/sci/ - Science & Math

first for platonism

Plagiarism is such an awful thing. Is anyone else bothered deeply by it?
Every time I remember that plagiarism exists I can't help but sink into this mental trap and obsess over all the ways it can manifest in society.
It's actually really bad for my mental health, but I can't control it. Maybe I need to get back on SSRIs (I've been too lazy to get my prescription renewed recently).
I've stopped self studying mathematics also. For some time I was quite into Lee's Smooth Manifolds, working my way towards MathPhys, but I feel 0 desire to do any math now. A switch has flipped and now I just can't be bothered.

It has been years since I last saw a number in my math studies.

It’s just letters and concepts and sets and sets of sets and sets of functions from sets to sets and spaces of sets, which can be defined in terms of some equivalence relation between sets.

I sometimes forget numbers exist.

Algebraic Number Theory is neat af, everyone who knows at least commutative algebra should learn the subject

>>11286368
Gröbner basis too

>>11286311
>I sometimes forget numbers exist.
But they don't anon, numbers are sets in ZFC.

>>11286371
I legit don’t know why Grobner bases were skipped during my algebra class. They are as useful as row echelon form is in linear algebra.

>>11286442
The C is supposed to go in front of the abbreviation, anon, not the end.

>>11286640
>constructivism

>>11286311
>doing math that doesn't have a single subscript in it
found the category theorist

>>11286294
ok, leave and never return freak

Are there any comfy work from home jobs in math? My job has tuition aid and I'm holding out for when I qualify for it to try to take some math courses but I'd rather study on my own in some ways. Is there any way to get college credit more advanced than CLEP exams? I would love if I could get a degree through testing and wrap it up with projects later on.

How do you find the sine/cosine of a non-standard angle (say 78 degrees) without using a table/calculator/other outside device? 30/45/60/etc are easy enough since you can just use the Pythagorean theorem

>>11286818
community college and transfer it over. but no, you generally have to take classes at an accredited school to get the accredited diploma

I figured this would be the right place to ask. Where do you get a mantle like that? I want to be a real mathemagician

>>11287048
use the formulas for cosines and sines of doubles, halfs, sums, etc.

>you will never be as based as Alexey Krylov
why live?

>[eqn]-\frac{\pi}{2} = \frac{3\pi}{2}[/eqn]
Trigonometry is stupid.

>>11287149
But you'll look like an ugly jackass.

>>11287149
I'm not saying you shouldn't search for the mantle. All I'm saying is that when the time comes, you won't need to. The mantle will come to you.

>>11287050
Alright. Is there any way I could get a remote job from doing that? I hate driving and it's such a waste of time. I was thinking of learning html code too but odds are it's oversaturated.

>>11287206
If you get a degree you can get into a computer science field.

If you are trying to learn programming, you are competing against a bunch of no life pajeets on H1Bs who will work for 1/4 the price

>>11287193
>what is injectivity

Does anyone know if there exists a solution manual for pic related?
I'm stuck on the following (excuse me if my formatting is bad its my first time using latex):
Let A and C be subsets of S, and let B and D be subsets of T. Prove the following statements about subsets of S × T:
...
[eqn](A \times B) - (C \times D) = (A \times (B - D)) \cup ((A - C) \times B)[/eqn]

Also, why don't I ever see this textbook ever recommended here? It seems really good for self learning since the whole textbook is basically "do it yourself". You're given some definitions and theorems but the majority of the chapters are exercises which require you to make intuitive leaps from the definitions and theorems.

>>11287215
I have no idea!

[eqn]-\frac{\pi}{2} = \frac{3\pi}{2} = \frac{7\pi}{2} = \frac{11\pi}{2}\\
-1 = 3 = 7 = 11 ...\\[/eqn]

[eqn]-\frac{2\pi}{2} = \frac{2\pi}{2} = \frac{6\pi}{2} = \frac{10\pi}{2}\\
-2 = 2 = 6 = 10 ...\\[/eqn]

[eqn]-\frac{3\pi}{2} = \frac{\pi}{2} = \frac{5\pi}{2} = \frac{9\pi}{2}\\
-3 = 1 = 5 = 9 ...\\[/eqn]

[eqn]-\frac{4\pi}{2} = 0 = \frac{4\pi}{2} = \frac{8\pi}{2}\\
-4 = 0 = 4 = 8 ...\\[/eqn]

Math is not science.

>>11287193
>>11287539
>the absolute state of brainlets incapable of understanding [math]\mathbb{R}\ne\mathbb{R}/2\pi\mathbb{Z}[/math]

>>11287048
You could use Taylor series also

>>11287048
use a differential

>>11287586
>>11287595
I have no idea what those are. Anything that a simple trig/algebralet could do?

>>11287598
open a book and read some

>>11287048
The smallest known nonzero angle on wikipedia is 1.5°.
That one's known exactly, see https://en.wikipedia.org/wiki/Trigonometric_constants_expressed_in_real_radicals#1.5%C2%B0:_regular_hecatonicosagon_(120-sided_polygon)
You can consequently get ALL integer multiples of that, too. Luckily, 78 = 52*1.5. You just need to apply the laws again and again. Values which can't be extracted geometrically somehow can be computed up to arbitrary precision by other means

>>11287382
Here’s solution, I omitted some orthography but it has everything you need to follow the idea.

>>11287710
Thank you very much!

