/mg/ - Math General - Integration edition.

[Anonymous No.14521211]

Previously >>14489025.

Talk math.

[Anonymous No.14521591]

>>14521211
Is Category Theory useful?

[Anonymous No.14521593]

Here's a relatively easy problem for /mg/.
Let me know if you tried to solve it but got stuck, I can give tips.

[Anonymous No.14521600]

>>14521591
For turning you into a tranny? yes—it's more effective than HRT and puberty blockers but less effective than computer science and anime. Hope that helps :)

[Anonymous No.14521616]

>>14521591
Category theory is based on the idea that an object is fully characterized by its relation with other objects. For example, if others support your delusion that you're a woman, then you're a woman.

[Anonymous No.14521629]

>>14521593
10

[Anonymous No.14521638]

>>14521593
Let a be the start term, then the sum is na + n(n-1)/2

So let 2na + n(n-1) = 2100, n(2a + n - 1) = 2100
Clearly then n is less than the square root of 2100. By a parity argument n is the number of factors of 2100 less than the square root of 2100, or just half the number of factors of 2100, which is 18.

[Anonymous No.14521642]

>>14521638
Mb, it's 12, forgot to remove factors which 2 divides and 4 doesn't

[Anonymous No.14521717]

>>14521600
>>14521616
That makes sense. Will geometric algebra also turn me into a tranny?

[Anonymous No.14521758]

How do you rate the following rule, morally and aesthetically

[math]A, (A\implies B)\ \vdash\ A\land B[/math]

[Anonymous No.14521763]

>>14521616
I thought category theory was just another 2nd order prop logic / group theory / zfc for dummies?
how could something be fully characterized by their relation with other of the same kind of thing?
Doesn't that mean that every object is just a set of relations, in a way? I can't imagine that would be possible except if relations themselves represented objects that weren't sets of relations.

[Anonymous No.14521766]

>>14521593
Brute forcing this is [math]O(n^2)[/math], you gotta ask for a way higher number before I start thinking about alternative solutions.
>>14521638
>>14521642
Slick.

[Anonymous No.14521772]

https://youtu.be/4CBFUojXoq4

Monthly reminder that the uncountability of the Dedekind reals depends on LEM or countable choice

[Anonymous No.14521774]

>>14521766
>Brute forcing this is [math]O(n^2)[/math]
Actually, no, I can brute force it in [math]O(n)[/math] by reusing the same sum and subtracting terms from the back and adding terms to the front.

[Anonymous No.14521796]

>>14521763
>in a way
I think wanting to formalize this statement of
>determined by "all" its relations
and thus turning the "all" into a predicate or set, takes you up a metalevel and complicates things. Let's not do that.

Anyway, if you take the category where objects are finite sets of naturals, then {1,2,3} and {6,7,8} are in bijection (isomorphic) and the categorical object language judges them "equal" in this way. So applying the category theory tools in that way at least doesn't describe the whole mathematical universe.
But here we presumed the different naturals as distinct standalone objects not coming from our theory.

If you take categories as foundations, then a notion of naturals comes about as arrows in a natural numbers object and here we deal with an arguably different kind of naturals. It's a bit tricky to talk about this since it's hard to characterize the "standard naturals as kids understand them" without invoking a platonic realm pictured as a heaven where numbers are objects floating in space.

[Anonymous No.14521813]

>>14521758
it's a shitty rule because of that motherfucker who wrote Alice in Wonderland, if your "⊢" is the same as "⟹".
otherwise, looks good.

[Anonymous No.14521836]

>>14521813
I don't know the Alice in Wonderland context, although I know the guy was a mathematicisan.

The ⊢ here means it's a rule of inference. X⊢Y means from X we can infer Y, where X and Y are composed of symbols in the object language.
https://en.wikipedia.org/wiki/List_of_rules_of_inference

Meanwhile the implication ⟹ is a part of the object language, i.e. that expresses implication in the language itself.
The thing would probably more pretty if I'd have used \to instead of \implies, since the latter gives that wide kerning.

[Anonymous No.14521840]

or part of rule of inference, the full examples are all more involved

[Anonymous No.14521846]

>>14521836
>I don't know the Alice in Wonderland context
it's pretty neat
http://fair-use.org/mind/1895/04/what-the-tortoise-said-to-achilles
>The ⊢ here means it's a rule of inference.
ah, ok. A new symbol that does a similar job as implication, but means something like "Write this." may help his cute dilemma.

[Anonymous No.14521860]

>>14521629
Wrong! I'm afraid that's wrong.
How did you get it, could you explain?
>>14521638
>>14521642
Correeectooo.
Nice job. Since you understand how to do it for 1050, I think it's fair to ask how to do it for some arbitrary natural number, given you know it's prime decomposition.
You don't have to give a very precise formula or anything . It has to do with its number of factors as you already know.
>>14521766
Well, you can certainly brute force your way through it. Infact I asked this to a discord server and that's how a few went about it. But clearly this isn't what the problem is about. It's not about 1050.

If you want to bruteforce it, go ahead. I don't lose anything but you don't really gain anything either unless you come up a pretty efficient algorithm or something.

[Anonymous No.14521881]

>>14521758
It's trivially true, so who cares?

[Anonymous No.14522011]

I hate statistic so much it's unreal.

[Anonymous No.14522162]

>>14521860
Fun problem

[Anonymous No.14522227]

>>14521758
That’s modus ponens isn’t it? Most fundamental rule in logic.

[Anonymous No.14522236]

>>14522227
Well modus ponens is implied by it if you adopt elimination of the conjunction.

>>14521881
Well all short theorems of propositional logic will be fairly trivial, but the validity depends on the theory.

E.g. in resource logics, stuff liek 'A and A' following from A is not taken for granted.

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

[Anonymous No.14522246]

What's the dual of the free group on n elements? (i.e. Hom(F_n, C*))
I'm talking about the regular free group, not the free abelian group (for which it's trivial).

[Anonymous No.14522258]

>>14522246
Some of you lads are so bad at algebra that you make me look decent, it's amazing.
[math]C^*[/math] is commutative, so any map [math]F_n \to \mathbb{C}^*[/math] factors through the abelianization. What is the abelianization, you might ask? The free abelian group.

[Anonymous No.14522359]

>>14521593
lazy way:
b(b+1) - a(a+1) = 2100
c = b + 1/2, d = a+1/2 -> c^2 - d^2 = 2100
for any factorization n = pq (p,q not necessarily prime), (p+q)^2 - (p-q)^2 = 4*n, so we search for all unique pairs from the factorization 525 = {3,5,5,7} and get {1/525,3/175,5/105,7/75,15/30,21/25} and their obvious swaps, so there are 12 representations

[Anonymous No.14522363]

>>14522236
>E.g. in resource logics, stuff liek 'A and A' following from A is not taken for granted.
I.e. pointless useless mental masturbation. I an declare A => A to be invalid. It wouldn't make me smarter.

[Anonymous No.14522379]

>>14521211
Calc II teacher here, AMA

Supposed to be writing the first exam but I'm on /sci/ instead

[Anonymous No.14522520]

>>14522363
Not really, those can provide the logics for type systems.
For resources, e.g.
https://en.wikipedia.org/wiki/Uniqueness_type

[Anonymous No.14523106]

>>14522379
Why in the world aren't you writing your first exam?

[Anonymous No.14523333]

Basic question
>>14523317

[Anonymous No.14523343]

>>14523333
you sure it's not 10/16 on the right side?

[Anonymous No.14523627]

>>14521763
if you care about foundation, maybe.
if you are a normal person, category theory is just a way to do algebra

[Anonymous No.14523693]

>>14521763
So you just got all your information on an entire subject of math just from memes? You can very easily look up what a category is it’s not that hard

[Anonymous No.14523744]

>>14522379
What do you have to say for yourself?
>>14523661

[Anonymous No.14523751]

>>14521763
>Doesn't that mean that every object is just a set of relations, in a way?
Yeah, that's basically Yoneda's lemma.

[Anonymous No.14523779]

>>14521600
>For turning you into a tranny? yes—it's more effective than HRT and puberty blockers but less effective than computer science and anime. Hope that helps :)
>>14521717
>That makes sense. Will geometric algebra also turn me into a tranny?
>>14521616
>Category theory is based on the idea that an object is fully characterized by its relation with other objects. For example, if others support your delusion that you're a woman, then you're a woman.
>>>/pol/
What is with the tranny paranoia

[Anonymous No.14523789]

>>14523744
I can't really say that isn't true, about 1/3 of the syllabus is just random fucking engineering applications we need to cover, however the fact is 3/4 of my class are engineering students and maybe having a different calculus for pure math students would be nice but that is the audience we need to teach to

[Anonymous No.14523868]

>>14523779
Why did you meme arrow their entire posts?

