. No real need to learn this stuff

[Anonymous No.14967816]

>>14967762
Sit in the back, don't interact, pay attention.

[Anonymous No.14967820]

>>14967539
Egyptians

[Anonymous No.14967853]

>he just ploots functions
>doesnt even try to solve differential equations
>just drinks and ploots
>but yet cant find another plooter in the whole place
>who can ploot functions
>like he ploots

[Anonymous No.14967858]

>>14967734
be yourself and remember to stay hydrated. This will improve your performance by a tenfold

[Anonymous No.14967886]

>>14967734
that game looks fun. I've done the kind of stuff you just did and it doesn't fucking matter, so just stop caring, you had fun.

although now I don't care about stuff like that that much and the studying is my "fun", so I don't know

[Mega Man No.14967900]

>>14966908
Howard Anton's book doesn't follow the standard function limit derivative integral format and has a picture based font that will make your Analysis soft it's Okay if you get it for cheap though

[Mega Man No.14967906]

>>14960838
Eat poison

[Anonymous No.14967910]

So after I prove these once I can just rote memorize them like a poem, right? So that they pop up instantly in my head whenever there's a chance I might need to use them, right?

[Anonymous No.14967929]

>>14967910
>o-o
>---

[Anonymous No.14967931]

>>14967910
>rote memorize
You're shooting yourself in the foot.
You need to UNDERSTAND what these mean. For example, sin^2 + cos^2 = 1 is just Pythagoras' theorem.
Visualize a circle and see why all of these are true, they're not hard.
Once you understand, you don't NEED to memorize "like a poem", because you would've internalized them.

[Anonymous No.14967939]

>>14967910
Better just remember
[eqn]e^{ix} = \cos(x) + i \sin(x)[/eqn]
You can derive all 5 formulas from this.

[Anonymous No.14968013]

>>14967931
yeah, you're right, these are the obvious ones, but for the two additions [math]\sin(A+B) = \sin A \cos B + \cos A \sin B[/math]
[math]\cos(A+B) = \cos A \cos B - \sin A \sin B[/math] I only see the algebraic manipulation and not some geometric intuition like the others. am I missing something?

>>14967939
I've heard about this before but I think I gotta brush up on my complex numbers first.

>>14967929
I don't get it

[Anonymous No.14968033]

>>14968013
They become obvious if you know about matrices. A rotation by the angle A+B is the same as a rotation by the angle B followed by a rotation by the angle A.

[eqn]
\begin{pmatrix} \cos(A+B) & - \sin(A+B) \\ \sin(A+B) & \cos(A+B) \end{pmatrix} = \begin{pmatrix} \cos(A) & - \sin(A) \\ \sin(A) & \cos(A) \end{pmatrix} \begin{pmatrix} \cos(B) & - \sin(B) \\ \sin(B) & \cos(B) \end{pmatrix} = \begin{pmatrix} \cos(A) \cos(B) - \sin(A) \sin(B) & -\cos(A) \sin(B) - \sin(A) \cos(B) \\ \sin(A) \cos(B) + \cos(A) \sin(B) & - \sin(A) \sin(B) + \cos(A) \cos(B) \end{pmatrix}
[/eqn]

[Anonymous No.14968034]

>>14968013
[math]e^{ix} = \cos(x) + i\sin(x)\\
\cos(A+B) + i\sin(A+B) = e^{i(A+B)} = e^{i(A)}*e^{iB} = (\cos(A) + i\sin(A))(\cos(B) + i\sin(B)) = (\cos(A)\cos(B)-\sin(A)\sin(B)) + i(\sin(A)\cos(B)+\sin(B)\cos(A))[/math]

Look at both ends of the equation, compare real parts and imaginary parts.

For the intuition, you can think of linear transformations: If you take the vector (1,0) and rotate it counter-clockwise by an angle of A, where does it end up? Where does (0,1) end up? Actually sit down and draw this and write down the matrix for this linear transformation.
The matrix for B is similar. Now, if you want to rotate by an angle of A+B, just multiply the two matrices. Where does (1,0) end up? Where does (0,1) end up? Now you have the formula for the angle sum.

