/mg/ - maths general

[Anonymous No.14877069]

formerly >>14866559

Which trigonometric function is the most fundamental? - edition

Talk math.

[Anonymous No.14877114]

fuck anime

[Anonymous No.14877117]

girls who are very sexy

[Anonymous No.14877120]

[math](\vec{n} \in \mathbb{R}^3 / \{0\} \wedge r \in \mathbb{R}) \implies\\ [\exists\, \vec{a}, \vec{b}, \vec{c} \in \mathbb{R}^3\, \exists\, \vec{p} \in \mathbb{R}^3 : (n_{1}p_{1} + n_{2}p_{2} + n_{3}p_{3} = r) \iff (\exists\, \lambda, \mu \in \mathbb{R} : \vec{p} = \lambda \vec{a} + \mu \vec{b} + \vec{c})].[/math]

[Anonymous No.14877140]

>>14877117
What about them?

>>14877120
Seems like the /{0} is not necessary - just take 0's for all the numbers that are claimed to exist too.
Feels like you can also go beyond dimension 3 with this, easily.

[Anonymous No.14877157]

Psst. Hey, kiddo. Come over here.

[math] \forall (x\in X). \neg \neg {\mathrm {LEM}} (P(x)) [/math]

where
[math] {\mathrm {LEM}} (A) := ( A \lor \neg A) [/math]

Since by a De Morgan's law, for any given [math]x\in X[/math], the statement [math] \neg \neg {\mathrm {LEM}} (P(x)) [/math] just says that [math] P(x) [/math] and its negation can't be true at the same time.

But consider now a more particular scenario.
The case where the [math] x [/math] are binary sequences and [math] P(x) [/math] is the claim that a sequence is forever constantly zero.

[math] X\ :=\ {\mathbb N}^{\mathbb N} [/math]

[math] P(x)\ :=\ \forall (n \in {\mathbb N}). x(n)=0 [/math]

If you prove something about an infinite object like a sequence, you can't possibly inspect all values, so much is clear anyhow. If you can prove something about an unending sequence, it's also a finite proof, so much is clear as well.
Given all the sequences and how complicated they can turn out to be, whether a sequence is the zero sequence surely can't be established for ALL the sequences.

[math] \neg \forall (x\in X). {\mathrm {LEM}} (P(x)) [/math]

I hope that helps.

[Anonymous No.14877162]

>>14877140
The textbook used [math]/\{0\}[/math] for the proof. Also it's necessary to say that [math]\vec{a},\ \vec{b}[/math] are not parallel

[Anonymous No.14877165]

Psst. Hey, kiddo. Come over here.

[math] \forall (x\in X). \neg \neg {\mathrm {LEM}} (P(x)) [/math]

where
[math] {\mathrm {LEM}} (A) := ( A \lor \neg A) [/math]

Since by a De Morgan's law, for any given [math]x\in X[/math], the statement [math] \neg \neg {\mathrm {LEM}} (P(x)) [/math] just says that [math] P(x) [/math] and its negation can't both be ruled out at the same time.

But consider now a more particular scenario.
The case where the [math] x [/math] are binary sequences and [math] P(x) [/math] is the claim that a sequence is forever constantly zero.

[math] X\ :=\ {\mathbb N}^{\mathbb N} [/math]

[math] P(x)\ :=\ \forall (n \in {\mathbb N}). x(n)=0 [/math]

If you prove something about an infinite object like a sequence, you can't possibly inspect all values, so much is clear anyhow. If you can prove something about an unending sequence, it's also a finite proof, so much is clear as well.
Given all the sequences and how complicated they can turn out to be, whether a sequence is the zero sequence surely can't be established for ALL the sequences.

[math] \neg \forall (x\in X). {\mathrm {LEM}} (P(x)) [/math]

I hope that helps.

[Anonymous No.14877173]

>>14877165
Are you trying to do magic?

[Anonymous No.14877194]

>>14877165
>[math] \mathbb{N}^{\mathbb{N}} [/math]
What? did you mean [math] \mathbb{N}^{\aleph_0} [/math]?

[Anonymous No.14877195]

>>14877173
Au contraire.
I'm claiming that whenever you acshually somehow map a sequence [math]x \in {\mathbb N}^{\mathbb N} [/math] to a single number [math]f(x)\in {\mathbb N}[/math], then this was only possible because you were expecting at most finitely many values of the sequence [math]x [/math].

[Anonymous No.14877201]

>>14877194
Isn't this the notation for all mappings on [math]mathbb{N}[/math]?

[Anonymous No.14877203]

>>14877194
The collection of all sequences

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

Ponder!

[Anonymous No.14877210]

Unfucking believeable.

[Anonymous No.14877215]

>>14877165
>are all the entries zero?
>no
>then one of the entries is nonzero
>WTF YOU CAN'T JUST ASSUME THAT

[Anonymous No.14877219]

>>14877069
sine obviously

[Ponder No.14877220]

>>14877194
I wrote binary sequences, but it doesn't matter. It's just all the sequences on N into some other set.

You can be more estoeric and think of it as the collection of
https://en.wikipedia.org/wiki/Choice_sequence
But any formalization wouldn't know until you postulate Browerian continuity. The mere rejection of the universally closed LEM over the infinite collection is weaker.

[Anonymous No.14877236]

>>14877195
What about just mapping x to x(0)

[Anonymous No.14877245]

>>14877215
Depends on your reading of "one of" and whether the sequence can be evaluated at all the n's at all.

[Anonymous No.14877249]

>>14877245
Every function can be evaluated at every n

[Anonymous No.14877250]

>>14877245

[Anonymous No.14877260]

>an experiment is repeated 900 times
>odds of success are 10%
>what is the probability of it succeeding 70 times?
Picrel is profs solution, where does he take the 0.5 from?

[Anonymous No.14877284]

>>14877249
But not at all n.

>>14877236
>What about just mapping x to x(0)
Evaluation at 0 is indeed expecting x at at most a finite number of values (namely at a single one)
Protip: You probably won't find counterexamples to Brouwers analysis among computable functions, since the theory can be realized/has models.

Note that it being possible to reject a universally quantified LEM claim shouldn't be too surprising.
E.g. you can implement the theorem by theorem consistency search for Peano arithmetic in Peano arithmetic and the theory can neither prove that it will find a match or never find a match.
Of course Peano arithmetic (as it's classical) proves that either of those holds for the search in it's entirety - but the search can't do transfinitely many steps and so that either of those is "true" is a useless claim. Dropping the latter assumption doesn't hurt.
Related,
https://en.wikipedia.org/wiki/Limited_principle_of_omniscience

[Anonymous No.14877291]

[math](\vec{n}, \vec{m} \in \mathbb{R}^3 \wedge r, s \in \mathbb{R}) \implies [\exists\, \vec{a}, \vec{b} \in \mathbb{R}^3 \wedge \vec{a} \neq 0\, \exists\, \vec{p} \in \mathbb{R}^3 :\\ (n_{1}p_{1} + n_{2}p_{2} + n_{3}p_{3} = r \wedge m_{1}p_{1} + m_{2}p_{2} + m_{3}p_{3} = s) \iff (\exists\, \lambda \in \mathbb{R} : \vec{p} = \lambda \vec{a} + \vec{b})].[/math]

[Anonymous No.14877292]

>>14877249
Every computable function, yes

[Anonymous No.14877304]

>>14877114
based anime fucker

[Anonymous No.14877307]

>>14877249
Yes, nevermind if you narrow it down to functions with \exists! in the definition then sure

[Anonymous No.14877324]

1+1 = 2 = a +b = x + y = z

[Anonymous No.14877325]

>>14877284
>Protip: You probably won't find counterexamples to Brouwers analysis among computable functions
>Meta-protip: If you live in Brouwer's analysis, all functions are computable, so your protip holds trivially.

[Anonymous No.14877420]

>>14877284
Being a finitist sounds boring. You can deny that infinitary statements have meaning, but I think it's significant that nobody has derived an inconsistency from infinitary mathematics after centuries of looking

[Anonymous No.14877459]

>>14877284
>since the theory can be realized/has models.
there are infinitely many computable functions. How do you propose to check infinitely many objects in order to verify you get a model of your theory?

[Anonymous No.14877480]

>>14877459
>there are infinitely many computable functions. How do you propose to check infinitely many objects in order to verify you get a model of your theory?
you mean like a fucking proof?

[Anonymous No.14877553]

>>14877480
What do gradient fields feel like?

[Anonymous No.14877590]

>>14877480
If you had some magical way of verifying that a proof can apply to infinitely many things than sure. But you don't. There are only a finite number of objects you can have access to, and therefore a finite number of objects you can make statements about

[Anonymous No.14877606]

>>14877459
In particular I mean like
https://ncatlab.org/nlab/show/effective+topos
or a type theory.
Of course you can always doubt (TM)

>>14877325
You're likely confused there, as recursive math is the school of Markov. In the Brouwerian school, the fan theorem (Königs lemma, basically, which is classical) holds, and this contradicts the constructive Church's thesis (which is probably the best way to read functions are computable).
https://en.wikipedia.org/wiki/K%C5%91nig%27s_lemma#Relationship_to_constructive_mathematics_and_compactness

Brouwers lawless sequences aren't recursive and I purposely always spoke of unending sequences and the collection of such (not of functions and sets) to not get into this.
(The protip would give info to that anon either way, no matter if all functions are computable)

Brouwer didn't have Markov's pricniple
https://en.wikipedia.org/wiki/Markov%27s_principle
and conversely, the Russians didn't have the continuity principle (pic related) either.

Clearly I'm memeing, I'm not defending Brouwer.

>>14877420
I don't think either of the big schools were finitists as we'd today want to understand them.
But that aside, the plenty of infinities are not even 150 years old and so I'm not sure it's fair to refer to
>infinitary mathematics after centuries

[Jealous No.14877626]

Relevant to my interests.

[Anonymous No.14877642]

>>14877626
Jealous=Tooker?

[Anonymous No.14877643]

Need good recommendations for books on geometry. I know there are multiple levels of study and that the field diverges, so I'll ask for anything you think is good, as long as it's geometry.

[Anonymous No.14877969]

Already forgot all the into to proofs content I should need before delving into abstract algebra, as I spent too much time on other courses. After calculus 3 I'll have a semester before I take differential equations, where I'm assuming ill forget everything again.
How do you even stop skill decay?

[Anonymous No.14878427]

>>14877969
>How do you even stop skill decay?
Do stuff

[Anonymous No.14878447]

>>14877643
do carmo's differential geometry book is an all-timer

[Anonymous No.14878626]

>>14877260
Its continuity correction from moving discrete to continuous distribution

[Anonymous No.14878903]

>Intro to analysis
>It's another proof due to triangle inequality theorem.