[Anonymous No.14524106]

check out these foci

[Anonymous No.14524272]

>>14521860
I just tried to bruteforce [math]1050 = \frac{n(n+1)-(n-a)(n-a+1)}{2} [/math] for all values of n and a

[Anonymous No.14524323]

>>14523779
People who’ve had too much /pol/ and it just ruins everything cute for them. Pretty cringe if you ask me because anime is cute and those things are not.

[Anonymous No.14524359]

What are you studying tonight /mg/? Anything interesting?

[Anonymous No.14524474]

>>14524106
Yep...there's nothing eccentric about it.

[Anonymous No.14524487]

>>14524359
I'm knocking out some questions from the text
by C.H. Edwards. Currently on chapter 1, section 4.

[Anonymous No.14524538]

Which areas of math should I study extensively to reach the highest level of theoretical physics? For reference, these two books are about as mathematical as physics gets:
Quantum Fields and Strings: A Course for Mathematicians by Deligne, Etinghof, Freed, Jeffreys, Kazhdan, Morgan, Morrison, and Witten Vol 1+2
https://libgen.rocks/ads.php?md5=CD6403D953AD25A6E66735B02F404313
https://libgen.rocks/ads.php?md5=C0DF19C49289AEAA2635B42A976F3234
From Classical Field Theory to Perturbative Quantum Field Theory by Dütsch
https://libgen.rocks/ads.php?md5=7A214CCA7350182EC3703A72E1B2A72C

[Anonymous No.14524541]

Retard here.
I'm trying to write an expression for the average of the last 4 numbers in a set of numbers.
e.g. 1,2,3,4,5,6,7,8
1/4(5+6+7+8)

What's the best way to show this? Picrel feels wrong, i is the current index (yes, this is comp-sci stuff).

[Anonymous No.14524605]

>>14524541
Keep i as the index and have them go from i = n - 3
to i = n. So, n would be the total amount of numbers
in the list and the fix always gives the last four
numbers in the list.

[Anonymous No.14524615]

>>14521717
Geometric algebra is based

[Anonymous No.14524620]

>>14521796
>it's hard to characterize the "standard naturals as kids understand them" without invoking a platonic realm pictured as a heaven where numbers are objects floating in space
it's easy, just define natural numbers as finite strings of the '|' symbol

[Anonymous No.14524621]

it seems like mathematical platonism pre-supposes quite a lot. "meaning", for example

[Anonymous No.14524625]

>>14521600
you spend too much time on twitter and/or /pol/
as a theoretical computer science phd I have met 1 tranny in my life and they were a number theorist

[Anonymous No.14524643]

why did he do it lads

[Anonymous No.14524649]

>>14521796
>platonic realm
I want this midwit meme to die. Just because a concept is abstract, it doesn't mean it's "platonic".

[Anonymous No.14524650]

>>14524649
indeed, we need a strict and valid construction of that object for us to be sure of its platonic existence. glad we agree anon

[Anonymous No.14524652]

whoa didn't realise feynman was a constructivist. very cool

[Anonymous No.14524653]

>>14524650
>platonic existence
I want this midwit meme to die. Just because a concept is abstract, it doesn't mean it's "platonic".

[Anonymous No.14524657]

>>14524652
Sounds more like an NPC. But then again his IQ was only in the 120 range.

[Anonymous No.14524658]

for some reason we had the only ultrafinitist in the department teaching real analysis and in the third week he had a total mental breakdown while recalling the limit theorem

[Anonymous No.14524660]

>>14524652
he forgot to add
>t. man who created nothing

[Anonymous No.14524706]

>>14524650
If you can construct the object, why is there a need for the object to exist in the platonic realm. Is constructibility not enough? Does it have to "exist" if there's no conscious beings around? I see no need for that.

[Anonymous No.14524718]

>>14524272
And what did you get? How long did it take you?
>>14522162
Well, this is certainly new. It seems alright but you need to give me a number. It's very simple, you don't need to split into cases for one. But uh, yeah, you can easily find the number by hand. And it has quite an easy calculation for all natural numbers, not just 1050, provided you can factorize it into prime powers.

[Anonymous No.14524724]

>>14521758
Morally wrong but so convenient.

[Anonymous No.14524800]

How to solve this?

I just can't into questions like this that say given <log equation> show that <log equation>. My professor got mad that my class couldn't solve questions like this and told us that he would include a lot of questions like this in the finals. How can I git gud and solve this kinds of questions? I think he's trying to fail us. Pls help.

[Anonymous No.14524816]

>>14524800
GTFO brainlet

[Anonymous No.14524857]

>>14524816

[Anonymous No.14524870]

>>14524800
>>14524857
>I just can't into questions like this
Get some middle school math textbooks and do some e-log-problems. Even the problem in your pic just boils down to applying exp to both sides and doing simple algebra, stuff like e^(log a + log b)=e^log a * e^log b =a*b. Or that e^ab=(e^a)^b, etc.

[Anonymous No.14524872]

thoughts? https://www.youtube.com/watch?v=xgsc7stSoUw

[Anonymous No.14524879]

>>14524657
only statlets believe in IQ

[Anonymous No.14524891]

how much of this physics babble is comprehensible to you mathematicians?

[Anonymous No.14524910]

>>14524879
If you reject IQ then please show me an 80 IQ brainlet who cannot rotate a cube in his head but who is also good enough at math to prove h-cobordism theorem.

[Anonymous No.14525152]

>>14523779
Anime tranny is the best poster.
Is she back yet? I hope she is doing well.

[Anonymous No.14525314]

>>14521211
do any of you have access to the proceedings of the london mathematical society, and if so can you get me this pdf
https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/plms/s3-23.3.532

[Anonymous No.14525351]

>>14525314
scihub/libgen

[Anonymous No.14525445]

>>14525314
I managed to find open access to this year's first issue
on one of the articles:
https://londmathsoc.onlinelibrary.wiley.com/toc/1460244x/2022/124/1

Past years can be found here:
https://londmathsoc.onlinelibrary.wiley.com/loi/1460244x

Other than that, >>14525351 could have those
journals there...nothing too current of course.

[Anonymous No.14525491]

>>14524800
Here you go, I wrote down every step. I think it's correct. In the exam, you probably won't have to do that and can be more practical. As for how you know what to do, you just kinda follow the rules you know for log. The answer will show itself in all likelihood. Let me know if I made a mistake or something is unclear.

[Anonymous No.14525492]

>>14524541
You mean like a trimmed mean sort of? I'd write it as a matrix personally or do as >>14524605 said and right it as a sum from n-3 to n.

[Anonymous No.14525521]

>>14524891
Not much of it, but I don't really use math like that anymore. The amount of times you need to use math like that is pretty small, so I normally just outsource the work to a university physics professor. They LOVE working on it and I make sure to give them plenty of credit while my organization praises the hell out of me. They aren't even expensive to hire either.

I mainly do it for complicated magnetic field problems because of the nature of my work, but it's all the same. From my perspective, problems of this nature are pretty rare and for their rarity there are actually more than enough people capable of working on them. I'm not saying the skill set is common or anything, just that these problems are rarer than the Physicists capable of solving them.

>t. Applied 'Mathematician' for the Navy

[Anonymous No.14525571]

>14 week summer calcII course is really an 8 week calc II course with the remaining 4 weeks being differential equations and linear algebra
>week 3, Hydrostatic force and volumes of revolution on irregular shapes and their general forms
>still trying to keep up with trig substitution inside partial fractions from last week.
JUST
FUCKING

[Anonymous No.14525577]

>>14525445
>>14525351
thank you, i got it. it's available on scihub

[Anonymous No.14525606]

>>14525492
>I’d write it as a matrix
Nigga it’s adding 4 numbers and dividing by 4

[Anonymous No.14525652]

>>14524891
can you tell us where that is from? looks like a pretty interesting and fairly advanced qft/mathphys course and i would like to see more

[Anonymous No.14525679]

>>14524891
While this uses some terminology from physics, it's mostly DG with some variational calculus and some functional analysis. I wonder what kind of exam this is, cause I doubt that students are expected to solve this properly in a few hours.

