/mg/ maths general

[Anonymous No.12588999]

Regular polytopes edition
Talk maths, formerly >>12570175

[Anonymous No.12589019]

>>12588999
First for checking the OPs digits.

[Anonymous No.12589087]

Bros, don't fall for the PhD meme

[Anonymous No.12589091]

>>12589087
What happened anon? I’m currently waiting to hear back from schools for fall 2021.

[Anonymous No.12589477]

>>12589091
I wasted my 20s being an indentured servant to professors who know jack shit about how the world works outside their ivory towers. Applying to jobs lately, I only just realized the hole I dug myself in and all the little things I need to learn/do if I want a job I'm not extremely overqualified for. Fortunately I have a couple years left, so I'll probably manage. A lot of grad students in my department make it all the way to their final year before reality hits them and they have to scramble just to get a shitty teaching/code monkey job. Grad school is like that, it puts you in a bubble if you're not careful.

>I’m currently waiting to hear back from schools for fall 2021.
Some advice for you:

-I highly recommend getting your masters and getting out. A PhD is 4 more years of your time and only marginally better.
-Take some "applied" courses: probability, machine learning, data analytics, etc. They're not as "sexy" as the main graduate sequences (many professors you meet will look down on them), but they're literally the only ones that matter after you graduate.
-Lrn2code; it's not just a meme, any job worth having is going to require you to code.
-Network as much as you can, even outside your department.
-ABSOLUTELY DO NOT plan on doing a postdoc.

[Anonymous No.12589585]

>>12589477
Why did you go to grad school if you’re not going into academia?

[Anonymous No.12590322]

Kann -mg- ein mehrsprachig gruppe sein?

[Anonymous No.12590347]

>>12589585
Not him but quite a few people think they'd like to go into academia, dip in their toes with a PhD and realize it's a shitshow they want no further part in.

[Anonymous No.12590370]

>We announce the 9th meeting of the "New directions in group theory and triangulated categories" series that is scheduled for Tuesday (Jan 19). We will have two talks by Henning Krause https://www.math.uni-bielefeld.de/~hkrause/ and Janina Letz https://www.math.uni-bielefeld.de/~jletz/..
>*Zoom ID*: 992 4902 2878 https://zoom.us/j/99249022878

>*Speaker*: Henning Krause
>*Title*: Local versus global representations of finite groups.
>*Time*: 1 pm GMT (2 pm CET, 8 am EST), Tuesday Jan 19.

>*Speaker*: Janina Letz <https://www.math.uni-bielefeld.de/~jletz/> (University of Bielefeld)
>*Title*: Generation in derived categories and applications to commutative algebra.
>*Time*: 2.15 pm GMT (3.15 pm CET, 9.15 am EST)


>>12590322
Nein.

[Anonymous No.12590464]

>>12590370
Aber warum nicht

[Anonymous No.12591466]

Anon doing his best to solve anitranny's challenge so he can drink her semen.

[Anonymous No.12591600]

>>12591466
What challenge?
>her semen
Anon girls don't produce that

[Anonymous No.12591677]

>>12591600
He promised a leg pic if someone solves his problem.

[Anonymous No.12591704]

>>12590347
I just find it frustrating, do people not think through or research shit before taking a decision? Like all the retards who take history in college because they kinda liked it in HS and then realize it isn't at all like their shit class they had.

[Anonymous No.12591718]

>>12591600
Given a connected T4 space (normal & Hausdorff) with two distinct points, show that there are uncountably many points.

>>12591677
I was not the instigator of that incident, nor did I believe anyone would have energy to do that. I gave a conditional yes and had to keep my half of the bargain.

[Anonymous No.12591726]

wtf i love measure theory bros why didn't my CS professors teach me about this

[Anonymous No.12591739]

>>12591600
>>12591677
This is a new one with this higher said prise, only she can decide the challenge.

[Anonymous No.12591768]

>>12591718
If you say so, bro.

>>12591739
Do we need to give him attention?

[Anonymous No.12591848]

Is Lang a good second text for abstract algebra or is something like Aluffi/Foote better?

[Anonymous No.12591893]

>>12591726
ok that's cool but my question is: can you give an example of an 0-1 valued nonatomic sigma-additive measure on a powerset of some set X?

[Anonymous No.12591913]

>>12589091
I'm waiting to hear back from schools too, honestly I'm pretty scared to get decisions. I'm seriously considering stopping after my masters and not continuing to a doctorate program. From what i've read, you can do what I want to do with just a masters, so why waste my time with a doctorate?

[Anonymous No.12592079]

>>12591913
>what I want to do with just a masters
Which is?

[Anonymous No.12592087]

>>12591893
>words
>>>/lit/

[Anonymous No.12592100]

Both Brans–Dicke theory and general relativity are examples of a class of relativistic classical field theories of gravitation, called metric theories. In these theories, spacetime is equipped with a metric tensor, g a b {\displaystyle g_{ab}} g_{ab}, and the gravitational field is represented (in whole or in part) by the Riemann curvature tensor R a b c d {\displaystyle R_{abcd}}

R_{abcd}, which is determined by the metric tensor.

All metric theories satisfy the Einstein equivalence principle, which in modern geometric language states that in a very small region (too small to exhibit measurable curvature effects), all the laws of physics known in special relativity are valid in local Lorentz frames. This implies in turn that metric theories all exhibit the gravitational redshift effect.

As in general relativity, the source of the gravitational field is considered to be the stress–energy tensor or matter tensor. However, the way in which the immediate presence of mass-energy in some region affects the gravitational field in that region differs from general relativity. So does the way in which spacetime curvature affects the motion of matter. In the Brans–Dicke theory, in addition to the metric, which is a rank two tensor field, there is a scalar field, ϕ {\displaystyle \phi } \phi , which has the physical effect of changing the effective gravitational constant from place to place. (This feature was actually a key desideratum of Dicke and Brans; see the paper by Brans cited below, which sketches the origins of the theory.)

[Anonymous No.12592101]

The field equations of Brans–Dicke theory contain a parameter, ω {\displaystyle \omega } \omega , called the Brans–Dicke coupling constant. This is a true dimensionless constant which must be chosen once and for all. However, it can be chosen to fit observations. Such parameters are often called tuneable parameters. In addition, the present ambient value of the effective gravitational constant must be chosen as a boundary condition. General relativity contains no dimensionless parameters whatsoever, and therefore is easier to falsify (show whether false) than Brans–Dicke theory. Theories with tuneable parameters are sometimes deprecated on the principle that, of two theories which both agree with observation, the more parsimonious is preferable. On the other hand, it seems as though they are a necessary feature of some theories, such as the weak mixing angle of the Standard Model.

Brans–Dicke theory is "less stringent" than general relativity in another sense: it admits more solutions. In particular, exact vacuum solutions to the Einstein field equation of general relativity, augmented by the trivial scalar field ϕ = 1 {\displaystyle \phi =1} \phi =1, become exact vacuum solutions in Brans–Dicke theory, but some spacetimes which are not vacuum solutions to the Einstein field equation become, with the appropriate choice of scalar field, vacuum solutions of Brans–Dicke theory. Similarly, an important class of spacetimes, the pp-wave metrics, are also exact null dust solutions of both general relativity and Brans–Dicke theory, but here too, Brans–Dicke theory allows additional wave solutions having geometries which are incompatible with general relativity.

[Anonymous No.12592102]

Like general relativity, Brans–Dicke theory predicts light deflection and the precession of perihelia of planets orbiting the Sun. However, the precise formulas which govern these effects, according to Brans–Dicke theory, depend upon the value of the coupling constant ω {\displaystyle \omega } \omega . This means that it is possible to set an observational lower bound on the possible value of ω {\displaystyle \omega } \omega from observations of the solar system and other gravitational systems. The value of ω {\displaystyle \omega } \omega consistent with experiment has risen with time. In 1973 ω > 5 {\displaystyle \omega >5} \omega >5 was consistent with known data. By 1981 ω > 30 {\displaystyle \omega >30}

\omega >30 was consistent with known data. In 2003 evidence – derived from the Cassini–Huygens experiment – shows that the value of ω {\displaystyle \omega } \omega must exceed 40,000.

It is also often taught[2] that general relativity is obtained from the Brans–Dicke theory in the limit ω ∞ {\displaystyle \omega \rightarrow \infty } \omega \rightarrow \infty . But Faraoni[3] claims that this breaks down when the trace of the stress-energy momentum vanishes, i.e. T μ μ = 0 {\displaystyle T_{\mu }^{\mu }=0} T_{{\mu }}^{{\mu }}=0 . An example of which is the Campanelli-Lousto wormhole solution.[4] Some have argued[who?] that only general relativity satisfies the strong equivalence principle.

[Anonymous No.12592114]

>I went into a phd knowing i could quit whenever i wanted but i didn't and now I hate my life don't do a phd guys its bad ok

[Anonymous No.12592117]

arXiv.org > gr-qc > arXiv:2101.05745v1

Help | Advanced Search
General Relativity and Quantum Cosmology
[Submitted on 14 Jan 2021]
Disformal transformations and the motion of a particle in semi-classical gravity
Sandip Chowdhury, Kunal Pal, Kuntal Pal, Tapobrata Sarkar

The approach to incorporate quantum effects in gravity by replacing free particle geodesics with Bohmian non-geodesic trajectories has an equivalent description in terms of a conformally related geometry, where the motion is force free, with the quantum effects inside the conformal factor, i.e., in the geometry itself. For more general disformal transformations relating gravitational and physical geometries, we show how to establish this equivalence by taking the quantum effects inside the disformal degrees of freedom. We also show how one can solve the usual problems associated with the conformal version, namely the wrong continuity equation, indefiniteness of the quantum mass, and wrong description of massless particles in the singularity resolution argument, by using appropriate disformal transformations.