[Anonymous No.14968035]

>>14968034
>>14968013
Trying again:
[math]e^{ix} = \cos(x) + i\sin(x)[/math]
[math]\cos(A+B) + i\sin(A+B) = e^{i(A+B)} = e^{i(A)}*e^{iB} = (\cos(A) + i\sin(A))(\cos(B) + i\sin(B)) = (\cos(A)\cos(B)-\sin(A)\sin(B)) + i(\sin(A)\cos(B)+\sin(B)\cos(A))[/math]

[Anonymous No.14968036]

>>14968035
>>14968013
This site is a whore:
[math]\cos(A+B) + i\sin(A+B) = e^{i(A+B)} = e^{i(A)}*e^{iB} = (\cos(A) + i\sin(A))(\cos(B) + i\sin(B)) = (\cos(A)\cos(B)-\sin(A)\sin(B)) + i(\sin(A)\cos(B)+\sin(B)\cos(A))[/math]

[Anonymous No.14968052]

>>14968013
Fuck it

[Anonymous No.14968179]

https://arxiv.org/abs/2211.02515
surprised this hasn't been mentioned yet
if verified would be huge result

[Anonymous No.14968193]

>>14968179
Imagine trusting a paper on a non peer-reviewed platform by an author named "Zhang".

[Anonymous No.14968208]

>>14968179
Oh shit, THE Zhang? Yitang himself?

[Anonymous No.14968261]

>>14968179
>https://arxiv.org/abs/2211.02515
virus

[Anonymous No.14968266]

sure you could matrix rotation sines and cosines. but if you were to just ploot them you would get a much more intuitive understanding of their phase relationships.
>he never even learned how to ploot

[Anonymous No.14968271]

>>14968266
>he never learned how to properly spell "plot"

[Anonymous No.14968274]

>>14968271
thats because im a plooter. plotting or graphing is what normies do

[Anonymous No.14968276]

>>14968271
he has no time for spelling lad, he has to PLOOT

[Anonymous No.14968289]

>>14968266
>signature on the ploot
plooters can't stop winning

[Anonymous No.14968293]

I hate teenagers.

[Anonymous No.14968294]

>>14967734
so how was the test, anon?

[Anonymous No.14968298]

>>14968294
It's only been 2.5 hours since the exam started. Could be 3 or 4 hours.

[Anonymous No.14968320]

Does anybody who matters even like number theory without the applications?

[Anonymous No.14968338]

>>14968298
I integrated this post in a program. What you said will forever be kept in a logfile somewhere on my computer's harddrive.

[Anonymous No.14968450]

https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics#Probability_theory
Someone finally added probability theory problem to the list

[Anonymous No.14968509]

Anyone have any examples/explanation on how to do picrel?

Professor has forgotten to post resources relevant to topic and lecture on this topic was about a month ago.

I took notes, but the in-class example was way easier and nothing like picrel.

[Anonymous No.14968531]

Is
[math]\{x\ |\ 1 \leq x \leq 1\} = \{1\}[/math]
an intervall?

[Anonymous No.14968536]

>>14968509
[eqn]
A \begin{pmatrix} 6 & 3 & 3 \\ 0 & -3 & 3 \\ -3 & 3 & 0 \end{pmatrix} = \begin{pmatrix} 4 & 1 & -1 \\ -2 & -5 & -1 \\ -5 & 1 & -4 \end{pmatrix} \\
A = \begin{pmatrix} 4 & 1 & -1 \\ -2 & -5 & -1 \\ -5 & 1 & -4 \end{pmatrix} \begin{pmatrix} 6 & 3 & 3 \\ 0 & -3 & 3 \\ -3 & 3 & 0 \end{pmatrix}^{-1}

[/eqn]

[Anonymous No.14968545]

>>14968536

Is it really that easy?
Anyhow, thanks anon!

[Anonymous No.14968682]

>>14968531
Yes, it is the interval [1,1]

[Anonymous No.14968687]

>>14968545
Can be done even more easily.
Each of these 3 equations is of the form Ax=b
To find the first column of A, you need add/subtract these equations to get x to be the column vector (1,0,0)

For example, add all 3 equations, and you get x to be (12,0,0), and you can divide by 12 to get (1,0,0).
The example here is slightly easy.