[Anonymous No.14525810]

is this normal first year uni calculus stuff or am i a brainlet? i've been going over my notes for ages and it still doesn't make sense to me. i'm getting filtered so hard by ODEs

[Anonymous No.14525822]

>>14525810
My dad told me math is a lot harder in college than it was 20 years ago. The new normal is programs geared for international superstar students on US Visas.

[Anonymous No.14525828]

>>14525810
Yes, this is trivial.

[Anonymous No.14526233]

>>14525810
This is highschool maths

[Anonymous No.14526240]

>>14525810
laplace transforms, i learnt them (taught myself) at 14, this is like a 2 mark question on my exams this year

[Anonymous No.14526311]

What does a Graduate Math Syllabus look like ? I know it depends on what you want to specialize in but I want to know the core even though I have a particular interest in Analytic number theory and partial differential equations.

[Anonymous No.14526323]

if the slope is rise over run, then can we call run over rise the lateralness or something else? if you call it the inverse slope you are a wordlet and need not reply.

[Anonymous No.14526383]

>>14525810
it's first semester DE stuff but hyperbolic notation is child abuse

[Anonymous No.14526610]

is the quality of ahlfors contingent on the edition? graduate who never took the heavy course for complex analysis and does weird number theoretic stuff posting

[Anonymous No.14526688]

>>14525571
Its not possible to actually learn in that course. I had a A and didn't actually learn anything until analysis.

[newfag No.14526699]

>>14522363
>I.e. pointless useless mental masturbation.
do you know what thread you're in? retard

[newfag No.14526730]

>>14521758
morally correct but aesthetically degenerate

[Anonymous No.14526767]

Do I need the well-ordering principle to prove the principle of induction?

[Anonymous No.14526773]

>>14521211
Need to learn about groups when considering matrices, jus got btfo in my discrete maths assignment. Theres not even a groups sections in my Discrete Mathematics with Applications - Epp,Susanna book...

[Anonymous No.14526984]

>>14526773
isn't that just Z3*?

[Anonymous No.14527025]

>>14524538
pls dont ignore me. I just dont want to turn into a physishit who's too retarded for math.

[Anonymous No.14527032]

So how should one go about reading math books? Do you read through them linearly? Or read/do what interests you and the rest once it interests you? I've thought about maybe just continuing with the next chapter in case I'm stuck at like #25 of Chapter 1's 50 exercises and do the rest while progressing. I feel like this could prevent burnout. Basically just doing it all, reading and working through problems, incrementally.

[Anonymous No.14527038]

>>14526984
idk one of the questions was {h}
is a subgroup of (O(2, R), ·) which is isomorphic to (Z4, +).
had just to spit the definition of subgroups back at them ...

[Anonymous No.14527052]

>>14527038
>1*1 = 1, 1*2 = 2, 2*1 = 2, 2*2 = 1
what gets me is when the groups all seem equally significant then something like A5 comes back to bite you months later

[Anonymous No.14527053]

Serge Lang's "Algebra" arrives tomorrow, what am I in for?

[Anonymous No.14527154]

>what if a mod m
>now what if z1 mod z2 where z1 and z2 are gaussian integers
>later what if z1 mod z2 where z1 and z2 are in the ring of integers of a weirder quadratic number field
i don't like it

[Anonymous No.14527170]

>>14526323
Rise over run = tangent = slope
Run over rise = cotangent = coslope

[Anonymous No.14527183]

>>14526773
>zoomers literally need to learn math with emojis because else their ADHD doesn't allow them to concentrate for more than 3 minutes
The absolute state of modern math education, lmao

[Anonymous No.14527186]

>>14526323
the spook
it prioritizes running over rising (to the top of the class) while a slope does the opposite
you asked for this

[Anonymous No.14527206]

>>14527183
I think it’s more on the professors trying to be cool. Every time I’ve seen a professor teach with emojis the students just get annoyed

[Anonymous No.14527223]

>>14526984
Z/2Z. Lion is 0, tiger is 1 and bear is +. Alternatively, 1, -1 and multiplication.

[Anonymous No.14527229]

>>14527223
Z/2Z is a ring, not a group
Z3* is >>14527052 and your alternate

[Anonymous No.14527247]

>>14527229
there doesn't exist a ring which isn't a group

[Anonymous No.14527312]

>>14527229
Lol retard seriously rings are abelian groups with extra monoid shit

[Anonymous No.14527315]

>>14527025
physicists are higher iq and more productive than mathematicians. if you are good at what you do they will kneel before you, always.

[Anonymous No.14527361]

>>14527315
This. Theoretical physics absolutely BTFO's pure math in terms of IQ needed

[Anonymous No.14527379]

>>14524910
IQ's correlation is non-linear. Effective for identifying mental retardation, that's all. In any case, here's someone without a brain and an IQ of 126

[Anonymous No.14527392]

>>14527229
>Z/2Z is a ring, not a group
Lmao. This is what happens when zoomers learn math with emojis.

[Anonymous No.14527409]

>>14527379
126 is midwit. As someone with IQ 160+ I can clearly say that talking to a 126 midwit feels to me the same way it feels for a 126 midwit talking to an 80 IQ retard.

[Anonymous No.14527597]

>>14524359
Just doing some statistics homework.

[Anonymous No.14527601]

>>14525571
Don't worry, you'll learn how to integrate and derivate in analysis. Anything before analysis is just a filler.

[Anonymous No.14528224]

>>14527247
>>14527312
>>14527392
>it's fine to call it a group because the group operation yields the same results
midwit move to assume the ring operation exists

[Anonymous No.14528242]

>>14524538
Linear Algebra, basic Group Theory, basic ODEs and PDES, basic Topology, Real Analysis (inlc some measure and probability theory), Complex Analysis, Fourier Analysis and Analysis on Manifolds are the basics.
Symmplectic geometry for classical mechanics,
Riemannian geometry for GR,
Functional Analysis and Representation theory for QM,
Differential Geometry and Gauge theory for QFT,
PDEs for fluid dynamics...
I could go one and go one: there are hardly any fields of math that arent used by some sub field of theoretic physics

[Anonymous No.14528676]

What is the most important sequence in combinatorics? Catalan numbers?

[Anonymous No.14528845]

>>14528224
It’s fine to call it a group because it simply is a group you fucking moron

[Anonymous No.14528883]

>>14527229
>Z/2Z is a ring, not a group
Actually, [math]\mathbb{Z}_2[/math] is a graded ring. You can't just call it a ring and assume that the gradation exists.

[Anonymous No.14528900]

>>14528883
i call it a ring and assume the gradation doesn't exist, there's no issue here
>>14528845
does the example have a second closed arithmetic operation? if not, it's not Z2

[Anonymous No.14528915]

>>14528242
Not him, but if you want to list more feel free
>Functional Analysis and Representation theory for QM
>PDEs for fluid dynamics...
Book rec for these two?

[Anonymous No.14528951]

>>14527229
Z/2Z is a field not a ring

[Anonymous No.14529013]

>>14528951
a field is a ring

[Anonymous No.14529024]

>>14529013
midwit move to assume division exists

[Anonymous No.14529036]

Okay faggots
1. Go to http://simpde.infinityfreeapp.com/
2. Find a cool looking PDE
3. Dump your Settings JSON (scroll down on the right) so we can try it out:
Example:
{
"laplacian": 1,
"cubic": 1,
"identity": 1,
"derivative": 1,
"noise": 3,
"defaultLaplacian": 40,
"defaultCubic": 1,
"defaultIdentity": 0.2,
"defaultDerivative": 0.3,
"defaultNoise": 2,
"inputStrength": 5,
"inputRadius": 30,
"colorSensitivity": 50,
"colorMixRatio": 0.13,
"colorCap": 0.98,
"colorPattern": 0,
"scaleX": 1,
"scaleY": 1,
"scaleT": 0.01,
"maxVal": 100000,
"speed": 3,
"delay": 6,
"boundaryCondition": 1,
"useCustomEquation": true,
"equation": "u_tt = abs(cos(0.1*x)) * u_laplace * Delta_u \n - u_cubic * u * u * u \n + 0.01 * sign(u) * sqrt(abs(u))\n - u_derivative * u_t\n + u_noise * noise \n",
"defaultEquation": "u_tt = u_laplace * Delta_u \n - u_identity * u \n - u_derivative * u_t \n - u_cubic * u * u * u \n + u_noise * noise \n",
"displayedQuantity": "u",
"initialDataFunction": "(x,y) => [0.0,0.0]"
}

[Anonymous No.14529042]

For [math] \Delta=(2\pi)^{12}\eta^{24} [/math] i get that both sides are cusp forms of weight 12 but how does that imply they are proportional and where does that constant factor really come from?