Comments: 18 Pages, LaTeX
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
Cite as: arXiv:2101.05745 [gr-qc]
(or arXiv:2101.05745v1 [gr-qc] for this version)
Submission history
From: Tapobrata Sarkar [view email]
[v1] Thu, 14 Jan 2021 17:47:28 UTC (24 KB)


https://arxiv.org/abs/2101.05745v1

[Anonymous No.12592119]

More than twenty five years ago, Bekenstein [1] showed that intheories of gravity where two distinct geometries arepresent, they are, in general, related by a disformal transformation, which is a generalization of the conformal transfor-mation. In such situations, the gravitational dynamics is controlled by the metric and is called gravitational geometry,whereas matter dynamics takes place on a geometry that is disformally related to the metric, and called physical ge-ometry. This is a notable departure from general relativity(GR), where the dynamics of both gravity and matter aredetermined by the metric, but is common in scalar-tensor theories of gravity, such as Brans-Dicke theory, in whichthe two geometries are related by a conformal transformation. The purpose of this paper is to establish the nature ofdisformal transformations in the context of Bohmian mechanics in gravitational backgrounds, and to show that it solvesa few important problems that arise in an usual treatment popular in the literature, that uses conformal transformationsinstead.

[Anonymous No.12592123]

Bohmian mechanics [2–4] is an important tool in a semi-classical understanding of the full theory of quantumgravity [5]. Formulating such a quantum theory of gravity isof course a formidable challenge, with the metric playingthe role of a quantum operator, and with quantization conditions on space and time. The somewhat simpler semi-classical approach, in which the metric is classical, has been popular over decades. In Bohmian mechanics, the particletrajectories are determined by suitable wavefunctions, and the statistical distribution of particle positions is given bythe modulus squared of this wavefunction. In this first quantized approach, one replaces the geodesic motion of freelyfalling particles in a curved space-time by corresponding Bohmian trajectories. In such situations, geodesic equationsare typically modified by an additional force term coming from a quantum potential [6–9]. This kind of reasoning hasbeen used to deal with the usual singularity problem of classical general relativity [6].

[Anonymous No.12592125]

In this context, an important question to ask is the following. If the physical geometry on which the particle movesis different from the gravitational geometry, can we perform an analysis similar to the one described above, where theparticle, moving in the physical geometry, is a quantum mechanical particle obeying Bohmian mechanics ? Is it possibleto incorporate quantum effects in the disformal factor as in the conformal case? We show it is possible, by deriving therelation between the acceleration equations and then relating the factors of the transformation with quantum potential.Next, in a minimally coupled scenario, we show that by using the equivalent description in the disformal frame, wecan solve some well known problems that are present in the conformal version of theory described before. For example,in presence of the quantum potential, the mass of a particle is modified to a variable one (known as the quantum mass ofthe particle), and this is not always positive definite, so that the theory may have tachyonic modes [3]. If we transformto a conformal frame where the quantum potential is absent, the particle mass becomes constant, but the transformationitself is not definite for such imaginary quantum mass. Furthermore the continuity equation in the transformed framedoes not have the desired form to define a suitable probability density [13, 14].

[Anonymous No.12592142]

One of the main contributions of this paper is to show that instead of transforming to a conformal frame, if we use a disformal transformation, all of the above mention problems can be solved. The modified geodesic equation and the continuity equation fix the transformation factors such that have positive definite values even for a particle with negative quantum mass.In the last part this work we address a related question. If the force on the particle due to it’s quantum nature is absent in the conformal frame, what happens for a massless particle moving in null trajectory in that frame. It is known that, by the nature of construction of conformal transformation the null geodesics remains invariant, they do not feel any force in any of the two conformally related frames. In particular what happens to the argument used to avoid the singularity problem. Namely, how can null trajectories not cross if they do not feel any quantum force? We shall show how to answer this question by using the fact that under a general disformal transformation, a null trajectory of one frame is not null in another frame [1, 15]. By doing a disformal transformation in a direction different from the wave vector of the photon, we show that photon does not moves in a null trajectory in the gravitational geometry, and hence can avoid the singularity.

[Anonymous No.12592147]

>>12592114
>quit whenever i wanted
Then you can never do a phd ever again.

[Anonymous No.12592158]

>>12592147
Lol what? Thats not true at all and even if it was so what? You'll kill yourself slaving for years just because if you quit you won't be able to do a phd again? See the faulty logic there?

[Anonymous No.12592275]

Let [math]{\mathcal B}({\mathbb R})[/math] be the banach space of bounded real functions with the sup norm. Let [math]f[/math] be a functional such that
[eqn]
\bullet \text{If } \lim_{x \to \infty} f(x) \text{ exists then } \phi(f) = \lim_{x \to \infty} f(x)\\

\bullet \phi(f) \geq 0 \text{ for positive } f \\

[/eqn]
Can I construct a [math]g(x)[/math] such that there exists [math] c \in {\mathbb R}[/math] with
[eqn]
\phi(g(x)) \not= \phi(g(x+c))
[/eqn]
I do know that [math]g[/math] must be non-measurable

[Anonymous No.12592279]

>>12592275
>I do know that gg must be non-measurable
What's the reason for this?

[Anonymous No.12592304]

>>12592275
The answer is Yes.
You're welcome.

[Anonymous No.12592309]

>>12591466
regular => urysohn qed

[Anonymous No.12592315]

>>12590370
Wth bielefield doesn't exist but has a uni?

[Anonymous No.12592343]

Let [math]n[/math] be a positive integer.
Let [math]r[/math] be an irrational in [math](0, 1)[/math].

Consider the sequence
[math]
n_0 = n\\
n_i = \lfloor r n_{i+1} \rfloor
[/math]
which ends when [math] n_k = 0 [/math].

Prove that [math] \lfloor \log_r n \rfloor \leq k \leq \lceil \log_r n \rceil [/math]

The upper bound is pretty obvious since the sequence [math] r^i n_0 [/math] drops slower than the original one and the first time it becomes less than 1 (meaning floor = 0) is [math]\lceil \log_r n \rceil [/math].

But what about the lower bound?

[Anonymous No.12592349]

>>12592343
Meant
[math]
n_0 = n\\
n_i = \lfloor r n_{i-1} \rfloor
[/math]

[Anonymous No.12592390]

>>12592343
The correct inequalities are with -k in place of k.
Just work out the details of one of them and I think you'll see how to prove the other one, it's pretty much the same reasoning.

[Anonymous No.12592415]

>>12592343
>>12592390
oops right
meant to write
[math]\lfloor -\log_r n \rfloor \leq k \leq \lceil -\log_r n \rceil [/math]

I've been trying to prove this for hours, I can't figure it out.
Best I could think of is to somehow prove this (if it even holds)
[math] r^{i-1} n_0 < r n_{i-1} < r^i n_0 [/math]
The left inequality is obvious.
The right inequality on the other hand... no idea if it's even true.

[Anonymous No.12592502]

>>12592415
There are counter-examples to the upper bound you wrote.
Isn't it (lower bound) = ceil, and (upper bound) = 1+floor ?
If so, this upper bound isn't difficult, and I think the other one follows similarly.
You just need [math]n_i < r^i n[/math], which follows by floor(x) =< x and iteration.

[Anonymous No.12592556]

>>12592502
I am specifically trying to show it for sqrt(2) - 1 but I believe it holds for any positive irrational less than 1.
Here's a python script showing evidence that it holds for sqrt(2) - 1 at least.

[Anonymous No.12592635]

>>12592315
BieleFELD not BieleFIELD, silly!

[Anonymous No.12592646]

>>12592556
and here it shows that it holds for at least up to 1 billion

[Anonymous No.12592666]

>>12592343
>>12592556
>>12592646
Ah shit nigga.
It doesn't hold for all 0 < r < 1

[Anonymous No.12592691]

>>12592666
For which r you think it failed?
I reviewed what I've done and I think I proved your inequalities, they do hold.
For the ceil you use n_i < r^i n, and for the floor you use n_i > r^i n - 1.
Start from the definition of floor and ceil of that -log. You'll find n_c < 1 and n_f > 0, f = floor, c = ceil.

[Anonymous No.12592862]

All of my PhD candidate friends are having trouble with their supervisors, dealing with some sort of abuse. How common is this? More than 80%, 90% of these relationships?

>>12586761
>you seem very likely to have this nagging voice in your head as well
Yes, I do have. Though I think it's different from yours in some ways. Long ago I have decided that I'll try until the end, until everything is clearly objectively ruined, so my inner demon isn't going to make me quit by my own will alone. But it makes it harder to keep on studying well and consistently, and to socialize. When I perceive myself being behind (usually my own goals, not other people), I tend to isolate from others. Comparing with others, I have good tolerance with being alone I suppose, but it doesn't help, it's extra weight for the snowball.
>It is not a completely trustworthy source of information
Definitely. I think we've "known" this for quite some time already, but "knowing" is not enough to manage it well in a daily basis. It's even easy to forget and listen too much, sometimes.
>Please do not let your own version of that voice demoralise you. It will definitely try to
Thanks. It feels comforting receiving this from someone else that deals with similar problems!

[Anonymous No.12592886]

>>12588999
Does anyone have any recommendations for a number theory book with a fast pace and really hard problems? I'm a math grad and I already know number theory but I'm currently giving some classes and I have realized that I am getting rusty. The intro textbooks that I know from college are too slow for what I need now and I would probably get bored with them.