All the results are uninteresting as well. When does analysis get interesting?

[Anonymous No.14878913]

>>14878903
measure theory/fourier
Undergrad analysis is pretty dry all around. Just look forward to complex analysis and functional analysis, that’s where it gets pretty neat

[Anonymous No.14878977]

>>14878903
How do you eat your corn cobs?

[Anonymous No.14878999]

>it’s another babby contrarian logic episode

[Anonymous No.14879008]

>>14878903
Read Abbott's Analysis. He doesn't talk about all the foundational rigour until appropriate (mostly at the end). So it picks up the pace pretty soon.

[Anonymous No.14879027]

>>14877165
>you can't possibly inspect all values
That's what non-standard models and filters are for. It doesn't matter if we can't inspect all the elements, we just need almost all of them to be able to know what we can and can't say.

[Anonymous No.14879032]

>mfw had sex with all the women I have dated (vacuously). See you later virgins.

[Anonymous No.14879034]

>>14878903
>When does analysis get interesting?
Non-standard/arbitrary measures are pretty fucking neat, imo.

[Anonymous No.14879049]

Can someone recommend me a resource to learn partial fraction decompositions

[Anonymous No.14879054]

>>14879049
https://www.youtube.com/watch?v=P78LfZTIFJg

[Anonymous No.14879084]

>>14879049
>>14879054
I am not a brainlet, I meant a book.
I am looking for a not necessarily rigorous formulation of it (over the reals only) which explains why it works. I understand it works for degree one polynomials because Ap(x) + Bq(x) forms a straight line, so if we can find A,B that is works for 2 distinct x's, it must work for all of them. But I don't understand the rules for others. Looking for a general algorithm.

[Anonymous No.14879102]

>>14879084
The key there is Bezout's identity.
The polynomial [math]g(x)[/math] factors into irreducible factors [math]g_j(x)[/math]. Now of course two different irreducible factors have a gcd of 1 so there are polynomials [math]u(x),v(x)[/math] with
[eqn]f(x) = g_1(x) u(x) f(x) + \left(\prod_{j=2}^N g_j(x) \right) v(x) f(x) [/eqn]
Using this you can split a part off
[eqn] \frac{f(x)}{g(x)} = \frac{g_1(x) u(x) f(x) + \left(\prod_{j=2}^N g_j(x) \right) v(x) f(x)}{ \left(\prod_{j=1}^N g_j(x) \right)} = \frac{v(x) f(x)}{g_1(x)} + \frac{u(x) f(x)}{\left(\prod_{j=2}^N g_j(x) \right)} [/eqn]
You can then inductively repeat the process until the fraction is fully split.
The polynomials [math]u(x),v(x)[/math] can be computed with the extended euclidian algorothm as usual.

[Anonymous No.14879135]

>>14877606
Fan theorem != WKL, if you phrase them correctly. They are the same only up to a tiny bit of classical logic. Basically, the Fan theorem is the positive statement of WKL.

[Anonymous No.14879152]

>>14879102
Exactly the kind of thing I am talking about. I have no idea what you have written because I never did precalculus properly. And now it's coming to fuck me over when doing some Analysis problems. I am looking for a book to learn all this polynomial algebra.

[Anonymous No.14879162]

>>14879135

[Anonymous No.14879172]

>>14879152
>I have no idea what you have written because I never did precalculus properly.
You aren't supposed to learn about Bezout's identity in precalc because it's something more related to number theory and abstract algebra, not precalc.

Bezout's identity says that if you have two integers x and y, then you can represent their gcd g as this: Ax + By = g, where A and B are integers.
This is something more general than just for integers and works for any principal ideal domain (you don't need to know what this means), which includes polynomial rings over fields (don't need to know this either), like polynomials over the reals or the complex numbers.
So basically you can replace "integer" in the statement above with "real/complex polynomial" and it'll work.

If we go back to the problem of partial fractions, then factoring g(x), you see that the factors are "prime" and cannot be factored further. Now these factors play the roles of x and y above, and because they're prime, their gcd is 1. Then you can find polynomials to satisfy the equation. From there you multiply both sides by f(x) and divide by g(x).

[Anonymous No.14879234]

>>14879172
Thanks I got it. I haven't read Abstract Algebra yet, but an introductory book on it should cover all this I suppose, something like [math] \textit{Topics in Algebra}[/math]?

[Anonymous No.14879309]

>>14879234
I like Pinter’s A book of Abstract Algebra

[Anonymous No.14879415]

>>14879135
>Basically, the Fan theorem is the positive statement of WKL.
you mean contrapositive.
>fan thm: no paths implies finite height
>wkl: infinite height implies paths
anyway you seem like you might be able to finally tell me: whats the actual difference between a fan and a spread.? whats the actual difference between fan thm and bar induction?

[Anonymous No.14879535]

>>14879032
Well played anon, well played.

[Anonymous No.14879539]

>>14879032
So you're still virgin, got it

[Anonymous No.14879599]

>magna cum laude
>zero research
Unironically, completely and utterly over for me.

[Anonymous No.14879874]

>>14877114
i fucking hate the touhou posters, they should go die in a ditch. they are literally repressed transvestites and homosexuals and are ashamed of their anime fetish. you know how i know? because they would never display it publicly to the world and can only post that shit anonymously

[Anonymous No.14879883]

>that classmate who won't stop trying to show off by showing off irrelevant knowledge
>is wrong half the time
>wastes everybody's time 100% of the time

[Anonymous No.14879885]

>>14879084
>I am not a brainlet, I meant a book.
Vinberg's "A Course in Algebra" has a chapter on this, i don't recall any other algebra book that does besides Van der Waerden, which is a bit old

[Anonymous No.14879900]

>>14879874
>homosexuals
That does not make sense because i like women, so that makes me heterosexual, if i was homosexual i would post pictures of cute boys instead of cute girls.
I can't understand how a picture of a cute anime girl can make someone mad, why do you have so much anger inside you anon?

[Anonymous No.14879924]

>>14879885
This book looks really nice. Thanks anon.

[Anonymous No.14879932]

>>14879599
>summa cum laude
>zero research
>doing masters at my undergrad school
it was over for me before it began

[Anonymous No.14879947]

Any book recommendations on the easiest, softest, babied introduction to navier-stokes, that can also be utilized as a reference?
The only content I have on it now that is within my grasp is derivation an discrete models in matlab, in a book titled "computational mathematics" by White.. Beyond use in the text, the only "theory" is a quick derivation.

[Anonymous No.14879949]

>>14879932
>doing masters online

[Anonymous No.14879953]

>>14879949
i-it's just as good as in person, r-right??

[Anonymous No.14879970]

>>14879953
I don't even care. I just want to do more math, I want to keep taking classes forever, but clearly I am not smart enough to do a PhD and I am not willing to live like a student for half a decade more, and I'm not willing to wait before starting a graduate program, so something has to give. I should I guess, be thankful that this opportunity even exists.
The main suck is that the lack of research from undergrad will feed into this loop of less and less research options.

[Anonymous No.14880215]

>>14879599
>magna cum laude
>summa cum laude
What the fuck does any of this mean you fucking Americans
What, they rate how loud you guzzle cum at your unis?

[Anonymous No.14880232]

>>14880215
>If a student's cumulative CU GPA (all coursework in the Undergraduate Career GPA on the CU transcript) is at least 3.700, the student will automatically receive a Latinate honor. A GPA of 3.700-3.799 earns the "cum laude" designation (a medal with a green ribbon is worn during graduation ceremonies), 3.800-3.899 earns "magna cum laude" (a medal with a red ribbon is worn during graduation ceremonies), and 3.900-4.000 earns "summa cum laude" (a medal with a purple ribbon is worn during graduation ceremonies).

[Anonymous No.14880238]

>trying to work out a number theory problem
>Manipulate the algebra
>Cancel our some terms
>Find that x=x
At least my manipulations are correct.
Without explaining my problem, where can I find info on the factors of some number x? (Generally speaking)

[Anonymous No.14880251]

>>14879883
I have a classmate who most likely has autism (no joke), and he makes comments all the time and sometimes talks over the professor.
Also when he makes mistakes with these comments, instead of saying "oh sorry" or "nevermind, I was wrong", he instead EXPLAINS IN DETAIL why he made those mistakes and the thought process he had.

Sometimes he CALLS me hours after class has ended and explains to me a mistake he made.
He just talks a lot in general. Between classes he talks to me and gets real close in my personal space, and I can feel the saliva when it shoots out of his mouth and hits my hand.

[Anonymous No.14880255]

>>14880238
>Find that x=x
Most likely you substituted the same thing twice.
As a general rule of thumb, only substitute once.

[Anonymous No.14880261]

>>14880232
I did a degree in CS and didn't have a high enough GPA to get any of these lmao.
Then I started my master's in math and I'm getting a 4.0 on literally every course.

[joyofsatan.org No.14880288]

>>14877069
>>14877114
How can you fuck an animation?

[Anonymous No.14880294]

>>14880261
Its all based on the school and doesn't have much meaning besides comparing within the school. Some universities give honors out to 30% of the student body, others are limited to very, very few top students.
https://registrar.uconn.edu/latin-honors/
An example, the cum laude cutoff for University of Connecticut is 3.751 for engineering students. Every year, the GPA requirements get higher and higher.
Most graduate schools will not allow more than one B grade in the entire program, so classes are just pass/fail, and if you pass you get an A, barely pass you get a B.

[Anonymous No.14880307]

>>14880288
I don't know enough set theory to shitpost using proofs, but I imagine you can construct a logical argument that follows the lines of if I masturbate while looking at a cartoon it is roughly equivalent or geometrically similar to having sex with a woman.

[Anonymous No.14880322]

How would you feel if you were locked in a cage and forced to study math all day every day?

[Anonymous No.14880327]

>>14880322
>they're_both_the_same_picture.meme

[Anonymous No.14880343]

>>14880232
for me, it's
>GPA >3.3, cum laude
>GPA >3.5, magna cum laude
>GPA >3.7, summa cum laude
is my school shitty?

[Anonymous No.14880383]

>>14880343
No like I said, its only use is for determining your standing within your school, and even then within your graduating year.

If a school has massive grade deflation, 3.3 in that school is comparable to a super grade inflated school cum laude of 3.8.
Grad admissions are bullshit too though, and committees have no idea what half the shit means. A guy on reddit was asking for top 3% subject GRE, when the maximum attainable was 89th percentile or some shit. Having some honor or distinction on your application just helps pad it.