[Anonymous No.14529050]

Help a brainlet out, how do I solve this type of question:

A man drives 60 miles per hour for 40 minutes. The man stops and heads back to the starting point, this time 40 miles per hour. How long does the man's car ride take?

T. Haven't done math in a decade, I feel like this should be fucking easy, but I just can't...

[Anonymous No.14529073]

>>14529024
??? yes i assume division exists its a field u retard i.e. precisely a commutative division ring

[Anonymous No.14529079]

>>14529050
What have you tried?
First of all, what is an hour? It's a useless word. Convert it to something appropriate.
How do these then compare? Is one, like, seven times bigger than the other? How about 125% bigger? (you understand percentages?)

[Anonymous No.14529087]

>>14529050
drive 60 down a road for 40 minutes. Time yourself. Then go back going 40. Time how long it takes you.

[Anonymous No.14529088]

>>14529050
60 miles per hour is a mile a minute, he drove for 40 minutes so he traveled 40 miles. He now needs to travel back 40 miles, and he’s doing so at 40 miles per hour, so it will take him one hour

[Anonymous No.14529094]

>>14529079
>>14529087
Nvm, it's 100 minutes. I had some retarded numbers on a similar task and the task was to done without calculator, it made no sense since the retarded decimals would be impossible for an average brainlet without calculator. Got me confused.

[Anonymous No.14529247]

>>14528915
Reed and Simon for FA, Hall for Representation Theory. Follands Abstract Harmonic Analysis is also good for stuff like that, and his QFT book is good as well imo.
For PDEs, I like Evans, but I am not sure if the application to physics is as natural as with the other ones.
In general, there are also a tons of connection between string theory and algebraic geometry and modular forms (mirror symmetry, moonshine), but i am less knowledgable of them. Microlocal analysis is another obvious topic that has direct use in QFT, stochastic calculus is obviously connected to physics (i.e. brownian motion), algebraic topology and topological solid state is a very modern and trendy connection and theres probably more that i dont know

[Anonymous No.14529248]

>>14525606
Yeah, but writing it as a matrix or at least in matrix form is preferable imo.
Studying Sx where S is a matrix and x the vector of observations is much easier and to me more fundamental than a summation.

[Anonymous No.14529284]

>>14529050
>>14529094
It would help if you knew how far the man went in the car. How would you calculate that? With that answer, how can you find out how long it was?

[Anonymous No.14529288]

>>14529024
i see you shadow man

[Anonymous No.14529293]

>>14529088
the ride takes 100 minutes because he goes there and back
read the problem closer next time

[Anonymous No.14529418]

>>14529042
Δ has no zeros except a simple one at the cusp, which means [math]\eta^{24}/\Delta[/math] is holomorphic and bounded at the cusp -- a modular form of weight zero, which must be a constant. Then you just pick some nice point to compute the constant.

[Anonymous No.14529613]

so tell me lads, are there any hot ladies in the platonic realm?

[Anonymous No.14530009]

>>14529418
Thank you very much, for some reason i had it stuck in my head that the quotient form you mention was merely meromorphic and thus Liouville theorom didnt apply. im doing something related to the j-invariant and so i hear weight 0 and think modular function ig.

[Anonymous No.14530152]

>>14521211
Doing some material science stuff, my professor wants me to find all planes perpendicular to the (1 1 0) plane. Is (1 1 0) perpendicular to (0 0 0)? Or does (0 0 0) not count as a plane?

I know its just the dot product of the two planes = 0 so (0 0 1), (1 -1 1), (-1 1 1) , (0 0 -1), (1 -1 -1), (-1 1 -1), (1 -1 0), and (-1 1 0) are solutions, but I'm not sure if (0 0 0) counts.

[Anonymous No.14530160]

>>14521616
>Category theory is based
Indeed

[Anonymous No.14530272]

Would Project Euler be a good way to up my math and programming skills at the same time?

[Anonymous No.14530314]

If you don't have a PhD by 24 why do you browse /mg/ anymore ? It's clear that you're NGMI

[Anonymous No.14530319]

>>14530314
>implying /mg/ is not for NGMIs

[Anonymous No.14530324]

>>14530314
I will never do a PhD because I reject the anti-intellectual atmosphere in acadummia. Autodidact master race.

[Anonymous No.14530419]

Math anons. Give it to me straight. How do you remember everything? I'd forget a sizable amount if I don't study/revise for a significant amount of time (~1 year) Is there a trick to remembering all the math you learn? Although I've found that it's easier to relearn stuff.

I finished khan academy recall (as the wiki said), but found that I couldn't do some problems in my precalc class intuitively. KA exposed me to a specific set of problems, but I struggled with different questions. Even if I knew the rules/ laws knowing how or when to apply them took a lot of practice. Is this normal?

Can you recommend good precalc books that thoroughly cover the topic and have hard question sets. I can do question sets from KA and Stewarts Precalc, but struggle with some hard questions that my prof gives.

Was a neet for 6 years and learned enough math to go to college and am getting ~B tier grades thanks to help from /sci/.

[Anonymous No.14530961]

I'm solving an RA question and it asks me to prove that a surjective, strictly increasing real function f: U -> V is continuous.
I don't see why the "strictly increasing" part is relevant, couldn't you prove that a surjective function cannot be discontinuous as, since the function is defined at every point of its codomain, V, the neighborhood (whose points belong to V) of any point that belongs to V is defined under f and has a corresponding inverse image.
Isn't this sufficient to deduce continuity, that a function is defined at every point in its real codomain and domain so that a corresponding delta could always be found?

[Anonymous No.14530966]

>>14530961
nvm I think it's because the function must be injective within the given interval, something that strict increasingness guarantees.
Would my statement be true if I replaced surjective with bijective?

[Anonymous No.14531008]

>>14530419
the trick is to not worry about remembering everything. i still have to look up definitions and precise statements all the time.
math isnt about how much you know its about what you do.

[Anonymous No.14531043]

Let K be a compact of a normed space and [math] (x_n) [/math] a series in K such that [math] ||x_n - x_(n+1)|| \rightarrow_(n -> /infty) 0 [/math]. Show that the closure of [math] x_n [/math] can't be written as a disjoint union of two closed subsets.

I tried this but blocked. I just have the intuition that the closure is a closed set and that for every element in the closure there exist a series converging to it so the fact they are disjoint already poses a problem I guess ?

[Anonymous No.14531049]

>>14531043
[math] ||x_n - x_(n+1)|| \rightarrow 0 [/math]

I meant ^^

[Anonymous No.14531083]

>>14531043
This statement seems to be wrong. Error in translation or did you miss to tell us an additional constraint?

[Anonymous No.14531096]

>>14530961
f(x) = x on the rationals, and -x on the non-rational reals
This function is surjective and nowhere continuous except at 0.

[Anonymous No.14531118]

>>14531083
[math] x_n [\math] is a sequence not a series
[math] || x_n - x_{n+1}|| \rightarrow 0[/math] is the condition.
Same question :show that the closure of [math] x_n [/math] can't be written as a union of two disjoint non null closed sets.

[Anonymous No.14531124]

>>14531043
>>14531118
It's still false.
Just screenshot the fucking problem.

[Anonymous No.14531136]

>>14531118
>>14531124
Actually what do you mean "non null"?
You didn't mention it earlier so I assume it's "non empty".

[Anonymous No.14531138]

>>14531124
Can you show why it's false ? If not stick to anime

[Anonymous No.14531152]

>>14531138
Sure can.
The normed vector space is [math]\mathbb{R}[/math].
[math]K = [-1, 1][/math].
[math]x_n = 1/n[/math].
The closure is [math]\{ 1/n : n \in \mathbb{N} \} \cup \{ 0 \}[/math], which can be expresses as [math]( \{ 1/n : n \in \mathbb{N} \land n > 1 \} \cup \{ 0 \} ) \cup \{ 1 \}[/math], two closed non-empty sets.

[Anonymous No.14531200]

>>14531152
Ok, my error. It's not the closure of [math] x_n [\math] but the set of limit points of [math] x_n [\math]

[Anonymous No.14531209]

This was fun!