>>11287764
You’re welcome! Once you’re done with basics try doing proofs with symmetrical difference operation, that one’s a major step up.

>>11287710
Wait, why do you say [math]y \notin D[/math] in line 3 but change it to [math]y \in D[/math] in the second half of line 4?

>>11287788
Oops, should be B instead of D. Sorry.

>>11287775
The proof of the associativity symmetric difference actually came before this in this textbook, but I never actually proved it rigorously. I kind of just did an "intuitive "proof"" and moved on.

>>11287794
I had one where you have to prove that A intersection (B sym difference C) equals (A sym difference C) intersection (B sym difference C), and also to show that with union instead of intersection it doesn’t stand... Real tough one.

>>11287149
The Eastern Orthodox Church.

When solving a linear system, is there a way to break down a really big Ax=b into smaller Ax=b's, solve them, and then recombine them somehow?

>>11287930
depends, if A comes in blocks (few off-diagonal elements), then sure

>>11287930
That sounds like either block matrices, Jordan form or the Kaczmarcs method.

>>11287930
Yes, using QR factorization, but believe me, it ain't worth it unless A is REALLY big. You'll end up with A=QR, so Qy=b, with Rx=y, and Q and R are triangular matrices (at least if A is square afaik), which makes it easier to solve

>>11287930
Yes. If your system has a compact symmetry [math]G[/math] such that [math]A\mapsto A^g = g^{-1}Ag = A[/math] for all [math]g\in G[/math] then you can decompose [math]A \in \operatorname{Hom}_\mathbb{R}(V,W) \cong V^*\otimes W[/math] into diagonal representation blocks [math]A= \bigoplus_\pi A_\pi[/math], where [math]A_\pi = P_\pi AP_\pi[/math] transforms under the irrep [math]\pi[/math]. Given the orthogonal projection [math]P_\pi[/math] onto the subspace [math]V_\pi \subset V[/math] for which [math]A_\pi[/math] acts irreducibly, we can then first solve the partial problem [math]A_\pi x_\pi = P_\pi b[/math] for each [math]\pi[/math] then combine them to obtain the solution [math]x = \bigoplus_\pi x_\pi[/math] to the original equation. If [math]G[/math] is finite then you only have finitely many partial problems to solve.

>>11288144
Yes, obviously. That is a translation of what I asked into a very elementary result which states existence but does not suggest an algorithm for determining such symmetries. Do you have anything interesting to contribute to my question?

>highlighted = covered in precalc
Should I bother with the non-highlighted parts or just do it in Calculus?

>>11288219
chapter 9 looks based

>>11288208
>That is a translation of what I asked
Not exactly, you asked for a way to decompose [math]A[/math] and I gave one to you. Please learn to read when someone graciously tried to help you.
>does not suggest an algorithm for determining such symmetries
Sure there is; if [math]W\cong V[/math] is framed then what I said immediately suggested you to look for subgroups of [math]\operatorname{Aut}V[/math] that commutes with [math]A[/math]. In particular, if [math]V[/math] is in addition oriented then you may ask what subgroup of [math]G\subset SO(n)[/math] commutes with [math]A[/math]. For this, you only need to check the action of rotations on [math]A[/math]; given a representation [math]\pi[/math] of [math]SO(n)[/math], I think even you can compute the commutator [math][\pi(g),A][/math] can't you?
I honestly thought this was obvious.

>>11286368
Recommend books pls

>>11288144
>>11288251
cringe

>>11287539
what is a periodic function

>>11288208
What compels people to make such responses?
What anger is build up inside you that makes you want to induce negative reaction in others as well?
To say
>Do you have anything interesting to contribute to my question?
after someone puts in more than a minute of thought to your question is not how you make the world (or your life) a better place.

>>11287382
>Also, why don't I ever see this textbook ever recommended here?
I don't know. It is one of the first math books I ever bought and it really helped me get started.
I love this "learn by doing" approach

Let's try to generalize the concept of characteristic functions for fun.
Let X be a set and P(X) its power set. We call:
[math] \chi: P(X) \rightarrow \{X \tightarrow \mathbb{R}_0^+ \}/math]
(functions X to [0,inf))
a characterization on X if:
(i) [math] \chi(\emptyset) = 0[/math]
(ii) [math] \chi(A \cap B) = \chi(A) \cdot \chi(B) [/math] for all A,B
(iii) [math] \chi(A \cup B) = \chi(A) + \chi(B) [/math] for all disjoint A,B.

Conjecture:
The only characterisations are the characteristic function
[math] \chi(A) = \mathbb{1}_A [/math] and 0.
If this conjecture is true then characterizations are always trivial!
So we should modify the axioms.
Suggestions:
[math] \leq [/math] in (ii) or (iii)
or
replacing an axiom by monotonicity:
(iv) [math] A \subseteq B \Rightarrow \chi(A) \leq \chi(B)}[/math]

>>11288747
>trivial zero
There's actually a trivial zero associated to every set.

Axiom IV: [math]\chi [/math] is injective.
Then, we have that, for any point of A, [math]\chi (A \cap A) = chi(A) \times \chi(A)[/math]. This implies [math]\chi (A)[/math] needs to be either 1 or 0 everywhere on A.
You should be able to finish showing this is equivalent to the classical characterization.

