/sci/ - Science & Math

I passed calc 3, thanks /sci/

If a polynomial takes integer values for an infinite number of integer arguments, must it take integer values for all integer arguments?

If it must, how can I prove it?

>>9394934
>If a polynomial takes integer values for an infinite number of integer arguments, must it take integer values for all integer arguments?
No, consider x/2.

>>9394949
Oh, obviously. I was going to use that as a lemma to prove that a polynomial that takes integer values at "increasing-digit" integers (e.g. 234 or 334556) must take integer values at all integers, but now I'm not sure how to proceed.

>>9395038
>prove that a polynomial that takes integer values at "increasing-digit" integers (e.g. 234 or 334556) must take integer values at all integers
Why do you think this is true?

>>9395046
It's a recreational math problem, and I thought it would be much harder to disprove than to prove. Also, the claim itself is pretty unique, so I suppose I was biased to think it was true.

>>9395060
Here's another fun one:
If a polynomial takes integer values for all integer arguments, does it necessarily have integer coefficients?

>>9395131
I'm thinking no. I'm trying to think of a parity argument by starting with p(x) = x/2 and multiplying by something that turns it into an integer, but I'm not sure how to without resorting to non-arithmetic functions

>>9395148
You are going in the right direction. I can give you a theorem as a hint if you want.

>>9395131
I was too impatient and looked it up after not having figured out a solution within 5 minutes. I'm such an embarrassing brainlet. How did a retard like me obtain a master degree with best grades? University education is fucked up. In a real educational system a moron like me should have no chance. I fucking hate myself and my fraudulent pseudo-intelligence.

>The “derived drift” is pretty unsatisfying and dangerous to category theory (or at least, to me)

https://mathoverflow.net/questions/289259/the-derived-drift-is-pretty-unsatisfying-and-dangerous-to-category-theory-or

>>9395397
>let mathematics develop without the guidance of physics
>it starts running around like a headless chicken

>>9395422
>hypotehesis

I want to go to grad school but my GPA is too low what do

>>9395441
Fuck. Fingers too fast.

>>9395291
>I fucking hate myself and my fraudulent pseudo-intelligence.
Welcome to the club.

Got around 12g of maths textbook pdfs on mega

Would I get in trouble for distributing them? (living in NZ)

>>9394546
Anyone willing to skim over this textbook and tell me how you'd rate it as learning material? I'm a bit more than halfway through it (Chapter 8) and wondering how long it should be taking me to work through it. I'm really keen to get a good foundation so I can hurry up and move on to higher and more interesting maths. Would I be good to move on to a calculus textbook after this? Or should I do a "pre-calc" one first? Trig? My ultimate goal here is to get the basics down.

>>9396079
Forgot link, sorry:
https://www.saylor.org/site/wp-content/uploads/2011/12/SAYLOR-MA001-TEXT.pdf

>>9396079
>how you'd rate it as learning material
3/10; horrible. The whole textbook seems to be phoning in trivial example after trivial example, so as to teach general algorithms and heuristics by rote learning. It's the plug and chug method. Avoid it.
>wondering how long it should be taking me to work through it.
1 or 2 months if you're in middle school (5th-7th grade or so).
1 or 2 days if you've finished high school.

>My ultimate goal here is to get the basics down.
Try Serge Lang's Basic Mathematics instead.

>>9396100
>Serge Lang's Basic Mathematics
Lang is a meme.

>>9396101
No. Lang is great. His books are "memes" for a reason.

>>9395422
>>>/r/taiwan/
>>>/r/dogs/

Anyone wants to discuss physics and dog-eating here? Is this the right thread?

>>9396121
>Anyone wants to discuss physics and dog-eating here? Is this the right thread?
It should be fine as long as it's mathematical discussion (i.e. the economics of the dog meat market).

>>9396121
Yes. We also discuss our deep physical intuitions here. Be sure to use cancerous avatars as well.

>>9396135
>economics
That's pretty mathematical. It should also be fine it's about applied combinatorics related to dogs.
Or maybe applied avatarfagging related to both physics and dogs? Or maybe applied black holes related to taiwan and dogs?

>>9396100
Sorry, I meant as review, not learning material. But yeah it still seems pretty low quality, a lot of the solutions listed in the book are incorrect, I thought I was crazy until realized I was just being gaslighted by typos.
>>9396101
What would you recommend instead?

What are some shit 2hu characters one could use for a disgusting avatar? I'm a physisict and I would like to shit up these threads with my avatarfagging if you don't mind.

>>9396151
>What would you recommend instead?
I would recommend Einstein's books on blacks holes and physics.

>>9396155
Come on anon why are you memeing me? I'm trying to learn, please give me a real answer.

>>9396151
see >>9396155
also keep bringing up how your a physicist preferably attaching images of the same character or characters related to you're character of choice to every post you make and you should keep doing that and getting angry when your posts get deleted for some reason??

>>9396160
>also keep bringing up how your a physicist preferably attaching images of the same character or characters related to you're character of choice to every post you make and you should keep doing that and getting angry when your posts get deleted for some reason??
Are you okay?

>>9396159
How is that not a real answer? Physics is really cool and fun, so are blackholes and astrophysics.

>>9396161
sorry, i don't speak taiwanese. couldn't read your post. maybe you should try communicating via images? preferably the same set of recognizable images.

>>9396159
To what extent do you know calculus?

>>9396161
It's an old troll. Just ignore "his" posts. This >>9396116 is where "he" made "his" entry in the thread.

>>9396159
Read Baez's Guage Fields, Knots and Gravity.
>have an oversimplified toy model of an interaction on a small scale, but get all these interesting phenomena after re-normalizing to a larger scale. I mean, this is essentially what's happening in QFT, right?
Not really.

>>9396168
Is "he" a "her"?

>>9396168
I agree, but I'll have to add the following.
It'll give you a superficial understanding of other areas of math and all you'll be capable of doing is abstract wank that serves no purpose. For instance there's no way for anyone to extract the definition of functional germs from the categorical definition of a sheaf, and the latter isn't nearly as useful (or even usable) in the algebraic geometry of Riemannian surfaces as the former.

>>9396167
Never been exposed to it at all. I had a pretty shit education.

>>9396116
Why do you respond to all of her posts with this?

>>9396175
>can't understand basic quantum mechanics
>wants to study string theory

>>9396176
Right and wrong. Those mathematicians that dislike the supposed "lack of rigor" in physics should also reject statements proven assuming generalized RH/CH.

>attend small, non-meme university
>got memed by my parents that apparently they had no money for uni
>work hard to get scholarships
>got off with $10k debt
>got into meme tier grad school with a world-tier meme prof who offered me a meme amount of stipend of $30k/year
>turned out my parents had prepared 30k in advance to pay off my tuition
>used 20k to pay for the downpayment of a flat in downtown Vancouver
>mfw now I own property at the age of 23

I love /mg/ drama.

>>9396183
>20k downpayment
>downtown Vancouver
You lie.

>>9395131
No. Sounds like what people would gather from skimming Griffith. Go read an actual QM book like Townsend, Sakurai or Landau-Lifshitz.

>>9396187
Assuming anything that is not proven (except axioms lol) cannot yield a proof. Any mathematician thinking otherwise is an idiot.

any recommendations on geometry books? looking for the most rigorous a book can get.

>>9395397
>using incorrect intuition to understand something yields "spooky" results
Wow who would've thunk??

>>9396177
Where did you get the idea that I want to study string theory? I said I wanted to learn the basics of mathematics, that I want to learn the foundations.

