/mg/

[Anonymous No.12002000]

Math general - SMBC edition

[Anonymous No.12002014]

>>12002000
>meme comic
>doesn't link the previous thread
I hate it.

[Anonymous No.12002018]

>>12002000
>Elliptic curves

[Anonymous No.12002042]

>>12002014
It was my first time making the thread. I linked forward but not backwards.

Previous thread:
>>11990339

Also, I always liked SMBC and it was the only good picture I had on my phone already, so fuck off. Plus I got trips.

[Anonymous No.12002044]

Previous >>11990339

[Anonymous No.12002045]

>>12002000
>SMBC

[Anonymous No.12002053]

Is this a real word?

[Anonymous No.12002054]

>>12002053
Yes.

[Anonymous No.12002055]

>>12002054
what does it mean

[Anonymous No.12002056]

>>12002053
https://en.wiktionary.org/wiki/paedagogically
It's very, very close. Just fucked up the da.

[Anonymous No.12002059]

>>12002055
https://www.thefreedictionary.com/pedagogically

¿Why are you asking this in /mg/?

[Anonymous No.12002062]

>>12002056
less funny now that it doesn't spell "paedo"
>>12002059
this isn't the word in the image
this is in a math book so it belong in /mg/.

[Anonymous No.12002065]

>>12002045
>le soulless wojack #20182918291974721

[Anonymous No.12002070]

Is Pinter actually good? It's in the new chart but I thought it was a beginner Dover book and not even close to Lang or Foote, or is it meant to come directly before i.e. Pinter then Lang/Foote?

[Anonymous No.12002071]

>>12002062
Next time please just type your word into a search engine. Even if it was a math word, you should have tried that first.

[Anonymous No.12002072]

>>12002065
>>le soulless wojack #20182918291974721

[Anonymous No.12002075]

>>12002000
>numerical methods for stochastic differential equations

[Anonymous No.12002076]

>>12002070
It's good as an introductory text. If you've already taken undergraduate algebra, then you won't get much from it.

[Anonymous No.12002077]

>>12002071
>Next time please just type your word into a search engine.
I did, the only things returned were the book I was reading, some retard on mathoverflow talking about ultrafilters and a book on Microelectronic Circuits.

[Anonymous No.12002083]

>>12002053
what book is this? Is this intro to topos theory?

[Anonymous No.12002087]

>>12002000
what do you think about suppressing isomorphisms and writing equalities instead? for example
[math]S^1 = U(1) = SO(2) [/math]
[math]\pi_n(S^n) = \mathbb{Z} [/math]
[math]\mathbb{Z}/2\mathbb{Z} \otimes \mathbb{Q} = 0 [/math]
[math]H^n(X;G) = \langle X, K(G,n) \rangle [/math]

[Anonymous No.12002088]

>>12002076
Does undergraduate come after Pinter or does Pinter come before graduate algebra in Foote or Lang?

[Anonymous No.12002089]

>>12002083
Topoi: The Categorial Analysis of Logic by Robert Goldblatt
it was shilled here a few days ago i think

[Anonymous No.12002115]

What are some good electives to take during Math undergrad?

[Anonymous No.12002119]

>>12002088
Mostly the latter. Pinter will give you all the groundwork that you'll need for grad level algebra. Going through all the chapters and working through the exercises will cover your standard algebra in undergraduate and a tiny bit extra stuff, although it doesn't cover some stuff like Gröbner bases and Burnside's lemma, but those don't seem to be standard topics covered from what I've seen.

[Anonymous No.12002128]

>>12002115
Philosophy

[Anonymous No.12002132]

>>12002087
thats just called working in the skeleton

[Anonymous No.12002141]

>>12002115
grad level modules

[Anonymous No.12002144]

>>12002128
this but unironically

[Anonymous No.12002145]

>>12002144
I was being completely serious. Math and philosophy are the two highest tier subjects.

[Anonymous No.12002161]

>>12002087
There's nothing wrong with it. A bunch of those barely even have "official" base sets.
[math]S^1 = \mathbb{R} / \mathbb{Z}[/math] versus [math]S^1 = \{ x \in \mathbb{R}^2 : |x| = 1 \}[/math], not even mentioning the different constructions of the real numbers thing.

[Anonymous No.12002177]

>>12002087
Like >>12002132 said, it's fine as long as you remember which category you're working in and don't start using properties that depend on elements.

[Anonymous No.12002178]

>>12002145
Good starting points for philosophy?

[Anonymous No.12002180]

>>12002178
Jordan Peterson, the greatest living philosopher.

[Anonymous No.12002185]

>>12002180
And what if I actually want to learn something?

[Anonymous No.12002188]

>>12002087
related question: which symbol do you use to denote isomorphisms? [math]\simeq \ \approx \ \cong [/math]

[Anonymous No.12002190]

>>12002178
Nietzsche's Philosophy in the Tragic Era of the Greeks.

[Anonymous No.12002199]

>>12002178
>>12002185
It mostly depends on what you're interested in (politics, metaphysics, aesthetics, etc.), but Plato's Five Dialogs (Euthyphro, Apology, Crito, Meno, Phaedo) are about as good a starting place as any. They're all very short and can be found online, but be wary of the quality of the translation.

[Anonymous No.12002201]

>>12002188
≅ is isomorphism
≈ is "approximate" like pi≈3
≃ is isomorphism for faggots

[Anonymous No.12002210]

>>12002188
The symbol for congruency.

[Anonymous No.12002214]

>>12002188
= of course

[Anonymous No.12002219]

>Commutative exponentiation
Does it exist?

[Anonymous No.12002229]

>>12002219
Define exponentiation.

[Anonymous No.12002239]

>>12002229
[math]x^y = \underbrace{x*x*x...x} _\text{y}[/math]

[Anonymous No.12002245]

>>12002239
This only makes sense in [math]\mathbb{N}[/math]

[Anonymous No.12002249]

>>12002000
This comic is so based, hence why you never learn economics until maybe high school/college despite the huge benefits it would have on individual freedom in our society to teach these things to everyone at a young age.