>>11288747
>>11288747
I wanna fix the latex.
Let X be a set and P(X) its power set. We call:
[math] \chi: P(X) \rightarrow \{X \rightarrow \mathbb{R}_0^+ \}/math]
(functions X to [0,inf))
a characterization on X if:
(i) [math] \chi(\emptyset) = 0[/math]
(ii) [math] \chi(A \cap B) = \chi(A) \cdot \chi(B) [/math] for all A,B
(iii) [math] \chi(A \cup B) = \chi(A) + \chi(B) [/math] for all disjoint A,B.
Suggestions:
[math] \leq [/math] in (ii) or (iii)
or
replacing an axiom by monotonicity:
(iv) [math] A \subseteq B \Rightarrow \chi(A) \leq \chi(B)[/math]

>>11288144
>>11288208
what yukarifag said is just a really convoluted way of saying "yes; if the matrix is similar to a block diagonal matrix then each of those blocks induces a system which you can solve". A particular case of this is when the matrix is diagonalizable -- for instance a matrix can be similar to its real Jordan form but not diagonalizable. Anyhow you'd need to diagonalize or find the Jordan form before solving those small systems, so it's up to you whether that is easier than solving the big system.

>>11288769
(IV) is too strong of an axiom I think.
Modifying (i) to be
[math] \chi(A) = 0 iff A = \emptyset [/math] also solves the problem with 0.
Now it would be interesting to find a minimal set of axioms that imply injectivity of the characterization

axiom (ii) is far too strong at the moment.
If we replace it with the [math] \leq [/math] version, we get that.
If [math] \chi [/math] fulfills (i) and (iii), and has values less or equal to one, it is a characterization.
Then we get that for any function X to (0,1] we have:
[math] \chi(A) := 1_A \cdot f [/math]
is a characterization.

>IV is too strong
IV is exactly strong enough to regain the classical characterization.
If you don't have IV, you did this:
[math]\phi P(X) \rightarrow P(X)[/math] where [math]\phi (A) = \chi ^{-1} (A) (1)[/math].
Then, we can translate your previous axioms as follows:
(i) [math] \phi ( \emptyset ) = \emptyset [/math]
(ii) [math]\phi (A \cap B) = \phi(A) \cap \phi(B) [/math]
(iii) [math] \phi (A \cup B) = \phi(A) \cup \phi(B)[/math]
Which is peak comfy, and has the inverse map [math]\chi (A) = \mathbb{1}_{\phi (A)}[/math] .

Changing the equalities into inequalities just removes the fun.

>tfw when stuck on a research problem since 2 weeks
just fuck me up senpai

I have an exam for "Probabilities and mathematical statistics" (idk what the direct translation is) in 1 week and I had a shit-tier professor so I literally don't know anything atm. The chapters I'm gonna be tested in are(sorry for the bad translations, idk what the original terms are :
1) Theory of probability(events,field of events, random variables, the law of large numbers, repartitions etc)
2) Mathematical statistics( Theorem of selections, estimation theory, corelation, regression etc)
Can you recommend me a book/ site to study this from please? I only have a shit romanian book that doesn't have most proofs and has awful examples.

>>11287149
Based and mantlepilled

>>11288925
>tfw stuck on the Riemann hypothesis ever since I was born

If the paper I'm working on doesn't ever see the light of day, I'm going to give up and join the military

>>11288251
Don't worry, I was just fucking around. I'm not the other guy. Your post was great, it's the asker I was mocking.
>>11288631
Try not to read into these things too much.
>>11288827
This is more along the lines of what might be useful to the guy who asked. Answer is basically "Jordan form is your friend." But I always enjoy Yukari's functional analytic generality.

>>11288882
But then can we proceed to do anythig interesting here?
I wanted to find axioms that can give me the classical indicator function but also other characterizations, and then we can try to find general properties that mimic properties of the indicator function

what is the intuition behind continuity in terms of preimages of open sets?

>>11289222
>But then can we proceed to do anything interesting here?
I haven't taken a closer look at you axiom IV yet, but before we go on, it might be worth pointing out that the crucial axiom of a Topos is, in fact, the universal characterization of characteristic functions (the other being sums, products, exponentiation):

If your theory has an object that behaves like the a singleton set (all arrows of type into it are the same)
and if your theory has a notion of injections/embeddings (j.f=j.g implies f=g)
then a notion of subobject, if it exist,
is given by a truth object Ω (and no, in general this doesn't have to be a two-element set, like {0, 1})
and, for each embeddings j:U->X from "smaller" objects U into "bigger" objects X,
a "characteristic function" chi such that only j makes

chi.j = take_True

The categories which have this thing are generalizations of logics, set theories and topologies.

https://en.wikipedia.org/wiki/Subobject_classifier
https://en.wikipedia.org/wiki/Topos#Elementary_topoi_(topoi_in_logic)

How do I get the taste for maths lads.. I really love the thought process behind it but I have a hard time with how they teach it at uni.

>>11289261
I never found one, I just got used to it

>>11289261
>>11289337
the intuition is that points in a neighborhood of a given point should be mapped into a neighborhood of that point's image. so if you look at a neighborhood of the point's image, some neighborhood of your original point should end up in here.
don't think about open sets, think about neighborhoods.

is [math]\omega^\omega[/math] the ordinal number of [math]\mathbb{R}[/math]?