[Anonymous No.14968689]

>>14961649
>this is a dodecahedron, right?
Dodecagon. It's a planar figure. "Hedron" refers to faces, not edges.

[Anonymous No.14968693]

>>14964279
That's not how I solved it, but interesting nonetheless.

[Anonymous No.14968979]

reminder to use lyx instead of texmaker

[Anonymous No.14969019]

>>14960838
how do I get.gud at commutative algebra? I'm taking a graduate level class in it right now with a year of college math experience under my belt. I love the material but I get stuck on any problems other than the first few in each chapter of Atiyah McDonald. Other resources (Matsumura) seem even more terse and inaccessible

For real though what the fuck is going on with Ass

[Anonymous No.14969101]

>>14967910
Unit circle.

[Anonymous No.14969135]

>>14968294
I took the entire 3 hours for maybe 8 questions total. I crashed, cried, had constant trombone champ intrusive thoughts. Pretty sure I got an A, or at least a B- on in though.
Got back home and actually played some trombone champ for a bit while drinking. Gonna go to bed now, early night as its only midnight.

[Anonymous No.14969200]

>>14968509
I fucking hate CSfags so much.

[Anonymous No.14969227]

>>14968034
[math] \cos(A+B) + i\sin(A+B) = e^{i(A+B)} = e^{i(A)}*e^{iB} = (\cos(A) + i\sin(A))(\cos(B) + i\sin(B)) = (\cos(A)\cos(B)-\sin(A)\sin(B)) + i(\sin(A)\cos(B)+\sin(B)\cos(A)) [/math]

[Anonymous No.14969499]

>>14968193
>non peer-reviewed

[Anonymous No.14969529]

[math]\frac {44}{14}[/math]

[Anonymous No.14969631]

>>14969227
Why didn't it work when I tried it?

[Anonymous No.14969762]

>>14969019
> I get stuck on any problems other than the first few in each chapter of Atiyah McDonald
It's normal if you're only getting started, just keep going, solve what you can solve and after awhile the harder problems will be as easy for you.

[Anonymous No.14969764]

Will all the homotopy groups of spheres ever be solved?

[Anonymous No.14969811]

Can you really generate all one variable rational polynomials with only the symbols [math] x, \; - \; ÷ \; ( \; ) [/math] ?

[Anonymous No.14969850]

>>14969811
can you name a "rational polynomial" tak you can't?

[Anonymous No.14969868]

>>14960838
is this from a paper or a textbook.

[Anonymous No.14969967]

>>14969811
If you're willing to write x/x for the polynomial 1, then sure.
Multiplication is just juxtaposition, so that makes things easier. You also have 1 by the above.
You can write -1-1-1 ... -1 to get -n. Then use parentheses and -1 to multiply -n by -1 and get n.
Now you can get all rational numbers as n/m.
Juxtapose copies of x to get x^k, juxtapose by a rational, and sum of them up (i.e. subtract the negative, if you'd like).

>>14969850
It's not immediately obvious.

[Anonymous No.14969969]

>>14969868
I think it's from a book.
Here are all the similar drawings:
https://pbelmans.ncag.info/blog/atlas/

[Anonymous No.14970071]

Helios help help help help help Help it’s calculus

[Anonymous No.14970079]

i take a calculus 1 class fully online, and i’m wondering if anyone would be interested in becoming mutuals on discord or telegram to whatever, so that when i’m taking an exam and let’s say i don’t know 5 of the questions on it, could i come to one of you for help and pay you for your help? discord is: abrasion#2306
telegram: soulwhirlingsomewhere

[Anonymous No.14970080]

>>14970071
anon..... its right there.
Its literally labeled u(x) and u'(x). Did you read the book? you will substitute u(x) with a new variable, and its derivative, u'(x), will cancel out.
So using the last one as an example...


[eqn] \int u'(x)/u(x) dx [/eqn]

[eqn]v = u(x) => dv= u'(x) [/eqn]

[eqn]\int (1/v) dv [/eqn]

read the chapters again.