[Anonymous No.12002279]

>One fourth

[Anonymous No.12002295]

>>12002128
If I can only take one of philosophy or linguistics, which should I take?

[Anonymous No.12002299]

>>12002245
Ok, let's define it as [math]z \in \mathbb{C}, a^z = \exp(z \log(a))[/math].

[Anonymous No.12002303]

>>12002279
Come fourth and take a nineth of the pi.

[Anonymous No.12002309]

>>12002299
what happens when zlog(a) isn't a natural

[Anonymous No.12002310]

>>12002299
Neither of those operations are commutative. Tell us a more interesting definition if you want commutative «exponentiation», otherwise the answer is either «it isn't» or «just take it to be some commutative operation».

[Anonymous No.12002312]

>>12002309
I don't know.

[Anonymous No.12002344]

>>12002219
[eqn]x \wedge y = x^{\ln y}[/eqn]

[Anonymous No.12002381]

>>12002295
Philosophy, lad.

[Anonymous No.12002403]

>>12002344
¿Why should I call that a kind of exponentiation?

[Anonymous No.12002419]

>>12002188

[math]\cong[/math]

[Anonymous No.12002420]

>>12002403
>¿
Hola gallego

[Anonymous No.12002444]

If I read math books and I understand the material would it add anything to also take a class in the subject? I’m asking cause I’m gonna be in a program in my uni that lets me skip prereqs for a class

[Anonymous No.12002465]

>>12002000
I have what I think is a compete proof that shows that P = NP, but Im an undergrad and I don't have the slightest clue how to publish. All the profs won't actually read my proof or give me valid criticism. Instead they just call me a hack or a dumb undergrad and won't prove me wrong.

[Anonymous No.12002467]

>>12002420
Lo siento, hablo solemnemente inglés pero me gusta usar estos marques de pregunta en mi idioma.

[Anonymous No.12002477]

>>12002467
Ah okay :(

[Anonymous No.12002491]

>>12002444
Do your textbooks give you access to someone with a PhD in math to freely ask questions to?

[Anonymous No.12002508]

>>12002465
>I have what I think is a compete proof that shows that P = NP
Spoiler: You don't.

[Anonymous No.12002529]

>>12002465
Every fucking thread you say this just put the proof on the internet with a cipher that, if decrypted would spell your name. If the internet accepts the proof, then publish the key so people can decode it as you and you get credit. If they think it’s bullshit never release the key so you don’t ruin your reputation. Also just in case I wasn’t clear you definitely didnt solve it

[Anonymous No.12002530]

>>12002491
Not OP, but surely stackexchange and /sci/ are sufficient for any questions outside of the learning material

[Anonymous No.12002535]

>>12002465
Publish it here and we can give feedback

[Anonymous No.12002545]

>>12002491
Do classes?

[Anonymous No.12002546]

>>12002545
Ideally.
Even then, a PhD student will know what they're talking about for undergrad classes.

[Anonymous No.12002551]

>>12002546
I was gonna make a post that read
>ideally
>usually
But then I noticed that you actually didn't write "a PhD student will usually know".

[Anonymous No.12002567]

>>12002491
That’s a valid point but I think if I were struggling with the material from the book I would take the class anyway. I was talking more about if I understood the textbook, would it be ok to move onto another class that has it as a prerequisite

[Anonymous No.12002600]

>>12002567
Cont.
also I just remembered I can drop classes with no penalty so never mind my original question

[Anonymous No.12002652]

>>12002465
They wont prove you wrong precisely BECAUSE youre a dumb undergrad
you would learn far more by proving yourself wrong than by having someone explain why youre a dumb undergrad

[Anonymous No.12002677]

Posting smug anime girls is just massive cope that you are never going to make it.

[Anonymous No.12002708]

holy shit, whats it like actually getting tilted by smug anime girls you fucking pussy?

[Anonymous No.12002742]

Is there a worse class to TA for than calc 2?

[Anonymous No.12002746]

>>12002742
Calc 1

[Anonymous No.12002751]

So what the fuck is SMBC?

[Anonymous No.12002760]

>>12002751
Saturday Morning Breakfast Cereal

[Anonymous No.12002763]

>>12002760
but it is wednesday

[Anonymous No.12002773]

>>12002763
I don't understand your objection.

[Anonymous No.12002777]

https://www.real-world-physics-problems.com/gyroscope-physics.html

You should be able to solve this

[Anonymous No.12002781]

>>12002201
this

[Anonymous No.12002790]

>>12002219
[math] \left( \{ 1 \} , \exp(x) \right) [/math] is an abelian group.

[Anonymous No.12002796]

>>12002087
I think the univalence axiom in homotopy type theory is a way of formalizing this.

[Anonymous No.12002817]

>>12002796
>type theory
quotients are a better way

[Anonymous No.12002879]

https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/


why is linear algebra the most chad branch of mathematics next to calc?

[Anonymous No.12002907]

>>12002879
this is some horribly low quality bait

[Anonymous No.12002944]

>>12002879
Algebra is the true chad field.

[Anonymous No.12002949]

>>12002790
>a single unary operation

[Anonymous No.12002985]

>>12002879
calc is not a 'branch of mathematics'
In fact, it has shit all to do with mathematics

[Anonymous No.12002988]

>>12002985
>Analysis isn't mathematics

[Anonymous No.12002992]

>>12002988
Calculus is not analysis

[Anonymous No.12003039]

>>12002992
But if I memorize enough integrals I'll be a top-tier analyst, right? Don't tell me I need to do algebra or some gay shit. I like integrals.

[Anonymous No.12003064]

>>12002087
Pretty much every mathematician does this anyway tbdesu

[Anonymous No.12003097]

>>12003064
No, they know when the difference between equality and isomorphism counts, they don't just ignore it everywhere.

[Anonymous No.12003100]

>>12003039
Maybe if you get an education you'll have half a shot of being a genius

[Anonymous No.12003109]

>>12003064
Nobody I know does this, not even physicists.