>>11289281
interesting but I only know a tiny bit of category theory so I dont fully understand it though. It seems though like that definition might be a special case of some stuff like topos or sheaves or something.
I like trying to come up with new, not necessarily useful definitions and seeing what simple lemmas one might find. Then after researching I find that something similar already exists.
It makes me wonder why it seems so hard to come up with a genuinely new mathematical structure. Has analysis, algebra, topology etc. just already "filled" the space of possible mathematical definitions?
How hard could it be to write down some genuinely axioms and make deductions, and the whole thing doesnt have anything to do with already existing math. But it's clearly not easy at all.

>>11289624
In what sense? Anyway, the answer is most certainly no.
Here's a few pointers:

[math] \omega^\omega [/math], or [math] {\omega_0}^{\omega_0} [/math], is a countable ordinal in the smaller to medium range.
You can describe the order type it represents in Peano arithmetic.
It represents, roughly, the collection of all arbitrary sized but finite lists whos entries are natural numbers.
As a countable ordinal, it's cardinality is that of the natural numbers, [math] | {\omega_0}^{\omega_0} | = |\omega_0| = | {\mathbb N} | [/math].
Consider the description of countable ordinal types beyond infinity here:
https://youtu.be/EAAC9dCV9_k

[math] { \mathbb R } [/math] is of size of the continuum,
[math] |{ \mathbb R }| = | P({\mathbb N}) | =| 2^{ | {\mathbb N} | } | = | | \{0, 1\}|^{ | {\mathbb N} | } | = | | \{0, 1\}|^{ | \omega_0 | } | [/math]
and [math] | P({\mathbb N}) | \ge | \omega_1 | [/math] where [math] \omega_1 [/math] is set holding all countable ordinals, i.e. the smallest uncountable ordinal. This one is uncountable, so long long past all the easily compresensible ordinals.

To make the comparison sharp, [math] | P({\mathbb N}) | = | \omega_1 | [/math], is to claim the continuum hypothesis.
The size of [math] { \mathbb R } [/math] w.r.t. to ordinals is independent of ZFC, there's no good answer to it.
So your question was doomed from the start...

>It seems though like that definition might be a special case of some stuff like topos or sheaves or something.
What is "that definition" in this sentence now? Sheaf-categories fulfill those properties, so the latter is the more general variant, for what it's worth.
I just wanted to point you to it, in case you're interested. I was a bit scared of looking at your formulas.
>Has analysis, algebra, topology etc. just already "filled" the space of possible mathematical definitions?
"No", but I think it's a matter of (Kolmogorov) complexity.

>>11289624
In what sense? Anyway, the answer is most certainly no.
Here's a few pointers:

[math] \omega^\omega [/math], or let's write [math] ({\omega_0})^{\omega_0} [/math], is a countable ordinal in the smaller to medium range.
You can describe the order type it represents in Peano arithmetic.
It represents, roughly, the collection of all arbitrary sized but finite lists whos entries are natural numbers.
As a countable ordinal, it's cardinality is that of the natural numbers, [math] | ({\omega_0})^{\omega_0} | = |\omega_0| = | {\mathbb N} | [/math].
Consider the description of countable ordinal types beyond infinity here:
https://youtu.be/EAAC9dCV9_k

[math] { \mathbb R } [/math] is of size of the continuum,
[math] |{ \mathbb R }| = | P({\mathbb N}) | =2^{ | {\mathbb N} | } = | \{0, 1\}|^{ | {\mathbb N} | } = | \{0, 1\}|^{ | \omega_0 | } [/math]
and [math] | P({\mathbb N}) | \ge | \omega_1 | [/math] where [math] \omega_1 [/math] is set holding all countable ordinals, i.e. the smallest uncountable ordinal. This one is uncountable, so long long past all the easily compresensible ordinals.

To make the comparison sharp, [math] | P({\mathbb N}) | = | \omega_1 | [/math], is to claim the continuum hypothesis.
The size of [math] { \mathbb R } [/math] w.r.t. to ordinals is independent of ZFC, there's no good answer to it.
So your question was doomed from the start...

>>11289635
>It seems though like that definition might be a special case of some stuff like topos or sheaves or something.
What is "that definition" in this sentence now? Sheaf-categories fulfill those properties, so the latter is the more general variant, for what it's worth.
I just wanted to point you to it, in case you're interested. I was a bit scared of looking at your formulas.
>Has analysis, algebra, topology etc. just already "filled" the space of possible mathematical definitions?
"No", but I think it's a matter of (Kolmogorov) complexity.

>>11288815
Did you mean what you typed out? Did you mean that [math]\chi(\emptyset) = 0[/math] as the number [math]0\in \mathbb{R}_{\geq 0}[/math] or as the zero function in [math]X\rightarrow \mathbb{R}_{\geq 0}[/math]? And by [math]\cdot[/math] and [math]+[/math] you mean point-wise multiplication/addition? If this is the case then how did you define the partial order [math]\leq[/math] in >>11288835?

Anyways, it may be worthwhile for you to look at spectral projections [math]P_A[/math] of a densely defined operator [math]A[/math]. They define operator-valued measures [math]dP_A(x)[/math] on a Banach space for which [math]f(A) = \int_\Omega dP_A(x) f(x)[/math] where [math]\Omega[/math] contains the spectrum of [math]A[/math]. In particular, we can define [math]\chi_A:P(\Omega)\rightarrow \mathbb{R}_{\geq 0}[/math] by [math]S \mapsto \int_S dP_A[/math]; basically [math]\chi_A(S)[/math] measures the "volume" of the continuous spectrum of [math]A[/math] contained in [math]S\subset \Omega[/math]. I haven't looked at your axioms closely but I think they are satisfied for [math]\chi_A[/math] for sufficiently nice operators [math]A[/math].