>>9395397
Category theory is irrelevant to most of mathematics anyway

>>9396192
Sakurai - Modern Quantum Mechanics
Townsend - A Modern Approach to Quantum Mechanics

>>9396192
Don't listen to >>9396198
Wrong on almost all accounts.
>classical mechanics
Landau-Lifshitz
>electrodynamics
Jackson
>quantum mechanics
Ballentine
>quantum field theory
Weinberg

>>9396194
So you think you know better than someone who has formalized one of the most successful physical theories in existence in sound rigorous mathematical ground?
I'm actually howling right now

Stop it you assholes. It's the winter break. Let's all get along, ok?

>>9396204
Physics is the ultimate intellectual pursuit. Prove me wrong.

Protip: You can't.

>>9396198
>>9396200
these are physics books, you're telling me i can learn geometry from these books?

>>9396198
BUT WHERE WAS LANDAU-LIFSHITZ???
>>9396200
This.

>>9395397

>I can't tell if /sci/ is being raided by CS troll threads or carrying on as usual.
>Will someone please tell me what is going on?
>>9396213
I see he's a fellow Taiwanese.

>>9396207
Schwarz - Topology for Physicists
Atiyah - Geometry and Physics of Knots

>>9396192
I liked the one where Yukari and Yuyuko raped this one village boy.

>>9395397
So... which one of you made that mathoverflow post?

>>9394934
>how can I prove it?
You don't, it's obviously true by physical intuition.

>>9396216
thanks

>>9396219
Kronecker.

>>9396222
how do you know the name of the guy who posts hibikek pictures?

>>9396226
From reading Sakurai and Townsend .

>>9396226
Domain wall defects caused by the ferromagnetic order parameter.

>>9396079
Try Sakurai or Landau-Lifshitz.

>>9396121
Can anyone explain me why physicists are said to eat dogs?

>>9396237
This is discussed in the following literature:
Von Neumann - Mathematical Foudnations of Quantum Mechanics
Shankar - Principles of Quantum Mechanics

>>9396197
Most of mathematics is irrelevant to category theory anyway.

>>9396237
You're fine with buzzfeed journalists who's never taken a course in physics and not beyond highschool math should write articles on black holes and string theory? It's kind of like that.

>>9396226
I didn't make that post although I empathise a lot with him, to the point where I was choking on tears while reading through that thread.

>reviewing notes
>on the part where I constructed rows of exact sequences in equivariant cohomology
>have vertical morphisms between them with an s written on the arrows
>flip through notes trying to find out what these s's are
>turned out they're just tildes drawn on the arrows to denote isomorphisms
>mfw
Fuck these "exact sequences" anyway, they are abstract wank.

>>9396248
>I empathise a lot with him
Why?

>>9396229
What?

>>9396264
Shankar - Principles of Quantum Mechanics

is this general nothing but weebs?

sup piggots

>>9396249
>Fuck these "exact sequences" anyway, they are abstract wank.
They really aren't, even physicists know what exact sequences are.

>>9396270
Welcome to 4chan.

>>9396256
I was attracted to cat theory for the exact same reason, as a window into "ideal"/"platonic" mathematics, a mathematics that is thoroughly elegant, free of impromptu case-by-case technicalities. I still think that this ideal is 'real' or achievable, but it is always outside my grasp.
I am a mediocrity or an abject failure (same difference really) academically, and am considering quitting maths as a consequence.
I'm at my parents' house right now, trying to forget about this sort of shit and clear my mind for a couple of days when here comes this asshole and makes a post about the same sort of existential/vocational issues.

Basically, I am a faggot and a brainlet.
Pic related.

>>9395397
Holy fuck this is hilarious
>waaaah I have to read a real argument mommy give me my deffies back

>>9396273
Fuck them. They aren't physical intuitions.

>>9396275
Schwarz - Quantum Field Theory and Topology

>>9396297
I don't really see the similarities between your post and that one.

>>9395038
>to prove
Don't. Use your concrete physical intuitions about totally non-fictional things (i.e. TQFT). Just read:
Taylor - Classical Mechanics
Goldstein - Classical Mechanics
Also use programming intuitions.

>>9396297
The cobordism hypothesis can be proved, so where are the proofs of this homotopy "hypothesis"?
Answer: there are none, because cobordism hypothesis is the cornerstone of something concrete (i.e. TQFT) while this homotopy hypothesis is the cornerstone of absolute algebraic wank.

>>9396363
Right and wrong. Physicists of the older generation are more likely to reject fancy mathematical constructs, but I'm sure this is about to change.
see Fujikawa - Path Integrals and Quantum Anomalies

>>9396297
What is your research? Quantum computing?

>>9396375
I'm researching the relation of Black Holes to concrete things such as TQFT. Currently reading Sakurai's book on Black Holes and their connections to number theory.

>>9395445
A good place to start is the Landau-Lifshitz series.
1. LL classical mechanics + Goldstein
2. LL E&M + Jackson
3. LL QM + Sakurai
I'm sure you can get through this over the summer.

>>9396382
Isn't this physics though?

>>9396385
>let mathematics develop without the guidance of physics
>it starts running around like a headless chicken

Why is the negation of [eqn]\forall \epsilon>0, \exists N\in\mathbb N :\forall n>N, |x_n-x|<\epsilon[/eqn]
This: [eqn]\exists \epsilon>0, \forall N\in\mathbb N :\forall n>N, |x_n-x|\geq\epsilon[/eqn]
And not this (note the exists before the n>N): [eqn]\exists \epsilon>0, \forall N\in\mathbb N :\exists n>N, |x_n-x|\geq\epsilon[/eqn]

>>9396451
This is caused by the existence of black holes. You can read about it in:
Sakurai - Modern Quantum Mechanics.

I have to take a course in Galois theory but I was pretty shit in my intro to algebra course (groups rings) and got by off of a curve.

How hard of a time would I have being an average student and what are the big ideas I should hit so I don't fuck up.
I'm more than likely going to take a numerical class just to mix it up sine I feel this ship is going to sink.

>>9396451
It's not.

Consider
[eqn] x_n = (-1)^n \\
x = 1[/eqn]
then you would have neither
[eqn]\forall \epsilon>0, \exists N\in\mathbb N :\forall n>N, |x_n-x|<\epsilon [/eqn]
nor
[eqn] \exists \epsilon>0, \forall N\in\mathbb N :\forall n>N, |x_n-x|\geq\epsilon [/eqn]

>>9396451
negation is
[math]\exists\varepsilon>0,\exists N \in \mathbb{N}:\forall n\geq N, |x_n-x|\geq\varepsilon [/math]

>>9396458
It should be fine if you start with Sakurai and Shankar.

>>9396451
Because the first statement is written wrongly.
The correct statement is:
[math] \forall \epsilon > 0 : \exists N \in \mathbb{N} : \forall n \in \mathbb{N} : (n>N \implies |x_n-x|<\epsilon ) [/math]

>>9396375
>What is your research?
Moduli spaces (https://ncatlab.org/nlab/show/moduli+space).).

>>9396475
and the negation of it is
[math]
\exists \epsilon > 0 : \forall N \in \mathbb{N} : \exists n \in \mathbb{N} : (n>N \land |x_n-x|\geq \epsilon )
[/math]
which means that:
"There exists an ε-ball around x, such that all the tails of the sequence [math] \{x_n: n>N\} [/math] don't lie completely inside that ε-ball"

>>9396451
Wait a minute, the one that you think is right is actually the right one
It shouldn't be all n>N. One suffices.

>>9396451
>>9396555
Like, for example. Take x_n=(-1)^n and x=1.
This sequence doesn't converge, but
for all N, for all n>N and n even, |x_n-x|=0<ε

>>9396192
don't listen to those trolls. Depends what geometry.