[Anonymous No.14970086]

>>14970079
No. Just so you know, if you start using crutches or cheating in Calculus 1, you will get destroyed in follow on courses where you are expected to have mastery over the material. If your degree requires Calculus and you aren't interested in Calculus, you are wasting your time on that degree program.

[Anonymous No.14970089]

>>14970071
Do you know the antiderivatives of these?
x^n
e^x
1/x

That's literally the answer.

[Anonymous No.14970099]

>>14970086
im sure it has some relevancy in my degree plan. thankfully its the only math course im required to take so i am just trying to make it out passing. im a cyber sec major
>>14970080
thank you

[Anonymous No.14970104]

>>14970079
>>14970086
This sort of niggerfaggotry is why entrance exams should be a thing.

[Anonymous No.14970112]

>>14970104
niggerfaggotry...

[Anonymous No.14970132]

>>14970104
Maybe entrance exams work in small European countries, but it just would not work in the USA, for some very sad reasons.
In the USA, k-12 is standardized at the state level, and no matter how smart you are, you will be dragged down to the level of education and curriculum of your state, unless your parents put you in some private school or go out of their way to drive you to a community college for additional courses while you're still in high school. There is a huge disparity between high school graduates in the USA, across states and even across counties.

In contrast to k-12, American universities are incredibly standardized in their undergraduate curriculum, and those standards also hold at an international level, so an average university math program anywhere in the USA, will provide the same level of education as an average university math program in UK, Germany, Japan, etc. Now the problem is that most American high school students are just not ready for the average university program (they're regionally accredited, so there really isn't a "bad" program, per se), so if there were entrance exams, the acceptance to university would be abysmally low through no fault of the students themselves. Thankfully, most universities offer remedial math courses like college algebra, trigonometry, or precalculus, which go over what students should have learned in highschool, but cover it at the rigor you would see in European high schools.

tl;dr,
I don't agree with uni entrance exams, USA unis are okay, USA high schools are fucking terrible.

[Anonymous No.14970148]

any other solution?

[Anonymous No.14970163]

>>14970079
just fail the exam and take it again
think about it
you trade one semester of progress for a lifetime of honest progress in mathematics
if you admit you fucked up now, you will HAVE to develop decent study habits in order to progress
if you don't, you can get by with SHITTY study habits for as long as you want by cheating, and then someone has to take you out in ten years so you don't cause any problems for society

[Anonymous No.14970164]

>>14970148
Dude...
You fucked up
https://www.wolframalpha.com/input?i=y%27+%3D+%28pi%2F2%29*y*%28x-1%29

[Anonymous No.14970166]

>>14970079
This stupid idiots don't realize how easy it is to solve math problem as long as you identify as a nerd who works hard
These assholes want to pass math exams and look like gangsters
Assholes like you should be tagged and culled
We should proactively find out which students want to look like gangsters and cheat at math exams and share their personally identifying information on 4chan

[Anonymous No.14970168]

>>14970079
Students that express a willingness to cheat at math exams should be identified and bullied until they change their habits or leave school

[Anonymous No.14970178]

>>14970132
>if there were entrance exams, the acceptance to university would be abysmally low
And that is a bad thing, why?
>through no fault of the students themselves.
Incorrect.

[Anonymous No.14970187]

>>14970166
im not trying to look like a...gangster anon.
im fully aware that cheating thru math will not benefit me. i'm a good student in all of my other courses. but math is just that one that i have had trouble with for years. since elementary..i was only passed because the teachers "felt bad" for me.. passed in middle school for the same reason. went to a shitty christian highschool, took algebra 1 and did alright but after that they didn't require i take any more math. then as a refresher i took algebra 2 my first year of uni and i struggled but made it by with tutoring. however i have zero past knowledge of how the fuck to navigate calculus and i frustrate myself to no end (crying,stress ripping out hair,hitting head on wall) when i cant figure it out and ive come to accept i cant fucking do it and i just need to get done with this one class. yeah im probably retarded ok

[Anonymous No.14970189]

>>14970187
You sure do like talking about yourself.