>>11289711
quickly trying to google this leads me to believe those are characters from a video game? Is this correct? Or, if it's a series, what's the name? Touhou? Should I watch?
I watched Liz and the Blue Bird two days ago. I guess I'm a weeb now and can go all in.

>>11289711
yes everythig is pointwise, so I just left put the (x) everywhere.
The order should also be pointwise <= for all x, so the function is below the other.
The thing eith operators seems interesting thanks.

>>11288144
You always post stuff like this, but this is the first time that I actually understood what you are saying

>>11289896
>2020
>not understanding everything Yukariposter says
No future, I tell you.
Might as well just give up.

>>11289740
touhou is a very very popular series of "bullethell" games, i.e. games where you dodge a lot of bullets, made by a japanese guy called ZUN. they have a lot of very memorable and popular characters, very very good music, and tons of spinoff games, manga/doujins, animations, and short anime. it's one of the most popular indie franchises ever to exist.
you probably know some of the characters and musical riffs, even if you don't think you do.
i highly recommend the games, they're a lot of fun. i'm shit at them but you get fairly competent pretty quickly and then it's a lot of fun. there are also 17 mainline games out right now, and a bunch of spinoff official games, and you can download them for free (with questionable legitimacy).
for a good idea of what touhou is like, i recommend this video of the newest game's boss fight:
https://www.youtube.com/watch?v=DVynhYziCxo

>>11289740
alternatively, enjoy this slightly longer but absolutely stunning classic stage, with a really intense boss fight against yukari yakumo (the character yukariposter uses)
https://www.youtube.com/watch?v=AUqeQxEQYYU

>>11289519
Open sets are neighborhoods

>>11289740
who am i kidding, i can't help myself. here's yet another great boss fight. too many good ones.
https://www.youtube.com/watch?v=JKWfIgL1-ZM
>>11289992
of course, but when you think of open sets you think global, and when you think of neighborhoods you think local.

>>11289977 >>11289985 >>11289999
Okay, got it. It's a little too flashy for me at first sight. I stopped playing video games in 2001 with Final Fantasy X

>>11290036
if you are not consumed by an immediate, raging ambition to humiliate the people who know how to play these games, they are not for you. touhou is just like mathematics.

>>11290036
>tutorial mode difficulty life.png

wat do if rejected from reu

>>11290050
an hero

>>11290050
Look into other research opportunities, they're everywhere, you just need to be active about finding them.
Or find something to work on yourself (with some other students in your uni).

>>11290118
>with some other students in your uni

what if your uni is full of chinese spies who sell your research to CPC?

>>11290124
ccp doesn't care about cohomology

>>11290124
then maybe you don't have a future in mathematics. maybe /x/ is more your speed?
>>11290134
no one cares about cohomology

>>11290138
>then maybe you don't have a future in mathematics. maybe /x/ is more your speed?

speed is the only speed for me. i don't know what you're taking.

I know this is 4chan, but asking can't hurt. Is getting a PhD in pure math a wise decision? Are you shit out of luck for a job if academia fails (like it does for most people)?

>>11290161
It's not a wise decision, but anyone with the gumption to do it doesn't give a shit.
If you're questioning whether or not you should, I'll tell you right now - you won't make it in academia.
But as long as you pick up some applied skills, specifically programming and some numerical analysis / stats / data science, you would be fine.

>>11290161
pure math into cs is god mode comfy

>>11290138
>then maybe you don't have a future in mathematics. maybe /x/ is more your speed?

if we're talking about speed, i prefer methylphenidate. it's good stuff, hoss.

academia is full of foreign spies.

>>11290165
shiet
>>11290166
Elaborate? I can't imagine a CS company hiring a math phd over a cs phd

>>11290184
CS PhDs are in short supply, and are not anywhere near as smart or as good at problem solving as a Math PhD with any trivial amount of training in coding.
The vast majority of these people are CS bachelors, and as a Math PhD you look a hell of a lot better than one of those. You could pick up the material from a CS bachelors in a month.

>>11290134

of course they do. they care about anything that makes the chinese look good and westerners look bad.

>>11290161
> Is getting a PhD in pure math a wise decision?
No
>Are you shit out of luck for a job if academia fails (like it does for most people)?
Not if you (a) are at a top-tier school and (b) have made connections/acquired skills relevant to non-acdemic jobs. otherwise yes

>>11290214
>top tier
i'd say mid tier, but no matter what connections and skills are paramount over mathematical ability

>>11290214
>>11290165
WTF why is anybody on /sci/ even studying math in university? Is /sci/ really filled with MIT geniuses?

>>11290238
/sci/ is mostly retards.
/mg/'s level is hard to gauge because usually when people post problems here, I don't feel motivated at all to do it, and I imagine most anons are the same.
I could be wrong and this thread actually only has two or three PhDs and PhD students, tho.

>>11290238
/mg/ generally has pretty smart people. The rest of /sci/ is garbage. I wouldn't say MIT geniuses because that implies that your average MIT undergraduate isn't a complete moron who is doing engineering and got in for some bullshit community service activity and made a shitty phone app.
>>11290265
>>11290265
/mg/'s level is not hard to gauge, you're used to being around smart people if you think /mg/ is questionable. Almost everyone who posts in this thread consistently is very, very smart. Some of the regulars are smarter than others.