Classical: From Euclidean to the others: Coxeter Geometry Revisited

For a more axiomatic approach: Hartshorne's Geoemtry: Euclid and Beyond

Differential geometry: Do Carmo's Differential Geometry of Lines and Curves then Riemannian Geometry or Lee's Smooth Manifolds

Topology: Munkres' Topology then Milnor's Topology from a differentiable viewpoint

Algebraic Geometry: General Algebra like Dummit and Foote, or Aluffi's Chapter 0, then Atiyah-Macdonald Commutative algebra, then Shafarevich's Volumes on AG

please help a brainlet out

>proof by induction
[eqn]
\sum_{i=1}^{2^n} \frac{1}{i} \ge 1 + \frac{n}{2}
[/eqn]
This is the proof (omitting base step [math]n_{0}[/math])
[eqn]
\begin{align}
\sum_{i=1}^{2^{n+1}}
&= \sum_{i=1}^{2^n} + \sum_{i=2^n+1}^{2^{n+1}} \\
&\ge 1 + \frac{n}{2} + (2^{n+1}-2^n) \cdot \frac{1}{2^{n+1}}\\
&= 1 + \frac{n}{2} + \frac{2^{n}}{2^{n+1}}\\
&= 1 + \frac {n+1}{2}
\end{align}
[/eqn]
The part I don't get is how he turned
[eqn]
\sum_{i=2^n+1}^{2^{n+1}}
[/eqn]
into
[eqn]
(2^{n+1}-2^n) \cdot \frac{1}{2^{n+1}}
[/eqn]

>>9396464
>>9396461
>>9396475
>>9396566
>>9396555
Is my lecturer retarded then?

>>9396655
He did not turn it into that. Notice that the inequality sign is being used.

All he did was use the fact that [math] \frac{1}{2} + \frac{1}{3} + \frac{1}{4} > 3 \times \frac{1}{4} [/math]

Also known as, a sum of k elements is larger than k times the smallest element of the sum.

>>9396669
Thanks you.

>>9396458
Only thing you need to know well for intro to galois theory (assuming they introduce all needed field theory during it) is basic group theory, including concepts like normal subgroups, solvability of groups, group actions like conjugation, and theorems about them. If you didnt some of these in your algebra class then i wouldnt worry too much, but definitely keep your group theory up to speed.

>tfw got my own imposter
Didn't know I hold this much power over people.

[math]f[/math] is a differentiable function in its whole domain, which is all real numbers. If [math]A(0,1)∈Cf[/math], calculate the following limit:

[math]\lim_{x\to0}\frac{f(x^2)-1}{x}[/math]

Any tips on how to solve this one?
Thanks.

>>9396694
You posted this in the SQT and you got the correct answer. Why are you posting this again?

>>9396698
because I can't use the chain rule.

>>9396700
Jesus fucking christ. Okay, I'll help you. But before I waste my time, tell me exactly what you can use.

>>9396705
Give a sec, I'll post some more info for the whole thing, I need to transfer the photos from my phone to my computer.

>>9396694
Let g(x) = f(x^2). Then g'(x) = f'(x) (2x) by the chain rule.
The limit is just
g'(0) = f'(0) (2*0) = 0
since anything times 0 is 0.

>>9396694
Can you use l'hopital?

[eqn]\lim_{x\to0}\frac{f(x^2)-1}{x}=\lim_{x\to0}\frac{f'(x^2)}{1}=f'(0)[/eqn]

>>9396719
wrong.

>>9396709
Okay, I got the same argument but without using the Chain rule. Hopefully, now you can be happy :

Let [math] u = x^2 [/math]. Then [math] \lim_{x\to0}\frac{f(x^2)-1}{x} = \lim_{u\to0}\frac{f(u)-1}{\sqrt{u}} [/math]. Now use l'hopital rule to prove this is equal to [math] \\ \lim_{u\to0}\frac{f'(u)}{\frac{1}{2} u^{-\frac{1}{2}}} = \lim_{u \to 0} 2\sqrt{u} f'(u) [/math]

Which then goes to 0. Your homework is showing why applying l'hopital's rule is kosher here.

>>9396719
oh damn forgot the chain rule factor, never mind

>>9396363
they seem pretty similar to me. both got stumped by the fact that math is not as "simple" as they wanted it to be and have a case of impostor syndrome.

>>9396719
>-1/0
>l'hopital
learn 2 math

>>9396738
>-1/0
I love how the guy you are answering to is wrong, but you are also wrong. I love it. It is like a chain of retardation.

Anyways, you have a 0/0 situation because f(0) = 1. Retardoid.

>>9396719
>>9396723
>>9396738
>hopital
He's called hospital not hopital. Why are so many americans unable to spell his name correctly?

>>9396723
Wouldn't it be then like pic related, or is [math](u)'=0[/math].

I can use the de l'hopital rule, but this was supposed to be solved without it, though there's no problem solving it with it.

>>9396752
Oh I fucked up.
[math](u)'=1[/math]
Also the pic.

>>9396758
>>9396752
Why are you talking about the derivative of u? I did a change of variable. Have you ever done u-substitution inside of a limit?

>>9396766
So we just treat [math]u[/math] as a number?

>>9396767
I know number is a very vague term, but I don't know shit about math in English.

Take for example the derivative of [math]c[/math]m with [math]c[/math] being a real number.

Then [math](c)'=0[/math]. Is it the same with [math]u[/math]? I can't explain it any better.

>>9396767
Yeah. Explaining why is best left to your neighbourhoods friendly analysis textbook. Let me give you an example. Consider:
[math] \lim_{x \to 2 \pi} \frac{\sin(\frac{x}{2})}{x - 2 \pi} [/math]

This limit goes to -1/2. But let's do a u-substitution to compute it. Obviously let [math] u = \frac{x}{2} [/math]. Notice that [math] u' = \frac{1}{2} [/math]. Then the limit is equal to.

[math] \lim_{ u \to \pi} \frac{ \sin(u)}{2u - 2 \pi} [/math]
Let's now use l'hopital to get
[math] \lim_{u \to \pi} \frac{cos(u)}{2} = -\frac{1}{2} [/math]

What would have hapened if I had multiplied by u'?

>>9396758
>2nd category
I f*cking LOVE Greek!

>>9396749
The correct modern spelling is l'Hôpital you impure maggot.

>>9396297
Can you link that other post? It seems I missed that thread. That way of thinking about category theory is really appealing to me.

>>9396789
>>9395397

>>9396749
>HEY. HEY PROFESSOR. IT IS CALLED HOSPITAL RULE
Haha okay Billy. Please study for your next midterm, you are failing precalculus!

>>9396370
https://ncatlab.org/nlab/show/homotopy+hypothesis#ForKanComplexes

>>9396775
I guess this?
[math]\lim_{x\to 0}\frac{u}{2(u-π)}[/math]
Which doesn't lead to anywhere? Why do I have to fuck up every time.

Also see pic related, it's the next sub-question. Did I fuck everything up or you have to solve it using something else?

Thanks for the help so far anon.

>>9395422
One of the big motivations for the development of spectral algebraic geometry, the most homotopic form of any of this derived stuff, is the study of elliptic cohomology and topological modular forms.

And this is as physically motivated as any of the other shit involved with TQFT.

" A properly developed
theory of elliptic cohomology is likely to shed some light on what string theory
really means." - Witten

>>9396805
>I guess this?
I don't even know what you are doing. But for your question simply let [math] u=2x [/math] Then the limit is equal to [math] \lim_{u \to 0} \frac{f^2 (u) - 1}{\frac{u}{2}} [/math]

[math] \lim_{u \to 0} \frac{f^2 (u) - 1}{\frac{u}{2}} = 2\lim_{u \to 0} \frac{f^2(u) - 1}{u} [/math] and then L'hopital to get [math] = 2 \lim_{u \to 0} 2f(u)f'(u) = 4f'(0) f(0) [/math]

And assuming we are still using the hypothesis of your previous problem, f(0) = 1.