[Anonymous No.14531216]

>>14531200
Right.
Assume the set of limit points can be written as [math]A \cup B[/math], where [math]A[/math] and [math]B[/math] are both closed non-empty. The distance between the two sets needs to be larger than zero: [math]d(A, B) > 0[/math]. The limit condition on [math]\| x_{n + 1} - x_n \|[/math] implies then that infinitely of the points in the sequence aren't in either set (because they're in the traversal, and the traversal can't be done in a single step). Then you can slap the equivalence between compactness and sequential compactness for metric spaces onto the problem to obtain limit points outside of [math]A, B[/math].

[Anonymous No.14531241]

Can someone describe Stewart Calculus? I have 'Early Transcendentals' and it's a really clunky book. Or is it just me? It's thorough, especially in it's intent. "Understanding." Where is this book used? I'm having a rough time with getting correct answers. Like, I have to keep retracing my steps and paving new ways forward. I do really like it and would recommend it though.

[Anonymous No.14531263]

>>14530961
The definition of continuous is that the preimage of every open set is open. You seem to be acting as if the definition is “the preimage of every open set exists” but that’s just always true

[Anonymous No.14531276]

>>14531216
>implies then that infinitely of the points in the sequence aren't in either se
why not stop the proof here ?

[Anonymous No.14531351]

>>14530961
The actual proof goes something like this. Let x be in R, and let epsilon >0. By surjectivity, there exist some points a,b in R such that f(a)=f(x)-epsilon, and f(b)=f(x)+epsilon.
Since epsilon is positive, we have
f(x)-epsilon<f(x)<f(x)+epsilon so
f(a)<f(x)<f(b) so
a<x<b
(strictly increasing means a<x implies f(a)<f(x), but here I used the reverse implication, you should prove why you can do this)
Now let delta=min( x-a, b-x).
Now use strictly increasing to fill out the rest of the proof

[Anonymous No.14531372]

So I just got Lang's Algebra but I guess I should read something like Halmos's Naive Set Theory as a prerequisite? Or just jump straight into it? §1 alone took a bit of time for me to fully understand, is that normal or should I read something else before going through it?

[Anonymous No.14531481]

>>14531276
>why not stop the proof here ?
Completeness.
Also because there's a minor issue with the way I posted it and I wanted to leave anon a hint.

[Anonymous No.14531594]

>>14524359
Refreshing on ring theory to start up commutative algebra (Hungerford, Lang, Matsumura). Then Hartshrone.

Also reading singular homology by Massey and when time permits Holdel's logic.

[Anonymous No.14531777]

>>14531209
>a+x-b-y mod 5 = (a-b)+(x-y) mod 5 = (0)+(0) mod 5 = 0
>ax - by = ax + (a+x) - by - (b+y) + (1-1) = (a+1)(x+1) - (b+1)(y+1), repeat until ax - by = (a-a)(x-a) - (b-a)(y-a) = (0) - (0) = 0
here, done

[Anonymous No.14531846]

>>14521763

from what I have read, the meaning of this statement is that you can understand all the properties of one mathematical object using another mathematical object.

For example, to understand a smooth manifold, suppose you want to know what is the manifold's curvature, you use a function that map R to the manifold, then you get a path on the manifold, then you calculate the magnitude of derivative of the unit tangent vector along the path and now you know the curvature of the manifold.

[Anonymous No.14531864]

>>14531777
Nice, also nice digits. Think I've got a similar thing for the first row, but I did the ax - by part differently. I don't quite understand your solution for that one, but I'll take some more good looks at it with a fresher head later.

[Anonymous No.14531964]

>>14531864
ax - by + 0 = ax - by + (a + x - b - y [by result (1)] +1 - 1)
if ax - by = (a+1)(x+1) - (b+1)(y+1), then it's equal to any (a+k)(x+k) - (b+k)(y+k), setting k = -a is acceptable because the inverse of a is guaranteed and the group is cyclic

[Anonymous No.14532032]

i'm calculating the expectation and variance of the random sum [math]\sum_{i=1}^NX_i[/math], where the [math]X_i[/math] are IID exponential with parameter [math]\lambda[/math] and [math]N[/math] is Poisson with parameter [math]\mu[/math] independently from the [math]X_i[/math]. the expectation i get is [math]E[N]\cdot E[X_1][/math], while the variance is [math]\frac{2\mu(\mu+1)}{\lambda^2}[/math]
does this look right? i'm pretty sure on the expectation, but not 100% on the variance

[Anonymous No.14532035]

>>14532032
yeah, and the variance is essentially [math]E[N^2]\cdot E{X_1^2}[/math]

[Anonymous No.14532093]

>>14531481
Another one. Show that if [math] u_n [/math] is a sequence in [math] \mathbb{R} [/math] such that [math] \sum u_n[/math] diverges show that there exists
a sequence [math] a_n [/math] that converges to zero such that [math] \sum u_n a_n [/math] still diverges.
My solution :
Since [math] \exists \space n_0 \in \mathbb{N}, \space \forall n \in \mathbb{N} \space n \geq n_0 \space \exists \space k \in \mathbb{R} \space[/math] such that [math] u_n \geq \frac{1}{kn} [/math]
thus [math] \exists \space \epsilon [/math] such that [math] u_n \sim \frac{1}{kn^{1-\epsilon}} \implies u_n \sim \frac{n^{\epsilon}}{kn} [/math] thus [math] n^{\epsilon}u_n \sim \frac{1}{kn} \rightarrow \infty[/math]

[Anonymous No.14532161]

>>14532093
>if a series diverges it's eventually larger than a multiple of the harmonic series
Don't think so. Unless I'm misinterpreting your first line.
There's probably a slick solution. Like [math]a_n = 1/ \sum_{k = 1}^n u_k[/math] or something similar.
Actually, check if what I just posted works.

[Anonymous No.14532162]

>>14532093
You might something, but the proof is full of false statements. For the first line, the ∃k is in the wrong place: the statement is almost meaningless, since k can depend on n.
Second, consider [math]u_n=\frac{1}{n\log n}[/math], then there is no epsilon, k so that [math]u_n\sim k^{-1}n^{\varepsilon-1}[/math].
Lastly, [math]\frac{1}{kn}\to0[/math], not infinity.

[Anonymous No.14532271]

>>14532161
Update: sudden inspiration.
That works, but the slickest solution is [math]a_n = \sqrt{1/ \sum_{k = 1}^n u_k}[/math]
Since [math]\sum_{n = 1}^N a_n u_n = \sum_{n = 1}^N u_n \sqrt{1 / \sum_{k = 1}^n u_k} \geq
\sum_{n = 1}^N u_n \sqrt{1 / \sum_{k = 1}^N u_k} = \sqrt{\sum_{n = 1}^N u_k}[/math]

[Anonymous No.14532344]

>>14532271
I see. How do I get to "see" tricks like this ? The provided solution is similar to yours
Let [math] S_n = \sum_{p = 1}^{n} u_p [/math]
take [math] a_n = \frac{1}{\sqrt{S_n} + \sqrt{S_{n-1}}} [/math]

[Anonymous No.14532367]

>>14532344
>I see. How do I get to "see" tricks like this ?
In this case I guessed, then I guessed again.
I think your book's author came to >>14532271 but wanted to allow [math]u_n \leq 0[/math] (in my head I was assuming we just zeroed all of those so they didn't matter), so he added the second term to the fraction.

[Anonymous No.14532476]

I have three hours to study sequences, series and topology. Should I just give up on Analysis for now and chill? It's clearly impossible...

[Anonymous No.14532858]

https://archive.org/details/mathematicalprob00wolsrich
if you have an undergraduate degree you should be able to solve these

[Anonymous No.14533288]

>>14524615
QRD?

[Anonymous No.14533766]

>>14521211
I am just about to graduate from a mechatronic engineering and comp-sci double major and I am definitely rusty on hand solving maths since we've done everything on computers for the last few years.

I honestly should have just studied math, I enjoy it more than the subjects I have just dedicated years to, oh well.

I'm thinking of running back through some of the math content I covered earlier on after I finish this last semester.

I'm thinking of working through 'All the Math you Missed' by Thomas A. Garrity, anyone know if this is a good book for recapping the shit I've now kind of forgotten?

>>14532858
Might save this and come back to see if you're right.

>>14530152
This was me too, still curious if anyone knows the answer.

[Anonymous No.14533821]

>starts exam
>tough problem
>get frustrated
>eventually figure it out
>dopamine hit
>finish problem
>look closer at earlier work
>forgot the negative
>mfw I have to do it all over again

i hate women so much it's unreal

[Anonymous No.14534097]

Is this the place to ask questions about mathematics?