>>11288223
It's too hard for teachers to teach in community college. It will affect the class GPA and teachers are all about passing as many students as possible.

>>11290272
To be fair, you must have a very high IQ to post on /mg/.

>>11290265
/sci/ shitposting is for when you open the laptop while a movie runs that turned out to be boring or when you're listening to experimental music. For me anyway.

I have a PhD and I'd write more nice answers if there was a point to it, but the anon-culture doesn't work greatly with science and math because you can invest 15 minutes thinking TeX'ing up a good response, only to have OP or the questioner abandon the thread, never respond and leave your text in the dust.
Everybody experiences this a few times and then it's not worth the "risk" of wasting your time like that.

So I come here to test my own ideas about some meta-mathematical position, shill concepts in various directions that I'm not convinced in myself and generally see what sort of spaghetti stick on the wall.

>>11290272
>you're used to being around smart people if you think /mg/ is questionable.
this is actually kind of true, people too inmersed in uni tend to forget just how retarded the average joe is

>>11290265
Just find another hobby and spend time on that board, it's a great reminder.
For me, it's /ck/.

>>11290311
I'm not into cuckholdry, but I'm willing to try it out if you have a good pitch

>>11290311
>its a great reminder
of what? just make a thread about something you’re interested in that would be relevant to a reasonable number of posters. we used to have a physics general but people stopped posting the thread so discussion died off. The spam and retards only predominate because the good posters grow our of 4chan or become discouraged.

>>11290272
>almost everyone
Rude.
>>11290311
No, that's bad for my pride.
As long as I'm not von Neumann, I'm a talentless hack who needs to study 18 hours a day to have a chance.

>>11289770
>everything is pointwise
Well, in that case we can endow even more structure to our [math]\chi_A[/math]. For instance, if we send [math]S\mapsto \left(y \mapsto \int_S dP_A(x) (x-yi)\right)[/math] for [math]S\subset \Omega[/math], then [math]\chi_A(S)(y) = \chi_A(S;y)[/math] is a nice parameterization of [math]A[/math] away from its Cayley transform [math]A \pm i = \int_\Omega dP_A(x)(x\pm i) = \chi_A(\Omega;\pm 1)[/math]. Since the denseness of [math]\operatorname{im}(A\pm i)[/math] gives us the self-adjointedness of [math]A[/math], regularity/analyticity (or lack thereof) of [math]\chi_A[/math] can detect obstructions to [math]A[/math] being self-adjoint.
If we in addition endow [math]\Omega[/math] with the structures of a continuum, we can perform calculus and relax our partial ordering to the [math]L^p[/math] sense: [math]S\subset T \implies |\chi_A(S)|_{L^p(\Omega)} \leq |\chi_A(T)|_{L^p(\Omega)}[/math]. If we also have [math]p=2[/math], then we can even relax axiom 2 to the convolution product: [math]\chi_A(S\cup T) = \chi_A(S) \ast \chi_A(T)[/math]. This allows us to treat distributions properly, and also gives you more elbow room for the characterization of such [math]\chi[/math]'s.

Taking graduate courses for the first time next semester (one in measure theory and another in algebraic topology). Wish me luck bros!

>>11290322
No, the physics general died because of schizos and cranks like that dude who denies QM.

>>11290166
The dark side:

(0.1+0.2) does not equal 0.3 by current computational methods.

Floating point is tricky, imagine you have a finite set of bits to represent all the rea...

Gradanons what made you decide to foray into higher education?
Just got my BS in computational mathematics a few weeks ago, looking for jobs and found some interested employers looking for people with numerical analysis and imperative programming experience which seems to suit me well. I still don't feel like my studies are over though, and I'm not sure what I should be looking for to decide I need a MS.

>>11289624
This question does not make sense. R is not well-ordered. You cannot associate a single ordinal to it.
However, it has a cardinal that you may write as [math]\aleph_0^{\aleph_0}[/math].
Do keep in mind that exponentiation on cardinals and ordinals are different notions. [math]\omega[/math] and [math]\aleph_0[/math] are essentially the same object, but [math]\omega^{\omega}[/math] as an ordinal is countable whereas the cardinal [math]\aleph_0^{\aleph_0}[/math] is uncountable.

>>11288144

thank you

>>11286089
Based

>>11288144

I am bit confused. Is W=V? Can I replace compact with linear reductive?

>>11288747
Conjecture isn't true, take [math]\chi(A) := \mathbb{1}_{A \cap S}[/math] for a fixed subset S not equal to X or the empty set.
(ii) [math]\chi(A \cap B) = \mathbb{1}_{(A \cap B) \cap S} = \mathbb{1}_{(A \cap S) \cap (B \cap S)} = \mathbb{1}_{A \cap S} \mathbb{1}_{B \cap S} = \chi(A) \chi(B)[/math]
(iii) [math]\chi(A \cup B) = \mathbb{1}_{(A \cup B) \cap S} = \mathbb{1}_{(A \cap S) \cup (B \cap S)} = \mathbb{1}_{A \cap S} + \mathbb{1}_{B \cap S} = \chi(A) + \chi(B)[/math] where A, B disjoint implies [math]A \cap S[/math], [math]B \cap S[/math] are also disjoint.