[Anonymous No.14970190]

>>14970189
im on adderall rn and also trying to prove that not all students that cheat do it because they are lazy or want to seem baller

[Anonymous No.14970200]

>>14970178
>And that is a bad thing, why?
Artificially limits the advancement of fields, by excluding persons that have the mental capacity and drive to contribute, but were never given the opportunity.

>incorrect
But I'm not. Children cannot decide what school they go to or what content they are exposed to, and they are limited by the influences around them such as their parents and school teachers.

As an example, think of Nathaniel Bowditch, he only became one of the premiere mathematicians in the USA because the intellectuals at the time noticed his interest and natural intellect, and gave him books, tutored him and such. What you're saying is if it were up to you, then people would be denied the opportunity to prove themselves or advance a scientific field by virtue of the unfortunate circumstance of their birth? Well, that just seems politically misguided. Since this is 4chan, the nature of the problem should be changed to fit better so..

Imagine a planet where everyone is a White, Nordic Aryan and they are all good. There is an a child of laborers, lets say miners, that is possibly gifted in mathematics, but his education until now was limited as he lived in a very rural isolated area. Would you deny this young man the opportunity to prove himself?

Not saying that US universities are are a perfect system, but other countries having entrance exams and artificially limiting the student body only happens due to the "free" university system. You're just limited financially, and restrict the student population because of it.

[Anonymous No.14970201]

>>14970187
everyone can do math, you just let the stress of currently not understanding something, overwhelm you. And instead of going simpler, or tracing exactly why you don't understand something, you simply give up and make cheap excuses.
>>14970190
> they are lazy
you are lazy because you don't want to put in the work to get over hurdles and understand it.
Now quit crying and get back to work, or take it to >>>/adv/

[Anonymous No.14970205]

>>14970187
Didn't read your post. Math is just hard work and discipline until you reach active research fields. Stop making excuses and put in the time, that is all it takes.

[Anonymous No.14970228]

>>14970200
>Artificially limits the advancement of fields, by excluding persons that have the mental capacity and drive to contribute, but were never given the opportunity.
If someone doesn't have the ambition to self study basic mathematics for an entrance exam, they don't have anything to contribute to any field lmao. They belong in some shitty trade school.

>but his education until now was limited as he lived in a very rural isolated area.
We live in the age of internet and free public libraries, everyone has access to education. Anyone who doesn't know basic math chose to ignore it. It is entirely their fault.
Funny you mention Nathaniel Bowditch.
>In 1786, age fourteen, Bowditch began to study algebra and two years later he taught himself calculus. He also taught himself Latin in 1790 and French in 1792 so he was able to read mathematical works such as Isaac Newton's Philosophiae Naturalis Principia Mathematica. He found thousands of errors in John Hamilton Moore's The New Practical Navigator; at eighteen, he copied all the mathematical papers of the Philosophical Transactions of the Royal Society of London.
Thanks for helping my argument.

[Anonymous No.14970238]

>>14970190
>not all students that cheat do it because they are lazy
I was required to take Chem 101 as a CS student.

I didn't understand shit in class, and I didn't like that I got shit scores in the first quizzes.
So I studied every night at dinner time. 8 to 9 PM, EVERY night.
My scores improved in the quizzes, and I got one of the highest scores in the lab, too.
When the final came, there was a one/two hour gap between my chem final and math final. I don't remember which was first, but whichever it was, it started at 8 AM. At dawn I studied both and kept frantically alternating between the books.
I went into both exams and aced them, and even found a mistake in the chem exam.
I ended up getting an A+ in the course. And I never touched chem again in my degree.

Stop making excuses, and study like you ought to.

[Anonymous No.14970241]

>>14970228
>If someone doesn't have the ambition to self study basic mathematics for an entrance exam, they don't have anything to contribute to any field lmao. They belong in some shitty trade school.
A kid doesn't even know where to start.

>Thanks for helping my argument.
The things he taught himself were by guidance, mentoring, and resources given to him the few academics around him at the time. I'm sorry if I can't properly express just how deep the void of American k-12 education is.

[Anonymous No.14970259]

>>14961493
Then why hasn't it been delegated to AI yet?