[Anonymous No.14880408]

>>14880322
You don't know many mathematicians do you.

[Anonymous No.14880551]

>>14877069
Opinions on the list of books im going to use to learn topology and differential geometry? Is there anything else that I should add?

[Anonymous No.14880568]

>hear about [X] Analysis course and how it's important for a mathematician to take
>get excited and register it
>get lost in all the "sequentially shit fuck epsilon compact" and "uniformly piss cunt delta continuous" definitions
>repeat cycle
Why is analysis both so fucking convoluted and boring?

Not a single redeeming quality.

[Anonymous No.14880572]

>>14879874
but touhou isn't anime

[Anonymous No.14880582]

>>14880568
Its pretty boring and bogged down with terms. Got trolled by the internet into going into pure math, huh? Should have gone into applied,taken only abstract algebra, and then numerical/functional analysis courses.
The way most real/complex analysis courses are set up are a real meme and will drop you off into category theory, where you memorize terms and phrases like "would you like fries with that?"

[Anonymous No.14880585]

>>14880582
not at all

[Anonymous No.14880594]

>>14880582
>Got trolled by the internet into going into pure math, huh?
Nope.
>Should have gone into applied,taken only abstract algebra, and then numerical/functional analysis courses.
I'm already an algebraist.
And applied shit is as bad as analysis, or even worse.

[Anonymous No.14880595]

>>14880585
Did you take Advanced Calculus I and II before taking analysis?

[Anonymous No.14880612]

>>14880595
The guy you replied to is not me. I'm >>14880568
I took both of these, along with real analysis (graduate), complex analysis, and functional analysis.
The only one out of these that's almost bearable is complex analysis. The rest can completely fuck off.

[Anonymous No.14880621]

>>14880612
>I took both of these, along with real analysis (graduate), complex analysis, and functional analysis.
>The only one out of these that's almost bearable is complex analysis. The rest can completely fuck off.
Ok just making sure, as some schools call advanced calculus I and II, their real/complex analysis for undergraduates.

Graduate real/complex I found unberable and useless, it was only functional analysis and undergraduate numerical analysis that were of any interest/useful.
Different Stokes I guess.

[Anonymous No.14880628]

>>14880621
I'll also add that most grad courses I had were unstructured mess. Graduate numerical analysis was focusing the entire time on elliptic boundary value problems and boundary integrals, it was so dumb and overdone.

[Anonymous No.14880639]

>>14880621
>some schools call advanced calculus I and II, their real/complex analysis for undergraduates
In my case, advanced calc I was undergrad real analysis, and II was multivariable undergrad real analysis.

[Anonymous No.14880647]

lol at me but i skimmed through lectures for calc 3
difq and line A and even a bit of diff geo and analysis and it was the most redundant boring thing i have ever seen in my life and i’m sad because i wanted it to be fun and it just wasn’t way too slow too much explanation not enough drawing and algebra everything is hand cranked and nothing was fun
sad

[Anonymous No.14880654]

>>14880647
>school doesn't offer 8 week courses
Combined with skipping lectures to watch online lectures at 2x speed is how I found my undergraduate courses to be more fun and not leave me falling asleep or daydreaming.

If you don't have that option and don't enjoy cranking, take advantage of the free time to volunteer for research. Ask everyone in the faculty you can, go in during office hours and see if you can get any "topics in X" courses added during a semester for you and other interested students.

[Anonymous No.14880856]

is there a function that graphs a cube? how does it map the rotations about the vertices?
can a point traversing the cube drawing a single unbroken line trace every point on the surface without going over any spot twice?

[Anonymous No.14880880]

>>14880215
'cum' is from Latin meaning 'with',
like 'Johnny with lately' or 'hotdog with buns'.

the level of the honors from smaller to greater
are cum laude (with praise), magna cum laude
(with great praise) and summa cum laude
(with highest praise). you can also say
3rd, 2nd, 1st order honors in its place as well

[Anonymous No.14880885]

>>14880856
>is there a function that graphs a cube?
[eqn](2x/l)^n+(2y/w)^n+(2z/h)^n=1[/eqn]

>can a point traversing the cube drawing a single unbroken line trace every point on the surface without going over any spot twice?
You mean like a integral to find surface area?

[Anonymous No.14881271]

>>14879415
>you mean contrapositive.
No, I really meant positive as in linear logic i.e. something that constructs a datatype, here an existential.
>whats the actual difference between a fan and a spread
I think this depends too much on the setting and on the author to get a definitive answer. I would personally use them interchangeably.

As for bar induction vs fan theorem, this is basically the same, barring (aha!) inter-author variability. Maybe "bar induction" should be reserved for the variant that describes the produced inductive tree as an actual inductive data rather than as some integer bounding said tree, but that's about it.

[Anonymous No.14881280]

>>14877210
the white man's contradiction symbol

[Anonymous No.14881306]

>>14880251
Why does this person have your personal cellphone number kek

[Anonymous No.14881360]

Can anyone please post the flowchart of the studying order of different branches of math and its sub-topics?

[Anonymous No.14881414]

>>14881360
Check out the charts from the /sqt/ thread and see if you can find it:
imgur.com/a/pHfMGwE
imgur.com/a/ZZDVNk1

[Anonymous No.14881445]

Is anyone worried that as they study math more they will lose creativity?

[Anonymous No.14881539]

>>14881445
No, math is all about creativity.

[Anonymous No.14881587]

>>14881539
It feels like the more I go through other people's books and education the less I am able to come up with new ideas on my own.

[Anonymous No.14881595]

>>14877069
Brahs are there any situations where the limit on one side of something is 0 and the limit on the other side is infinity?

[Anonymous No.14881607]

>>14881595
Consider [math]f(x) = \frac{H(x)}{x}[/math] where [math]H[/math] is the Heaviside function.
[eqn]\lim_{x \to 0^-} f(x) = 0 \\
\lim_{x \to 0^+} f(x) = \infty[/eqn]

[Anonymous No.14881764]

>>14880594
>And applied shit is as bad as analysis, or even worse.
Despite the perception among many pure mathematicians, applied math is not about using mathematical techniques without proving anything. It's more about proving things about these techniques — e.g., accuracy, stability, rate of convergence — and that requires lots and lots of (you guessed it) analysis.

[Anonymous No.14881797]

>>14881764
>It's more about proving things about these techniques — e.g., accuracy, stability, rate of convergence — and that requires lots and lots of (you guessed it) analysis
Hence why it's as bad or worse.

[Anonymous No.14881800]

>>14881306
We're classmates. Sometimes we need to coordinate stuff, e.g. our classes are small, so the professors have us agree amongst ourselves on times for exams and such, or moving our class to a different time/location.

[Anonymous No.14881997]

>in calc class
>chain rule time
>d/dx (x^2+4)^100
>teacher brings up analogy
>consider your tools when trying to solve a problem
>would you rather expand this or use the chain rule?
>how would you like to take on Manny Pacquiao?
>i would much rather face him in chess
>student: whats your elo on chess.com?
>i use lichess, chess.com is.... not it
>kid in back says "based"
which one of you is it??

[Anonymous No.14882107]

>>14881271
>aha!
Is that an exclamation of laughing somewhere?

[Anonymous No.14882121]

>>14881997
Me.

[Anonymous No.14882179]

>>14882121
Then tomorrow say "feeling fit, buddy"

[Anonymous No.14882187]

>Remember back when I was I grad school
> Advisor sits down with me
>"You gotta relearn all of these separation axioms before you can get any further in algebraic topology"
>Crammed six chapters of Patty in eight days
>four years later
>still never used any of them
Was that week wasted?

[Anonymous No.14882385]

>Enumerate all sequences of natural numbers
>All sequences of length 1, all sequences of length 2, ..., all sequences that can be bijected with N, all sequences that can be bijected with 2^N, ...
This looks countable to me, what's the problem?

[Anonymous No.14882393]

What's with the sudden hate for anime all over 4chan?

[Anonymous No.14882406]

>>14882385
Suppose you have a list of all sequences of natural numbers
[eqn](a^{(1)}_1 , a^{(1)}_2, a^{(1)}_3, \ldots ) \\
(a^{(2)}_1 , a^{(2)}_2, a^{(2)}_3, \ldots ) \\
\vdots
[/eqn]
Then consider the sequence [math](b_1,b_2, \ldots)[/math] with
[eqn]b_n = 1 + a^{(n)}_n[/eqn]
Clearly for every [math]k \in \mathbb{N}[/math] the sequence differs from [math](a^{(k)}_n)[/math] as [math] b_k \neq a^{(k)}_k[/math] so [math](b_n)[/math] is not in the list above. Contradiction.

[Anonymous No.14882443]

>>14880551
The ones I've read in that list are nice.
>Is there anything else that I should add?
Dunno how much Bredon covers, but probably something beefy on differential topology like Hirsch.

[Anonymous No.14882450]

>>14882443
nta but thoughts on Sternberg's lectures on differential geometry? I bought it since I was told Lee doesn't cover some important topics

[Anonymous No.14882466]

>>14882450
Never read it but the big reference book for dg is Kobayashi-Nomizu, if you want to just cover as much ground as possible.

[Anonymous No.14882474]

Is there a [math]\LaTeX[/math]-ed version of baby rudin or should i stick with the djvu from libgen?

[Anonymous No.14882480]

>>14882474
the modern German editions were written in it.

[Anonymous No.14882499]

>>14882474
Amaan & Escher have a [math] \LaTeX /[math] version.

[Anonymous No.14882538]

Is Lax's Linear Algebra book a meme? I thought about going through it since I've never had a proper Linear Algebra course but use it frequently and heard it's fairly comprehensive.

[Anonymous No.14882574]

>>14882538
>done with vector spaces by page 10
Yeah seems like a meme alright. If you want an introductory course that also talks about applications: Friedberg, S.H., Insel, A. J., & Spence, L.E. (1979). Linear algebra, is your best bet. If you want a pure theory course: Rao, R.A., & Bhimasankaram, P. (2000). Linear algebra. I'd suggest the latter, since it has better exercises. In fact, Lagrange interpolation which the former has dedicated a subsection to, is discussed in an exercise of the latter.

[Anonymous No.14882633]

LEM plus dependent choice is the most kino pair of principles and most correct way of doing maths

[Anonymous No.14882643]

>>14882633
>most kino
You mean LEM or not LEM?
Because if you have LEM and Dependent choice, how is that different than what every normie does?
I don't think full choice sees much use beyond some ideal existence claims.