>>11290861
good point. With a strengthened axiom (i) that states chi(A) = 0 iff A = empty we get that:
chi(S\A) = 0 but S\A nonempty

>>11288747
>>11290861
Wait a second.
What did you two lads think I meant when I specifically said
>>11288769
>there's actually a trivial zero associated to every set

You didn't ask anything, so I thought you'd understood it. Correcting that to get the classical situation is exactly the point of Axiom IV.

>>11286076
Is there such a thing as a "dark ring"? Intuitively, for every ring [math]A[/math] you'd have some kind of object [math]\mathscr{A}[/math] with properties similar to dark matter in physics, i.e. most of the "elements" in [math]\mathscr{A}[/math] are in some sense "invisible", it has "dark-nilpotents", multiplication need not make sense everywhere, and so on. It is expected that this operation of darkening a ring would not have an inverse; although something like [math]\mathscr{L}^\flat(\mathscr{A}) \cong A^\times[/math] should exist, where [math]\mathscr{L}^\flat[/math] takes any dark ring to a forcibly "ligthened" version of that ring.

>>11290861
>>11290958
this is gay, I want to see an actual proof (with a minimal strengthening of axioms) now.
Ive been trying for half an hour and it's not as trivial as it seems.

>>11291073
ok I think I've found a counterexample for all versions presented so far, even axiom (IV). {x}(a) means chi({x})(a)
X = {x,y}
{x}(x) = 0, {x}(y) = 1
{y}(x) = 1, {y}(x) = 0
{x,y}(x) = 1, {x,y}(y) = 1

>>11291104
There's a condition on the support in the first post lad.

>>11291109
Wait, there isn't.
Anon literally forgot the most basic characteristic of characteristic functions.

In that case, Axiom IV isn't strong enough and you can just do swapperoos.

>>11291104
Intuitively this makes me believe we can easily find counterexamples to the hyptohesis that the indicator function is the only characterization, by setting
[math] \chi(A)(y) := 1_A(x + y) [/math] for a fixed shift x.
Then [math] \chi(A) = 0 => 1_A = 0 => A = \emptyset [/math]
[math] \chi(A \cap B)(x) = 1_(A\capB)(x + y) = 1_A(x+y) * 1_B(x+y) = \chi(A)(x) * \chi(A)(x) [/math]
[math] \chi(A \cup B)(x) = 1_(A\cupB)(x + y) = 1_A(x+y) + 1_B(x+y) = \chi(A)(x) + \chi(A)(x) [/math]
Even more generally it seems like
[math] \chi(A)(x) := 1_A(f(x)) [/math] works for an arbitrary bijective f? wait wtf.

>>11291114
well so how do we fix it.
I mean saying [math] \chi(A)(x) = 1 or \neq 0 [/math] duh seems kinda gay to me.
How about requiring only
[math] \chi({x})(x) = 1[/math]

>>11291120
[math]\phi (A) \subset A[/math].
Analogously, [math]\chi (A) \leq \mathbb{1}_A[/math].
Showing that the only possibility is trivial is one line from this >>11288882 characterization.

>>11291120
Also, [math]\chi({x})(x) = 1[/math] is already strong enough.
Specifically, assume [math]x \in A[/math], then [math]\chi(A)(x)=\chi(A\ \{ x\} )(x) + \chi ( \{ x \})(x)=1[/math].

Actually, demanding that is enough to remove the need for Axiom IV and completely trivializes everything.

>>11291131
I dont get this right now but what you could also do is say:
CONJECTURE:
The only characterization is the indicator function up to bijection of X, so
[math] \exists f:X \rightarrow X: \chi(A)(x) = 1_A(f(x)) [/math]
Then my previous counterexamples dont work.
I wanna see proofs now, I am sure that axiom (IV) (injectivity) should not be necessary for the conjecture

>>11291149
No, it is, you can just do [math]\phi (A) = B \cap A [/math].
Satisfies axioms I through III, satisfies the support condition. In fact, every [math]\chi[/math] that satisfies I through III and the support condition has this form.
With Axiom IV, you just gouge out this >>11291140

I'm getting sorta bored, my next reply will probably be the last one.

>>11291140
why should the first term after the equality be 0?
[math] \chi(A - x)(x) = \chi(A - x)(x) * \chi(A)(x) [/math].
[math] \chi(A)(x) = 0 \rightarrow \chi(A - x)(0)[/math]
othereise we are done too. Okay it works.

>>11291167
It was supposed to be [math]\chi(A - \{ x \} [/math], but I forgot bars disappeared.
>why should it be zero
Because it can't be one, otherwise they sum two and the previous argument falls in.

This discussion is interesting all, but I'm not going to put the energy and try and interpret the original broken TeX mess that is the axioms to find out what problem you are talking about...
Write it up properly in one post.

>>11291180
We call
[math] \chi: P(X) \rightarrow \{X \rightarrow R\} [/math]
a characterization on X if some of these axioms hold. I don't know what the best axioms are.
[math] (ia) \chi(\emptyset) = 0
(ib) \chi(A) = 0 iff A = \emptyset
(ii) \chi(A \cap B) = \chi(A) * \chi(B)
(iii) \chi(A \cup B) = \chi(A) + \chi(B)
(IV) \chi injective [/math]
The conjecturenis that the indicator function is the only characterization up to bijections on X before applying it.