[Anonymous No.14970267]

>>14970259
WolframAlpha.com

[Anonymous No.14970269]

how do I into math?

[Anonymous No.14970274]

>>14970259
It hasn't. He's someone that has never done any math outside of an academic setting.

[Anonymous No.14970414]

>>14970274
>if I say it that'll make it true
The coping mechanisms of a computing monkey

[Anonymous No.14970418]

>>14970414
The ego of a student.

[Anonymous No.14970441]

>>14970418

[Anonymous No.14970453]

>>14965027
Thank you so much, anon. You are amazing.
>>14964279
How did you solve it, anon?

[Anonymous No.14970475]

>>14965027
Thank you so much, anon. You are amazing.
>>14968693
How did you solve it, anon?

[Anonymous No.14970514]

>drank a bottle of gin and just fuckin plooted again last night.
please help this plooter find a woman who can break my bad habit

[Anonymous No.14970632]

>>14963602
Source?

[Anonymous No.14970796]

>>14965507
what book?

[Anonymous No.14970813]

>>14970132
>an average university math program anywhere in the USA, will provide the same level of education as an average university math program in UK, Germany, Japan, etc.

Those programs must really suck then because many bachelor's degrees in math are granted every year to people who can't do basic linear algebra, analysis, or topology.

[Anonymous No.14970985]

im new [math]\wedge[/math] retarded. how bad did i do? be honest

[eqn]\exists \eta \left ( \eta\in \mathbb{N} \right )\forall \mu \left (\left ( \mu\in\mathbb{N} \wedge \mu\neq \eta\right) \right )\left ( \eta> 1 \right )\wedge\left ( \eta/\mu\neq \mu \right )[/eqn]

[Anonymous No.14970986]

>>14970985
for c. and i messed up the brackets for [math]\mu[/math].

[Anonymous No.14970992]

[Anonymous No.14970998]

>>14970985
>>14970986
Why did you use eta instead of n?
Also what's that goofball definition of prime?
[math]\forall r \forall s (r \neq 1 \land s \neq 1) \implies rs \neq n[/math]

[Anonymous No.14971002]

>>14970998
>Why did you use eta instead of n?
first time using latex and that looked like n
>∀r∀s(r≠1∧s≠1)⟹rs≠n
thank you anonsama but it has to have an existence assertion for all is the next question

[Anonymous No.14971064]

>>14970985
>there exists an n in N such that for all u in N, u =/- n
good luck

[Anonymous No.14971102]

>>14970985
There is m and k, both greater than 1, such that mk = n.

[Anonymous No.14971640]

>>14970632
Only if you answer the question, first.

[Anonymous No.14971657]

>>14970632
Answer the question, first.

[Anonymous No.14971743]

>>14971657
You should be reading a real linear algebra text like Hoffman and Kunze 2/e.
They're called projecTIONS not projectors.
When was that shit written?

[Anonymous No.14971759]

>>14971743
>my book is better because it calls it something else
This is the brain of your average /sci/ user.

[Anonymous No.14971862]

How can visualize a morphism geometrically? For example, how’s you visualize

phi: a -> log(a)

between the groups (R, +) and (R, *)?

[Anonymous No.14971869]

>>14971862
https://www.desmos.com/calculator/n4l5iqi3kf

[Anonymous No.14971870]

>>14970992
Let C,D be sectors and e : C -> D,f : D -> C calcs. The *binary twister* started at (c,d) for c <- C,d <- D is the sequence
>(c,d,e,f)
>(f(d),e(c),e^c,f^d)
>(f^d(e(c)),e^c(f(d)),e^{c f(d)},f^{d e(c)})
>...
if the nth item in this sequence is X_n = (c_n,d_n,e_n,f_n), then the recursion is
>c_{n+1} = f_n(d_n)
>d_{n+1} = e_n(c_n)
>e_{n+1} = e_n^{c_n}
>f_{n+1} = f_n^{d_n}

[Anonymous No.14972068]

>>14960838

[Anonymous No.14972111]

>>14971862
>How can visualize a morphism geometrically?
No general way. But if you can visualize the order-preserving homeomorphism between R and an interval by means of tan / arctan, then you're pretty safe.