In this task im supposed to determine the x-values between the interval of 0 to 4 pi. I need to give the solution in dg and rad.

Sin(x) = 0,46947
>28 dg
>0,15 pi
So far so good
for the next intervall id say its
208dg (180+28) but the solution says its 152dg (180-28)
for 2pi its again: 388dg (360+28)
and 3 pi is: 512dg (360+180-28)
Why do i remove 28dg on 1pi and 3pi?
Its hard to write about maths in english, so please excuse my retardation.

[Anonymous No.14534203]

>>14534097
It's not true that [math]\sin(x)=\sin(x+180^\circ)[/math], but instead [math]\sin(x)=\sin(180^\circ-x) = -\sin(x+180^\circ)[/math].

[Anonymous No.14534229]

This one had me stumped for a bit and then I figured it out. What's the name of a proof like this where you go through every possible case to show something only happens in one case, so that you can "go both ways" afterwards?

[Anonymous No.14534243]

>>14534229
>What's the name of a proof like this where you go through every possible case to show something only happens in one case, so that you can "go both ways" afterwards?
When you say ", so that", are you saying the first part (checking cases) is required to show the converse?

[Anonymous No.14534270]

>>14534243
Yeah, you check the three possible cases a, b, c, and determine A is only true for a, and then you can say if A is true, then the case falls under a.

I'm probably not explaining it in the best possible way, but that's why I'm trying to pick up the vocabulary by asking a question.

[Anonymous No.14534278]

>>14534270
You're not correct if you think that
>if A is true, then the case falls under a
is required to answer the question.

The "axiom" that every integer is represented in either of the three cases (a, b and c) just changes the scope of the question. It then remains to show that A holds for all those cases a, b and c. (Note that A is of the form X=>Y, so A also holds for a case in which X is false.)
There is no going back to the cases from A.

[Anonymous No.14534282]

To be more explicit
A(n)
is
X(n) => Y(n)
where
X(n) := n^2 is divisible by 3
and
Y(n) := n is divisible by 3

You need to show that A holds for all n.
And the first sentence just says that you really only need to show the three more specific propositions
A(3k) for all k
A(3k+1) for all k
A(3k+2) for all k

[Anonymous No.14534395]

>>14534229
Name of the book ?
My Solution :
Suppose that every positive integer [math] p [/math] can be written as [math] 3k [/math], [math] 3k +1 [/math] or [math] 3k + 2[/math].
Then if [math] p = 3k [/math] it's trivially divisible by 3
If [math] p = 3k + 1 [/math] then [math] p^2 = 3k' = 9k^2 + 6k + 1 = 9k^2 + 3k + (3k+1)[/math]. Thus [math] 3k + 1 = 3k' - 9k^2 -3k [/math]. So divisible by 3
If [math] p = 3k +2 [/math] then [math]p^2 = 3k' = 9k^2 + 12k + 4 = 9k^2 + 6k + 2(3k+2) [/math] Thus [math] 2(3k+2) = 3k' - 9k^2 - 6k[/math]. But 3 does not divide 2. Thus it divides [math] 3k + 2[/math]

[Anonymous No.14534435]

>>14534229
It's called proof by exhaustion
Also 君は頭がよくない

[Anonymous No.14534440]

>>14534395
How did you fuck up that badly

[Anonymous No.14534443]

>>14534229
>every possible case
x = 3k + a, x^2 = 9k^2 + 6ka + a^2, 3|x^2 -> a^2 = 0 mod 3 -> a = 0 mod 3 -> x = 3k

[Anonymous No.14534533]

Is the appendix on integral calculus in "Infinite Jest" any good?

[Anonymous No.14534534]

>>14534533
DFW was a brainlet. I read his book on infinities and it was complete nonsense in every page. He doesn't understand math.

[Anonymous No.14534663]

>>14522379
Vefa? How are you?

[Anonymous No.14534682]

>>14534534
I know how you feel. anon. I tried to read some books written by W. Shakespeare.
He did not know how to write either.

[Anonymous No.14534720]

>>14534682
You are not as smart as you think you are.

[Anonymous No.14534879]

>>14534278
>>14534282
Think I got it, thank you! Shame the book doesn't really note all this explicitly like you did, but I guess the author is saving space for explaining more stuff and I figure things like this will be second nature to me too once I make my way through a bunch of books.

But I guess doing it this way is not bad either for the time being, we could say I got to explore a bit on my own.

>>14534395
pic rel

>>14534435
Thanks!
日本語喋れないのに煽るなばーかw

[Anonymous No.14534886]

>>14533766
I would honestly work through a classical mechanics text for physics students. It'll probably more easily engage your mind and all the problems for undergrads should be solvable by hand.

At the graduate level (at least in applied math) the big skill you end up gaining is recognizing when to do something by hand and when to do something by computer. They should train this better at the undergrad level but they don't, it tends to be math and physics majors trained to solve everything by hand and the other stem fields overtly relying on computer and already derived equations.

[Anonymous No.14534985]

>>14534440
What do you mean ?
>>14534879
Ok, thanks

[Anonymous No.14535002]

Anons, I was doing Serge Lang's Basic Mathematics and got stuck on some problems in Linear Equations. This makes me embarassed as hell. I'm starting college and can't do basic algebra stuff. How do I get better at it?

[Anonymous No.14535077]

>>14535002
post the problems

[Anonymous No.14535324]

>>14534097
sin(x) = sin(180-x), cos(x) = cos(-x), tan(x) = tan(180+x)

[Anonymous No.14535430]

What kind of job did he get?

[Anonymous No.14535470]

>>14535430
Naive set theory is the bare minimum for understanding the notation in any graduate analysis course.

[Anonymous No.14535506]

>>14535470
all right, but I thought that for anyone who went through university the word "industry" means non-academia. would such a job change involve graduate analysis courses?

[Anonymous No.14535507]

>>14535430
he's clearly not a mathematician, and most probably he got a job related to applied discrete math

[Anonymous No.14535543]

>>14535430
chef at mcdonalds

[Anonymous No.14535579]

Let M be a matrix with full row rank.
Suppose that Mx = 0 has no solution x such that every coordinate of x is >=0, other than x=0.

Is it always possible to find an invertible matrix B such that BM is a non-negative matrix ? (ie such that every coefficient in BM is non-negative).

[Anonymous No.14535811]

>Topic A is more difficult than topic B
not quoting anyone in particular, haven't read the thread, but I've called this mindset out numerous times always leading to animosity and dismissal.

But the fact remains: If you are a mathematician who asserts that "Calculus" is "harder" than "highschool algebra" or whatever you like: A > B, but you have no ability to back up that assertion, then I have to consider you an enemy.

But really, despite my humorous consequent, if you are going to assert that one thing is "harder" than another, then shouldn't you have a framework of evaluating the two?

In fact, with the nature of mathematics building upon itself, I argue that no topic in mathematics, by its very nature, can actually be "difficult".
Theorems rest on lemmas and definitions and axioms. Lemmas and definitions rest on axioms.
There's no hand-waving. There's no room for "difficulty."

Yet mature mathematicians will throw this around: so-and-so topic is "difficult", so-and-so topic is "easy."
Shameful, really, without a concrete basis to stand on.

[Anonymous No.14535819]

>>14535811
Kolmogorov formalized probability
when will we formalize "difficulty"?

[Anonymous No.14535843]

Statistics made me quit math undergrad and become a webdev. I found it harder than real analysis.
Fuck gamma, beta and chi-squared distributions

[Anonymous No.14535850]

>>14526311
>PDE by Evans
>Complex Analysis Ahlfors
> Algebra Lang
>Real and Complex Analysis Rudin
>Functional Analysis Rudin
>Algebraic Topology Hatcher
>Smooth Manifolds Lee
>Basic Algebraic Geometry 1 Shafarevich
>Multiplicative Number Theory Davenport

This should cover a 1st year master course

[Anonymous No.14535852]

>>14535843
If you were to assign a difficulty measure to webdev, and a difficulty measure to real analysis, on what criteria would you proceed?

[Anonymous No.14535878]

>>14535852
I would grade my subjective suffering and perplexity in front of a problem/challenge.