[Anonymous No.14882649]

>>14882385
None of the sequence in your attempt is infinite.
For example, the (very low Kolmogorov complexity) sequence given by alternating 3 and 7 is not in your list.
3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, ....

[Anonymous No.14882689]

algebra exam today bros please wish me luck

[Anonymous No.14882693]

>>14882689
Algebra? That's easy bro. Just remember the quadratic formula.

[Anonymous No.14882749]

What's THE starting book for undergrad Math? I read some of the beginner books posted here and could easily understand and solve them, yet when I pick up random undergrad book, i'm failing badly. It's like there's a missing link in-between. What book should I look for?

[Anonymous No.14882764]

>>14882393
Smug anime posters who makes you seethe/they are probably trannies

[Anonymous No.14882777]

>>14882749
All undergrad math is equally easy... once you take the most important course of all: A proofs course.

Find any book that teaches proofs. Proofs are quite literally a language to learn. Once you know how to read and write proofs, then you can clearly understand where an argument is going and even foresee how it's going to go.

Find something that covers the following: Logic, proofs (direct, contradiction, contrapositive, induction), relations (equivalence, partial order, total order), functions (injections, surjections, bijections), cardinality (countable/uncountable). Then after that maybe go to calculus and understand epsilon-delta proofs.

I looked up my uni's course and they use this book: Mathematical Proofs, A Transition to Advanced Mathematics.

[Anonymous No.14882779]

>>14882749
What books did you read?

[Anonymous No.14882781]

>>14882749
>when I pick up random undergrad book, i'm failing badly.
You're supposed to struggle.

[Anonymous No.14882787]

>>14882781
>t.

[Anonymous No.14882792]

>>14878903
Read Rudin's RCA L^p chapter. You will realize how easily he proves the triangle inequality holds for a pretty big ton of spaces.
Read convex analysis then, optimization by methods of convexity. Derivatives are way too fucking strong, it's almost uninteresting to do hard analysis because you just know it's true but it doesn't necessarily give you a useful method

[Anonymous No.14882796]

>>14878913
>Undergrad analysis is pretty dry all around.
Is there even a point to this? when I got to the later ears I got mad that we even had to go through analysis in such a cryptic way with a stupid professor that didn't know the intuition either. Analysis is similar to Linear Algebra in the way that both have obvious results but the notation of the theory might work against you if you didn't know the geometric intuition (translating between symbols and intuition is quite important)

[Anonymous No.14882800]

checking to see if my proof of transitivity of separability is correct (i.e. if [math]L\supset E\supset K[/math] are fields and [math]L/E[/math] and [math]E/K[/math] are separable, so is [math]L/K[/math])
firstly, we need only prove this for characteristic [math]p[/math], because in characteristic [math]0[/math] all algebraic extensions are separable and [math]L/K[/math] is algebraic by transitivity. let [math]S[/math] be the separable closure of [math]K[/math] in [math]L[/math], i.e. [math]K[/math] adjoined everything separable in [math]L[/math].
we show that [math]L/S[/math] is purely inseparable, i.e. if [math]\alpha\in L\setminus S[/math], then [math]\alpha[/math] is inseparable over [math]S[/math]. it is known that in characteristic [math]p[/math] there exists a [math]k\geq0[/math] such that [math]\beta=\alpha^{p^k}[/math] is separable over [math]K[/math], i.e. [math]\beta\in S[/math]. therefore the minimal polynomial of [math]\alpha[/math] over [math]S[/math] divides [math]x^{p^k}-\beta[/math] in [math]S[x][/math], but the latter factors as [math](x-\alpha)^{p^k}[/math] in [math]L[x][/math], so the minimal polynomial has multiple roots and [math]\alpha[/math] is inseparable over [math]S[/math].
coming back to what we had before, by assumption [math]E/K[/math] is separable, so we have [math]E\subset S\subset L[/math] and every [math]\alpha\in L\setminus S[/math] is inseparable over [math]S[/math]. but all such [math]\alpha[/math] are separable over [math]E[/math] by assumption and enlarging the base field does not break separability, so we have a contradiction and [math]L\setminus S[/math] must be empty, i.e. [math]L/K[/math] is separable.

[Anonymous No.14882804]

>>14882749
The two most important things to learn are
>Real Analysis
>Linear Algebra
because you will need them for almost everything and they require no knowledge of other math areas.
Another thing you can study right away is
>Elementary Number Theory
Most universities don't offer courses in it anymore as most results can be gotten as special cases from more advanced theorems in Algebra but knowing Number Theory beforehand will make learning Algebra much more easily.

[Anonymous No.14882805]

>>14880612
>almost bearable is complex analysis.
lol that's because the basedplex numbers form a field and their "differentiation" is just differentiation from R^2 to R^2 with the additional property that they solve a differential equation.
It's quite a large class of functions and they have applications, but the techniques used in complex analysis itself doesn't generalize well outside of it because of how specific it is.
Measure Theory, Probability, Functional Analysis, etc are better

[Anonymous No.14882811]

>>14882781
Nah, I mean struggling as in the author expects me know something that I don't. I think I covered my basic high school math, yet it feels like I'm missing something.

[Anonymous No.14882818]

>>14882805
No, it's because algebra came to the reals and unfucked them by giving them algebraic closure.

[Anonymous No.14882822]

>>14882811
Do you have this feeling when reading specific parts, e.g. proofs? Maybe you just need to get used to axiomatic reasoning and formal logic first. At least I wasn't taught that in high school and did that first when I went to uni.

[Anonymous No.14882824]

>>14882779
I redid my high school math books, abd looked into Basic Mathematics(Lang) because it seemed like the most recommended book in the chart.

[Anonymous No.14882826]

>>14877165
What is LEM

[Anonymous No.14882830]

>>14882826
Law of excluded middle.
It says that every statement is either true or false.
Some people hate it, because using it means you don't get the explicit solution.

[Anonymous No.14882834]

>>14882800
Hehe nice Star Game

[Anonymous No.14882838]

>>14882777
Thanks. Nice trips.
>>14882804
How do you transition to Calculus from there? I seem to struggle with it the most. And non-Euclidean geometry too.

[Anonymous No.14882839]

>>14882830
Thanks so much, you're awesome. :)

[Anonymous No.14882842]

>>14882822
>axiomatic reasoning and formal logic first.
Any book on this.

[Anonymous No.14882848]

>>14882834
what?

[Anonymous No.14882873]

>>14882818
It's ok to cope, many mathematicians have taken their cope to their grave like you. Reality is that if you aren't getting because of your theories then your theories only have a narrow margin for being applied, probability, measures, etc are used a lot and have become such a meme you can now become a "data scientist" by just knowing the applications like a monkey, but it doesn't take from the theory. Complex Analysis is nice, but it's a specific tool

[Anonymous No.14882919]

>>14882873
>then your theories only have a narrow margin for being applied
Don't care.

[Anonymous No.14882927]

I am about to finish my math undergrad without taking real analysis. I took abstract algebra and numerical analysis instead.
Am I fucked?

[Anonymous No.14882940]

>>14882927
Analysis is for faggots

[Anonymous No.14882945]

>>14882940
Tell 'em, sister!

[Anonymous No.14882949]

>>14882927
>without taking real analysis.
>numerical analysis instead
How does this fucking work?
How do you prove that a numerical method converges without knowing what a limit is?
How do you numerical integrate something without knowing what a integral is?
How do you use Newton's method without knowing derivatives or analyze it without Taylor's theorem?

[Anonymous No.14882950]

>>14882945
>Muh I wanna find the answer
Shits so cringe. I literally could not care a modicum less about analysis. The fact that most universities lock real math behind intro analysis courses is a nice filter but otherwise cringe.

[Anonymous No.14882965]

>>14882927
Is it a math degree? Then how the fuck does your college even allow you to do this? I don't get American education. They just let you take and skip whatever course you like, but just add math after the BSc.?

>>14882749
>>14882811
The only thing introductory undergraduate books expect you to know is high school mathematics and proof writing. But I don't know about American high schools, since American colleges teach Calculus (a high school subject) in college for some reason.

So, first and foremost you need to be good at proof writing, which is something you can only improve by doing more undergraduate math. But you can get a head start by reading a book on proofs. The shortest book I know on it is:
>Vellman, D.J. (1994). How to prove it.
But this should not be enough, since this barely teaches you any real math, so you barely solve any actual problems. But it should get you to expect what proof writing is all about. What you need is a specific proof based subject to do to prepare you for proofs; the best for that is Number Theory and hence:
>Long, T.C. (1965). Elementary introduction to number theory.
You should also pick up a book on high school mathematics that is not meant for brainlets. Most Olympiad books are like this. I recommend:
>Barbeau, E.J. (1989). Polynomials.
Now it's time to test your skills in high school mathematics. For this, you should solve problem books written for Olympiad students like:
>Skopenkov, A. (2021). Mathematics via problems Part 1 - Algebra (S. Shubin, & P. Zeitz, trans.).
If you do all this, it should prepare you for all introductory undergraduate books.

Btw, the ideal sequence for undergraduate subjects is:
>Abstract algebra
>Linear algebra
>Univariate real analysis (would be helpful to read a book on inequality first)
>Topology
>Analysis on manifolds
If you are ever going to tackle either Linear Algebra or Real Analysis, I would suggest you watch 3blue1brown's series on those first.

[Anonymous No.14882972]

>>14882949
>How do you prove that a numerical method converges without knowing what a limit is?
This was covered in our calculus courses? The definition of a continuous function on a metric space and compactness/connectedness is a calculus I topic.

>How do you numerical integrate something without knowing what a integral is?
Is this a joke or are you a german that calls their calc I and II, analysis I and II?
Calculus II covers integrals, starting from the Riemann sum. Taylor's theorem is also a calculus II topic....
I am right now taking the numerical analysis course, and the syllabus covers error analysis, lagrange interpolation, fast fourier transforms, B-splines, euler summations, gaussian integration. [I am here], linear equations/sparce matrices, iterative m ethods/bairstow method, eigenvalue problems, ODE boundary-value problems and finite-element method, poisson euqation iterative methods ADI-method.

>>14882965
>Is it a math degree?
yes, applied maths.

>>14882965
>I don't get American education.
I think we call our courses different things.

[Anonymous No.14882976]

What do /mg/ bookshelves look like?

[Anonymous No.14882977]

>>14882976
Bookshelves.

[Anonymous No.14882981]

>>14882976
Not at home but mostly philosophy and a few "classic" works of fiction. I have a nice copy of elements and a couple of math books but I don't care to study text as much as discuss it with others

[Anonymous No.14882984]

>>14882972
>compactness/connectedness
A calculus course should not talk about topology.