[Anonymous No.12003110]

>>12002087
What does the third equation mean? How can a tensor product of nonempty spaces be empty?

[Anonymous No.12003115]

>>12002145
Philosophy is infantile nonsense.

[Anonymous No.12003117]

>>12003115
but you can teach

[Anonymous No.12003121]

>>12002295
You should think for yourself
>>12002567
Yes. Doing all the exercises in a sufficiently advanced undergrad textbook is a more thorough introduction to the material than what nearly all math majors would be exposed to. If you don’t believe me look at the problem sheets and exams from any top uni in America with an open courseware program. They cover surprisingly little and ask even less on exams.

[Anonymous No.12003134]

>>12003110
take any (a, b) in the product, then (a, b) = (a, 2* b/2) and then (2a, b/2) = (0, b/2) = (0,0)

[Anonymous No.12003163]

>>12003134
Wow

[Anonymous No.12003170]

>>12002879
Explain

[Anonymous No.12003278]

Is teaching the only way mathematicians can make money? Like are there grants for research, and if so how lucrative are they? Is there a huge difference in salary between a mathematician progressing his field and a professor just teaching?

[Anonymous No.12003347]

>>12002985
Calculus is the application of Analysis brainlet

[Anonymous No.12003361]

tips/advice for a complete brainlet taking introductory undergrad real analysis?

[Anonymous No.12003381]

>>12003347
>application
That’s exactly why it’s not math

[Anonymous No.12003432]

>>12003361
Take your time reading the textbook - make sure you 100% understand things. If you have doubt about something, you can always move on for a little bit, but just remember to go back. And do plenty of problems ig

[Anonymous No.12003453]

>>12002087
Like all things, it depends on the context. There's no universal rule to this.

[Anonymous No.12003480]

why do apostol and spivak get their dick sucked so much

[Anonymous No.12004084]

Does a weak homotopy equivalence [math]X\to Y [/math]induce isomorphisms [math]K(Y) \to K(X) [/math]?

[Anonymous No.12004096]

>>12003361
If you don't understand something the first time, don't give up or get frustrated. It'll take some time. The most important thing is to keep going on

[Anonymous No.12004100]

>>12004084
If it does that for ordinary cohomology, then it does it for extraordinary, too. I can't remember if it happens for all spaces, but in the CW-case yes.

[Anonymous No.12004115]

>>12004100
>in the CW-case yes
yea, I know. I wondered if it's true for arbitrary topological spaces

[Anonymous No.12004125]

>>12002000
Sell me on studying dynamic systems, chaos theory and the like. Where should I start and where should I branch of.

[Anonymous No.12004164]

Is Birkhoff and Maclane's Algebra any good as an intro to Abstract Algebra? And is it any better than the typically meme'd Aluffi Chapter 0 book?

[Anonymous No.12004343]

>>12003097
>>12003109
Maybe it depends on the field, but almost every mathematician I've met writes e.g. [math]H^1(S^1)=\mathbb{Z}[/math] or [math]\hom_{\mathbb{Z}}(\mathbb{Q},\mathbb{Z})=0[/math].

[Anonymous No.12004368]

>>12002053
Use a search engine retard

[Anonymous No.12004373]

>>12004343
That's irrelevant and not mutually exclusive. Your statement says that the cohomology group IS, literally, this particular group.

[Anonymous No.12004477]

>>12004373
[math]H^1(S^1)[/math] is well-defined set theoretically and not intrinsically equal to [math]\mathbb{Z}[/math].

[Anonymous No.12004508]

>>12004477
The same can be said about Z. It's accepted notation and 99% of textbooks use it - as opposed to the complete substitution of 'equal' and 'isomorphic' for which you (or someone) argued above.

[Anonymous No.12004511]

>>12004477
For what construction of [math]S^1[/math] and for what construction of the real numbers?

[Anonymous No.12004536]

>>12004511
That doesn't matter as much as being able to keep track of cohomology class representatives when you go to use the cup product.

[Anonymous No.12004542]

>>12002201>>12002781

all wrong

[Anonymous No.12004577]

>>12004508
I'm not sure what point you're trying to make here. My point was that many mathematicians play fast and loose with = and only stress the difference between = and [math]\cong[/math] in introductory algebra courses.

>>12004511
Irrelevant. [math]H^1(S^1)[/math] is defined as a quotient of a set of functions to [math]\mathbb{Z}[/math].

[Anonymous No.12004588]

>>12004577
>irrelevant
If you change [math]S^1[/math]'s base set, this changes [math]C_n[/math]'s base set, which changes [math]C^n[/math]'s base set, which changes [math]H^1 (S^1)[/math].

[Anonymous No.12004594]

>>12002087
>>12002161
>>12002796
>>12004373
>>12004477
>>12004508
>>12004511
>>12004577
This is why noone likes set theory

[Anonymous No.12004605]

>>12004577
>only stress the difference between = and ≅ in introductory algebra courses.

That's totally incorrect. In many contexts the difference matters because being isomorphic in one category doesn't meam you have isomorphic objects in every relevant category. The integers and the compact surfaces might be the same as groups, but I can't find the tangent bundle of an integer.

[Anonymous No.12004612]

>>12002072
>imagine bothering to search and find le sohyjack 56782556 just to post it on 4chan

[Anonymous No.12004636]

>>12004605
I agree

>>12004588
If you know of a construction of [math]\mathbb{Z}[/math] under which [math]H^1(S^1)=\mathbb{Z}[/math], I'd be interested to see it. For all the usual constructions of [math]\mathbb{Z}[/math] (e.g. von Neuman ordinals), equality fails.

[Anonymous No.12004665]

>>12004636
Anything is possible if you define [math]\mathbb{Z}[/math] as the unique non-finite cyclic group (up to isomorphism).

[Anonymous No.12004686]

>>12004665
¿Do you understand the difference between an algebraic structure and its isomorphism class?

[Anonymous No.12004688]

What non-research jobs could someone get if they enjoy Mathematical Physics?