[Anonymous No.14972261]

For someone who doesn't know Calculus, assuming that they have a strong foundation on all the basics, what is the best textbook to go through to learn Real Analysis? I want to get into Big Boy Maths from a pure and more rigorous way and I remember a thread a while back where anons were talking about not having to do the whole Calculus thing and instead just learning Real Analysis.

[Anonymous No.14972282]

>>14972261
Amann Escher Analysis I-III

[Anonymous No.14972323]

Hi /mg/.

So, in functions (f(x); real or complex) containing algebraic equations, can I always see 'x' as the algebra of distances (plus phase if complex) from its corresponding root? Does this intuition break at any point in applied mathematics?

[Anonymous No.14972345]

>>14972261
>I remember a thread a while back where anons were talking about not having to do the whole Calculus thing and instead just learning Real Analysis.
yeah its a bit slower though, since you have to build up the intuition for these concepts by hammering your head against analysis text, rather than having your hand held in calculus. Spivak is a good middle ground if you want to do this, or really just any Honors calculus textbook, and then read it alongside whatever analysis textbook you choose. Rudin?

[Anonymous No.14972347]

There once was a cult of Pythagoras. What texts did they have? Has it ever been recreated?

[Anonymous No.14972349]

>>14972261
Why wouldn't you want to learn the calculus thing? Basic derivative / integral rules will pop up in advanced math all the time

[Anonymous No.14972351]

>>14972349
Pseuds get trolled by ego tripping retards on 4chan and discord into only doing the most "pure" and "intellectual" math. Similar to how idiots on /g/ waste their entire day on obscure linux distros.

[Anonymous No.14972353]

>>14972068

[Anonymous No.14972361]

>>14972261
>I remember a thread a while back where anons were talking about not having to do the whole Calculus thing and instead just learning Real Analysis.
Do calculus before. It will save you a lot of time.

[Anonymous No.14972410]

I'm majoring in math and just downloaded LaTeX but it looks geeky as fuck (I got TeX-Works or whatever)
How can I rice this shit? I want it to look like I'm a hacker, some fancy interface with black borders and sleek design. Is there some version I can download that's basically this by default?

[Anonymous No.14972437]

>>14972410
if you're majoring in math, you should be intelligent enough to figure that out.
If not, you'll drop out.

[Anonymous No.14972488]

>>14972437
Wow anon you were right I just had to believe in myself thanks

[Anonymous No.14972587]

is there a way to solve for x in x-ab*arctan(a/b*tan(x))=c? (a, b, c all positive) I'm trying to do this thing with some ellipses and circles and been stuck here for a couple of weeks. I can rewrite this in many ways but can't seem to get it to terms of only x or tan(x).

[Anonymous No.14972822]

is there no mistake in this proof? i feel like i'm taking crazy pills.
if x is an element of a Sylow subgroup (i.e. of prime-power order), how the hell can it have order pm? shouldn't it be [math]o(x)=p^m[/math] and [math]o(x^{p^{m-1}}=p[/math]?
i actually wrote to the author and informed him of this mistake, but he wrote back to me saying that everything is correct

[Anonymous No.14972857]

>>14972282
Thanks anon, will check them out
>>14972345
>read it alongside whatever analysis textbook you choose. Rudin?
That's what I'm asking about
>>14972349
It's not that I don't want to, it's just that wouldn't I learn them anyway through Real Analysis?
>>14972351
Don't call me out like that :(

[Anonymous No.14972867]

>>14972857
I should add that I'm also going through Rosen's Discrete Maths text so the proof and logic aspects wouldn't be foreign to me

[Anonymous No.14972942]

>>14972822
Everything is correct. A power of p is divisible by p so there is an integer m with o(x) = pm.

[Anonymous No.14972954]

> Zero times zero equals 1
Okay which one of you know it all nerds added that bullshit into math class

[Anonymous No.14972972]

>>14972857
3blue1brown's series on Calculus is really all Calculus knowledge you need to start reading Real Analysis. I never read a book on Calculus either. I would advise you against Amann & Escher. You should instead read Abbott's Analysis as a first treatment.