[Anonymous No.14882988]

>>14882984
I never took topology, those were just the words my professor used to describe it over a metric space, which was covered in our very first intro to math program course (into to advanced math) that I took before calc I for math majors.

[Anonymous No.14883006]

>>14882988
It's still topology
>metric space
Even more topology
Caclulus + topology is real analysis. Sorry, Anon but have you have to come to terms with the fact that you were raped: unconsensually studied Real analysis.

[Anonymous No.14883011]

>>14882574
>Rao, R.A., & Bhimasankaram, P. (2000). Linear algebra
This one's cheap so I'll take a look at it. Lax's book seems to be more of a refresher, according to the wiki, at least. I'll just read both.

[Anonymous No.14883023]

>>14883006
I don't think so. Maybe real analysis terms were used for convenience, but I did not take analysis my freshman year. Its a requirement for pure math majors, but for applied maths I had other options which I found more interesting.

[Anonymous No.14883048]

>>14883023
What books did you use for it?
>inb4 I never read books
Then yeah you are fucked, but for other reasons.

>>14883011
Yeah it's Indian, so very cheap. I think they are partnered with Springer or something, they publish Terence Tao's analysis book as well at a cheap cost.
>Lax's book seems to be more of a refresher
Looking at the contents, I am sure it is not for someone who has never taken a Linear Algebra course. Also, you should watch 3b1b's series on Linear Algebra if you already haven't.

[Anonymous No.14883054]

Analysis and all other branches of math are just tools to solve PDEs

[Anonymous No.14883061]

>>14883048
>What books did you use for it?
Spivak, as that was when I was doing the honors track, before I dropped it in favor of applied maths.

[Anonymous No.14883072]

>>14883061
So the book, author of which regrets calling it Calculus and not Real Analysis? Nice going there.

[Anonymous No.14883102]

>>14883006
>>metric space
>Even more topology
These are even covered in multivariable calculus for engineers when completing transforms.

[Anonymous No.14883120]

>>14883102
Don't troll. Engineers don't even know the definition of limit.

[Anonymous No.14883172]

>>14883120
They love to puff up complex numbers but ask them to check the Cauchy Riemann equations and they give you that thousand lines in Python stare

[Anonymous No.14883702]

squaring a number maps to one number but square rooting maps to two?

[Anonymous No.14883968]

>>14883702
To make it a function you have to pick a branch, but at the same time you restrict the range. Like complex log function

[Anonymous No.14884380]

>>14883702
There are two numbers that square to the same number, but if you wanna make a *function* that goes back, you have to pick only one of them.

[Anonymous No.14884450]

I have a math problem that I'm trying to work out. On this graph, you can see four colored coordinates. For each coordinate, I want to combine their X and Y values in some fashion that then I can arrange the four coordinates in ascending numerical order with "Red is the lowest value, Blue is second, Green third, and Purple is the highest value."

[Anonymous No.14884454]

>>14877069
Would one of you fine fellas be so kind as to take a look at this for me? >>14884415

[Anonymous No.14884464]

>>14884450
Just map every pair (x,y) to y + (1/2) * (1 + x/(1 + |x|)) and then use the normal order relation of the reals?

[Anonymous No.14884470]

>>14884450
You can do the dictionary ordering. First you look at the x value and compare, then if they are the same you use the y value as a tie breaker. There are many ways to order R^2 so if you need it to fulfill a specific purpose, tell us what that would be

[Anonymous No.14884512]

>>14884450
Sort them based on x+2y

[Anonymous No.14884544]

combinatorics question

This is a question in my textbook:

A basket of fruit is being arranged out of apples, bananas, and oranges. What is the smallest number of pieces of fruit that should be put in the basket to guarantee that either there are at 'least eight apples or at least six bananas or at least nine oranges?

The answer they give is 8 + 6 + 9 - 3 + 1 = 21, which they say the use the strong pigeonhole principle for:
Let q1, q2,..., qn be positive integers. If q1 + q2 ... + qn - n + 1 objects are distributed into n boxes, then either the first box contains q objects, or the second box contains at least q2 objects, ..., or the nth box contains at least qn objects.

I've no clue how this works, can someone explain?

[Anonymous No.14884554]

>>14884544
Take a pic of the question and solution. Because the way it's phrased implies the answer is six (bananas).

A statement of the form "[something] or [something] or [something]" means only one of the three things has to be satisfied and the others are optional. So the smallest number of fruit required is 6 by choosing 6 bananas.

[Anonymous No.14884558]

>>14884554
Here is the image of the part i'm referring to.

[Anonymous No.14884561]

>>14884544
You look at the worst case. What is the biggest amount of fruits you can have without fulfilling the condition? Of course it's (8-1) apples, (6-1) bananas and (9-1) oranges. So take one more fruit and one of the conditions has to be fulfilled
(8-1) + (6-1) + (9-1) + 1 = 8 + 6 + 9 - 3 + 1 = 21

[Anonymous No.14884565]

>>14884558
Ah okay, I get it now. The question is just weirdly worded. So it's NOT up to you how to choose the fruit.

I'm gonna try to present it in a different way.
Imagine someone is giving you a random basket of fruit comprised of some combination of apples, bananas, and oranges. You don't know what's inside. Though you can ask for a certain total number of fruit, call that T.
Suppose you want at least 8 apples, or at least 6 bananas, or at least 9 oranges.
What's the smallest number for T that guarantees one of these is satisfied, no matter the combination inside?

Think of the opposite: What's the BIGGEST number you can have where it's POSSIBLE that none of these conditions are satisfied?
Well to do that, you fill the basket with the biggest number of apples, bananas, and oranges you can WITHOUT satisfying the condition. So you put 7 apples, 5 bananas, and 8 oranges, which is a total of 20.
If this is the biggest number where it's possible to get away with NOT satisfying the condition, then the number after that is the SMALLEST where it's GUARANTEED to have one satisfied. That answer is 21.

[Anonymous No.14884573]

>>14884561
>>14884565
My question is why can't there be 21 bananas for example in the fruit basket.

[Anonymous No.14884574]

>>14884573
This is a stupid question, after reading the explanations I understand now. It has been a long night.

[Anonymous No.14884695]

I'm thinking of buying either Hungerford's or Lang's textbook on Algebra. I've read a decent comparison here:
>https://www.physicsforums.com/threads/algebra-texts-hungerford-vs-lang.134992/
But would most definitely appreciate a second opinion from the distinguished posters of /mg/.
HELP PLEASE!

[Anonymous No.14884740]

I have devised a system to compute anime maids. Two things have become apparent.

There are an infinite number of anime maids.

If we live in a Cellular Automata like Wolfy thinks, then it probably isn't being used to compute anything important. Most computations aren't important.

[Anonymous No.14884896]

Any Indians here, what do you think of using NCERT books(9-12) as background for maths, before you start an undergraduate course, does it cover everything?

[Anonymous No.14884983]

>>14884896
It is retarded to study math unless you are doing it in ISI, CMI or TIFR. But NCERT clearly is not enough to prepare for their entrances, especially considering it has little focus on proof based math. You have to follow an Olympiad book like the one's recommended in CMI's entrance exam syllabus.
Also, you need to be 18 to post here.

[Anonymous No.14885019]

[math]\sum_{n = 1}\frac{x^n}{n}[/math] is divergent for all [math]x < -1[/math], right?

[Anonymous No.14885039]

>>14884983
I'm in my late 20's, never completed my graduation. These are the books I found on CMI's site.
>V. Krishnamoorthy, C.R. Pranesachar, K. N. Ranganathan, B.J.Venkatachala, Challenge and Thrill of Pre-College Mathematics, New Age International Publishers.
>M.R. Modak, S.A. Katre, V.V. Acharya, An Excursion in Mathematics, Bhaskaracharya
Pratishtan (Pune).
>D. Fomin, S. Genkin, I. Itenberg, Mathematical Circles: Russian experience, Universities
Press (Hyderabad) 1998.
Are these the olympiad books you mentioned?

[Anonymous No.14885077]

>>14885019
your series is the formal integral (i.e. termwise integral) of [math]\sum_{n\geq0}x^n[/math] and its known that the formal integral/derivative of a power series have the same radius of convergence as the original

[Anonymous No.14885118]

the meme to end all arguments

[Anonymous No.14885130]

>>14885039
>late 20's
Then forget about it. Just join the college with the hottest bitches, and slay some underaged pussy. NCERT should be enough for your average Indian college. But prepare for master's entrance of these colleges. The master's syllabus is lot more structured and has more canonical books + more time + less competitive.

Or if you need money, then yeah, these are your only options + IISc (but that has a retarded 4 years long course). These all pay you and don't require fees. IISc entrance has a completely different syllabus I think, where you need to study some more Physics, Biology and Chemistry retardation. It's practically JEE. TIFR does not have any bachelor's course. ISI and CMI have the same syllabus I think, but the latter is far more difficult (also is a more difficult course).

I think those books should cover everything except Calculus (for ISI and CMI). I have never studied elementary Calculus (only Real Analysis) nor have I prepared for any undergraduate exam, but I suppose Spivak is what people would recommend for Calculus. You can look for resources online, there are a bunch of books people recommend, aside from those. The most common are:
>Hall and Knight, Algebra.
>Loney, Plane trigonometry.
>Engel, Problem solving strategies.
>Maron, Problems in one variable calculus.
And of course, ISI's TOMATO is the best problem book you can find for these exams.

The main question is how the fuck are you gonna prepare for all these at this age? Preparing for these exams is gonna take a year for a student with free time, given they are already done with NCERT. Don't you have a job or anything, or do you have NEET money covered by your parents? How much time can you invest?

[Anonymous No.14885219]

>>14885130
Thank you for replying. I'm pretty well off actually. We run a family business that I took over 7 years ago. Dad wants me to do an MBA to sound legitimate to prospective brides, but it really doesn't make a difference from business perspective. I on the other hand have always been interested in Math. I was lurking in this threads for weeks now, and it has only raised my curiosity. I'll have a lot of free time, so I want to do it properly.

[Anonymous No.14885242]

If [math]f : [-1; 1[ \to \mathbb{R}[/math] with [math]f : x \to \sum_{k = 1} \frac{x^k}{k}[/math], then what is [math]f'(x)[/math]?

[Anonymous No.14885247]

When [math]f : [-1; 1[ \to \mathbb{R}[/math] with [math]f : x \to \sum_{k = 1} \frac{x^k}{k}[/math], then what is [math]f'(x)[/math]?