You know, this problems are routine calculations. If you can't do them then I am not helping you by showing you the steps. Just go back to your textbook, learn the rules of the calculations, and then come back to do the problems. There is no reason to be doing problems if you do not yet understand the rules you are supposed to apply.

I got a B in Calculus I with Analytical Geometry. I reviewed my errors on my exams and understand where I went wrong immediately.

How fucked am I for Calculus II?

>>9396821
Well, B stands for Bad obviously but if you understand your mistakes then you shouldn't have a problem.

My only recommendation for you is that in the break you go over differentiation until the point you can find the derivative of any elementary function without even thinking about it. Like a computer. If you can't do that by the time you get into calculus 2 then you are going to learn what being fucked in the ass feels like.

>>9396819
Those aren't supposed to be calculated using de l'hopital's rule. I fucked up by not putting the exponent as a factor, I've been studying since noon and I'm still behind schedule for all this shit.

I used this, which is what they encourage us to do when there's sin(x) in a limit:
[math]\lim_{x\to 0}\frac{sin(u)}{u}=1[/math]

>>9396817
Okay? So what's your point? My point was that category theory serves fine as a tool for other areas of study (which I presume you agree going by how many buzzwords you put into your post) but it's pointless as a self-contained field. There's nothing to guide people towards studying the right thing without external perturbations.

>>9396297
Where is the elegance in category theory? The only elegance I've seen is when you skip tedious algebro-topological proofs by refering to some category theoretical fact. Otherwise it's just technical and tedious per se.

>>9396837
>which is what they encourage us to do when there's sin(x) in a limit:
Yeah, that is also a good method.
>I fucked up by not putting the exponent as a factor
Okay, then it was an innocent algebra mistake. So maybe you can do these problems on your own. Good luck.

>>9396839
>physishit
Entire post ignored.

I like category theory a lot especially Baire's theorem :))

What is the current research on the category of all axioms?

>>9396846
Just saw that you had written [math](u)'[/math] instead of [math]u[/math]. Makes a lot more sense now.

Thanks for all your help, hope I didn't bother you much, most of the mistakes I did was because I've been studying for too long and I can't think very clearly. Have a pape, it's a photo I took.

>>9396858
>>physishit
Who are you quoting?

>>9396866
see >>9396858

>>9396864
No problem. It is not good to study too much, at least not continuously.

>>9396863
>What is the current research on the category of all axioms?
It's been a while since I've spoken to my department's axiom category theorists, but last time they were working on the derived category of derived axioms and the [math]\infty[/math]-category of [math]\infty[/math]-axioms

>>9396839
The MO post was complaining about how the development of category theory has drifted to fit the needs of homotopy theorists and people studying derived geometry, and the result of this is a bunch of competing models for what the "right" definition for these higher categorical constructions should be. Almost all of these models are very simplicial/homotopical in nature and look (at least at first glance) quite different from ordinary category theory.

Your post seemed to imply this was because there was no physical motivations for any of these constructions, which is not entirely true.

I'm a brainlet, but is there any actual point in reading Apostol or Spivak for calculus, or will an Advanced Calculus course or textbook still teach you the same thing only better?

>>9396957
>but is there any actual point in reading Apostol or Spivak for calculus
No.

>>9396957
>>9396957
In general I think Spivak is a very good introduction to mathematical methods and ideas, but the focus is a fair bit narrower than apolstol or really most calculus books to the point where you'll need to pick up another book anyway when you want to work on multivariable or analytic functions.

To me combining doing Apolstol then Flanigan's complex variables and a beginners analysis book such as Bartle and Sherbert is the superior way to go in learning calculus than spivak first because of vol 2. of Apolstol

Either way they're good books

Does there exist a discontinuous linear functional [math]f: \mathbb{R}\to\mathbb{R}[/math]?

>>9397053
No. Every linear map on a finite dim. space is continuous.

>>9396876
>derived category of ... and the ∞-category of ...

Those terms should really mean the same thing. Unless the ∞-category is stable and "derived category" refers to the underlying triangulated category (i.e. the homotopy category of the stable ∞-category).

>>9397172
>those terms should really mean the same thing, except when they don't
Scientifically speaking, what did he mean by this?

>>9397217
>he

>>9397217
The term "derived category" does not really have a standard definition outside of the classical notion of "derived category of an abelian category".

Classically the derived category of an abelian category is given by localizing the category of chain complexes at quasi-isomorphism.

Viewing the category of chain complexes as a model category, with quasi-isomorphisms as the weak equivalences, this is the homotopy category of the model category.

To every ∞-category we naturally define an associated 1-category, called the homotopy category of the ∞-category .

When the ∞-category is presentable by a model category, the homotopy category of the ∞-category is the same thing as the homotopy category of the model category.

A stable ∞-category is a sort of higher categorical version of an abelian category, and its homotopy category has a structure of a triangulated category (just like the classical derived category). So sometimes this may be referred to as the derived category of the stable ∞-category.

However ∞-categories are naturally developed from a derived/homotopical point of view, so they may just be referred to as "derived" versions of categories.

>>9395397
>https://mathoverflow.net/questions/289259/the-derived-drift-is-pretty-unsatisfying-and-dangerous-to-category-theory-or
Any psychologists on /sci/?

What would you diagnose this category theorist with?

>>9397461
Doing category theory requires proving a bunch of things that are essentially trivialities.

Doing higher category theory requires proving actual theorems in (simplicial) homotopy theory.

Clearly the category theorist is scared for his future because he can't do actual math.

>>9397053
Get a Hamel base [math]B[/math] and assign to each [math]b\,\in\,B[/math] a non-null [math]\lambda_b[/math]. Finish by introducing [math]f:\sum_{b\,\in\,B} x_b\,b \,\longmapsto\, \sum_{b\,\in\,B} \lambda_b\,x_b\,b[/math]. If all [math]\lambda_b[/math]s are equal, you get the classic [math]f:x\,\longmapsto\, \lambda\,x[/math], otherwise you get something so ill-behaved its graph is dense in the plan.

>>9396067
>Would I get in trouble for distributing them?
Not if you don't get caught, just distribute it to people you trust and no one else, to be honest I've never heard of someone actually getting in trouble for downloading a book, hell many of my teachers have acknowledged that students do this and admit that if a student has downloaded a textbook as long as they don't tell the prof then no harm, no foul.
>>9396192
I'll second a lot of what >>9396645 said but add some
Classical Geo: Berger Geometry I & II
Diff Geo and topology: Anything by Fomenko, Jost, or Milnor
AG: Holme is good for undergrad, Vakil is good for grad

Also what the fuck happened in this thread? Holy shit. Also I'll share a math joke I saw that was pretty funny. A good paper is a like a miniskirt, short enough to be interesting, but long enough to cover the subject.

>>9396668
Yes, and you should tell him so.

>>9397846
How do I prove (or disprove?) that a polynomial that takes integer values at "increasing-digit" integers (e.g. 234 or 334556) must take integer values at all integers?

>>9397863
Define "takes integer values at 'increasing-digit' integers (e.g. 234 or 334556)."

>>9397866
\forall x (expressed in base 10) \in Z such that for every digit d_i of x (going left to right), d_k \leq d_{k+1}, p(x) \in Z.

>>9397872 let's try this in LaTeX
For all x (expressed in base 10) [math] \in \mathbb Z [/math] such that for every digit [math] d_i [/math] of x (going left to right), [math] d_k \leq d_{k+1} [/math] , [math] p(x) \in Z [/math].

>>9397879 More rigorous now
For all x (expressed in base 10) [math] \in \mathbb Z [/math] such that [math] \forall k \in \mathbb N, \lfloor \frac{|x| \pmod{10^k}}{10^{k-1}} \rfloor \geq \lfloor \frac{|x| \pmod{10^{k+1}}}{10^{k}} \rfloor [/math], [math] p(x) \in \mathbb Z [/math], where p(x) is a polynomial.