[Anonymous No.12592902]

All of my PhD candidate friends have to deal with sorts of abuse from their supervisors. How common is this? 80% of the cases? 90%?

>>12586761
>you seem very likely to have this nagging voice in your head as well
Yes, I do have. Though I think it differs from yours in some ways. Long ago I made the decision that I'll keep going until the end, until it's objectively clear that it's all ruined. So my inner demon isn't going to make me quit, but it makes it harder to keep on studying well in a daily basis, also socializing. When I perceive that I'm behind my goals (sometimes even others, even though I try to not compare with them), I tend to isolate myself. I think I have good tolerance with being alone when compared to other people in general, but this doesn't help. It's extra weight in the snowball.
>It is not a completely trustworthy source of information
Definitely isn't. I think we've "known" this for quite some time, but "knowing" is not the same as managing to deal with it whenever it arises. It's even easy to forget and go on listening to it.
>Please do not let your own version of that voice demoralise you. It will definitely try to
Thanks, it's really comforting when I hear this from someone else with similar problems!

[Anonymous No.12592909]

>>12592902
>All of my PhD candidate friends have to deal with sorts of abuse from their supervisors. How common is this? 80% of the cases? 90%?

Academia is full of unhappy people who themselves get bullied by administrators. I'd say it's approaching 100% fast.

[Anonymous No.12592911]

>>12591726
Can I study that textbook even if I have no background in probability theory? I already know measure theory and real analysis.

[Anonymous No.12592968]

>>12592902
I'm half a year into my PhD and I haven't been bullied so far. Hopefully it stays this way.

[Anonymous No.12593104]

>>12592691
It fails for sqrt(3) - 1 for example, see here >>12592666
It seems that it fails when r > 1/2

> n_i > r^i n - 1

I think it should be like:
[math]
n_i = \lfloor r n_{i-1} \rfloor > r n_{i-1} - 1 \\

n_{i-1} > r n_{i-2} - 1 \\
[/math]
etc.

So,
[math]
n_i > r (r n_{i-2} - 1) - 1 = r^2 n_{i-2} - r + 1\\

n_{i-2} > r n_{i-3} - 1\\

n_i > r^2 (r n_{i-3} - 1) - r + 1 = r^3 n_{i-3} - r^2 - r + 1\\

\vdots\\

n_i > r^i n_0 + 1 - \sum_{j=1}^{i-1} r^j
[/math]

[Anonymous No.12593120]

>>12593104
Ah and when r < 1/2, then
[math]
\sum_{j=1}^{i-1} r^j < \sum_{j=1}^{\infinity} \frac{1}{2^j} < 1
[/math]

Therefore [math] n_i > r^i n_0 + \delta [/math] with [math] 0 < \delta < 1 [/math]

Now, after that I don't know...

[Anonymous No.12593156]

>>12593104
Yeah, I thought I improved the estimate you showed but I forgot a term.
By the way, you seem to assume that the ceil is equal to 1+floor, but that is false when the floor's argument is an integer - which can happen in this case if r is something like n^{-1/m} for example.
The problem is with the lower bound, I think you can get one using this inequality, making it depend on [math]R := \sum\limits_{j\ge 0} r^j[/math].

[Anonymous No.12593167]

>>12592968
*bullies u*
What now idiot?

[Anonymous No.12593184]

>>12593156
>By the way, you seem to assume that the ceil is equal to 1+floor
It's because the argument can't be an integer. if the argument n*r was an integer m, then r = m/n meaning that r would be rational.

I'll try it a bit more. Thanks fren!

[Anonymous No.12593186]

>>12593104
>>12593156
Oh I just saw mine seems to be sharper:
[math]n_i > r^i n - \sum\limits^{i-1}_{j=0} r^j[/math].

[Anonymous No.12593192]

>>12593184
The argument is that -log_r n.
If r = 1/sqrt(n), then -log_r n = 2 is an integer.

[Anonymous No.12593201]

>>12593192
oohh I see

[Anonymous No.12593225]

>>12593104
>>12593201
I was going to repost everything together correcting a mistake.
The inequality I got [math]n_i > r^i n - r^{i-1} - r^{i-2} - \cdots - r - 1[/math] doesn't have your +1, so it's not sharper, but there shouldn't be a +1. Look at the RHS of your first equality (first row) in that chain of inequalities.

[Anonymous No.12593275]

>>12593167
i think i'm gonna change my gender now

[Anonymous No.12593292]

/mg/ I have to do some stuff with algebraic curves and I don't have much time to learn all the subject, so I'd appreciate if someone can help guide me.

Let's say I have a smooth curve [math]C[/math] in [math]kP^2[/math] with field of rational functions [math]k(C) = k(x)[/math] for some [math]x\in k(C)[/math]. How do I show that [math]C\cong kP^1[/math]?
I guess [math](x_1 : x_2) \mapsto (x(x_1, x_2) : 1)[/math] could be a field homomorphism between their function fields, but does that must come from a single morphism between the curves? I think there is a condition for this...

[Anonymous No.12593369]

>>12592635
I like bielefield more, sorry.

[Anonymous No.12593482]

>>12592902
>All of my PhD candidate friends have to deal with sorts of abuse from their supervisors. How common is this? 80% of the cases? 90%?
Mine is very sweet and nice to me.
>Yes, I do have...
Does your effort pay off on average? I think your demon is trying to help you, although not in the most sophisticated social way. I can relate to the isolation part, all the accumulating stress and stuff. There is a risk of burning out if you keep going like that when coursework is replaced with independent work on whatever it will be you are to do. Please do control the urge to follow your demon's commands too much.
>Thanks, it's really comforting when I hear this from someone else with similar problems!
No problem! I can't promise you a bright future, but I can tell you that you will do fine during your studies if someone like me can.

>>12593369
And I like the old Blofeld more than that grumpy one in the new James Bond.

[Anonymous No.12593490]

>>12593482
>Mine is very sweet and nice to me.
Sounds like he wants to abuse your asshole.

[Anonymous No.12593547]

>>12593490
Hopefully not. He is hot in the way well matured men are, but it would be extremely awkward and wrong in so many ways.

[Anonymous No.12593565]

>>12593292
>I guess [math](x_1 : x_2)\mapsto (x(x_1,x_2) : 1)[/math] could be a field homomorphism between their function fields,
Just realized I wrote shit.
[math]t := x_1/x_2[/math] and [math]x[/math] are both transcendent over [math]k[/math], so I have an isomorphism [math]f(t)\mapsto f(x)[/math], for any fraction of polynomials [math]f(Y) \in k(Y)[/math].
Can I get an explicit isomorphism of curves, though?

[Anonymous No.12593598]

>>12593547
I don't know. Maybe fall asleep in his office one day with your ass sticking out. Then just measure how much your asshole hurts while you walk home after he "just woke you up". It's the only mathematical way to prove it.

[Anonymous No.12593610]

>>12591893


Let X={1\n: n natural}. P(X) is equivalent to [0,1], call this equivalence f. Define the measure m on [0,1] by m(S)=1 if f^-1(S) has finite complement and zero otherwise. This is a nonatomic, sigma-additive measure and you are gay.

[Anonymous No.12593642]

>>12592117
>let's incorporate solvability in our energy-momentum tensor guise.

t. Bohm

[Anonymous No.12593664]

>>12593610
bro...
it's not sigma additive...

[Anonymous No.12593665]

>>12593598
If you insist...

[Anonymous No.12593702]

i dream of becoming a tranny so that i can go to a mathematical conference and whore myself as hard as possible to all the mathematicians present there. then after i fucked all of them, i have a talk on category theory scheduled for last day of the conference, but i cant concentrate on talking because i feel their cum sloshing in my bussy

[Anonymous No.12593791]

>>12593702
Why is category theory so good at turning young men into trannies?

[Anonymous No.12593827]

>>12593791
it makes me feel like a dumb slut that's playing with her dumb toys, waiting for real men who do real maths to use me

[Anonymous No.12593832]

>>12593791
>appeared after WW2
>all sorts of homo topics
coincidence?

[Anonymous No.12594095]

>>12593827
Where can I find one of you, but biologically female?

[Anonymous No.12594104]

>>12591704
no one teaches you to take controle of your life now a days. You have to trip up badly in order to realize its merit.
>why?
its convenient to have a shitload of NPC's at your disposal. there are probably some higher up dudes with little to no respect for humanity. I mean, i cant see why the system would be this way otherwise

[Anonymous No.12594155]

It's easy to prove that [math]S_3 = Aut(S_3)[/math], so I thought what is the smallest [math]m[/math] for a given [math]n[/math] such that [math]Aut(S_n) \le S_m[/math]? By Cayley theorem we have [math]m = n![/math], is there any lower bound?

[Anonymous No.12594269]

>>12591848
Dummit and Foote should have been your first text

[Anonymous No.12594277]

>>12592911
yes you are the target reader

[Anonymous No.12594281]

>>12594155
Try using the presentation [math]S_n = \langle (1,2), \; (1,2,\dots,n) \rangle[/math].

[Anonymous No.12594282]

>>12590370
>linguistics
naw thanks

[Anonymous No.12594331]

>>12594155
Take K = set of 2-cycles in S_n, then there are exactly n*(n-1)/2 2-cycles. Since all elements of S_m are represented by justapposition of 2-cycles (generally not disjoint) all automorphism are such that permutes the 2-cycles. Therefore Aut(S_n) = group of permutations of K = S_m with m = n*(n-1)/2.