[Anonymous No.14535888]

>>14535878
So the topics carry no inherent "difficulty"

[Anonymous No.14535891]

>>14535850
>real and complex analysis Rudin
>functional analysis Rudin
Do you people really read the whole Rudin trilogy?
I remember picking up Rudin's functional analysis back in the day, working through a hundred pages and thinking that the subject selection was basically random and that the book was garbage.

[Anonymous No.14535897]

Pick two topics or even problems in mathematics and tell me why one is more difficult than another.

It's not a trick, I want to get to the bottom of this.
I think difficulty is axiomizable but I think it will take some work.

[Anonymous No.14535901]

>>14535891
>Calling Rudin garbage
>Anime pic
Fucking tranny piece of shit, you will never succeed in academia, you will never be japanese and you will never be a woman.

[Anonymous No.14535902]

>>14535897
I think what you mean is complexity of one expression over the other, go on anon, make up a definitions or an axiom

[Anonymous No.14535908]

>>14535902
it's not just about complexity of an expression, unfortunately. Though I think Kolmogorov complexity will play a role in a general theory of difficulty.

[Anonymous No.14535910]

A general theory of difficulty seems right now to be unfortunately not exclusively mathematics, as the pedagogy element plays a large role.

[Anonymous No.14535916]

do you fags go over "hand made" math bullshit every once in a while?

I've been babied by my Ti CAS that i've forgotten how to do triple integrals..

[Anonymous No.14535918]

>>14535891
I keep his series as reference material myself, but definitely not the book I learned from. The axiomatic route of measure theory is so dry.

[Anonymous No.14535922]

>>14535908
Well then your sense of "difficulty" here is useless, or else you misunderstood what kind of definition of "complexity" I was on about, which is similar to the algorithmic complexity.

[Anonymous No.14535923]

>>14535916
Is there something more to this than integrating three times? I don't see how you can forget that if you still know antidifferentiation rules.

[Anonymous No.14535926]

>>14535850
Is this legit ? Seems incomplete

[Anonymous No.14535934]

>>14535922
If you say "calculus is harder than arithmetic"
then I expect this A > B to be codified, and supported in some way

[Anonymous No.14535949]

>>14535918
>The axiomatic route of measure theory is so dry.
I personally really like it.
The formalism and the exposition is half the flavor. Like Euclidean geometry.

[Anonymous No.14535978]

>>14535850
davenport seems kind of silly and not useful for practical applications
is there a book that just lists all the ways FLT progressively went wrong over centuries and how people corrected for each problem along the way?

[Anonymous No.14535979]

>>14535926
what do you think is missing?
only criticism is that some of that stuff should have been done in undergrad already

[Anonymous No.14536168]

>>14521211
>integration edition
>not a single integral problem posted

[Anonymous No.14536360]

>>14535077
many from picrelated
it's not so much the specific maths problems thats the issue. Thing is, I'm stumbling quite frequently when trying to learn from the book. I have a feeling I'm doing something wrong and am not actually learning anything.
Another problem is, when we were taught maths, our country had a completely different system of teaching and words questions in a very different way. Which is why, I can't even understand some of the questions. Only now in college, I am learning basic stiff that you were supposed to learn in USA middle school.

[Anonymous No.14536369]

Anons, I just started EE undergrad and the level of maths being introduced makes me feel like a fucking retard. Everyone else in my class seems to understand the stuff easily but I'm struggling. How do you guys keep yourselves from being overwhelmed in such situations?

[Qanon No.14536381]

Do you know this formula?

[Anonymous No.14536468]

>>14536369
just do the exercises and believe in urself

[Anonymous No.14536476]

>>14536381
Its trivial to prove from trig identities.

[Anonymous No.14536481]

>>14536468
>believe in yourself
pls dont make fun of me. How am I supposed to cope with and learn so much stuff?

[Anonymous No.14536510]

>>14536381
>mixing degrees and radians
>parenthesis multiplication with the number on the end
aaaaaaaaaaaaaaaaaaaa

[Anonymous No.14536656]

in all serious, what is up with the number of trannies in maths these days
like if i ever find myself on twitter, amongst the first things i see is something like this
just getting a bit grim at this point to tell you the truth

[Anonymous No.14536657]

>>14535926
You could definitely fill a year with this, although hopefully you'd come in knowing some of it already.

[Anonymous No.14536706]

>>14535926
It's missing Linear Algebra by Hoffman.

[Anonymous No.14536861]

sort of accidentally became a logician

[Anonymous No.14536935]

Consider a parabola [math]y^2 = 2px [/math]. Start with a point [math] P_n(x_n, y_n) [/math] different from the summit (here [math] (0,0)[/math]).
Consider the intersection of the normal to the tangent of than point with the parabola to be [math] P_{n+1}[/math].
Does [math] \sum \frac{1}{y_n}[/math] converge ?

[Anonymous No.14536936]

>>14536481
Unless you're a prodigy it's literally just hard work.
Sit down and take your time to learn the concepts properly, don't try to get a surface level 'close enough' sort of understanding. Especially not if you actually want to ever work in the field.

I got shit grades in my first few years of Uni because I coasted through high school and high school was piss-easy. Uni throws much harder content at you that you really do need to pay attention to. After realizing that I started taking it more seriously and did fine. I failed 3 subjects in my first year, by the way, now I'm an HD student. You CAN do it.

Having said that, I'm typing this to procrastinate wrapping up my thesis which is due in ~24 hours. So I'm far from perfect, but its a continuous process of improvement.

[Anonymous No.14536955]

How old were you when you started your Masters/PhD?

[Anonymous No.14537021]

>>14536935
Working out the algebra, I get [math]y_{n+1}=-\bigl(1+\frac{2p^2}{y_n^2}\bigr)y_n[/math].
Clearly, y_n alternates in sign and grows in magnitude to infinity, so the sum converges by Leibniz's criterion.

[Anonymous No.14537023]

I'm about to spend $75 on this book. Should I pull the trigger?

[Anonymous No.14537028]

>>14537023
Not if you can pirate it, which you usually can.
If not, you can get it used, which you also usually can.

[Anonymous No.14537035]

>>14537023
Forgot the pic.
>>14537028
I don't do piracy, sorry.

[Anonymous No.14537038]

>>14537035
Grow up. http://libgen.rs/book/index.php?md5=0257BEC2F45D299A6C7CDBC37075906C
If you don't wanna pirate, what reason could you have for not buying a book you need?

[Anonymous No.14537039]

I just got a B on my bachelor's thesis. Love u frens

[Anonymous No.14537069]

>>14537038
not him, but he didn't specify that he /needed/ the book, and maybe he wanted some opinionated anons to shill him some other book(s) instead

[Anonymous No.14537099]

>>14537023
>>14537035
It's my preferred graduate algebra brick.
You might fucking hate it because you don't like the subject selection or the funny jokes or whatever, I dunno.
Print the first chapter out. Compare and contrast with Lang/Rotman/whatever.

[Anonymous No.14537130]

>>14537099
Do you buy books or just pirate them?

[Anonymous No.14537165]

>>14537130
I just pirate them unless I can get better quality pdfs with institutional access or if I can get them from the library.

[Anonymous No.14537539]

Maybe I'm dumb, but I don't understand the point of proofs or of abstraction really. Like I can do it and I've done well in my math 'career', but I've never really seen the point of proofs or a lot of abstractions seen in 'pure' math.

Are there cases where these things have helped with specific problems? I can understand proofs on more specific problems, but once things start to become abstract I just get lost as to why I should study them. In my experience, most 'applied' problems are so specific that abstract proofs kind of become a waste of time. Not because they aren't true mind you, but because they're pretty trivial to show, prove or see in the more specific problem.

I guess I've just never seen a case where highly abstract thinking helped in a specific problem. Maybe it's because I'm already abstracting and seeing generalities without thinking about it because I've taken all these sorts of courses before.

[Anonymous No.14537720]

>>14536656
societal decay

[Anonymous No.14537733]

>>14537539
Without logic the universe wouldn't exist.

[Anonymous No.14537772]

>>14536656
Has more to do with trannies on twitter than trannies in math

[Anonymous No.14537784]

>>14536656
Dysgenics

[Anonymous No.14537790]

>>14536656
>waaah waaah, someone i dont like is also doing math
you are pathetic

[Anonymous No.14537797]

>>14536656
Surprise surprise, math is for everyone. Even for a chud incel loser like you :).

[Anonymous No.14537870]

>>14537720
>>14537772
>>14537784
>>14537790
>>14537797
This samefagging is too obvious and sad.