[Anonymous No.12004722]

>>12004594
>cant appreciate a very simple distinction between being the same set and being algebraically indistinguishable
stick to analysis

>>12004636
>If you know of a construction of Z
just define the circle first and then form the set of homotopy classes of loops
call Z that set of classes

[Anonymous No.12004734]

>>12004722
>just define the circle first and then form the set of homotopy classes of loops
>call Z that set of classes

That's immoral.

[Anonymous No.12004850]

>>12004734
It isn't, since [math]\mathbb{Z}[/math] acts on [math]\mathbb{R} \rightarrow \mathbb{R / Z}[/math] canonically through deck transformations.

[Anonymous No.12004885]

>>12004850
Just because there is an action doesn't mean that's the right thing to do. Swapping out a definition like that is bad practice. Let elementary objects be what they are and show isomorphisms where relevant. Don't try to pull a fast one by suppressing them and redefining basic concepts after you already used them.

[Anonymous No.12005485]

Best introductory complex analysis text?

[Anonymous No.12005556]

how many hours of math do you do everyday?

[Anonymous No.12005564]

>>12005485
"Funktionentheorie" by Klaus Jänich

[Anonymous No.12005576]

>>12005556
like uh 0 right now but usually between 2 and three, not counting university of course

[Anonymous No.12005669]

>>12005564
>only available in German

welp

[Anonymous No.12005690]

>>12004636
>von Neuman ordinals Z
?

What do you mean by equality?

[Anonymous No.12005720]

good afternoon /mg/, any good resources for me to learn more about 4-dimensional geometry? I'm a non-math brainlet but with decent high school maths knowledge so I understand there's probably pre-requisites I need to fulfill, but my goal is as stated above.

[Anonymous No.12005733]

>>12005720
4 dimensional only sounds kinda boring, why not arbitrary dimensional?

[Anonymous No.12005750]

>>12005733
Actually 4 is very special and more challenging than the higher-dimensional versions in many cases. There are exceptional regular polytopes in dimension 4, for example.

[Anonymous No.12005752]

>>12005750
Wasn't the 4D case the missing link in the Poincare conjecture until Perelman?

[Anonymous No.12005753]

>>12005750
yeah, but generally, you might want to learn the general higher dimensional case before.

[Anonymous No.12005771]

>>12005564
Got anything in English?

[Anonymous No.12005778]

germans should be rangebanned from /mg/, and more generally alienated from the mathematical community.

[Anonymous No.12005805]

>>12005720
>I understand there's probably prerequisites
Do you also understand that it'll take a few years to learn the necessary prerequisites?

[Anonymous No.12005816]

>>12005805
not if he's motivated and dedicates himself to that goal.

[Anonymous No.12005833]

>>12005778
This.

[Anonymous No.12005834]

how to get reference from retired academic advisor from 4 years ago
do I just email and hope?

[Anonymous No.12005873]

>>12005805
Yes, I am prepared to undertake any period of study however long.
>>12005750
>>12005733
I am interested in arbitrary dimensions, yes, but particularly interested in 4D structures.

Any recs anons?

[Anonymous No.12005928]

>>12002309
Just use the series definition bro, sum(x^n/n!). You can prove convergence in C, the law e^(ab)=(e^a)(e^b), and thus that e^z = e^x * (cos y + i sin y) for z=x+iy. Super basic complex analysis.

[Anonymous No.12005998]

This is from an mit lecture on qm
The swirly drawings are from the previous lecture
What was the previous class, what are these swirly drawings from, pls pls pls

[Anonymous No.12006010]

>>12005998
Those look like electron orbitals

[Anonymous No.12006179]

>>12005998
>>12006010
those are definitely electron orbitals

>>12005873
https://www.springer.com/us/book/9780387215075 this looks neat

[Anonymous No.12006257]

new to math here.

learning statistics at uni first semester. kinda fun and interesting desu. hope to be smart like you bros some day

[Anonymous No.12006265]

>>12006257
Intelligence comes from your parents, their parents, and so on. Mathematical mastery comes from the confluence of breeding and conditioning of the mind. You only have control over the latter and little else, besides of course accidents of history, separates you from the people you admire that you perceive as mathematically adept.

I wish you luck in achieving your goals

[Anonymous No.12006285]

>>12006265
I’ve never heard anyone as obnoxious as you. The guy just said he’s enjoying learning and wants to get better. Keep believing that your entire family lineage was conspiring to create you, the greatest mathematician in history while you’re on 4chan

[Anonymous No.12006447]

>>12006257
> hope to be smart
Years of practice, discipline, self-reflection. Talent is a meme excuse for lacking skills. Spend time doing shit -> level up.

[Anonymous No.12006478]

>>12006447
This.

[Anonymous No.12006488]

>>12006265
brainlet cope

[Anonymous No.12006510]

>>12006285
>>12006488
i don't know what the problem is guy basically said be realistic and train hard

[Anonymous No.12006557]

>>12006257
Being good at math is about working diligently and not giving up. In 8th grade I was one of the worst performers in my algebra class, and my teacher was very worried about my future. I began studying math in my free time during high school (nothing too fancy, mostly doing puzzle-like math problems akin to those found on math competitions), and by the time senior year came I was the best in my AP Calculus BC class. I continued working hard and now I'm taking graduate level classes in math at a very good university. Keep grinding, OP, and don't give up. The only way to get ahead is to get started. Good luck.

[Anonymous No.12006569]

>>12006557
Algebraist?

[Anonymous No.12006649]

>>12005778
Don't worry, bro. Math will soon be abolished in German schools and universities.

[Anonymous No.12006678]

>>12006569
Nope, I'm a geometry person. My first two years of college I was definitely an algebraist in that I was obsessed with commutative algebra, algebraic geometry, and representation theory. Then, junior year I started taking geometry classes like algebraic topology and differential topology and got hooked. Now I'm very interested in stuff like: smooth 4-manifolds (work of Donaldson and Witten), quantum field theory, complex geometry, geometric quantization, etc. It would've been funny if I did become interested in algebra, though!