[Anonymous No.12594362]

>>12594331
This ain't it chief

[Anonymous No.12594375]

Is discrete geometry a death field?

[Anonymous No.12594530]

Let [math]C[/math] be a smooth algebraic curve in a two-dimensional projective space over an algebraically closed field [math]k[/math], such that we have a [math]f\in k(C)[/math] with just a single pole and a single zero, both simple. Why does this imply that [math]k(C) = k(f)[/math]?

[Anonymous No.12594618]

>>12592902
Mine is very nice and conscientious, no issues at all

[Anonymous No.12594642]

>>12593702
so you want to get railed by pic related
>>12594375
That's essentially combinatorics by now, isn't it?

[Anonymous No.12594681]

>>12594530
I can finish by using (2) of this Proposition from Fulton's book, since I also know that the pole of my [math]f[/math] has Riemann-Roch dimension greater than 1.
But my professor didn't present this and the proof is complicated, instead, he suggested to find a morphism [math]\varphi[/math] associated to this extension and show that its degree is 1 by using what we have and those basic relations between divisors, pullback and pushforward, like [math] \text{deg}(\varphi^* D) = (\text{deg }\varphi) (\text{deg } D)[/math]. I don't see a solution here... I thought of trying to define [math]\varphi[/math] by [math]Q\mapsto (x_1(Q) : x_2(Q))[/math] for suitable [math]x_1, x_2\in k[C][/math] with [math]x = x_1/x_2[/math], but I don't even know if this is well-defined.

[Anonymous No.12594771]

>>12591726
i got confused so i switch to this lol. i like soviet books though anyway

[Anonymous No.12594920]

>>12594681
You can think of f as a morphism from C to P^1, the hypothesis that it has a single zero of order 1 imposes degree 1 because of the formula you mention

[Anonymous No.12594962]

>>12594920
Thanks anon, I did pretty much what you said.
Though it's sort of unnecessary to go to divisors since in the end the formula I needed to use was a previous one relating the degree of the morphism with the ramification indexes.
Now I can sleep in peace.

[Anonymous No.12594977]

>spent a few months without lurking on /mg/
>missed anime tranny posting her leg apparently
Life is nothing but pain, on the bright side I had a lot of time for putnam problems

[Anonymous No.12595495]

>>12594642
none of them will achieve anything worth noting anyway like most posters itt

[Anonymous No.12595550]

>>12595495
Look at the smug cunt in the nekopara tee and tell me he hasn't achieved anything by dabbing on all the serious nerds who placed below him.

[Anonymous No.12595683]

Why the hell are these so similar? I understand why they stay close to each other on the positive reals, but I've never seen this kind of similarity on C. Did I forget complex analysis while doing algebra?

[Anonymous No.12595686]

>>12595683
>Chrome for android

[Anonymous No.12595694]

>>12593791
Is this meme true? What the odds of getting my dick wet with sweet boypussy if I go into mathematics?

[Anonymous No.12595696]

Courant vs Spivak vs Apostol. Which one is the best rigorous calculus textbook?

[Anonymous No.12595705]

>>12595683
x = 10
x^19 = 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10
19! = 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

[Anonymous No.12595708]

>>12595696
According to the head of mathematics at Edinburgh back in 2014, Kolmogorov & Yushkevich

[Anonymous No.12595709]

>>12595705
Yes, it obviously applies for the positive reals. Why are the graphs so similar across the complex plane?

[Anonymous No.12595713]

>>12595708
What's the name of that textbook?

[Anonymous No.12595715]

>>12595696
What do you want to learn?
Rigorous lower division math? Apostol.
Problem course in basic analysis? Spivak.
Introduction to calculus and analysis? Courant.
Read multiple textbooks. If you want to solve every problem and prove every theorem in any of these books it will take you 6 months. If you want to solve every problem and prove every theorem in all of these books it will take you 9 months.

[Anonymous No.12595724]

>>12595709
Use the identity from the reals -1 -> i^2

[Anonymous No.12595734]

>>12595694
>Is this meme true?
Yes. Category "theory" is a language. Useless in almost all cases it's being used for, easy to publish a lot of obfuscated bullshit by just adding a "higher" in front of literally anything and drawing arrows. Hence, attracts many retards and non-ables, in particular trannies. Furthermore degenerates like Baez pushing for (((diversity))) and trannies. Oy vey. Not completely shitting on Baez though, has some nice introductory articles on his homepage.
>What the odds of getting my dick wet with sweet boypussy if I go into mathematics?
100% It's almost only dudes. Roughly 10% are gay, so like normal, but more males means more gay faggot males. Funny story had a course taught by a postdoc once who was so fucking gay he always popped semis while teaching (cause, as expected, room full of men). Great mathematician and cool course though.

[Anonymous No.12595750]

>>12595734
>100%
Ok I just enrolled in all math classes for Spring.

[Anonymous No.12595758]

>>12594977
Rebost

[Anonymous No.12595759]

>>12594642
>Chad in nekopara shirt
Holy fuck

[Anonymous No.12595767]

>>12595758

[Anonymous No.12595768]

Anybody knows a good sum up of linear algebra?

[Anonymous No.12595809]

>>12595715
I want to learn both calculus and analysis in one go but still include important applications. I find Courant's book pretty good, but he writes strangely and the exercises are a lot harder compared to either Spivak or Apostol.

[Anonymous No.12595920]

>>12592902
It's very common. It's at least half, and I think 80% is probably quite a good estimate.

[Anonymous No.12595958]

>>12595734>>12595694

i love how atheists cant stop cramming sex and politics into maths. No wonder their republic is so shit.

[Anonymous No.12595980]

>>12595768
it's the description of how finite linear things behave.

[Anonymous No.12596023]

>>12595980
thanks, now i feel like i can ace the upcoming test

[Anonymous No.12596026]

>>12588999
>Regular polytopes
Is there a strict definition of a polytope?

[Anonymous No.12596040]

>>12595958
>maths
>asexual britnigger talking about how america is a failed state
Rent-free

[Anonymous No.12596057]

>>12595767
Even if she looks like a man I want to fuck her. I want to rape her. I want to dominate her. The only thing better would be to turn a weak male into a broken cum doll of a femoid. This is my base desire and it is good. I also like to read linear algebra textbooks.

[Anonymous No.12596094]

>>12596057
There's no turning back now, you're a degenerate

[Anonymous No.12596105]

>>12596057
me too bro

[Anonymous No.12596141]

>>12596057

[Anonymous No.12596164]

>>12595809
I have the book for you: Zorich's Mathematical Analysis I and II.

[Anonymous No.12596170]

>>12596141
If I see one of you homotopic posters at my local uni, I'll irreversibly deform your torus up to isomorphism

[Anonymous No.12596177]

i posted this in /sqt/ but i think it fits this one better.
is pic related going to be as fun as it looks? (after I finish linear algebra with applications by gilbert strang)
any comments?

[Anonymous No.12596200]

>>12596177
There's
>Abstract Algebra: codes, ciphers, and discrete algorithms 2 edition - hardy richman walker
Looks like a pretty neat book, and fred richman is a cool guy, eh proves fta without choice and doesn't afraid of anything.
libgen (dot) rs/book/index.php?md5=0EB5359E3A9D2E3930CB889C4DA47559

[Anonymous No.12596209]

>>12596200
Shit I meant
>applied algebra
Instead of
>abstract algebra

Also good review on MAA

[Anonymous No.12596212]

>>12596200
i already bought pic related tho

[Anonymous No.12596231]

>>12596212
Are you forced to use it?

[Anonymous No.12596234]

>>12596231
yea. it cost money and i can't return it.

[Anonymous No.12596239]

>>12596234
As in buyer's remorse or a course that requires it?

[Anonymous No.12596243]

>>12596239
woa, is it really that bad?

[Anonymous No.12596255]

>>12596239
>>12596243
>>12596239
yeah, buyers remorse?
i thought it looks fun.
that's the question.

[Anonymous No.12596258]

>>12596243
What, the book? I don't know, but it's probably not very good seeing how there's no academic reviews of it (and foid author). Staving off your buyer's remorse is probably not that important in comparison to not having to suffer through multiple mediocre books. Also It'll be an expensive lesson not to buy books available on libgen (if you look it up, it's right there, in color with ocr and fully bookmarked).

[Anonymous No.12596263]

>>12596258
dude, I buy books for a few different reasons. It's easier to study a physical book. and it supports the author.

[Anonymous No.12596266]

>>12596263
Why would you buy a book if you don't know if it's even good?

[Anonymous No.12596270]

>>12596266
I'm going to use what I buy, and it was the cheapest technical abstract algebra book that covered the topics I want to study.

[Anonymous No.12596282]

>>12596266
look, why are you interrogating me?
I asked about the book.
I don't really want to talk about anything else.

[Anonymous No.12596285]

>>12596270
That's fine, I recommend that next time you choose among the books that are used in courses at good unis, or at least the ones that have academic reviews

[Anonymous No.12596291]

>>12596285
Cambridge University Press is bad?
check this out, fren:
https://www.cambridge.org/us/academic/subjects/mathematics/algebra/abstract-algebra-applications?format=AR

[Anonymous No.12596296]

dear anons, please help me understand why can't I make this example like pic rel? I know the correct way of doing it (by multiplying the thing with short multiplication formulas) BUT why doesn't pic rel work?!

[Anonymous No.12596326]

>>12596291
CUP is usually on the better end, and it's good that there's a review. Would be even better if someone used it in an actual course, but that's not always open to the public. Just don't do what you said in your original post and buy books because they're new and the cover is pretty. Even the big name publishers shovel mediocre shit to bloat the "new arrivals" shelves.