[Anonymous No.14885248]

>>14885242
Power series can be differentiated termwise. So
[eqn]f'(x) = \frac{1}{1-x}[/eqn]
for all [math]x \in (-1,1)[/math].

[Anonymous No.14885256]

>>14885248
Why did excluding [math]-1[/math]? The series converges for this value.

[Anonymous No.14885262]

>>14885219
If you have all the time in the world and are truly interested in mathematics, I'd suggest take the long route. You will have a lot less holes in your concepts. I am assuming you are done with NCERT. So first pick a book on proofs like Velleman, How to prove it.
Then move on to Number Theory.
>Long, T.C. (1965). Elementary introduction to number theory. (till chapter 4)
Then theory of equations.
>Barbeau, E.J. (1989). Polynomials.
After this you should do the entirety of:
>Krishnamurthy, V., & Pranesachar C.R. (1996). Challenge and thrill of pre-college mathematics. (very comprehensive)
And I suppose Modak as well. You could do the preceding books simultaneously.

Now you only have Calculus left. I would suggest just watch 3blue1brown's series on it, and jump straight to Real Analysis (although it is a bit overkill for entrance). Real Analysis is basically Calculus but more rigorous.
>Abbott S. (2000). Understanding analysis (till chapter 5)

For entrance, you also do problem books like:
>Engel, A. (1998). Problem solving strategies.
>Fomin, D., Genkin, S., & Itenberg. I. (1996). Mathematical circles (Russian experience).
>TOMATO
And obviously past year papers of ISI and CMI.

These ought to be enough.

>MBA
My faggot dad wants me to do it as well, but I have no interest in business faggotry.

[Anonymous No.14885274]

>>14885262
Thank you for the detailed reply.

[Anonymous No.14885283]

I don't see any point in olympiad stuff. Never did any of that stuff and still am doing just as good as former olympiads as a PhD student. People really overstate the importance of this elementary material. Many mathematicians, like Peter Scholze, I think, even learned math top-to-bottom.

[Anonymous No.14885300]

>>14885283
Olympiads makes it easier to get into top unis, plus you get to know like minded people. You can also get to research faster than others, because you already have a strong base before undergraduate.

[Anonymous No.14885312]

>>14885283
>like Peter Scholze, I think, even learned math top-to-bottom.
What do you mean by that?

[Anonymous No.14885349]

>>14885312
he apparently started with algebraic geometry without even knowing linear algebra, more or less looking up everything he didn't understand. I think he even mentioned never even taking an actual linear algebra course. It's basically starting with a complex topic and filling in the gaps.
>>14885300
I've never had any issues as a non-olympiad where I'm from. Maybe this is the case in 3rd world countries.

[Anonymous No.14885364]

>>14885283
You can be good at math through practice, but reaching the level of Scholze or Green is something you're just born with.
The most hypercope groomed for success you can reach is Tao level, but he still gets mogged by people who just walked into it one day. There will always be someone better, so the value of humility can never be overstated.

[Anonymous No.14885367]

>>14885349
Literally never said you need to Olympiad. I never did Olympiad, but doing it would have given me a head start.

>3rd world countries
Literally the opposite because standards of school mathematics is much higher in 3rd world countries.

[Anonymous No.14885376]

I can't find this anywhere nor do I know if it even exists, but is there an accessible collection of USSR K-12 Kolmogorov method mathematics textbooks?

[Anonymous No.14885404]

me >>14884450
Sorry for the silence

>>14884464
>(x,y) to y + (1/2) * (1 + x/(1 + |x|))
I went with this. You're my savior. Thank you so much

I don't know how you came up with that, but it really does the trick for this video game engine sword trail effect that I came up with. I'm programing the coordinates of a flat plane and the way numbers for the vertices were assigned is basically random, so I had to bring order to the chaos by coming up with a way to order them from the bottom, left to right, to the top and now I have a perfect script that will work no matter how many times I subdivide the plane. Your formula made it possible.

[Anonymous No.14885528]

So I'm in my late 20's and never learned Calculus. Lately I've been wanting to finally try and learn it just to say I did. I've also been thinking about trying to get my Bachelors in CS so there's another reason. My math skills are very, very rusty though and I'm having a hard time trying to relearn mostly everything leading up to Calculus. I've been dicking around with Khan Academy, a couple math YouTubers, and some shitty self study Algebra I & II book but I feel like I have no structure and I'm all over the place...because I am. Does anyone have any recommendations for me on how to be more productive? My main problem is just figuring out how to progress in a logical, linear way to reach my goal. I always end up needing to back track to some forgotten element of elementary math and I feel like I'm not really progressing.

[Anonymous No.14885534]

>>14885528
Can you start a sentence without using a first person pronoun? Do you ever stop talking about yourself?

[Anonymous No.14885650]

>>14885528
From my experience in life, the best way to "be more productive" is to stop worrying about being productive and just put in the work hours in whatever form you're able to at the moment. If you keep learning new things, and put in a reasonable amount of time, you'll eventually reach your goal, whatever it is.

There's not much instant gratification in this field most of the time, you gotta get used to the "slow burn".

[Anonymous No.14885668]

Is it true that if I came up with a solution to one of those 6 unsolvable problems, someone else will instantly steal my work.

[Anonymous No.14885743]

>>14885668
No, you'll have timestamps from when you created it and saved files on google drive or something. Those problems don't mean anything to people outside of math/physics world, so all you get out of it is really a possible tenure track position, if you have the other credentials to qualify.
The million dollar thing first of, isn't a lot of money, and second, it comes with tons of strings attached.

[Anonymous No.14885763]

>>14885743
>comes with tons of strings attached.
Interesting. Such as?

[Anonymous No.14885836]

>>14885256
The limit doesn’t exist at the boundary because it can’t be approached from both sides, so it has no derivative there

[Anonymous No.14885848]

>>14885836
I should specify, f(x) exists at -1 but lim (f(x+h)-f(x))/h doesn’t exist so it’s not differentiable at -1

[Anonymous No.14885940]

>>14885836
It vacuously exists.

[Anonymous No.14885953]

>>14885940
Maybe if your head is vacuous

[Anonymous No.14885984]

>>14880885
[eqn](2x/l)^n+(2y/w)^n+(2z/h)^n=1[/eqn]
what are LWH and n?
xyz=lwh? basis vectors?
each of the areas of the plane would be like
(xy+ xz + yz) * 2
would give 6 faces but why dividing?

[Anonymous No.14886008]

a singularity's location necessarily changes over time so it contains a vector as well

[Anonymous No.14886013]

>>14885984
should maybe also ask here what the function defining a square is?
can i use law of cosines and define angles? is it a projection of the 3d vectors onto their component planes? is it one of the partial derivative of a sphere?

[Anonymous No.14886123]

>>>Brits on the internet are convinced that Americans don't cover proofs of delta-epsilon, Rolle's theorem/Intermediate Value Theorem/Extreme Value Theorem, etc. during first year math courses
Why are they so egotistical? Do they really think that Americans are graduating with a bachelors in mathematics that isn't equivalent to theirs? They always present oxford/cambridge/warwick as examples of what their curriculum is, but get upset when you compare it to MIT, Princeton, Harvard.

[Anonymous No.14886266]

>>14885262
>My faggot dad wants me to do it as well, but I have no interest in business faggotry.
Respect your father. Now.
>>14885283
It's mostly useful and was originally intended for generating interest and giving students encouragement through accomplishment (which you don't get in math otherwise until you're well into your career). As for learning math top-to-bottom, it's possible if you have the talent but most people are better served going the standard way imo.

[Anonymous No.14886590]

[math]|\mathbb{A}| = |\mathbb{N}|[/math]

[Anonymous No.14886621]

>>14879883
Oh shit that's literally me.
>>14879152
>I never did precalculus properly. And now it's coming to fuck me over when doing some Analysis problems
How tf can you study Analysis without having properly covered everything from Precalculus (elementary Algebra and Analytic Geometry) to Calculus I-III?
Don't Calculus books teach partial fraction decomposition methods too?

[Anonymous No.14886643]

Can anyone tell how these are equivalent? [math]F[/math] is a field and t is transcendental. I can see how [math]ad-bc\neq0[/math] implies the conditions, but not the other way around. I can tell this is a stupid question, but it's late and I'm not seeing something...

[Anonymous No.14886659]

>>14886643
"Sharing no positive degree factor" means that at+b is not a multiple of ct+d, in which case at+b = m(ct+d) and so a = mc and b = md. Then ad-bc = 0.

Btw, these are linear-fractional transformations (Mobius transformations) and you can write them as 2x2 matrices, and they're invertible precisely the matrix is invertible, i.e. ad-bc is not 0.

[Anonymous No.14886719]

>>14886659
it's 3am and my brain isn't working (which is why i must be stuck here), can you check my thinking:
we need to show ad-bc!=0 is equivalent to a,c not both 0 AND (at+b.ct+d)=1
if a=c=0 or (at+b,ct+d)!=1, we get ad-bc=0
for the converse, let ad-bc=0. if a=0, then bc=0, so c=0, otherwise u=0\in F, which can't be. if c=0, then ad=0, so a=0, otherwise we'd be dividing by 0, so if ad-bc=0, then a=0 iff c=0. now assume a,c both not 0, then b/a=d/c and if e is either of these, we have at+b=a(x+e) and ct+d=c(x+e), so we have (at+b,ct+d)!=1
is this correct or am i missing something
>>14886659
>Btw, these are linear-fractional transformations (Mobius transformations) and you can write them as 2x2 matrices, and they're invertible precisely the matrix is invertible, i.e. ad-bc is not 0.
yup, i know

[Anonymous No.14886722]

Is there an agreed upon notation for the set of all units in a ring [math]R[/math]? My supervisor uses [math]Units(R)[/math] but I've also seen a textbook that uses [math]R^\times[/math].

[Anonymous No.14886735]

>>14886722
i don't think it's an iron-clad standard, but the one i've seen most commonly by far is [math]R^*[/math]. a professor i had used to denote with [math]R^\times[/math] the set of non-zero elements of [math]R[/math], i.e. according to him [math]R^\times=R\setminus\{0\}[/math]. so in his notation you'd have [math]R[/math] is a field if and only if [math]R^*=R^\times[/math]. this tracks, because in analysis you denote the nonzero reals/complex numbers by [math]\mathbb{R}^\times[/math] and [math]\mathbb{C}^\times[/math]
>My supervisor uses Units(R)
kek

[Anonymous No.14886757]

>>14886621
>Don't Calculus books teach partial fraction decomposition methods too?
Impossible to finish calculus II without it.