[Anonymous No.12006698]

>>12006649
That could never happen here

[Anonymous No.12006848]

>>12006179
thanks anon

[Anonymous No.12006900]

>>12005720
There is an excellent series of educational videos made by french artists and msthematicians callef dimensions. You can find it on youtube by searching for a playlist called dimensions. It uses stereographic projections to faniliarize your thinking especially with 4 dimensional objects. Ive been into math for some time, did diff geo and stuff in R^n without much geometric intuition and this videos i felt were based.

[Anonymous No.12007562]

>>12005564
Basiert und rotgepillt

[Anonymous No.12007602]

Is it worth churning through every example in a textbook?
I'm using hughes-hallett for single var calculus (first year), and it takes me about at minimum 1 minute to do a question.
Is it possible? Have people done it? And is it worth it?

[Anonymous No.12007605]

It's kind of crazy how few people actually do math. I've never seen a math board on an imageboard survive for very long.

[Anonymous No.12007609]

>>12007602
>Is it possible?
Yes.

>Have people done it?
Yes, for some books.

>And is it worth it?
Generally no. You'll understand the material in a book very well long before you read a whole book or do every exercise. Like to the point you can sensibly try publishing something in the area in some cases.

[Anonymous No.12007612]

>>12002072
>>>le soulless wojack #20182918291974721

[Anonymous No.12007666]

Do you anons solve Project Euler stuff?
Has it taught you some nice tricks?

[Anonymous No.12007687]

>>12007666
depends on your level and what are you looking to learn

[Anonymous No.12007699]

Which fucking retard thought that passing function arguments through subscript and superscript was good idea?

[Anonymous No.12007715]

>>12007699
Me.

[Anonymous No.12007721]

>>12007699
The same one who had us compose functions in the opposite direction to the one in which we write.

[Anonymous No.12007723]

>>12007721
boo, f(g(x))

[Anonymous No.12007729]

>>12007723
xfg ftw

[Anonymous No.12007737]

>>12007729
I bet you write 1+2=3+7=10

[Anonymous No.12007744]

>>12007737
¿How would someone so new to math even know about the composition-order debate?

[Anonymous No.12007749]

how do I know an idea is good enough to start trying to write a paper on it

[Anonymous No.12007752]

Does anyone know if they're jewish? Henri looks kinda jewish but Elie not so much.
Wikipedia and MacTutor doesn't mention anything about them being jewish.

[Anonymous No.12007753]

>>12007744
There is no debate, science has settled.

[Anonymous No.12007776]

>>12007687
I think playing with simple probability and number theory and even finding some arithmetic tricks is just fun.
I was more asking if people here do the challenges and found out something interesting possibly.

[Anonymous No.12007784]

>>12007729
you mean xgf?

[Anonymous No.12007816]

>>12007737
>1+2=3+7=10
Replace = with =: and the problem disappears.
>>12007729
I prefer indicating composition/application explicitly with x;f;g so that instead of single letters, more meaningful names may be used.

[Anonymous No.12007979]

>>12007784
What does it mean for a curve in the space of distributions to be smooth? That is if I have a function [math]\gamma:I\subseteq\mathbb{R}\to\mathcal{S}'(\mathbb{R}^N)[/math], in many applications sometimes the derivative of such a curve is computed using the chain rule, but what notion of differentiability is appropiate in this context?

[Anonymous No.12007986]

>>12007979
Didn't meant to reply >>12007784

[Anonymous No.12008004]

What are the differential forms of variational calculus?

[Anonymous No.12008070]

>>12007753
Math isn't science, and notation isn't even math, properly speaking.

[Anonymous No.12008130]

>>12002000
I've got a dumb question here. If I've got a holomorphic function [math]f[/math] two small numbers [math]\varepsilon[/math] and [math]\delta[/math] then if I want to expand [math]f[/math] in a Taylor series, does it matter whether I expand it with respect to [math]\varepsilon[/math] or [math]\delta[/math] even if one is an order smaller than the other?

[Anonymous No.12008136]

>>12008130
Sorry, meant to say does it matter whether I expand [math]f(\varepsilon+\delta)[/math] as a power series in [math]\varepsilon[/math] or [math]\delta[/math] (if, let's say [math]\varepsilon[/math] is an order smaller than [math]\delta[/math])

[Anonymous No.12008158]

>>12007979
>[math]\subseteq[/math]
>not just using [math]\subset[/math] and letting the reader figure it out

[Anonymous No.12008176]

>>12008130
>>12008136
Let me tell you a secret that physicists for some reason don't seem to understand. A function just for being smooth to certain order has a Taylor expansion of that order https://en.wikipedia.org/wiki/Taylor%27s_theorem#Taylor's_theorem_in_one_real_variable you just have to consider the remainder term. The thing about your parameter being small has to do with control of the remainder term if you want to approximate your function by it's taylor expansion, but is not a condition to represent it like that. Now , if you put your function as depending on two variable [math]f(z_1+z_)[/math] yes you can taylor expand however you want and as it is analytic any expansión will converge.

[Anonymous No.12008192]

>>12008176
Condescension aside, thank you. I'm just tired and wanted someone to confirm this for me since I've been out of uni for a long time now.

[Anonymous No.12008213]

>>12007979
https://en.wikipedia.org/wiki/Gateaux_derivative

[Anonymous No.12008229]

>>12002065
Got some bad news for you if you don't like wojaks bruh... There's at least 2000 of them.

https://www.memeatlas.com/wojak-memes.html

[Anonymous No.12008288]

>>12007816
>Replace = with =: and the problem disappears.
I've never seen := used for anything besides definitions. What are you talking about?

[Anonymous No.12008292]

>>12007784
g(f(x)) can be written as xfg

[Anonymous No.12008300]

>>12008158
faggot

[Anonymous No.12008327]

>>12002381
Super based was thinking about that myself the other day
>It is what it is because is has to be
t Morpheus

[Anonymous No.12008352]

Why is the strong operator topology not the strongest topology? Why this retardation with the name?