>>9396845
You're mistaking category theory with its usage in other fields.

>>9397686
>what the fuck happened in this thread?

I see two possibilities: either the guy who posts with those anime pictures is suffering from some sort of dissociative personality disorder, or some other autist went to the trouble of saving his images and analysing his posting style in order to convincingly reproduce it for the purposes of (you) farming. In short, it's just /mg/ business as usual.

>>9398228
>went to the trouble of saving his images and analysing his posting style in order to convincingly reproduce it for the purposes of (you) farming.
That's some premium autism right there.

Well I might as well throw this out to all of /mg/, what are you working on right now? Any research or text? What's the subject? Enjoying the holidays?

Why is combinatorics so comfy lads

>>9398369
>combinatorics
>comfy
Are you a robot?

>>9398369
Since with deals with such basic questions that are omnipresent in all of mathematics it lends itself to having a lot of interesting interactions with other fields from algebraic topology, ergodic theory, graph theory, number theory, hopf algebras, and more. I would also say that the type of arguments in combinatorics have a certain charm to them, frequently they are quite clever and help give you a new preservative on many types of problems that have a similar structure, as lots of problems in math can be reduced to counting problems

>>9398256
>Enjoying the holidays?
Speaking of holidays, what music does /mg/ listen to? Do you listen to music while you work/study?

>>9398428
>what music does /mg/ listen to?
Most music really, I find that most genre have at least one song you'll like. I really like classic rock, jazz, swing, comedic music (Tom lehrer and flight of the Conchords mostly), Cabaret, and some other music of which I have no idea what genre they really belong to.
>Do you listen to music while you work/study?
Depends, when I'm thinking a research question I usually have some background music playing while I pace around, I just put on whatever I in the mood for but won't overly excite me. I put on music I especially like anytime I'm writing/typing up a solution since I'm actively listening to it then. I don't put any music on when reading papers/books though, it gets too distracting.

>>9398428
>what music does /mg/ listen to?
https://www.youtube.com/watch?v=LWDVnWWmk8c

>>9396957
My opinion is that "rigorous calculus" texts are stupid ideas.
Lots of people aren't ready to read them by the time they need a calculus book (mostly those who never took calc in high school, and/or those who never got any real exposure to elementary math).
If you are ready to read it, you can handle a proper analysis book and shouldn't bother wasting your time on a book that tries to disguise analysis as baby calculus and butchers both in the process.

>>9396888
>The MO post was complaining about how the development of category theory has drifted to fit the needs of homotopy theorists and people studying derived geometry
I don't understand why this upsets him so much.
Category theory was born with the purpose (more or less) of making homology not aids. It's always been an integral partner of algebraic topology; the "d00d so abstract and d33p" version of category theory has never even existed except as a meme.
It's like he thinks the people who created his theory are somehow hijacking it for their own purposes.

>what are you working on
Trying to determine homotopy groups for certain classes of moduli spaces (stacks) of quartic (hyperelliptic) curves.
>Any research or text?
You could check out Shigeru Mukai's An Introduction to Invariants and Moduli for exactly what it says on the tin if you're interested in the subject.
>Enjoying the holidays?
Yeah. Well, I'm mostly lazing about, but I needed this. I was planning to go skiing sometime these days but I'm not really sure if it's a good idea after considering it some more. (It's too crowded this time of the year.)
>what music does /mg/ listen to?
https://www.youtube.com/watch?v=dCSny4eRzYI

>>9398563
Some of us are actually yearning for a "deep" theory that is more than a "meme". I guess you will never understand because you seem to look for getting something else entirely out of mathematics. Maybe doing math is no different from solving a fun puzzle to you, but know that there are people out there for who the practise is closer to a prayer than a game.

>>9398572
>>9398563
Some of us are actually yearning for a "deep" theory that is more than a "meme". Maybe doing math is the same as solving a fun puzzle to you, but know that there are people out there for whom the practise is closer to a prayer than a game.

>>9398586
>"deep" theory
What does this mean?

>>9398590
A (foundational) theory that explains why mathematical stuff is the way it is, instead of merely providing an elementary toolbox or a walled garden for mathematics as is commonly practised.

>>9398572
That book actually looks cool, might check it out, the suite you posted is enjoyable. You a grad student? You said you needed this so I imagine it must've been a rough semester, well at least that's the sort of experience I've been having.

>>9398599
>A (foundational) theory
So merely an encoding of mathematics as is commonly practiced?
>why mathematical stuff is the way it is
How does a mathematical theory answer such philosophical questions?

>>9398586
>Maybe doing math is the same as solving a fun puzzle to you, but know that there are people out there for whom the practise is closer to a prayer than a game.
cringe

>>9398601
>that's the sort of experience I've been having.
I don't know what else to say but hang in there anon. I'm not one to give advice since I am not sure how I'll deal with my own impediments myself.
>That book actually looks cool
It helps if you have at least a passing interest in classification problems and like to construct objects. I think they also have applications in physics but I couldn't care less about that shit.
>You a grad student?
Something like that.

>>9398428
Lately I've been listening to stuff like these:
https://youtu.be/t3wGQME-V9s
https://youtu.be/igMxJ-66CmA
https://youtu.be/HyImgF-1NPw
https://youtu.be/SW8oGnusHUo I know it's not Christmas anymore, but this is the most appropriate Couchereau for today. Also, I listened to Jussi Björling with my granny, like we do every year. His interpretation of "O helga natt" is her favourite.
Stuff to listen to while writing, but not so much while reading.

>>9398256
Slowly starting the book on algebraic homotopy by Baues. I like his style, I like how he explains various approaches of homotopy theory, and makes some remarks on the implicational relationships between various axiomatizations.

>>9398572
What would the prerequisites be like for that book?

Just how much of a brainlet am I if I can never prove Minkowski inequality without looking it up? I always get stuck at Hölder, even though I kinda remember what kind of tricks you're supposed to use.

How the fuck did the people come up with this shit back then?

>>9398586
Thank you for this post. It's very rare for me to see other mathematicians who share my viewpoint, which you managed to capture in a very concise way.
I've always thought that mathematicians can be classified in three broad categories: First, there are the mathematical physicists, who see mathematics just as a toolbox that can be applied. Those are the people from whom you are most likely to hear jokes such as "mathematics is the language of nature", implying that mathematics has no use unless it can be directly applied to some physical model. Then there are the "computer scientists" (even if they don't actually do CS), the mathematicians who see math as a game or a puzzle to be solved. One that is particularly interesting and hard, and which can offer the player enduring fame and glory, but a game nonetheless. Finally, there is the philosopher (in the etymological sense of the word, not necessarily one who practices philosophy as understood today); the lover of knowledge, the mathematician who has a belief (faith) that mathematics is one of the few disciplines where humans can attain understanding. The author of that mathoverflow post seems to understand this viewpoint in a way similar to mine.
For the record, I am not claiming at all that one of those types is better than the rest. My own bias is evident, but that can't be helped for a matter as personal as this.

>>9398817
Your classification is retarded.
Most mathematicians would not fit into any of those designations; an operator theorist is very unlikely to think he's just solving Erdos-style puzzles but he's also not jerking off over the meaning of meaning of meaning of mathematical meaning.

>>9398834
Yes, I agree with you. I forgot to mention that those categories are not meant to be mutually exclusive at all (indeed, most mathematicians share characteristics of at least two of those categories), but I maintain that there is one "main" category that corresponds to the "reason" why a person does mathematics. My descriptions where meant to be about the canonical example of a mathematician in each category (Erdös is indeed who I had in mind for the second one, Feynman would be close to the first one even though he is not a mathematician, and Grothendieck fits the last one). So an operator theorist would fall between 1 and 2 or 2 and 3 depending on how interested he is in applications to quantum mechanics.