[Anonymous No.14887050]

>>14886621
>How tf can you study Analysis without having properly covered everything from Precalculus?
I derive things on the fly. Only brainlets need separate books for precalculus. I never studied Calculus either btw.

[Anonymous No.14887055]

>>14885836
Why are you considering points outside the domain to calculate limit? Are you retarded?

[Anonymous No.14887057]

>>14886266
>Respect your father. Now.
I hope your dad dies in his sleep tonight. Faggot.

[Anonymous No.14887173]

Set Theory Time. Given the following Properties:

\[a + 0 = a \]
\[a + b_+ = (m + n)_+ \]
\[a * 0 = 0 \]
\[a * b_+ = a * b + a\]
and the fact that addition is commutative, prove a * 1 = a

I'm confused on how to do this prove. My first thought was saying 1 is the natural successor to 0, and then going from 0 to 1 algebraically, but I think that's wrong.

[Anonymous No.14887191]

>>14887173
Retrying my latex

[math] a + 0 = a [\math]
[math] a + b_+ = (m + n)_+ [/math]
[math] a * 0 = 0 [\math]
[math] a * b_+ = a * b + a [\math]

[Anonymous No.14887211]

>>14887173
>Doesn't post in /sqt/ instead
>Broken Latex
>Set Theory Time when it's a purely algebraic problem without any sets
Anyways here is the solution so you can leave and not post here again.
[eqn]a * 1 = a * 0_+ = a * 0 + a = 0 + a = a + 0 = a[/eqn]

[Anonymous No.14887327]

>>14887055
Yeah actually I’m retarded

[Anonymous No.14887421]

>>14877114
fpbp
>Verification not required.

[Anonymous No.14887501]

>tell mom I'm running out of notebooks
>she buys me a bunch
>get corona, self study habits break down
>haven't filled a single notebook
how do I get back on the wagon and make her proud? only way I can repay her favor

[Anonymous No.14887610]

>>14887501
>mean value theorem
>tfw no nice value theorem
why do the meanies always win /mg/?

[Anonymous No.14887621]

>>14887610
I didn't mean to reply to you >>14887501, and for some reason i can't delete my post

[Anonymous No.14887690]

>latest edition of cohen's precalc book has no appendix
>uc davis' custom edition based on the latest edition has the appendix with review
lol weird

[Anonymous No.14887713]

bros, someone help me figure this out. i'm reading Keith's note on the existence of algebraic closure https://kconrad.math.uconn.edu/blurbs/galoistheory/algclosure.pdf.. what he does is build an algebraic extension [math]L/K[/math] such that every monic polynomial in [math]K[x][/math] has a root in [math]L[/math]. he then says that we could theoretically iterate this construction and enlarge [math]L[/math] step-by-step until it becomes algebraically closed, but it's actually unnecessary because [math]L[/math] ALREADY IS algebraically closed. to do this, he shows that every irreducible of [math]L[x][/math] divides an irreducible of [math]K[x][/math]. if the latter were to split, the former would too, so the rest of the proof is devoted to showing that what we already know about [math]L/K[/math] implies this (i.e. every irreducible of [math]K[x][/math] with a root in [math]L[/math] actually splits in [math]L[x][/math]). this takes him ~1 page to show
but we already KNOW that [math]L/K[/math] is such that every monic of [math]K[x][/math] has a root in [math]L[/math], doesn't splitting follow from that? that's literally how the Fundamental Theorem of Algebra is used to show [math]\mathbb{C}[/math] is algebraically closed (every complex polynomial has a root in [math]\mathbb{C}[/math], therefore by induction on degree it splits in [math]\mathbb{C}[x][/math]). i assume something must be wrong with this reasoning, otherwise Keith wouldn't waste a whole page proving this proposition, so what am i missing?

[Anonymous No.14887719]

>>14887621
Retarded phone poster

[Anonymous No.14887725]

>>14885836
Then why didn't you exclude [math]\sup \{x\ |\ 0 < x < 1\}[/math]. The same argument is valid for this value.

[Anonymous No.14887757]

>>14885836
>>14885848
>>14885256
a right-sided derivative exists at [math]-1[/math] and it's [math]\frac{1}{2}[/math]
you have that [math]f'(x)=\frac{1}{1-x}=\Big(\log\frac{1}{1-x}\Big)'[/math] on [math](-1,1)[/math]. since their derivatives coincide on an interval (a connected set), you get that [math]f(x)=\log\frac{1}{1-x}[/math] on [math](-1,1)[/math]. the latter is dense in [math][-1,1)[/math] and [math]f[/math] is continuous in [math]-1[/math] (Abel's theorem), so you get [math]f(x)=\log\frac{1}{1-x}[/math] on [math][-1,1)[/math]. the RHS obv. has a derivative in [math]-1[/math], so the LHS has a right-sided derivative there. so in fact you have that [math]f'(x)=\frac{1}{1-x}[/math] on [math][-1,1)[/math]

[Anonymous No.14887759]

>>14887725
what? That is just 1?

[Anonymous No.14887773]

Hey bros, how do you publish a book? I have a bunch of unique differential and difference equations and unique solution methods for them lying around and I originally though of organising them in a manuscript and then analysing it to come up with a new more general theory on solving differential equations that would also hopefully make a lot of the unsolved problems trivial but I didn't get around to actually doing that for a few years plus I don't think the examples I have are sufficient to actually form such a theory, they mearly just hint at it plus I don't actually study mathematics so I just thought of just throwing the equations and the solutions out there in a book. I estimate it wouldn't be more than 50 pages long but it would certainly have previously unsolved and maybe even unimagined differential equatuons, about 20 in number, all original work by me. Is it too short? Should I just come with a couple more to throw in there? Also I have an idea of a general method but so far I have only managed to apply it in one case which is also solvable via traditional methods, should I throw that in there too? I don't think the math I know is capable of further development of this idea

[Anonymous No.14887783]

why didn't people figure out all these things about prime numbers thousands of years ago? it doesn't take computers or anything

[Anonymous No.14887794]

>>14887783
What do you mean by "all these things"?

[Anonymous No.14887803]

>>14887794
I found a book called The New Book of Prime Number Records. The only theorems and knowledge I know of from more than 2000 years ago were basic sounding facts about primes. But there seems to be a more expansive knowledge about them today. But they could have discovered this five thousand years ago.

[Anonymous No.14887812]

>>14887803
I think part of the reason is due to (lack of) notation.
Just look at how long it takes to write out the solution of quadratic equations in Al-Khawarizmi's time.
Having compact notation makes it easier to communicate and work off of each other. And most importantly, it's easier to use pattern recognition. You look at an equation/formula in the compact notation and you can recognize something similar from something else you've seen previously and deduce you could use that result here.

[Anonymous No.14887824]

>>14887812
It could also be the more boring answer of people not having enough time or productivity to be enlightened enough to ask certain questions

[Anonymous No.14887886]

>>14887713
There are far more polynomials in [math]L[x][/math] than there are in [math]K[x][/math]. It's not obvious that if something is true for all elements of the small set [math]K[x][/math] is also true for all elements of the big set [math]L[x][/math].

[Anonymous No.14887905]

>>14887773
Are you in academia? You can discuss it with a professor in Differential Equations and see if it's worth publishing a paper on.

[Anonymous No.14887919]

>>14887886
true, but that wasn't my question. Keith intends to show that all irreducibles of K[x] split in L[x] and because every irreducible of L[x] divides some irreducible of K[x], the fact that L is alg. closed follows. to that end he spends about a page proving this (every irreducible of K[x] splits over L). but we already know by construction that L/K is an extension such that every monic of K[x] has a root in L. wouldn't it automatically follow that every element of K[x] (in particular the irreducible ones) split over L? i'm guessing there must be some fault in my reasoning, but i can't find it

[Anonymous No.14887933]

>>14887905
>Are you in academia?
No
>You can discuss it with a professor
Why would I let that fucker get credit for it?
>publishing a paper on.
But I don't want to publish a paper, I want to write a book. Though it would be quite short. Also I looked over my notes and only approximately 4 of the equations use original methods (the rest use existing but not well known ones in original equations so I assume the may have been solved before). Some of these, I think, only work in the specific equations because of the special form of the equations so they probably aren't that usefull overall. I also saw that I also derived known results using similar methods, for example the general solution to [math]x_{n+1} = rx_n(1-x_n) [/math] when [math] r=4 [/math]
It probably isn't enough to write a book or notable enough to write a paper, though I wouldn't be interested in the latter

[Anonymous No.14887936]

>>14887905
Shut the fuck up worthless talentless PDE kiddie

[Anonymous No.14887947]

>>14887933
There is a very high chance that even if what you have is correct, it is trivial stuff that any student could notice. You don't have enough background to understand how little math you know. This is quite common, but by all means feel free to consider yourself an unsung genius whose ideas are worthy of being "stolen" by a mathematician.

[Anonymous No.14887952]

>>14887933
you could give just a sample and even still you would probably understand it better even if you told him

[Anonymous No.14887955]

>>14887057
NGMI. I think your dad is right about the MBA, since that seems to be the peak of your potential
>>14887773
typeset it and, if you care about it being attributed to you, upload it to github with your name as the username. you're probably not going to get a legit publisher on board without a university behind you (and even then it's hard).

[Anonymous No.14887961]

>>14887936
>PDE's and legit million dollar ideas with wide reaching applications to engineering
>for kiddies

>arguing about which infinity is bigger or if .9999=1, "real" pure math

Insufferable children.

[Anonymous No.14887967]

>>14887961
Worthless talentless college kiddie I'm talking about pure math and highly abstract ideas, not PDEs

You are a worthless talentless trash taking what I wrote in your own context

[Anonymous No.14887969]

>>14887961
You are a worthless talentless little child worthless talentless no intelligence worthless kill yourself I will torture you figuratively for being less intelligent than I am.

[Anonymous No.14887972]

>>14887967
>>14887969
>>14887936
worthless talentless pilled.
when I solve .9999=1, PDE worthless talentless will be sorry for being worthless talentless.

[Anonymous No.14887975]

>>14887947
>consider yourself an unsung genius whose ideas are worthy of being "stolen" by a mathematician.
Literally me btw (pic related)
>trivial stuff that any student could notice
Some of it is, I think
>>14887952
I don't like colaborating anyway. Plus I have a personal feud with the differential equations department in my uni (they don't know about it)
What would I gain out of doing that?
>>14887955
Can't I just go to a book store and tell them to print 5 copies of this book or something?