[Anonymous No.12596331]

>>12596326
This is your most sensible post, thank you. Will take note. ^_^

[Anonymous No.12596342]

>>12596331
Last thing, try to only buy books that have errata or a dedicated page somewhere online. It's the worst when you have no way to know if there's an error in some exercise because no one heard of the damn thing.

[Anonymous No.12596360]

>>12595734
Lol, what course was that and why did you fucking NOTICE

[Anonymous No.12596368]

>>12596026
The union of finitely many simplices.

[Anonymous No.12596384]

>>12596296
You're implicitly using the product limit law incorrectly. Namely, n^2 has no real limit, so you can't substitute n^2 for n^2(1+(1/n)).

[Anonymous No.12596413]

Currently doing a bsc in physics, first year. Recommend me a book that'll let me understand math on another level. Something that will improve the foundation of my mathematical understanding greatly.

[Anonymous No.12596421]

>>12596413
Artin's Algebra should be accessible, fun and give you a new perspective

[Anonymous No.12596440]

>>12596413
I got just the thing for you

[Anonymous No.12596508]

>>12592275
>using "construct" in this context,

lol

[Anonymous No.12596550]

>>12596508
>the virgin show
>the Chad Construction

[Anonymous No.12596556]

>>12592275
it depends on the functional Phi. your conditions don't define it uniquely.

[Anonymous No.12596600]

>>12596164
Have you finished Vol I and II? If so, how long did it took you, and how hard was it?

[Anonymous No.12596719]

Degenerates...

>>12596141
Nice one, made me chuckle a bit.

>>12596413
Maybe some nice introductory text on topology like Mendelso(h)n's book, or just Vrill the Coming Race.

[Anonymous No.12596755]

>>12589087
bachelor chads rise up. fuck phd, fuck masters, and most importantly fuck universities.

[Anonymous No.12597029]

yes i study the homology where are the homos

[Anonymous No.12597097]

>>12596023
no problem senpai.

[Anonymous No.12597250]

>>12589087
Why not just learn2code and all those applied skills on the side and pursue a Ph.D anyway? Worst thing that happens is you become a NEET.

[Anonymous No.12597348]

>>12588999
a 2d Lotka–Volterra describes predator prey, what does a 3d Lotka–Volterra represent?

[Anonymous No.12597361]

>>12589477
would you say a bachelors good enough? i'm likely to get a 1st and struggling with the cope of uni and being isolated, doing really know if i can do another year

[Anonymous No.12597383]

>>12596368
Is union of 2D simplex, 3D simplex and 4D simplex a polytope?

[Anonymous No.12597418]

>>12596755
based fellow bachelor chad. jewniversity is a waste of time

[Anonymous No.12597625]

I am a retard :)

[Anonymous No.12597638]

>>12597361
You can try without a bachelors if doesn't work out for you, get into masters.
You can always self teach master-level subjects. It's not much.

[Anonymous No.12597671]

>>12589477
Would you recommend finishing a bsc in physics and running away from uni because its a corrupt system to create office drones instead of really teach humanity the sciences, and then proceed to read occult books whilst practicing old pagan rituals and write books linking theoretical physics to said rituals, metaphysical structures and ideas?

[Anonymous No.12597716]

>>12597671
go for a masters(outside of america) if you can

[Anonymous No.12597776]

>>12596755
fuck you too groupfucker ringger, go embed a homosexuomorphism into the faggotoid group of the wheel over your torushole

[Anonymous No.12597779]

>>12597716
i can, i do not know what'll be though. in order to do a masters in exact sciences, we have to find a lab and apply. does it work that way where you from as well?

[Anonymous No.12597788]

>>12597776
This made me think, don't Grothendieck and Foucault look kind of similar? Maybe this is not a coincidence?

[Anonymous No.12597860]

>>12597779
idk for maths I just applied to the department

[Anonymous No.12598200]

>>12597788
>Grothendieck
unironically Imagine not being able to calculuate anything, give any interesting example of theorems and can't even into prime numbers
>le 57 prime
and convincing other people that you are a mathematician until your impostor syndrome breaks your mind and you become an insane hermit.
LMAO

[Anonymous No.12598203]

>>12594269
Foote is a meme. Aluffi is god tier.

[Anonymous No.12598262]

>>12598203
Isn't Aluffi a category theory text and not really abstract algebra? What is category theory anyway?

[Anonymous No.12598448]

>>12596413
>Physics
Unironically, pic rel

[Anonymous No.12598470]

Noob at combinatorics here. How does one see that [math]C(n,r)=C(n,n-r)[/math] intuitively (i.e. without resorting to algebraically manipulating the definition)?

[Anonymous No.12598495]

Some o can help me to derive the Poincaré group? When I add the translation constants to form the group, I can't get the Lorentz transformation by minkowski metric invariant.

[Anonymous No.12598515]

>>12598470
Say you have n different stuff.
Picking k of them, is the same as deciding leaving out the rest n-k stuff. .

Like, if you have {a, b, c, d, e}, then picking {b, d}, is the same as leaving {a, c, e} out (and vice versa).

[Anonymous No.12598525]

>>12598515
I see, thanks. I will need to work on this for harder problems.

[Anonymous No.12598550]

Let [math]\omega = dt[/math] be a differential form of the algebraic curve [math]\mathbb{C}P^1[/math], [math]t:=x/y[/math] in its field of rational regular functions. Is there a short and simple way to compute [math]\text{div}(\omega)[/math]? The order at the zero or the pole where easy through a few results given, but at the other points I did a long and cluncky calculation.
Is [math]\text{ord}_P(df) = 0[/math] if [math]P[/math] is not a zero nor pole of [math]f[/math]? Maybe it's this general property and I didn't see it yet, wouldn't know why.

[Anonymous No.12598728]

>>12598550
Well t is a local coordinate for CP1 on the chart {y != 0}. In that chart, we have w = dt, which has no zeroes nor poles.
Now, z = 1/t is a local coordinate on the chart {x != 0} and, in that chart, we have w = -dz/z^2 which has a double pole at 0.
Hence, in summation, div(w) = -2 [\infty].

And yes, by definition of the order of vanishing at a point, ord_P(f) = 0 if P is neither a zero nor a pole, as it implies that f assumes a nonzero value at P (and therefore is invertible in the local ring of your algebraic curve at P)

[Anonymous No.12598749]

>>12598495
It's not clear what you're talking about.
The Poincaré group is a group, what do you want to derive? Do you want to derive that it's the symmetry group of some object? If your goal is to derive it's the symmetry group of [math]g_{\mu\nu}dx^{\mu}dx^{\nu}[/math], then just start by actually plugging things in.

[Anonymous No.12598853]

>>12598749
Actually is to show that x'=x-
_0 + ax + bt and t'=t_0 + cx + dt is invariant under minkowski metric. But I can't show that the constants are the Lorentz transformation plus translation term.
Thanks anyway.

[Anonymous No.12598885]

>>12598728
You seem to be using that if P is in a chart, then I take the affine coordinates for this chart and write my differential form in terms of the differentials of these coordinates and then compute the order at P with the functions that are coefficients of the diferentials.
I didn't see this result, if it is one, what I have is that if t is a local parameter for the curve at P, then writing w = g dt gives ord_P(w) = ord_P(g). (In fact, it was defined this way.)

>And yes, by definition of the order of ...
Not sure if you mistook f for df. If the local ring is at P, then I know ord_P(f) = 0 by what you mentioned, but I don't see how to connect this with df. I'd be able to directly apply the definition I showed if P where a zero of f, but it isn't.

[Anonymous No.12598937]

>>12598262
reddit math. "look all these disparate mathematical disciplines feature connections between their basic structures!"

[Anonymous No.12599059]

>>12589477
I am thinking about getting a PhD but only because it seems impossible to know anything in the field I am interested in without going really deep into it. But the field I am interested in seems mostly applied, not sure it's an ivory tower subject. Any thoughts on getting a PhD just so you can get the point where you network with people who know what they're doing so you can hopefully participate?

[Anonymous No.12599117]

>>12593482
>Mine is very sweet and nice to me.
I thought so. You and >>12594618 are luckers!
>Does your effort pay off on average?
Let's see some stats. Almost half of the courses at PhD level I took until now had more than 2/3 of the final grade based on conventional tests (some, more), and I think I came close to giving my all on those, unfortunately couldn't get As (all Bs). Those are one of the hardest there, most people agree. And (fortunately?) they aren't 100% related to AG. In another almost half of courses, the grading was hybrid in terms of exercise lists and tests, they had tests based on lists of exercises given beforehand, I got As. The rest were entirely based on exercise lists, got As too.
I rate not exceptional, but with potential to get somewhere between mediocre and a good (not "very good", just "good"). Ofc, weak indicatives.
>I think your demon is trying to help you
Maybe I sounded completely antagonistic or disagreeable towards my demon, but it's really not the case. He is a part of me, in fact there are positives in having this. It makes me hunt for problems, mistakes, prevent or prepare to worst case scenarios. I can't proceed completely without him, I must know all my wounds and look them naked and clearly, every detail. Problem is when I see more than there is there.
There's this widespread idea of "success iff great confidence, self-steem, etc", and while I think there's a minimum necessary, there are counter-examples, people that tend to be often pessimistic/uncertain/worried and won't just believe they can pull shit off. Like Knuth, he said in an interview that he started to shine during uni because he got so afreid of failing courses that he'd channel the fear into completely solving books, books, and more books. These are exceptions, but they exist, and I like to hear about them because it motivates me. I don't have to completely change into someone I currently am not.
I think you may also think/behave in similar ways.