[Anonymous No.14537894]

>>14536656
Of all fields in university, it is math and CS which have the highest incel and autist density. Anyone who studied in these departments will confirm this immediately. The conclusions to draw are obvious then.

[Anonymous No.14537978]

>>14537870
Yep. Some loser from leftypol probably, I don’t know why these faggots target /sci/ of all places

[Anonymous No.14538022]

If I want to be a Finance Quant GOD, what are books you recommend?

I want to study tons of analysis, Papa and Grandpa Rudin and maybe Ahlfors. But from there, or on the side what are the good books in Stochastic Processes and Statistics? I see a lot of bad books written for retards from non-math degrees.

For PDE's I've heard Evans is good, but it looks kind of like the ODE books which are boring as fuck (lots of methods on how to solve different kinds of DEs instead of a theory.) I heard Brezis is better because of the Functional Analysis approach.

Please, I want good recommendations that aren't shitty recipes for engineers

[Anonymous No.14538027]

>>14536706
I want linear algebra for more advanced courses like Differential Geometry and Functional Analysis, what would be better? Halmos or Hoffman?

[Anonymous No.14538030]

>>14537870
>>14537978
unironic schizo posts

[Anonymous No.14538100]

>>14538027
Halmos is a meme, it would be the equivalent of studying Classical Mechanic with Newton's Principia.

[Anonymous No.14538135]

>>14538030
sad tranny
>>14538100
So what else is good? It should have a treatment on tensors

[Anonymous No.14538143]

anyone likes this one ?
https://www.amazon.com/gp/product/0486471896/
(Basic Algebra, Jacobson)

[Anonymous No.14538180]

>>14538100
>Halmos is a meme, it would be the equivalent of studying Classical Mechanic with Newton's Principia.
What is it with people coming into /mg/ to post COMPLETE FUCKING NONSENSE out of LITERALLY ABSOLUTELY NOWHERE?

[Anonymous No.14538183]

>>14538143
That book is honestly way too hard and outdated. I can't understand anything on Volume 2.

[Anonymous No.14538240]

>>14538180
You're free to post your arguments refuting if you can.

[Anonymous No.14538282]

>>14538240
nigger

[Anonymous No.14538501]

>>14537733
And? I don't disagree.

[Anonymous No.14538550]

>>14538135
>everything i dont like is a tranny
take your meds schizo

[Anonymous No.14538573]

>>14538180
still better than anitranny and his posting

[Anonymous No.14538622]

>>14538573
Most of what anitranny posted had some basis in reality.

[Anonymous No.14538672]

Math bros i'm screwed., I took to many subjects this period and i don't even have time to breath, but thats not the real problem, The subject that take away more time is some faggotry Data Science Subject, i tried to drop the curse but my uni doesn't answer me. I want to die.

[Anonymous No.14538711]

>>14533288
Guys I'm still looking for the pill on geometric algebra

[Anonymous No.14538721]

Does anyone know any well written texts on co-induction and co-recursion that is specifically not targeted at computer science f-words?
It's already hard enough to find good stuff written on regular induction and recursion as it seems to be scattered around in random books and articles and seems to kinda just have become mathematical folklore.
To give an idea on what I'm looking for: the section on induction and recursion in Hinman's Logic book (+ anything he mentions in later chapters like how what he refers to as induction systems relate to monotone maps and their fixed points) was a nice elementary read.
Is there anything like this but also going over co-induction and co-recursion (and how they relate to regular induction and recursion)?
I come across inductively defined sets in all the time (finite ordinals, transitive closure, language of FOL, deductive closure, kleene closure, entailment relation for hilbert systems, reduction relations in LC, you name it). What are some common co-inductive definitions in mathematics? Would the interior of a set w.r.t. a topology be an example of a set defined by co-induction?

[Anonymous No.14538776]

Is my correlation function wrong or does this look like it should be as low as 0.04?

[Anonymous No.14538783]

>>14538672
lol is it numerical analysis with 20 page homework assignments every other week?
the course is no problem but that crap is tedious

[Anonymous No.14538792]

>>14538776
You're fit is fine up until a point then it is no longer linear. A transformation or higher terms may be useful. Try an exponential fit or a quadratic fit.

[Anonymous No.14538794]

>>14538672
Sounds like someone is a pissy baby. I hope your gpa gets fucked and you have to retake that data science course

[Anonymous No.14538799]

>>14538776
Also, plot the residuals vs the fitted values. It's much easier to see if your shit is right (and also get ideas for transformations) from that. Ideally you should just see random noise centered around zero in the residual vs fitted values (i.e. no pattern.

[Anonymous No.14538968]

what's the cleanest way to represent [math]\left(\frac{p}{q}\right)\left(\frac{q}{p}\right) = (-1)^{\frac{p-1}{2}\frac{q-1}{2}}[/math] as a declarative statement? is there any way to do it without a branch?

[Anonymous No.14538981]

>>14538968
math didn't work but quadratic reciprocity (p/q)*(q/p) etc.
the legendre symbol takes the form of a number just fine yet isn't really a number and shouldn't really be multiplied or have negatives

[Anonymous No.14539005]

>>14538711
Here's the qrd with nice pictures:
https://m.youtube.com/watch?v=60z_hpEAtD8

Book sources for further reading are also mentioned there.

[Anonymous No.14539154]

>>14539005
That was very cool and helpful.
I am trying to read Geometric Algebra for Physicists by a couple of the authors he referenced, but am having trouble with it.

[Anonymous No.14539735]

>>14536360
Regular/remedial K-12 students don't see that before 8th/9th grade. If they're magnet-school / honors-level / gifted-&-talented they would be shown the same for the first time in 5th/6th/7th grade.

Many people forget MOST math stuff that they did just over a year ago, even if they spent a couple of years drilling over the material.

[Anonymous No.14539821]

>>14525810
If you go to ANY Ivy League [or other top school] for your typical 8 semester Bachelor's degree and start at the first basic calculus course, you would NEVER see 2nd order ODEs until the very end of the second semester. In the first semester you would only see simple 1st order ODEs. The non-STEM students who do more math than their mandatory 1 statistics course wouldn't even see this until their third semester [out of 8] in linear algebra plus differential equations [condensed into one] course.

The only way you would see this in your very first university calculus course is if you placed high with AP or IB Calculus. Or if you are in a weird college where a single class runs from September to the beginning of June.

[Anonymous No.14539956]

>>14539821
Yeah but ivies have a big problem with avoiding problems that require dirty calculations. It's a serious weakness with a lot of the courses imo

[Anonymous No.14540269]

>>14524872
>In terms of information*, each 1 card is slightly larger than 1 card for learning a vocabulary word of a foreign language.
Makes sense.

*(measured by time spent reading the card, as implied by the YouTube video)

[Anonymous No.14540549]

>>14536360
>do #11 first and just plug in with "see #11" on most of the other ten problems

[Anonymous No.14540930]

>Open physics book
>Go to glossary
>Elementary field:A dynamical variable of a classical field theory
>Dynamical variable: An elementary field that is allowed to vary, and whose derivatives enter into the classical equations of motion
Cool, so elementary field is defined using dynamical variable, and dynamical variable is defined using elementary field

[Anonymous No.14540950]

>>14540930
>Open physics book
Sir, this is a math thread.

[Anonymous No.14540975]

>>14540930
read takhtajan, deligne or so if you want rigor in physics

[Anonymous No.14541028]

I'm reading a sex scene in a vn and I feel guilty for not spending this time on learning math. This one is even making me feel a bit lonely while math right now is like pure fun for me. Why do I do this...

[Anonymous No.14541131]

hi guys ive got this bachelors in math, wpi, basically graduated, pretty cool i guess
how do I turn it into money tho. like what’s the best way
I’ve been working as a deckhand this summer and I’m starting to miss solving problems… I feel like this work made for 90iq people is making me actively dumber

[Anonymous No.14541171]

>>14540975
That one was deligne, that example I gave might just be a fluke where he accidentally defined things circularly. I’ll check out the other author though

[Anonymous No.14541337]

>>14541028
soon you will have both brother.

[Anonymous No.14541779]

A last cheeky one
Given that [math] a_n [/math] is a sequence of strictly increasing positive integers and [math] a_n \rightarrow \infty [/math]. Plus [math] \frac{a_{n+1}}{a_n} \rightarrow 1 [/math].
Show that [math] \sum \frac{a_k - a_{k-1}}{a_k} \sim ln(a_n) [/math]

[Anonymous No.14541959]