>>9398817
>mathematical physicists
>mathematicians
Stopped reading right there. You are retarded.

>>9398859
>Stopped reading right there. You are retarded.

>>9398851
I don't think Groot took nearly as pretentious an attitude toward mathematics as you think he did. There are quotes from Recoltes et Semailles where he describes his work as playing a game.

>>9398772
> prerequisites
A solid grip on algebra, basic arithmetic/number theory, knowing your way around geometry on manifolds, and some category theory.
It's a pretty terse book.

>>9398871
'Pretentious' is a loaded term.

>>9398871
"Yet it is not these gifts, nor the most determined ambition combined with irresistible will-power, that enables one to surmount the “invisible yet formidable boundaries” that encircle our universe. Only innocence can surmount them, which mere knowledge doesn’t even take into account, in those moments when we find ourselves able to listen to things, totally and intensely absorbed in child’s play."
Maybe that's one of the quotes you had in mind? I accept that my post sounds pretentious, but that has more to do with my incompetence in making myself clear than with my own intentions. Anyways, the kind of play Grothendieck mentions here is definitely in line with what I have in mind, the key words being "child's play" and "innocence". The intentions of the puzzle solver feel more "impure" to me, since his single-minded objective of solving a problem makes him less receptive to the worlds he explores. Again, I'm not quite satisfied with how I'm describing this distinction, but it will have to do for now.

>>9398876
Thanks. I could try to make myself comfortable with manifolds the next spring. You mentioned geometry. Which kind?

>>9396081
>pic
>be engayneer
>can't get As without trying
brainlets, all is brainlets
t. ee bachelor math phd

Gonna need an extraordinarily QUICK rundown on the beef of finite dimensional vector spaces.

Also, what are some common proof tactics when proving things in linear algebra?

>>9398952
>proving things in linear algebra
direct proof method

>>9398952
Basis, basis and... basis.

>>9396327
An exact sequence in the derived category of a calabi-yau can be interpreted physically as a bound state of D-branes in the topological B-model.

>>9398572
>homotopy groups for certain classes of moduli spaces (stacks)


How do you define homotopy groups of a stack?

>>9396327
A short exact sequence in the derived category of a calabi-yau can be interpreted physically as a bound state of D-branes in the topological B-model.

>>9398991
>string theory is physics

>>9398993
It is

What's Australian cateogry theory?

>>9398915
>You mentioned geometry. Which kind?
From curves and surfaces to abstract projective spaces. You also need to be familiar with stuff like vector bundles and elementary sheaves, basic differential geometry notions, de Rham cohomology etc.
It's an algebraic geometry textbook written for graduate students and researchers that's meant to serve as an introduction to invariant and moduli theory. Anything in it that doesn't directly pertain to that will either be introduced in a very summary way ("recall that...") or simply be given a reference for to some other book.

>>9399002
It's something subhuman physishit avatarfags such as yourself should ask on >>>/r/eddit/

>>9398991
>short exact sequence
Abstract algebraic wank which isn't based on any physical intuitions. Didn't even read past this point.

How do I prove (or disprove?) that a polynomial that takes integer values at "increasing-digit" integers (e.g. 234 or 334556) must take integer values at all integers?

>Anon, please define "increasing-digit integer"!
For all x in Z, x is an increasing-digit integer if [math] \forall k \in \mathbb N, \lfloor \frac{|x| \pmod{10^k}}{10^{k-1}} \rfloor \geq \lfloor \frac{|x| \pmod{10^{k+1}}}{10^{k}} \rfloor [/math]

If ya'll nibbas wouldn't be in the field of maths, what would your second choice have been?

>>9399053
>If ya'll nibbas wouldn't be in the field of maths, what would your second choice have been?
Theology

>>9399069
Why, and in what way does maths win out?

>>9398986
For example via the topos associated to the étale sheaves of the stack, but you can also do it purely abstractly since algebraic stacks are a 2-category and the 2-morphisms between them behave like homotopies. This is the general idea in any case, the details are what I'm trying to figure out.

>>9399016
gimme a break, I had googled it but didn't get any result

>>9399098
religious truths come second only to mathematical truths

>>9399025
I think you can prove that such a polynomial has rational coefficients by repeatedly applying polynomial division. But this doesn't make any essential use of the increasing digit property.

>>9399025
This is neither true nor false.

>>9399124
>religious truths ≠ mathematical truths

>>9399025
Reductio ad absurdum.

>>9396370
>programming intuitions
what exactly did you mean by this?

>>9396655
Might be worth pointing out that you see the exponential 2^n=m there because that sum up to m (harmonc numbers H_m) asymptotically are, roughly
1/2 + log(m)

>>9398851
I agree with >>9398871 and think Grothendieck was more driven by being better than others than by "how pure math is" as a get-go.

I have a strong disagreement with the guy in the Mathoverflow post at the end, where he says that to study philsophy and reason about ethics theories, you must know about simple mathematical theories such as linear algebra. Mathematical, formalized logics don't have a monopoly on reasoning - in fact I think the core formalization that exists since Frege is good and the most effective one to get to a point where we can build iPods, but there are many good non-formalizable notions of reasoning. You can use logic and math to work out staticas of some data you gather, but logic won't help you with a good timely (!) theory about ethics any more than it will help you when you have a fight with your girlfriend. Knowing
(A => B) => (not B => not A)
helps me even beyond math, but that doesn't mean it's necessary to reason as a human. I wouldn't go into this fuzzy talk if the guy in the MathOverflow post not literally cry about death and the reason to live.

>>9398369
I think it's a cool subject because it gives procedural meaning to plain propositions. You see some sum formula where terms cancel each other and you may algebraically prove it, but you can alsouse inclusion-exclusion and see what the cancelations actually amount to. Or in some cases you device a counting procedure where you pocket items in this and that way (double counting). This is refreshing in the same way that geometric "proofs" of the pytagorean theorem (or similar things) give meaning to equalities.
That being said, combinatorics can also be ugly in the way that number theory is - ad hoc proves left and right.

>>9396859
:^)

>>9399227
>Grothendieck was more driven by being better than others
And you base this on what exactly?

>>9398817
Where does a brainlet like me get access to mathematics that deepens my knowledge?
I have never thought about math as a discipline, and more as a tool (like you mentioned).
I love acquiring knowledge but I merely lurk most of the times here on /sci/ (I mostly browse /lit/ and /his/) so I have no idea where to start.
Please elaborate and share your thoughts.

>>9399233
In the bonus DVD behind the scenes extras of Dodgeball: A True Underdog Story, Ben Stiller reveals that he spent months researching Grothendiek in order to perfect his role as Globo Gym leader White Goodman.

>>9399227
>:^)
>using avatars
Reddit filth is not welcome here.
>>>/r/eddit/

>>9399233
stories of the in-fights for acknowledgement in french academia, with Delinge and the bunch.

Here's a short public bio and discussion, but I'm not sure that's the source where I picked this idea up
http://xahlee.info/math/i/Alexander_Grothendieck_cartier.pdf
There's also a book, but I didn't read it.

>>9399312
I've been using Emma Stone pics on /sci/ since 2009, would be dishonest to discontinue it

>>9399363
You being a subhuman redditor since 2009 is not an excuse.
>>>/r/eddit/

>>9399363
Idiot Grothendieck hated this aspect of academia and he even wrote a book about it: Recoltes et Semailles

>>9399379
You can be a capitalist businessman and still cry and complain about the system.
Hey, I'm a big fan of jerking off Grothendieck myself, but I find it equally as likely that he was fame driven genius.
Gauss was as well, going as far as coming up with theories, letting it spit out theorems and conjecturing a bunch of unheard of things before releasing the corresponding theory to the public only years later.