[Anonymous No.12599147]

>>12593482
Oh, here's another aspect on what I was commenting about. Courses and grades.
In my uni some people would babble about how caring about grades is ridiculous, that they should be seen as almost irrelevant etc (some of them were good students, they had ideological inclinations to think that way). I also lowkey despised the dick-measuring contests etc, but I did care about grades, a lot. Because they are external confirmation (though obviously quite imperfect) on how well I'm doing. It's an evaluation from someone else, a professional paid to do that. This was also a way of measuring how wrong my demon usually was, in the vast majority of times he'd bet on lower grades. But also because of him I worried, studied harder and got better. How did you view grades?
>There is a risk of burning out if you keep going like that when coursework is replaced with independent work
Did you adopt different habits to get more balance?
>No problem! I can't promise you a bright future, but I can tell you that you will do fine during your studies if someone like me can
I would conjecture the converse at most haha
What matters now is that I'm doing it regardless, and I have work to do. I have to deliver. I must. It's now or never!

[Anonymous No.12599153]

>>12599117
Is the best way to perform in math exams to just do lots of problems?

[Anonymous No.12599159]

>>12599153
Yes. Consider the problem of finding integer pairs a,b such that a^(b^2)=b^a. If you solved that it would incrementally improve your math ability

[Anonymous No.12599166]

LOOK GUYS! TOUHOUS!

[Anonymous No.12599174]

>>12599159
That is one of the easiesf IMO problems

[Anonymous No.12599207]

>>12599159
Aren't IMO problems just all about tactics and tricks? Would it be good to work through all the problems in a book like 'Putnam and Beyond'?

[Anonymous No.12599220]

Hey guys,

I’m in computer science and my math is trash. Currently a second year (my uni is 3 years) and I feel for the up coming semesters. I’m currently going through a discrete math for cs students book, but I was wondering if anyone can recommend further readings or general resources (my math isnt the best)

[Anonymous No.12599290]

>>12597788
They came from very similar genetic backgrounds so it should be no surprise

[Anonymous No.12599311]

>>12597383
Yes, though not a unique one

[Anonymous No.12599328]

i just found this out while doing some schizophrenic maths

(a + b) + (a - b) = a * 2 ALWAYS

[Anonymous No.12599383]

>>12599328
Wow, brilliant.

Here's another cool equation:

(a - b + c) - (a - b + c) = 0 ALWAYS

[Anonymous No.12599385]

>>12599328
hm i guess cuz that is simplified 2a lol, is there a way to find ab with adition and subtraction only no loops?

[Anonymous No.12599388]

>>12599383
haha i get it now

[Anonymous No.12599427]

i fucking suck feminine penis when it comes to proof writing. but the "proofs for dummies" books are all so boring. am i going to regret just powering through the books i'm actually interested in such as >>12594771 and >>12595715 ?

[Anonymous No.12599434]

>>12599328
you're just proving for all a there is some number -a such that a + (-a) = 0 (trichotomy law)

[Anonymous No.12599530]

>>12599385
It's a longstanding conjecture that the answer to this question is "no."

[Anonymous No.12599777]

Am I a total dum dum if I think I can jump into studying rewriting systems (in context of mathematical logic and syntax) with barely any prerequisites? It looks easy to me.

[Anonymous No.12599831]

>a nontrivial mathematical problem comes up
>the solution requires one or more steps which are not obvious
>all the brainlets cry OH NO THAT PROBLEM DOESN'T COUNT IT'S A FUCKING TRICK
ever heard about pythagorean theorem? well if not, then don't worry - it's just a fucking trick with cutting up squares into triangles and rearranging them
or do you know how to solve the quadratic equation? it's a fucking olympiad-tier trick with completing the square, so don't worry, no need to learn this
now category theory that's real maths

[Anonymous No.12599926]

>>12599831
If I study cat theory, will I become better at finding those crazy hacks that solve difficult problems?

[Anonymous No.12599931]

>>12598262
>What is category theory anyway?
it's language and way of thinking which everyone going deep into algebra/algebraic geometry/algebraic topology etc. must learn sooner or later. it's a language only for adults though, and children trying to speak it are fucking ridiculous.

[Anonymous No.12599935]

>>12599926
No lol.
Category theory is the art of moving data around to fit some schemes. If you have no data to move or schemes to fit, you'll be spinning endlessly in circles. You get those from other fields of mathematics.
CT is best picked up along the way as needed.

[Anonymous No.12599970]

>>12599935
Is categorical logic at all a replacement for set theory in describing structures? I don't mean totally not using sets btw

[Anonymous No.12599976]

>>12599831
Without exception trick= part of the solution they don't understand.
They are simply revealing their own ignorance.

[Anonymous No.12599977]

>>12599970
While this question is vague on all ends, the answer to your question is likely Yes.

[Anonymous No.12600085]

>>12599970
Yes and no -- structural sets can replace material sets, if that's what you ask, but you're always going to have something set-like no matter where you start. Sets are structures to be described, too.

Structural sets are the kind of sets category theory talks about, and are a lot like types. They have elements, morphisms (functions) from the set with one element, but elements don't have internal structure. That is, there is a unique set with one element. It doesn't matter how you label the elements of a set as long as they're distinct.
The difference between structural sets and material sets comes from (or, if you come at it from another angle, implies) separating the concept of a set from the concept of a subset of a set.
The set of subsets of a set will have elements that have internal structure: they're predicates on a set, classifying elements of that set. Labeling now matters, as the set of labels is now fixed, and the structure you're interested about is in distinguishing how the predicate responds to specific labels. Since you also must have a fixed universal set of labels when talking about subsets, you also get to talk about arbitrary intersections without problems.

Material set theories like ZFC collapse this distinction. Other than that, they're pretty much equivalent, structural sets are simply nicer to work with and make a clearer distinction of the two concepts.
That being said, it's easier to work with structural sets as a type theory than categorically.

[Anonymous No.12600101]

>>12600085
That's what I meant, only using structural sets in formal definitions. But to describe the same notions as in material sets, it's a shitton more busywork isn't it? At least I got that impression when translating definitions from classical set theory based ones to some type theory

[Anonymous No.12600134]

>>12600101
Not really, you never actually use much of material set theory in ordinary mathematics.
Have you ever had to worry about whether your natural numbers were encoded by Zermelo naturals or von Neumann naturals? Have you ever worried over whether two for-the-purpose-at-hand-disjoint sets A B had some elements that are for-the-purpose-at-hand-distinct but are actually encoded by the same material set?
You already implicitly assume there exists an appropriate encoding of material sets for your sets that distinguishes all their elements. You're already working with structural sets. The only difference is that sometimes what you should call a subset of a set, you call a set.

The bias comes from the fact that people assume that the divide between informal "material" set theory and formal material set theory isn't that large, but when introduced to structural set theory, they're also encouraged to stay close to the formalism to get a feeling for it. This is possible for structural sets BECAUSE the formalism is so much closer to informal practice that you only need some additional busywork to make it formal, whereas fully formal material set theory would make your rather shoot yourself than do any mathematics at all.

[Anonymous No.12600215]

>>12600134
Now that I think about it, it's hard to imagine the kind of shitpile you'd have to produce in ZFC to describe relatively basic structures. Just to clarify, describing a set using anything beyond the standard set operations and cardinalities already counts as a having structure?

[Anonymous No.12600321]

I just flunked my abstract algebra exam, I'm on the verge of tears right now. I failed...

[Anonymous No.12600326]

>>12600321
It's not a final though right? What's it worth?

[Anonymous No.12600356]

>>12600326
Yes, it's just the first exam of the year, there are two more, but this is still a pretty bad sign. Now we're going to study rings but I barely know much about groups, I'm still fucked.

[Anonymous No.12600359]

>>12600356
Get Pinter, and fucking READ. Then solve the problems. Pinter makes things easy and it's not long. You can do it in 1 weekend if you FOCUS

[Anonymous No.12600362]

>>12600356
Not a big deal then, just put it behind you and resolve to do better.

[Anonymous No.12600386]

>>12600356
James Simons got fucked in his first abstract algebra exam at MIT, then got an algebra book to read for some weeks and aced everything and decades later he had abandoned mathematics to be a billionaire in the very front of the quant revolution on financial markets; anitranny failed tests in group theory, studied very hard and now she's doing schizo homological algebra. Many cases!
Now it may be your turn, where are you going to end up? We can only wonder.

[Anonymous No.12600412]

>>12600085
Just prove the basic things once and replace all the busywork with an instruction for the reader to refer to the pile of tedious basic proofs

[Anonymous No.12600417]

>>12600386
>anitranny failed tests in group theory
Source? That would motivate me, I look up to him.

[Anonymous No.12600509]

This guy wore it better honestly

[Anonymous No.12600518]

>>12600417
>>12577027
>At first it was total Hebrew to me, and I even failed the first course. Then I had to retake the exam, spent a lot of time trying to get a grip on the stuff, and that's when it started to make sense.

[Anonymous No.12600565]

>>12600417
In the other thread she had never seen what a degree n map of the 2-sphere looked like and more importantly brought this up without using the tools which she should have to describe what they are in terms of other familiar objects. Sometimes what she says sounds impressive to undergrads because there are many new words to them, but she's actually pretty fucking new mathematically speaking.

[Anonymous No.12600584]

>>12596368
Terrible.