[Anonymous No.14973383]

sup /g/oy here
can someone help me prove that lg N * M^(1/lg N) is basically 2 * lg N if M is a power of 2?

[Anonymous No.14973385]

>>14973383
>https://youtu.be/2g9OSRKJuzM?t=1484
link to youtube

[Anonymous No.14973433]

>>14973383
Why do you use two different variables when the professor only uses 1?

You want to prove n^(1/lgn) = 2
Say n = 2^k. You don't have to assume n is a power of 2 (i.e. k can be any real number, not just an integer).
Then lgn = k, and the expression n^(1/lgn) becomes (2^k)^(1/k) = 2.

[Anonymous No.14973436]

>>14973433
fuck, im really retarded
you made it look so obvious, thanks
also is latex broken in this board now?
not seeing a single use of it here

[Anonymous No.14973440]

>>14973436
It's working fine, e.g. >>14970080
Maybe check if you're using an extension that messes with it, or try switching browsers.

[Anonymous No.14973467]

Is J. T. Knight's Commutative Algebra textbook any good? I am in need of a good commutative algebra textbook but right now I only own Zariski's two-volume textbook.

[Anonymous No.14973473]

>>14973467
>I am in need of a good commutative algebra textbook
Atiyah and Macdonald
Kaplansky
Matsumura

Those are what my advisor (who works in commutative algebra) recommends.

[Anonymous No.14973516]

>>14973473
Yeah but they're pricey as fuck.
Though I guess I can just download for free and print my own copy, but somehow that feels less nice.

[Anonymous No.14973560]

>>14973473
Hang on, which Kaplansky book, "Commutative Rings"? Or "Field and Rings"?

[Anonymous No.14973577]

I'm getting filtered by this, lol. How should I solve it bros?

Determine f(x), if [math]f(\frac{x}{x+1}) = x^2[/math]

[Anonymous No.14973586]

>>14973577
y = x/(x+1)

then

x = y/(1-y)

so

f(y) = f(x/(x+1)) = x^2 = (y/(1-y))^2

[Anonymous No.14973620]

>>14973586
Thank you a lot, anon, I can see it now.

[Anonymous No.14973639]

>>14972111
>No general way.
Do you have proof for that? Or are you just making it up since you aren't being graded on this?

[Anonymous No.14973701]

>>14972942
oh fuck, now i see what he meant, he's just writing the order p^k of x as p times p^{k-1} and calling the latter m, FUCK

[Anonymous No.14973763]

So should I do 10 rotations of each point for 200 extra points drawn in total or should I do one rotation for each for 10 extra points drawn total?

[Anonymous No.14973827]

>>14973763
You should do one or two examples and then go to the next exercise. There is no point in doing mindless busywork.

[Anonymous No.14973832]

>>14973763
For each point in exercises 11-20 you need to draw a picture for each rotation in exercises 1-10. So it will be 100 pictures in total. Good luck!

[Anonymous No.14973850]

>>14973832
kek I can't even multiply two numbers properly
>>14973827
I'll do one for each point, like 11 rotated by 1, etc. you're right that there's no point being autistic (also I checked the solutions in the back and it seems that Lang doesn't expect me to go 10x10 autist mode)

[Anonymous No.14974062]

>>14973516
Libgen.rs

>>14973560
Which do you think...

[Anonymous No.14974360]

>>14961031
number 7 is not true for any ring doe, there are many rings with both idempotent and nilpotent elements. Plus 0 is also an idempotent element of any ring?

[Anonymous No.14974531]

>>14974360
I think it was written by a non-mathematician, because the title of 7 says "idempotent unit" and "nilpotent unit" (even though "unit" is a separate term). They use "idempotent unit" in the title to mean "idempotent", and "nilpotent unit" to mean "nilpotent".
But then, in the body, when they say "no nilpotent unit", they mean "nilpotent" and "unit" in the normal sense. Same for "only idempotent unit is 1".

Nilpotents are zero-divisors, so they can't be units (unless in the zero ring).
If x is idempotent and a unit, then x^2 = x, divide both sides by x, and you get x = 1.

[Anonymous No.14974801]

New thread: >>14974666