[Anonymous No.12008356]

The irrationality measure of a real number x is the largest real number u such that there are infinitely many integers p, q with 0 < q and 0 < |x-(p/q)| < 1/q^u. Suppose we define the base-b irrationality measure of a real number x as the largest real number u such that there are infinitely many integers p, q with 0 < q and 0 < |x-(p/b^q)| < 1/b^(q*u). Can you find a number with infinite base-b irrationality measure for every natural number b?

[Anonymous No.12008383]

>>12008327
The Matrix takes quite a bit of influence from Leibnizian metaphysics.

[Anonymous No.12008398]

>>12008383
What the fuck does plato cave has to do with monadism?

[Anonymous No.12008412]

>>12008292
Yes, but the original was f(g(x))
So in that notation it would be x;g;f

[Anonymous No.12008413]

>>12008398
>A movie can only draw inspiration from one philosopher

[Anonymous No.12008427]

>>12008352
It’s the strong operator topology not the strongest operator topology

[Anonymous No.12008446]

>>12008412
f(g(x)) is an abomination

[Anonymous No.12008453]

>>12008446
Not really.

[Anonymous No.12008456]

>>12008446
Its elegant and easy to comprehend the action of the operator

[Anonymous No.12008484]

>>12008413
Not him but holy shi the matrix doesn't even attempt to portray what that faggot wrote. It is literally le brain in a vat + platos cave. Yes Leibniz work is related to these question because he was a rationalist so you can just mention his view over these questions and say that the movie means this, but then I could use Spinoza's philosophy for that matter and claim the exact same thing.

[Anonymous No.12008511]

>>12008427
It still feels like it should be stronger than the norm topology

[Anonymous No.12008534]

>>12008288
1 + 2 =: 3 is to be interpreted as a construction of 3 from 1 and 2 (in the sense of Book II of the Elements, if you like), and the chaining of =: corresponds to composition in the category of Bishop presets and prefunctions.

[Anonymous No.12008552]

>>12008456
No, using g for the first applied function is what's offensive.

[Anonymous No.12008561]

>>12008552
Agreed, desu

[Anonymous No.12008565]

>>12008446
[math]f(g(x))[/math] doesn't qualify for abominability since it isn't a notation, it's literally the definition.

[Anonymous No.12008590]

>>12008565
Unironically this.

[Anonymous No.12008593]

>>12008565
¿The definition of what?

[Anonymous No.12008609]

>>12008534
Never saw this before. As far as I can tell it goes with the outmoded practice of writing every algebraic structure as a set with an equivalence relation and compatible operations. I'm not sure why anyone would want this.

[Anonymous No.12008615]

>>12008593
Jesus Christ, I know I am the single most cancerous poster on this board, but I still hate these inverted question marks so much.

[Anonymous No.12008616]

>>12002075

fuckoff code monkey

[Anonymous No.12008618]

>>12008615
You aren't the drunk slav tranny posting about homotopy and his bf. You aren't the most cancerous.

[Anonymous No.12008652]

>>12002773
Saturday is not isomorphic to Wednesday in the category of the DoW, you fag.

[Anonymous No.12008655]

>>12008618
I'm neither of those, God bless.

[Anonymous No.12008660]

>>12008652
:(

[Anonymous No.12008684]

>>12008593
stay in mexico and use doschan

[Anonymous No.12008691]

>>12008652
well, what would the morphisms in DoW be
i would think the morphisms are a -> b if b comes after a
but weeks are cyclic so every thing would have an arrow
then Sat -> Wed -> Sat would be id wouldnt it be

[Anonymous No.12008701]

>>12008691
>but weeks are cyclic
[citation needed]

[Anonymous No.12008704]

>>12008691
No, no, no.
You take the usual [math]\mathbb{Z}[/math] category.
The week day category has the elements of [math]F_7[/math] as its objects, the morphisms of [math]\mathbb{Z}[/math] with the normal composition, but the domain and codomain maps are composed with [math]f: \mathbb{Z} \rightarrow F_7[/math]

[Anonymous No.12008878]

>>12008691
wth, this is the most basedboy cat theory argument i've ever seen.
your category (naturally not DoW) states that Wed follows Sat and viceversa, but that's tautological. By definition of DoW, Wednesday and Saturday are not isomorphic.

[Anonymous No.12008916]

>>12008704
That doesn't make sense.

[Anonymous No.12008978]

What’s the redpill on parabolas? When I was a youngster they simply taught us to think of parabolas as the graphs of polynomials of the 2nd degree, ax^2+bx+c

I am reading an older text and it introduces parabolas as the equation of points (x,y) such that each point is equidistant from the directrix and the focus. So with the focus being (0,p) and the directrix being y = -p we have x^2= 4py or y = x^2/4p

Is there any reason to choose one representation or the other?

[Anonymous No.12008989]

>>12008978
Think about specifically what you’re asking for longer than a day.

[Anonymous No.12009058]

>>12008916
[math]\mathbb{Z}[/math] is a poset. Posets have a standard category.
Being explicit, [math]\mathbb{Z}[/math]'s morphisms are pairs [math](a, b) \in \mathbb{Z}^2[/math] such that [math]b \geq a[/math]. The domain is [math]a[/math], the codomain is [math]b[/math]. Composition is given by [math](b, c) \circ (a, b) = (a, c)[/math].
The days of the week category has as its objects [math]F_7 = \mathbb{Z} / 7 \mathbb{Z}[/math]. Its morphisms are pairs [math](a, b) \in \mathbb{Z} ^2[/math] such that [math]b \geq a[/math]. The domain is [math]a \mod 7[/math]. The codomain is [math]b \mod 7[/math]. Composition is given by [math](b, c) \circ (a, b) = (a, c)[/math].