[Anonymous No.12600587]

>>12599117
I don't know how important grades are on that side of the ocean, but your situation doesn't sound too bad with those A's and B's, especially if they are from high level stuff. Another thing I know nothing about is how important your uni's ranking is compared to your supervisor's name when applying for a post doc. You should still definitely be able to spend a few years doing what you seem to enjoy with such grades, I think.

Your relationship with your demon seems pretty good if you put it like that. Instead of Marbas, you made a pact with Sun Tzu (not the remainder theorem guy!). I don't know who this Knuth is, but I don't think confidence is necessary. Sure, you will have to play the social game and present yourself, but you can fake it till you make it. I failed my first spring completely, and then I did a lot of work to compensate that, so I guess we have something in common yeah.

The grades are not irrelevant per se, as they are something the reference letter folk will look at when they are writing them. They may remember who you are, they may remember your good questions and comments, but they will still need some objective facts, and the grades provide those. Also, that pressure thing you mentioned is true. I think my department had the requirement that one must have at least 4/5 as their GPA to be accepted into a PhD program, so I used that as a universal rule that I need to have at least 4 as my skill level on any course I took.
>Did you adopt different habits to get more balance?
I had a one year break studying stuff independently, so I just kept doing things the same way.
>What matters now is that I'm doing it regardless, and I have work to do. I have to deliver. I must. It's now or never!
Well said! You have my permission to succeed or fail but not to give up.

>>12600565
Not new, just dumb and inefficient.

[Anonymous No.12600628]

FEAR DOES NOT EXIST IN THIS GENERAL, DOES IT?

PAIN DOES NOT EXIST IN THIS GENERAL, DOES IT?

DEFEAT DOES NOT EXIST IN THIS GENERAL, DOES IT?

STUDY FIRST. STUDY HARD. NO LAZINESS.

[Anonymous No.12600636]

>>12600628
I want a textbook written by you

[Anonymous No.12600646]

[Anonymous No.12600695]

>>12600646
Just use morse code next time

[Anonymous No.12600735]

>>12600587
>just dumb
If you're dumb then I have a room temperature IQ.

[Anonymous No.12600762]

>>12593702
Hot anime bitch
>>12594642
Why can't mathchads look like actual chads? Someone should get working on that

[Anonymous No.12600770]

>>12595696
Apostol is dry as shit but has multivariable (although I never read the second tome). Spivak has a bit more real analysis, and is way more fun to read. The starred exercises are pretty tough I thought. Never used Courant

[Anonymous No.12600774]

>>12599427
I think most people here never read a proof book. Straight up, reading about conditionals/watching Michael Penn's new proof videos and just diving into the book should be just fine.

[Anonymous No.12600781]

>>12600770
Shit opinion. Spivak is weak, but Courant is too strong. Apostol is the perfect middle ground between both. Pick Spivak if you're dumb, pick Courant if you're a genius and pick Apostol if you're a normal person.

[Anonymous No.12600797]

>>12596057
Baste as fuck
>>12596342
Pretty important
Doubly so if you are going to use a translated text

[Anonymous No.12600807]

>>12600781
The 1935 version of Courant's Calculus seems to be much more readable.

[Anonymous No.12600815]

>>12600781
Spivak is definitely not for dummies though, conversational tone aside.
I used Apostol mainly, but the proofs for the theorems don't follow as naturally from the text as they do on Spivak's text. That's about it for it's difficulty I think.

[Anonymous No.12600816]

I'm starting Calc 3 and a couple problems use infinite fractions which I've never seriously encountered before. Can somebody link something that I can read to understand them in an hour?

[Anonymous No.12600870]

>>12600816
Retard

[Anonymous No.12600938]

>>12600816
wikipedia

[Anonymous No.12600975]

>>12600735
Hopefully not. 21 would be quite a low score. Nevertheless, some seemingly trivial things are completely out of my league, like that degree n map of the 2-sphere and the use of stereographic projection to get it. It should be obvious after maybe 20 minutes, but nope, I would never ever have thought of using it. I'm closer to a warning example than anything inspiring.

[Anonymous No.12601074]

>>12600646
=/= = 0 <=> |X| in {0,1}

[Anonymous No.12601092]

>>12600359
Pinter has like 33 chapters, it would take at least a month for a noob

[Anonymous No.12601095]

how do i get good at math, i feel like I'm too slow

[Anonymous No.12601103]

>>12601092
I didn't mean all of it, just like the first 5-10 chapters that cover group material which probably was part of the class so far. But my bad, now I see that it sounds like I suggested the whole book

[Anonymous No.12601129]

>>12601095
Kill yourself and be reborn with at least 130 IQ in a first world country.

[Anonymous No.12601200]

Hello frens, I’m going back to school and I’m taking trigonometry, pre calculus and then calculus. I want to ace these classes despite always having been a total brainlet when it comes to math, is there a site I can use to generate random problems to solve so I can practice outside of homework? I’m serious about mastering math

[Anonymous No.12601238]

>>12600215
As soon as you need more structure from the elements of a set than merely being a label for its elements, you're working with a subset.
Ask yourself whether these questions make sense:
Does it make sense to ask whether an element is NOT part of the set?
Do you have a reference set that includes all the elements you're talking about?
Are you STATING that an element is part of a set? "Let x be a ..." Or are you PROVING that the element is part of it? "therefore, x is/is not in ..."
If instead of working with a set, you work with a predicate, does it still make sense? "a \in {x \in A | P(x)}" <-> "P(a) is true for some P : A -> Prop"

Also note that cardinalities are seldom useful, what is useful about them is the injections and surjections between sets that they imply. Work directly with them, as the conversion to cardinality is lossy.

[Anonymous No.12601243]

>>12601200
I recommend you start with the basics. This book with it's plentiful exercises will give a you strong starting point for learning trigonometry followed by calculus.
Don't worry about the jargon in the description, it's just formalism and chest-puffing. This is one of those foundational textbooks that anyone, total beginner to grad student, can benefit from.

[Anonymous No.12601282]

>>12601238
That clears it up a bit, thanks. Yeah, I meant that cardinalities are often used as substitute for structure in material set formalisms.

[Anonymous No.12601563]

I'm going to do every problem in this book. How long will it take assuming I spend 4 hours a day?

[Anonymous No.12601598]

>>12601563
Around 6 months or so, unless you're a genius then maybe 4 months or so?

[Anonymous No.12601639]

>>12601598
6 months sounds like what I'm thinking. Probably more like a year; not a genius but algebra mostly clicks for me. I've already had formal courses in abstract algebra and group theory. I'm trying to learn more and also possibly couple it with pic related for AG.

[Anonymous No.12601742]

>>12601639
Yeah, I think I was being generous saying 6 months, it will probably be more since it's a huge book and not an easy one. Unless you really study it 4h every single day non stop, then I think 6 months is doable, but this requires tremendous discipline.

[Anonymous No.12601777]

>>12600774
thanks anon

to thank you, here's a pic of me and some of my buddies that study category theory

[Anonymous No.12601856]

>>12601777
me in the jeans and black t shirt

[Anonymous No.12601859]

Combinatorics is the cure to mental illness

[Anonymous No.12601868]

>>12601859
this is hands down the most based post in this edition of /mg/
big ups to u sir

[Anonymous No.12601892]

>>12601639
Matsumura was pretty hard if I remember correctly. Maybe Eisenbud on the side for reference.

[Anonymous No.12601906]

A group is a set of elements with binary operator (•) with the following properties (for each exists b s.t.):
i) Associativity ab(c) = a(bc)
ii) Identity ab = a
iii) Inverses b s.t. ab = ba
iii) Inverse ab

[Anonymous No.12601960]

Be me
Need to study german
Get distracted by fourier transforms instead

So can anyone help me pl0x. I wanna decompose a parabola from -1 to 1 into sines, how do I do et :P

[Anonymous No.12602214]

>>12601563
Strange, I was planning the same thing, even with Matsumura.

[Anonymous No.12602227]

>>12600975
>the use of stereographic projection to get it
As I told you before that was posted, just suspend a degree n map on the circle. You know what suspension does to homology, right? You may prefer thinking about it that way.

[Anonymous No.12602312]

>>12601960
Kys

[Anonymous No.12602321]

>>12602227
I know, yes. I know how those things work in the algebraic setting, but it just extremely difficult for me to imagine the spaces or how the shape affects the homology or homotopy. Something as simple as [math]\pi_1 (\mathbb{R}P^2) \cong \mathbb{Z}/2\mathbb{Z}[/math] took me a day or two to visualise. It follows easily from the bundle, sure, but to see it instead of just writing some magick runes on paper. I hate topology and geometry.

>>12601906
Yes.

[Anonymous No.12602409]

>>12602321
You need more examples, and maybe even more differential topology, in your life.

[Anonymous No.12602415]

So the thing I dont get with fourier series is doesnt the method assume the function can be decomposed into sines? It makes sense if it can be, but what if it cant be?

[Anonymous No.12602467]

>>12602415
The Fourier series, just like the Taylor series, need not converge to the given function.

[Anonymous No.12602483]

>>12602415
Thinking about it a bit more we could try this:
Given a mapping of a function F around the circle, it is the unique mapping that outputs its amplitudes-periods. We can see this by comparing two functions, getting their components, and seeing that the difference also has components. Here still assuming that each is decomposable but thats... trivial I think. Like a matter of testing it.

[Anonymous No.12602489]

>>12602483
Oh nevermind its not trivial. We need to show that the difference will have a component and thats easy, we just need to find any periodicity within it and all functions have that at the inflection points, just average out the inflections

[Anonymous No.12602528]

>>12602214
Study group?