>>9398871
Grothendieck was also a bit up his own ass, he also describes in his book his realization that he was "working for the establishment" is that a bunch of kids basically said he "with the man" cause he worked at IHES. He was such a fucking autistic contrarian that he had to go live in the fucking mountains to prove that he was a true authoritarian.
>>9399363
I'm gonna need some sauce on that pic anon

>>9399379
I can confirm this, he told it to me personally.

>>9399407
https://www.instagram.com/dubnitskiy_david/

[math] \int_0^t {\mathrm d} \sqrt{s} = \sqrt{t} [/math]

>>9399053
i see it clearly

suicide

>>9399053
>ya'll nibbas
Stop speaking like a nigger

How to get into analytical number theory? Apostol's?

>>9399014
Maybe I should read some introductory alg geo text then. Thanks for helping!

Higher Theory and the Three Problems of Physics
Antti Veilahti
https://arxiv.org/abs/1712.09454

According to the Butterfield--Isham proposal, to understand quantum gravity we must revise the way we view the universe of mathematics. However, this paper demonstrates that the current elaborations of this programme neglect quantum interactions. The paper then introduces the Faddeev--Mickelsson anomaly which obstructs the renormalization of Yang--Mills theory, suggesting that to theorise on many-particle systems requires a many-topos view of mathematics itself: higher theory. As our main contribution, the topos theoretic framework is used to conceptualise the fact that there are principally three different quantisation problems, the differences of which have been ignored not just by topos physicists but by most philosophers of science. We further argue that if higher theory proves out to be necessary for understanding quantum gravity, its implications to philosophy will be foundational: higher theory challenges the propositional concept of truth and thus the very meaning of theorising in science.

>>9399772
Moi Antti!

>tfw undergrad

What's the most efficient way to integrate over a high dimensional simplex? Monte carlo integration?

>>9396176
How assblasted are you? Yukariposter came in you so hard that even after months you are still recovering and butthurt? Stop embarrassing yourself

what is Grothendieck's Tohoku paper about and what are the prerequisites (besides being able to read french) ?

>>9400306
>How assblasted are you? Yukariposter came in you so hard that even after months you are still recovering and butthurt? Stop embarrassing yourself
Did you reply to the wrong post?

>>9400310
>what is Grothendieck's Tohoku paper about and what are the prerequisites (besides being able to read french) ?
Homological algebra
https://en.wikipedia.org/wiki/Grothendieck's_T%C3%B4hoku_paper

>>9399751
It would help but it's not exactly necessary.

>>9399772
Why is a sociologist writing about math and physics?

>>9400277
pls respond

>>9400438
I don't know. Not my field.

>>9394546

>Talk maths

flaming homo detected

>>9400465

XD

>PhD in mathematics
>300k starting salary

tfw you cabt into math :•|

Seriously wish I paid more attention to stats or something early on in Life. Things wouldve be so much different...

>>9400277
>>9400438
Most of the methods in this article
http://web.maths.unsw.edu.au/~z2265001/preprints/DKS2013_Acta_Num_Version.pdf
should be adaptable to simplices

>>9400468
Why the transphobia?

>>9400311
yes i did!! sorry anon
>>9396116
See: >>9400306

>>9399747
Montgomery and Vaughan is the gold standard but it's also a bit of a brick, and probably intended for grad students (not to say it's inaccessible to undergrads).
If you want a quick and not-too-hard intro there's a really cool book called the Prime Number Theorem by Jameson which just develops (shocker) the prime number theorem and some applications.

>>9398946
I'm sorry that you have some form of autism that enables you to do that.
t. suicidal EE undergrad

>>9400306
>Yukariposter
Is that the avatarfag dog-eater from C*nada? Why would anyone stop despising such a pathetic being?

This is the best general on 4chan. All the autistic drama is the cherry on top of the cake. Seriously.

>>9400668
>This is the best general on 4chan.
Every general is fucking trash, so being the best simply means being a general.

>>9400673
Stop being a prissy faggot. Embrace the gutter.

>>9400668
>All the autistic drama is the cherry on top of the cake
Autist drama _is_ the cake anon. Just like any general.
There's no actual discussion of math here, it's just a front.

>>9400680
>Embrace the gutter.
I prefer to leave those sorts of activities to vulgar peasantry (of which I am not a part).

>>9400688
> (of which I am not a part)

>>9400484
But that doesn't address the question of which integration method is most efficient.

>>9400697
A vulgar peasant not being able to see the truth is rather obvious.

>>9399779
Please record yourself speaking and post it to vocaroo or someshit. I like highly vocalic languages a lot.

https://www.youtube.com/watch?v=OSacz4GHQjs

>>9397247
Narf

>>9400729
I'd rather not, I hate my voice. But I will give you something else. The poet on whose poem this is based was a master of words, his stuff often sounds like Quenya: https://www.youtube.com/watch?v=VDZHVmlwm6E

What are the most important tools from linear algebra with respect to projective geometry?

>>9400680
>faggot
Why the homophobia?

How is everyone doing?

>>9400923
Determinants.

>>9400923
So far what ive done in projective geom is all things to do with the resultant which is just determinants so yeah

>>9401046
>>9401079
Determinants pop-up all over the place in projective geometry. From obvious stuff like coplanarity conditions, which are expressed as the vanishing of some (k+1) by (k+1) determinant, where k is the dimension of the projective space (just think about [math] \mathbb{P}^2 [/math]), to less trivial things like projective invariants, which are expressed as rational functions of determinants.
Come to think of it determinants are one of the most important tools to come out of linear algebra, period.

>>9401112
>muh linear algebra done right

>>9401116
What did he mean by this?

[math]f[/math] is a strictly increasing function, for which the following relation is true for all real numbers:

[math]f^3(x)+2f(x)=x+1[/math]

I need to find the range of [math]f(x)[/math], which I can tell is [math]\mathbb{R}[/math].

Please help I am tired.

what's a good book on the properties of real functions? no calculus, just stuff like parity, periodicity, injective/surjective definitions

Every analysis book I've looked for just defines the concept of a function and immediately skips to continuity.

>>9401138
wikipedia

>>9401135
idk but I agree that it seems like R
I don't see why it wouldn't be

>>9401152
I still need to prove it, though.

>>9401135
Well, if f is continuous only thing that could restrict the range would be horizontal asymptotes? So maybe show that there can't be one?

>>9401162
I need to prove that [math]f[/math] is continuous, and I haven't been taught asymptotes yet, so I can't use them, can you think of any other way?

>>9401135
what's clear is that x=-1 is the only zero and the derivative is
[math] f'(x) = \dfrac{1}{2+3f(x)} [/math]

Since the derivative tends to zero for large x, it's not completely clear that it would diverge there (e.g. the error function doesn't), but indeed mathematica gives results that have all of R as image.

Hope that helps.

You can probably also show that
f(x) = (x+1)/2 + x^3 * g(x) + g(-1)
for some g, but I'm not sure if that helps

>>9401169
try solving for f(x) and subbing it back in
maybe after taking the derivative three times to get f'''(x)

>>9401176
If there is an upper asymptote a>0 then f(x)<a for all x. Now fix x', then f(x')(f^2(x')+2)=a(a^2+2)-e=x'+1
Now choose x''>x'+e, then f(x'')(f^2(x'')+2)=x''+1>x'+e+1=a(a^2+2) which means that f(x'')>a.

>>9401176
>>9401178
It's not mentioned that [math]f[/math] is differentiable, so you can't assume that [math]f'[/math] or any greater derivatives exist.