[Anonymous No.14887986]

>>14887975
>Can't I just go to a book store and tell them to print 5 copies of this book or something?
I mean yeah you could and in fact you can do this all online, the question is why?
Why not post a bit of it here by the way?

[Anonymous No.14887987]

>>14887972
That's literally not what I propose.

You don't even know who I am.

What the fuck are you talking about worthless talentless stupid college child.

You are A FUCKING COLLEGE CHILD.

Nobody who studies pure math cares about your applied bullshit.
The best that you could do with your inferiority was studying calc 1

[Anonymous No.14887989]

>>14887972
You should accept that you are worthless and less intelligent than i am as if we were graded in an exam.

Your grade is smaller than mine.

I will try to abuse you by words and call you names for being inferior

[Anonymous No.14888018]

>>14887986
>the question is why?
I initially kept my ideas secret but since I didn't have enough time to develop them further and I gradually lost the hype to do so, it seems I won't be working on them for a while so there is no point in keeping them secret anymore. Also they are just sitting there being useless. I saw a youtube video of someone writting in latex and making a nice looking pdf so I thought I want to write a book
>Why not post a bit of it here by the way?
I would post the whole thing here as long as it doesn't contain my real name. The real question now is should I put my name on it? If its content is silly then it would be shamefull to bear my name. If it is important what do I gain?
I might just make a "lite" version of it and post it here

[Anonymous No.14888020]

>>14887987
>>14887989
Literally worthless talentless college child.

[Anonymous No.14888021]

ok i’m tired of being lied to redpill me on the dot product

[Jealous No.14888022]

>>14877642
indeed

[Jealous No.14888030]

>>14877642
What is your pic from?

[Anonymous No.14888036]

>>14888018
can you post just a little bit now no matter the format?
>>14888022
>>14888030
you are wasting time posting nobody cares

[Anonymous No.14888042]

>>14877069
Everybody asks what numbers are but they never ask why are numbers? Why are there numbers instead of no numbers? Did we invent numbers or did we discover them? I think once someone tried to answer this questions for me in terms of Rocks and Pianos, but I didn't care about numbers in those days. I only studied computers in those days because I wanted girls to think I was smart because I knew I wasn't going to make a good football player.

[Anonymous No.14888043]

>>14888036
>can you post just a little bit now no matter the format?
Why?

[Anonymous No.14888045]

>>14888043
Nice to have OC for once

[Anonymous No.14888048]

>>14888042
because something at nothing is a point

[Anonymous No.14888055]

>>14888042
>never ask why are numbers
shut the fuck up, retarded troon faggot.

[Anonymous No.14888080]

>>14888045
Well check this out:
https://en.m.wikipedia.org/wiki/Master_theorem_(analysis_of_algorithms)
I understand that for algorithms they care about big O and Theta etc but with my method I know how to find exact solutions to these equations (some involving [math] \Sigma [/math]), even to the ones not covered by the master theorem. I don't understand why they don't just find the exact solution as a proof of the theorem

[Anonymous No.14888084]

learning about induction with mr Lang. do these equations/equivalences in 1, 2, 3 have some kind of name? did people just stumble upon them? are they useful elsewhere or are they like little party tricks?

[Anonymous No.14888087]

can someone explain to me what the proof in pic related accomplishes?

[Anonymous No.14888089]

>>14888080
>I don't understand why they don't just find the exact solution as a proof of the theorem
Because when you have a huge algorithm and you wanna know how bad in general it is, you don't wanna focus too much on the details because it can get out of hand.
Just take what you need.

[Anonymous No.14888093]

>>14888089
I meant getting the exact solution is easier than remembering all the cases of the theorem. Also I've never seen proof of this theorem. Looking it up, it looks like to prove it they do a bunch of other things instead of just solving the equation

[Anonymous No.14888104]

>>14888055
>guy asks math question in math questions thread
>gets called troon instead of an answer
Maybe internet censorship isn't always bad. You added nothing to the conversation and deleting your participation would make this space nicer for the people engaging in the conversation.

[Anonymous No.14888114]

>>14888084
well I don't know if they have names, but they are quite well known closed form solutions. People didn't really stumble onto them, refer to the story of how gauss calculated the sum 1+2+3..+100. (100+1 + 99+2 + 98+3 +...)
Same thing for the square and cube sums.

[Anonymous No.14888118]

>>14888104
>>guy asks math question
It is not a math question.

[Anonymous No.14888133]

Wtf did i just find in the back of Frenkel's book.

[Anonymous No.14888200]

>>14888118
How is it not a math question?

[Anonymous No.14888215]

>>14888133
Art imitating art.

[Anonymous No.14888242]

>timed pop quiz
>"solve the following problems without the use of Green's theorem"

[Anonymous No.14888309]

When you were in high school did you do every single problem in the math textbook? Most teachers only assign half of the problems for homework so I'd assume that if I do all of them I will get good enough at math to do something impactful like become a quant/engineer who actually designs things. Most mistakes in higher math come from inadequacies in skill in the lower levels.
>t.high school dropout who is trying to master maths

[Anonymous No.14888322]

>>14888242
The purpose of the quiz was to prove you are bitch-made.

[Anonymous No.14888327]

>>14888309
>Most mistakes in higher math come from inadequacies in skill in the lower levels
where do you get these opinions about higher math as a highschool dropout? anyways no highschool math is not worth spending a load of time on, do half the exercises or whatever and move on

[Anonymous No.14888343]

>>14888309
They only assign half because the other half is essentially the same problems.

Math up to high school and undergrad calc is just treating students as calculators, it's in no way a representative of what the rest of math (the vast majority of it) is like. A better name to it is "computation" rather than "math".
Math requires creativity. It's not like lifting weights where "if you do the exercises enough you will get better".

[Anonymous No.14888353]

>>14888114
yeah, "Gauss summation" was the example in the chapter, and that one is pretty simple to understand, but I haven't figured out how the others are made up "intuitively"

[Anonymous No.14888386]

>>14888343
That is a poor view of math.
>just treating students as calculators
There is near zero reason to use a calculator during the calculus series, the arithmetic involved is simple.
>it's in no way a representative of what the rest of math
If you aren't a master of the basics of undergraduate calculus, linear and abstract algebra, analysis, you can do nothing at the higher levels. This is beaten in your head so that it become second nature. You do the exercises to build intuition.
You have a very common fart huffing mentality of a midwit. There is a reason the way you think things should be is not how they are taught or structured in universities. Your opinions are nothing, which is equivalent to what you've contributed or actually know about math. Before you go on dismissing and disparaging everything in favor of empty philosophical categories, you should have actually done something to warrant the inflated ego.(I know you haven't)

[Anonymous No.14888433]

>>14888343
>A better name to it is "computation" rather than "math".
Oh yeah, of course.
>"computation, yikes! not real math"
>"Non-representational Qualia!, now that is REAL mathematics :)"

Hey anon, could you solve this trivial computational non-mathematical problem.

[Anonymous No.14888438]

>>14888433
What has this have to do with solving 200 quadratic formula problems with different coefficients in high schools as opposed to only doing half of them?

[Anonymous No.14888439]

>>14877069
Did numbers exist before the big bang?

[Anonymous No.14888444]

>>14888343
I do not understand what point there is in your telling what areas of math you believe are "computation rather than math". You do not seem to be that well versed in them, so we (and you yourself...) should take your judgements of them with a bit of care. Indeed, your argument is more or less based on your not knowing what (what you call) computation is for; do you know what kind of computations are carried out by algebraic number theorists?

[Anonymous No.14888461]

>>14888438
No one is assigned 200 problems on quadratic formulas for home work. There aren't even that many total problems at the end of each section.

If you believe less problems should be assigned to students, you are welcome to perform your own studies and present it to textbook companies so that they can optimize their textbooks to facilitate student learning.

[Anonymous No.14888483]

>>14888439
Did they? What do you think?

[Anonymous No.14888486]

>>14888343
>all the seething highschool/calc teachers in the (you)s
lol

[Anonymous No.14888487]

>>14888439
just one of them

[Anonymous No.14888494]

>>14888386
>There is near zero reason to use a calculator during the calculus series, the arithmetic involved is simple.
Wolfram's a calculator. And that's what the students are treated as.
>If you aren't a master of the basics of undergraduate calculus, linear and abstract algebra, analysis, you can do nothing at the higher levels.
And if you don't know your ABC's, you can't write a novel. Yet writing a novel isn't about ABC's.
And I said "up to undergrad calc", and linear algebra, abstract algebra, and analysissy are already beyond that.
>There is a reason the way you think things should be is not how they are taught or structured in universities
When did I say anything about "how things should be structured", you illiterate moron?

The gist of your post is that you're huffing and puffing about shit I didn't even say.
Rage less.

>>14888433
What, some sort of ellipse in the unit disk under the hyperbolic metric?
Chuck it in Wolfram anyways and have it draw the set.

>>14888444
>do you know what kind of computations are carried out by algebraic number theorists?
I already studied algebraic number theory.
Oh no, tell me about how I don't know what a ramified Galois extension is, oh mighty one.

[Anonymous No.14888508]

>>14888486
It all just sounds like the same mong raging three times.

The funny part is that I'm actually teaching calc this semester. I'm speaking from experience that calc is all computation, because we're literally teaching it with programming.

[Anonymous No.14888528]

>>14888508

>tfw will never learn numerical integration with no proofs in anon's class.

[Anonymous No.14888534]

>>14888528
Both numerical and symbolic.
"Calculators" can do that.

[Anonymous No.14888544]

>>14888084
Faulhaber's formula

[Anonymous No.14888613]

>>14888544
Nice, thank you. Hope you enjoyed your meal and I wish you good night, pal.

[Anonymous No.14888674]

What are some good diff equation textbooks?

[Anonymous No.14888718]

>>14888674
VI Arnold's Ordinary Differential Equations (guessing you mean ODEs)

[Anonymous No.14888761]

>>14888718
Cheers

[Anonymous No.14888792]

how is the anti derivative of acceleration velocity if the derivative of acceleration is velocity

[Anonymous No.14888796]

>>14888792
>if the derivative of acceleration is velocity
You got it backwards.
The derivative of VELOCITY is ACCELERATION.

[Anonymous No.14888823]

>>14885650
Thanks anon, I'll keep grinding away at it!

[Anonymous No.14889102]

>>14886735
Alright, thanks, that was helpful, anon.
>kek
Don't bully my supervisor lel.

[Anonymous No.14889145]

>>14888792
Forgot about those applications. Only took the two required physics courses and nothing more.
Wasn't it velocity -> acceleration ->jerk?