[Anonymous No.12602706]

>>12602409
I actually did a course on differential topology and all the atlases gave my brain torsion. Examples would be/have been good, but I had to essentially study everything on my own other than the very basics due to the awfully minuscule amount of relevant courses offered by my uni, and thus I had no one to ask help from. At least algebra is easier.

[Anonymous No.12603088]

>>12588999
I wanted to relearn maths, what would you anons recommend?

[Anonymous No.12603095]

>>12603088
Youtube

[Anonymous No.12603109]

>>12603088
If you want to start before calculus then either go with https://Openstax.org, Khan Academy or Lang's Basic Mathematics, which is on libgen.
If you want to start at Calculus or thereabouts, skim Lang's Basic Mathematics to make sure you know everything there already and then read one of Apostol's Calculus, Spivak's Calculus or Courant's Calculus.
If you wanted to start from a point beyond this you wouldn't be asking that question.

[Anonymous No.12603239]

>Calculus is easier than Pre Calc
Is this a joke?

[Anonymous No.12603288]

>>12602415
it's not easy to prove that the fourier series converges to a given function. you can only do it in certain situations for certain kinds of convergence (but it turns out there are plenty of situations, and plenty of kinds of convergence, you just need to be careful with them).
the convergence of fourier series is a fascinating topic with dozens of detailed, complicated theorems and techinques. the most basic results are truly beautiful, and the more difficult results are just brutal to prove. for example, there's carleson's theorem which says that the fourier series of a square-integrable function converges almost everywhere. it's much easier to show that the fourier series of a square-integrable function converges in L^2, i.e. that the integrals of |f_n - f|^2 converge to 0 where f_n is the first n terms of the fourier series.
with this in mind, almost any periodic function you can come up with will have a fourier series which converges in some useful manner or another.

[Anonymous No.12603297]

Does anybody here know of any interesting generalizations of compass and straight edge to three dimensions? Where instead of constructing arcs you have a way to construct spherical caps or something?

[Anonymous No.12603387]

>>12603239
>local phoneposter still hasn't committed suicide
Is this a joke?

[Anonymous No.12603411]

>>12602528
Haha, I'd probably hold you back, but it's a nice idea.

[Anonymous No.12603424]

>>12603387
how can you tell?

[Anonymous No.12603435]

>>12601859
Explain how does one into combinatorics

[Anonymous No.12603489]

Is this the best pure maths curriculum online?

https://hbpms.blogspot.com/

[Anonymous No.12603571]

>>12603489
https://www.openstax.org

[Anonymous No.12603581]

>>12603571
HBPMS is much better than this I'm afraid in terms of courses listed and order.

[Anonymous No.12603595]

What's stopping you /mg/?

[Anonymous No.12603599]

>>12603595
cute puffy nips

[Anonymous No.12603652]

What a tiresome day. I hate "quantic definitions/notations", especially when the expositor doesn't even explain how to navigate from one to another. Another instance of a mathematical version of "physicist's freestyle manipulation of differentials as mere simple numbers".

>>12599153
The best way I learn is through attempting a lot of problems. And at least on courses up to masters, you should be able to go well by doing that. Some people study by building intuition, mental maps and asking and answering their own questions about the subject, though. I didn't really attempt this yet, so I guess I can only say it didn't come naturally to me.

>>12600587
>Another thing I know nothing about is how important your uni's ranking...
Is there an easy way to find how it ranks globally? In terms of PhD program. Never searched about.
>I don't know who this Knuth is
Donald Knuth, he's one of the giants in the intersection of math and computer science (from what I know). I've found the said bit of interview (see from 4:16 onwards): https://www.youtube.com/watch?v=YjyaYCLJQXw&list=PLVV0r6CmEsFzeNLngr1JqyQki3wdoGrCn&index=9
>Sure, you will have to play the social game and present yourself...
This is the hard part, and where he plays very against me. But I'm being a broken record at this point.
>You have my permission to succeed or fail but not to give up
Roger! Luckily we'll meet in Algebrahalla.

I think I'll stop pestering you with all my repetitive bs for a while, thanks for the attention. : )

[Anonymous No.12603656]

>>12603489
Aren't most uni curriculums online? Just search for a good one.
>>12603571
Doesn't go high enough. The books don't even have proofs

[Anonymous No.12603712]

Can I teach Gelfand's books to brainlets? They've also published the newest addition to the series: Geometry, and so I am currently going through that to tutor some brainlet finance majors about precalculus.

[Anonymous No.12603735]

>>12591704
people go to grad school out of college because it's the default next thing to do and they have no initiative or independent thought. these are exactly the worst students for grad school so they sink into depression and impostor syndrome.

[Anonymous No.12603791]

>>12603712
Unless you mean LibGen availability, how the hell have they recently published anything? Israel Gelfand died years ago.

[Anonymous No.12603806]

>>12603571
Is this a meme or something? They just have high school stuff.

[Anonymous No.12603822]

>>12601243
I'm working through this text now. It's quite difficult lol. I wonder how many /sci/ posters looking to brush up on trigonometry have been tricked into learning about the p-adics instead.

[Anonymous No.12603857]

>>12603822
Janny clean this up immediately. We can't have newfags in on it.

[Anonymous No.12603866]

>>12594771
i am enjoying this book thus far

cozy soviet texts hnnnngggggg

[Anonymous No.12603879]

Is combinatorial optimization a good topic for me to dive in if I want money and not a lot people know about it?

[Anonymous No.12603887]

>>12603879
if all you want is money study probability theory, stochastic calculus and financial methods

[Anonymous No.12603895]

>>12603887
It's not 1995 anymore, unless you combine this with a Ph.D. from Harvard or similar you won't get a job in this field, and you can't do it on your own either.

[Anonymous No.12603933]

>>12603895
>unless you combine this with a Ph.D. from Harvard or similar you won't get a job in this field,
This isn't exactly true. I know a few kids just with bachelors that landed quant roles. Moreover the good masters programs in financial engineering (e.g. Baruch or similar) place very well.

The larger concern is how well you do once you actually get on the desk. You're competing with the best in the world for ever diminishing alpha. The tech companies frankly offer a better proposition in terms of lifestyle / expected earnings / etc.. People fawn over the starting salaries at Jane street and the like, but once you're making over 200k (which is typical of any good new-grad job in tech or finance) it doesn't much matter anyway.

[Anonymous No.12603948]

I need to decide between taking euclidean geometry or linear algebra 2. Any thoughts on which will be more interesting and/or easy? They're both only offered online and I'm trying to avoid the potentially more difficult class if possible given the circumstances.

[Anonymous No.12603957]

I need to decide between taking euclidean geometry or linear algebra 2. Any thoughts on which will be more interesting and/or easy? They're both only offered online and I'm trying to avoid the potentially more difficult class if possible given the circumstances.

[Anonymous No.12604011]

>>12603791
Springer recently published his Geometry book. It was completed years ago before he died, but it wasn't published.
Overall it's pretty good as expected of Gelfand.

[Anonymous No.12604018]

what the fuck?
>https://www.ebay.com/itm/A-Comprehensive-Introduction-to-Differential-Geometry-3rd-ed-5-vols-M-Spivak-/223832628687
>US $7,450.00

Is this how much Spivak's differential geometry goes for now?

[Anonymous No.12604030]

>>12603933
Well yeah, I guess I should have said make big money instead of get a job.

[Anonymous No.12604067]

>>12604011
If only Springer had decent binding and wasn't 99% print-on-demand garbage though...

>>12604018
Nah, the 3rd edition is still being published by Spivak himself and the prices are around 50, 60 usd. see his website https://www.mathpop.com/

[Anonymous No.12604189]

Hello I'm a retarded civil student.

I want to know automate determining the wavelength of the tiny oscillation superimposed on the bigger oscillation in the graph. It's plotted as a line but it's discrete evenly spaced points. I think I need to do a discrete fourier transform to get the frequency and amplitude of the two waves right? I'm not quite sure how I calculate wavelength with that...

[Anonymous No.12604220]

>>12604011
>in [current year] we're still getting new Gelfand books
It's almost as if the Soviet Union never collapsed.

[Anonymous No.12604515]

>>12603652
>Is there an easy way to find how it ranks globally? In terms of PhD program. Never searched about.
There are some rankings that let you choose also subject specific rankings and show research impact etc., but that's all I know.
>Donald Knuth...
Oh right, I knew the man but couldn't connect him to any name. He seems like a nice guy on this video. He's a big guy, I wouldn't compare myself to him.
>This is the hard part, and where he plays very against me. But I'm being a broken record at this point.
Fake t till you make it!
>Roger! Luckily we'll meet in Algebrahalla.
At the great feast hosted by Thor, the god of thunder and thorsion free modules.
>I think I'll stop pestering you with all my repetitive bs for a while, thanks for the attention. : )
No, thank you for giving me something to do.

[Anonymous No.12605221]

>>12598728
>>12598885
How off am I? Can you shed some light?
I'm going to try and prove what you seem to have done.

[Anonymous No.12605339]

The real numbers are a psychological warfare operation to make you doubt your own sanity.

[Anonymous No.12605445]

>>12603088
Depends on what you know

[Anonymous No.12605491]

>>12605339
Were Dedekind and Cauchy servants of the Mental Warfare Commanding Emperor? https://www.youtube.com/watch?v=5VaSygBt6Pc

[Anonymous No.12605541]

>>12605538
new
>>12605538

[Anonymous No.12605632]

>>12598728
I got it now, the local parameters differ by adding a constant, so their differential is the same. Thanks.