[Anonymous No.12009078]

it has been a long time since I've had to do geometry, but I needed to find the area of our pool so I can find out how many gallons it holds. unfortunately it's not a simple rectangle or this wouldn't be a problem, it's got a weird bend in it. I'm pretty sure I've got this right, but I wanted to double check. the angles in my diagram aren't exact, but I did scale the image so I could set the line lengths to their actual measurements in feet so it should be pretty close

[Anonymous No.12009081]

>>12009078
and here's the diagram with just the lengths of the sides

[Anonymous No.12009094]

>>12009058
How will you send your integers to weekdays then? You can send each integer to some fixed weekday and have all the morphisms be sent to identity, you will have to be "locally onstant", or else you will have to treat the week as a preorder instead of a poset. This will not cause any harm, though. It will require adding an extra morphism from Sunday to Monday, but all morphisms will still be unique. In fact, there will then be a unique morphism between any weekdays.

[Anonymous No.12009175]

>>12009094
I thought you were kinda dumb earlier, but I was wrong, you are as dumb as a brick.
Like, I could forgive everything if you just said that the construction is retarded, but this is an extremely small-brained response.

[Anonymous No.12009182]

>>12009175
I almost care about some fat fuck's opinion on me.

[Anonymous No.12009185]

The homotopy group of SO(2) is Z. The homotopy group of SO(3) should be trivial. Can someone describe a homotopy that turns a full rotation around some axis in 3D space into the trivial loop?

[Anonymous No.12009198]

Wow people weren't kidding about the second half of baby Rudin. This is so incredibly dull. Didn't even bother with chapter 11 and just went straight to stein and shakarchi.

I was thinking of taking grad analysis I next semester but if it really gets this boring I might stick to algebra.

[Anonymous No.12009201]

Just finished learning about derivatives and their applications, very interesting stuff, i love it !

[Anonymous No.12009205]

>>12009175
>you are as dumb as a brick.

[Anonymous No.12009207]

>>12009175
I finally got what you initially meant. Your terminology will get better if you keep studying. Anyway, you are basically describing a category with 7 objects and a morphism from any one to any other one.

[Anonymous No.12009208]

>>12009185
>The homotopy group of SO(3) should be trivial
It isn't, that's kinda one of the most important examples

[Anonymous No.12009214]

>>12009198
Just stick with algebra. Analysis is simply not fun.

[Anonymous No.12009221]

>>12009214
>>12009198
Obviously a hard subject like analysis is not fun for people who are not willing to grind enough to reach the fun parts.

[Anonymous No.12009240]

>>12009207
>Anyway, you are basically describing a category with 7 objects and a morphism from any one to any other one.
NO
NO IT ISN'T
WHAT'S WRONG WITH YOU DUDE

[Anonymous No.12009256]

>>12009240
What is it then?

[Anonymous No.12009276]

>>12009256
Not him but the morphisms themselves are from ZxZ, so there are an infinite number of them, the source and target are calculated based off of mod seven. I’m not sure though I literally read one category theory book and am about to be a freshie undergrad so

[Anonymous No.12009281]

>>12007666

[Anonymous No.12009295]

>>12009276
The problem is that his construction has to be one of the following:
>week poset and a constant functor
>week poset and a functor constant on all but at most 6 pairs of consecutive integers
>week preorder and any order preserving functor
If his functor would map n to Monday in the case of a poset, then any m<n would need to be sent to Monday as well, and similarly sending n to Sunday would force the same for m>n.

[Anonymous No.12009299]

>>12008229
based link, needs hazmats tho.

[Anonymous No.12009310]

>>12007666
I'm noone to answer this but I did like, two problems

[Anonymous No.12009382]

>>12008609
>Never saw this before.
I'd be surprised if you did, since it's an interpretation that I made up on the spot (albeit I'm not claiming originality, since the univalent foundation people would have almost surely thought of something equivalent as well).
That said, in terms of algebraic structures, the intention of this interpretation is that =: is working in its internal logic in an automatically constructive manner, by identifying the construction of a term with its definition.

C.f. the HoTT book for example, which treats definitional equality as a primitive notion, and distinct from type-theoretic equality =. As long as you don't interpret expressions containing both := and =, my proposed semantics for definitional equality should be benign (read: paradox-free).

[Anonymous No.12009388]

>>12002000
>smbc
never post this again

[Anonymous No.12009476]

>>12009388
I don't get it

[Anonymous No.12009478]

>>12009476
exactly

[Anonymous No.12009509]

>>12009476
The snowperson is male because it expects to be thanked for not harassing anyone.

[Anonymous No.12009587]

just watched a bunch of videos on projective geometry and it sparked my autism and I'm working on a desmos setup for viewing arbitrary functions projectively
pic related projective parabola which becomes an ellipse when viewed this way
I also picked up Projective Geometry: An Introduction by Rey Casse. Good choice or is it shit?

[Anonymous No.12009607]

>>12009587

[Anonymous No.12009615]

>>12009607
aesthetic

[Anonymous No.12009656]

>>12005576
>2 and three
>When your gender changes half way through the sentence

[Anonymous No.12009667]

>>12009476
Muh male ego

[Anonymous No.12009676]

>>12009476
That's because you're a racist, cis-, heteronormative, white male. If you weren't so evil, you'd understand.

[Anonymous No.12009691]

>>12009058
I'm the original guys, mapping to cosets fucks welldefinedness up the ass, probably what the other guy was trying to say
Taking cosets would have 1 and 8 map to the same object in DoW, so 1<7<8 => M < S < M which is fuck shit we were trying to avoid
The right construction is just taking {1,2,...7} as the objects and taking the morphisms as the restriction of the one on Z^2

But even then you have a choice to define what the first day of the week is
Say you choose to start the week on Sunday and i choose Monday
Then by comparing our categories Sun < Mon in yours, and Mon < Sun in mine
But this is just because i took a different representative for Sun, i took 8 = Sunday, if the rest of our days match up

Also this is just taking a specific run of 7 days as a category, so i find it inappropriate to call it "The Days of the Week" category
its just "The Days of A Week"

in conclusion, fuck cosets, all my homies choose specific representatives and then redefine their operations from that new set.