The inverse function of [math]f(x)[/math] is this one:

[math]f^-1(x)=x^3+2x-1[/math]

Would this be a valid answer:
Since the domain of [math]f^-1[/math] is the range of [math]f[/math], which is all real number (since I didn't have to take any restrictions for x while I was solving for [math]f^-1[/math]), then the range of [math]f[/math] is all real numbers.

>>9401196
but f must be differentiable because of the f^3(x)
is that not the third derivative?

>>9401205
No it's [math]f[/math] to the power of 3.
I was told that from the third derivative, or greater, we use this one:

[math]f^(3)[/math]

>>9401196
how'd you get that inverse? just swap x and f(x) then reduce?

>>9401214

>>9401135
is f arbitrary, so long as it's increasing? consider exponential function, the range is certainly not [math]\mathbb{R}[/math]

>>9401157
>I still need to prove it
Why? It's fucking obvious from using basic physical intuitions.

>>9401431
>fucking
Why the vulgarity?

>>9401411
the inverse is a polynomial

>>9401431
>HURR DURR ITS OBVIOUS YOU FUCKING STUPID OR SOMETHING GIVE ME MUH MATHZ DEGREE NOW !1!!!!111!!1!

>>9401462
>>HURR DURR ITS OBVIOUS YOU FUCKING STUPID OR SOMETHING GIVE ME MUH MATHZ DEGREE NOW !1!!!!111!!1!
Who are you quoting?

>>9401475
>ask question on /sci/
>smartass doesn't know the answer to a question but has to say something
>spits out a wanna-be smart answer
>get told for his bs
>gets mad

who would have thought
why do ppl have to shitpost on this board as well

>>9401481
>>ask question on /sci/
>>smartass doesn't know the answer to a question but has to say something
>>spits out a wanna-be smart answer
>>get told for his bs
>>gets mad
Who are you quoting? Did you mean to quote a different post?

>>9401483
I am confused at this point. You aren't baiting.
What is "physical intuitions", I couldn't find anything on Google apart from some irrelevant articles, nor could I link it to anything in my language apart from gut feeling.

>>9401481
Do not respond to posts above your physical intuition maturity level. It's in bad taste.
>>9401489
>What is "physical intuitions"
see Sakurai - The Topology of Black Holes via Number Theory

>>9401234
Incorrect. See Kolenkow & Kleppner - An Introduction to Mechanics page 157 for an explanation.

>>9401196
Sounds like what people would gather from skimming Griffith. Go read an actual QM book like Townsend, Sakurai or Landau-Lifshitz.

>>9401506
this has nothing to do with solving the sub-question

what kind of answer is this

>>9401517
In what way does that post not answer your question? Have you ever been to a CS conference? Their shit's even more fucked up lmfao

>>9401515
>>9401510
>>9401520
>look mum, I am an internet bad guy

>>9401489
>What is "physical intuitions"
It is a popular proof technique used in physics. You can use it to drastically simplify almost all proofs by reducing them to one use of the "physical intuition" inference rule.

>>9401526
Why does one shitposter try to come out as many

>>9401536
Sorry?

>>9401539
literary can't find anything that matches what you suggested it means

>>9401539
>Sorry?
For what?

>>9401550
It is pretty well known in the physics community. But it's not consistent with classical or intuitionistic logic since modus ponens does not hold in general, so it is mostly taken as an informal principle rather than an inference rule.

>>9401571
>modus ponens
not science or math

>>9401576
Wrong on almost all accounts.
It is discussed in:
>classical mechanics
Landau-Lifshitz
>electrodynamics
Jackson
>quantum mechanics
Ballentine
>quantum field theory
Weinberg

For once the aping shitposter did a good thing. That little shit thought we'd solve his homework. Boy was something coming his way!

HAHAHAHAHAHA
Please kill me.

>>9401713
Assuming anything that is not proven (except axioms lol) cannot yield a proof. Any mathematician thinking otherwise is an idiot.

>>9401732
That's not technically correct.

>>9401747
Right and wrong. Those mathematicians that dislike the supposed "lack of rigor" in physics should also reject statements proven assuming generalized RH/CH.
As for the correctness of my statement, see Sakurai & Einstein - Mathematical Foudnations of Black Holes

>>9401437
Read Sakurai, he explains it in great detail.

>>9400923
The most important tool would be a linear black hole. I suggest Von Neumann's "Principles of Quantum Mechanics" if you wish to understand them. It was written so that even someone of your intelligence would be able to follow.

>>9399747
The best choice is Sakurai - Spin, Statistics and All That. Though that is not to say that you won't struggle with it.

>>9400465
>can't understand basic quantum mechanics
>wants to study string theory

>>9401135
Let's argue by contradiction
Assume there exists some [math]M\in \mathbb{R}[/math] such that [math]\sup_{x\in\mathbb{R}} f(x)=M[/math]. Further since the function [math]g(y)=y^3+2y[/math] preserves the sign of [math]y[/math] we have that [math]M\in\mathbb{R}^{+}[/math]. This assumption is clearly false since if [math]f(x)[/math] is bounded then so is [math]x+1[/math] since [eqn]x+1=f^3(x)+2f(x) \leq M^3+2M[/eqn] which is clearly false, so [math]f(x)[/math] is not bounded above, by similar arguments it follows that [math]f(x)[/math] is not bounded below either. Now let's prove that [math]f(x)[/math] is continuous. We know that [math]f^3(x)+2f(x)[/math] is continuous by definition, so it makes sense to use that to prove that [math]f(x)[/math] is continuous. Let [math]x,x_{0}\in\mathbb{R}[/math] be arbitary points in [math]\mathbb{R}[/math] with [math]x_{0}[/math] being fixed and choose [math]\epsilon > 0[/math], then we have
[eqn]\delta > |x-x_{0}|=|x+1-(x_{0}-1)|=|f^3(x)+2f(x)-[f^3(x_{0})+2f(x_{0})]|=|f^3(x)-f^3(x_{0})+2f(x)-2f(x_{0})|=|[f(x)-f(x_{0})][(f(x)^2+f(x)f(x_{0})+f(x_{0})^2]+2[f(x)-f(x_{0})]|\ge|f(x)-f(x_{0})||(f(x)^2+f(x)f(x_{0})+f(x_{0})^2+2|>|f(x)-f(x_{0})|[/eqn] so if we choose [math]\delta[/math] to be equal to [math]\epsilon[/math] we have our desired result. To finish things off consider some interval [math][a,b][/math] that gets mapped to [math][c,d][/math], by continuity we can apply the intermediate value theorem to get surjectivity, by being unbounded both above and below we can extend this interval arbitrarily to the whole real line, thus the function is surjective.

Hope this helps!

>>9402063
>Assume there exists
>""by contradiction""
Engineer spotted.

>>9402063
Nice

>>9402084
>Be me, make standard analysis argument that any math major would be expected to make
>Engineer spotted.
>???

>>9402199
Only an engineer would call a proof of a negation a proof ""by contradiction"".

>>9402211

or anyone not educated in the US smartie pants

>>9402211
>proof of a negation
Surely, you jest! Literally no human bean would ever use a term that stupid. This, in turn, implies that if you do, you are not a part of mankind. Assuming this person >>9402252 with xêr comment on the US is correct, my claim of not being human is even more factual, as there is no reason at all to consider Americans people.

>>9402252
>US
So basically a nigger? No.
>>9402263
>Literally no human bean would ever use
Good thing I'm not human. I am a holy existence.
>a term that stupid
The only thing which is stupid about it is it being a term in the first place. But that's mainly because of engineers such as >>9402063 misusing the term "proof by contradiction".

>>9402306
>nigger
Why the racism?

>>9402339
The what now?

Whats a good linear algebra book that isn't a meme like Apostol or Spivak?

>>9402385
Sakurai - Quantum Mechanics Done Right
Atiyah - Linear Algebra for Physicists