[Anonymous No.12009695]

>>12009691
There's nothing wrong with cosets.

[Anonymous No.12009715]

>>12009695
most of the time, yeah

[Anonymous No.12009894]

http://milesmathis.com/power.html

[Anonymous No.12009907]

>>12009894
What his endgame bros?

[Anonymous No.12009947]

>>12007605
they usually keep busy other ways then turning to boards to be condescending and pity other people.
rare are the cases where these self-entitled geniuses even think of teaching or passing their "knowledge" ahead. they normally die and all of their delusions of grandeur end in some dust-covered book nobody reads because their insufferable condescendence makes their writings horrible and terrible to read.

[Anonymous No.12009950]

>>12009907
Exposing mathematics for the lie that it is

[Anonymous No.12009954]

>>12009388
this is pretty good

[Anonymous No.12010003]

>>12009894
>As it turns out, proving the calculus with limits is not only unnecessary and inefficient, it is false. It breaks rules and finds fake numbers.
i was fine with him until this part

so hes just too dumb to realize that Finite Difference calc is the same fucking thing as normal calc, and so thinks its infinitely better?

[Anonymous No.12010007]

>>12002000
I fucking hate when women try to write comics none of them are funny and its always blatantly obvious that some dumb bitch wrote it

[Anonymous No.12010010]

>>12010007
ok incel

[Anonymous No.12010011]

>>12009947
>pity
we don't pity people here. no one will receive mercy on this site.

[Anonymous No.12010013]

>>12010010
found the whore

[Anonymous No.12010015]

>>12010013
Have you tried having sex?

[Anonymous No.12010020]

>>12009954
I love how these comics are always a total inversion of reality. A nigger teaching math and a white male being portrayed as a retard when most niggers cant even pass beginners algebra.

It's always hilarious to see the ethic demographic of university level math classes all asian and white with all of the niggers in the low level math classes that should have been completed in high school.

[Anonymous No.12010032]

>>12010020
cool story bro

[Anonymous No.12010035]

>>12010032
2008 called it wants its internet vernacular back

[Anonymous No.12010039]

>>12010035
https://www.youtube.com/watch?v=DBslFRbCXnw

[Anonymous No.12010152]

>>12010020
black science man would like a word with you

[Anonymous No.12010348]

I'm a non-mathfag wanting to work my way through the meme math chart. Thing is, I'm from a non-burger country where some principle of undergrad maths were taught to us in high school. Should I skip Spivak's calculus or should I just power through it? How do I judge?

[Anonymous No.12010380]

>>12002178
Kant: "Act only on that maxim which you can at the same time will that it should become a universal law."

[Anonymous No.12010531]

>>12004125
Differential equations and linear alg leading into systems of differential equations, phase spaces, etc

[Anonymous No.12010539]

>>12010007
go to bed randall, your comic/blag is incredibly subpar

[Anonymous No.12010543]

>>12009185
>The homotopy group of SO(3) should be trivial
why would you think that?

[Anonymous No.12010549]

should I be thinking about differential equations in terms of their solutions, or is there a way to think about them before looking at methods to solve them?

[Anonymous No.12010558]

>>12010549
diff eqs = vector fields

[Anonymous No.12010565]

>>12010348
If you're very familiar with the topics, you can skip it. It's a pretty elementary text albeit convoluted and if you wanna work through the chart I'm sure you have the mathematical maturity to skim over it.

[Anonymous No.12010567]

>mathematical maturity

[Anonymous No.12010573]

>>12010567
?

[Anonymous No.12010603]

>>12010565
Thanks anon. Appreciate the insight. I find it hard oftentimes to judge whether or not I'm 'ready' for a book, if that word even makes sense. What's a good rule of thumb? Obviously I make sure to read the preface and pre-requisites + read chapter 1 to see if it starts off on familiar ground.

Is there really no other way than to rely on meme charts + recs from others? The sheer number of meme charts coupled with the time-sink makes choosing a book a big decision for me. Not sure if it's my 'tism kicking in but I want to make sure I'm making the 'best' choice so to speak when I pick up a text.

sorry for blogpost

[Anonymous No.12010727]

Does anyone here has a link to download a pirated version of Magma?

[Anonymous No.12010740]

>>12007752
they're protestant.

[Anonymous No.12010755]

>>12010007
The author is a male. But his wife also looks very manly and is quite unattractively androgynous.

[Anonymous No.12010909]

>>12010727
Just use Sage.

[Anonymous No.12010916]

>>12010020
that's an indian polcel

[Anonymous No.12010917]

>>12010909
>announcing sage
enjoy your ban

[Anonymous No.12010922]

>>12010917
Mods might be banning left and right on /b/, but I won't be banned for mentioning software.

[Anonymous No.12011048]

>>12010011
pity and mercy are two different things, you condescendent ass.

[Anonymous No.12011056]

>>12010380
This.

[Anonymous No.12011083]

>>12010020

[Anonymous No.12011203]

>>12010727
>magma
iirc you can find it on rutracker. If you don't want to register try simply googling rutracker magma. Also fuck the magma dev cunts, seriously.

[Anonymous No.12011225]

>>12011203
What'd they do to you?

[Anonymous No.12011234]

>>12011225
Being dicks. Like
>no you are not allowed to run our shitty program on two separate hpc's
>oh and also not on multiple cores lololol
No wonder everone pirates this shit.

[Anonymous No.12011268]

[math]exp(x, 0) = x^0 = 1[/math]
[math]exp(x, y) = x^y = x \times x^{y-1}[/math]

[Anonymous No.12011278]

>>12011268
I like you, now someone use induction to prove that the product of exponents is the exponent of the sums

[Anonymous No.12011390]

What do you do when you are working on your research, and stumble upon a problem (worth a lemma) from a different branch that you are not familiar with?
Read books, do exercise, learn relevant ideas just to prove a lemma? This might take 6 months.
Consult other people in that field?
It's basically my situation right now.

[Anonymous No.12011397]

>>12011389
new thread