>>11291195
>>11291180
fuck
We call
[math] \chi: P(X) \rightarrow \{X \rightarrow R\} [/math]
a characterization on X if some of these axioms hold. I don't know what the best axioms are.
[math] (ia) \chi(\emptyset) = 0[/math]
[math](ib) \chi(A) = 0 iff A = \emptyset[/math]
[math](ii) \chi(A \cap B) = \chi(A) * \chi(B)[/math]
[math](iii) \chi(A \cup B) = \chi(A) + \chi(B)[/math]
[math](IV) \chi injective [/math]
The conjecturenis that the indicator function is the only characterization up to bijections on X before applying it.

Who is /mg/?
http://www.strawpoll.me/19199678
are we mostly self taght enthusiasts or math students/MSs/doctors?

>>11290322
A reminder that you're doing pretty okay for yourself. Chill out.
>>11290327
At some point you just get used to oscillating between "talentless hack" and "god's gift to mankind" mentalities, they're both useful in different situations and if you can wield them both you can improve yourself very efficiently.

>>11287816
I am seriously considering this. Were there any mathematicians who were also members of the clergy?

>>11291201
This seems like something primed for a truly atrocious counterexample.

>>11289677
>>11290717
Yes, my bad. I've lacked the proper understanding of ordinals.

>[math]\mathbb{R}[/math] is not well-ordered
I do believe that every set can be well-ordered.,,

>>11291310
That guy is a schizo, ignore him or he will shit up the thread.

Let [math]X,Y[/math] be real-valued RVs with joint density function given by [math]f_{X,Y}(x,y)=\frac{1} {y} [/math] if [math]0<x<y<1[/math], and [math]f_{X,Y} (x,y)=0[/math] otherwise.
My calculations show that the CDF of both [math]X,Y[/math] is given by [math]F(t) = \chi _{(0,\infty)} (t)[/math] (i.e. indicator function of [math]\mathbb R _{>0}[/math]). Am I in the wrong here? It seems counter-intuitive.

Hints would be very much appreciated.

Let [math]X,Y[/math] be real-valued RVs with joint density function given by [math]f_{X,Y}(x,y)=\frac{1} {y} [/math] if [math]0<x<y<1[/math], and [math]f_{X,Y} (x,y)=0[/math] otherwise.
My calculations show that the CDF of both [math]X,Y[/math] is given by [math]F(t) = \chi _{(0,\infty)} (t)[/math] (i.e. indicator function of [math]\mathbb R _{>0}[/math]), which seems absurd. How would you go about calculating their CDFs?

Hints would be very much appreciated.

>>11291380
>How would you go about calculating their CDFs?
Integration.

>>11291275
I'd be interested in a more fine grained poll, with majors+degrees+level or occupation

>>11291201
First thought:
- you can delete posts for at least 5 minutes, you don't have those cripples to spam your own agenda
- you can make spaces even in math mode

>>11291201
Third thought, if the image of chi are functions, what's 0 and *?

>>11291293
Reverend Thomas Bayes

i can access the highs i can access the lows i can bing dong bicky dicky ding dong doh

>>11291443
Constant zero and pointwise multiplication.

Came across this fat text entirely dedicated to the Baker Campbell Haussdorf formula, incl. Dykins expansion (and in terms the freely generated tensor algebra of a topological space over characteristic zero), including a few special case (finite cutoffs, I think, and normed spaces). It has the history of the theorem since 1890 and 6 proofs of different flavours.

>>11291447
Okay, fair enough. But given that you didn't write down, in that post, that the union axiom is to be considered only for adjoint sets, I'll not risk spending time on it only to later hear you change the rules of the game.
I'd also express the pointwise statements formally, e.g.
forall x. chi(A u B)(x) = chi(A)(x) * chi(B)(x)

>>11291471
I didn't write it down in that post because I didn't write that post at all, fool.
>I'd also express the pointwise statements formally, e.g.
Fuck off.

>>11291487
>Fuck off.
Wut. Well it will help if we state what we mean, no?

>>11291526
Anon, unless someone is putting a fucking satanic start [math]f \bigstar g[/math] between real functions, they mean pointwise multiplication, and not quantization of a Poisson algebra or whatever the fuck you could possibly be thinking of.

We consider a smooth manifold [math]M[/math] with an involution [math]I \in Aut(M)[/math].
We define, for [math]f, g \in C^{\infty}(M)[/math] the operation [math]f \star g (x) = f(x) \times g(I (x))[/math].
Tell me something about the star operation's Lie bracket.

>>11291444
>In probability theory and statistics
Pretty sure he/she meant mathematics, not "probability theory" and "statistics".

>>11291534
It wasn't even 100% clear to me whether he means what he wrote.

>>11291551
Satanic.
You mean End(M)?
Looks like
-g star f = -id circ (f star g) \circ I
so maybe there's a way to write the bracket as something along the lines of that.
Something something good algebra?

>>11291585
I meant something something hopf algebra, it autocorrected to good

>>11291583
Okayish bait, I rate it 4/10

>>11291471
my friend, you are free to do what you want

>>11291625
>free to do what you want
but what if he isn't a hedonistic degenerate?

>>11288219
They're important, but it depends on your current exposure already. Prioritise the highlighted, and if you have time then go for the others

>>11288507

>>11287382

>>11288219
Literally everything there other than matrices was taught in my algebra II class as a high school freshman. Precalc was a huge waste of time.

>>11290265
Have you *seen* yukarifag?
There are definitely PhDs here

>>11291439
Make it and post it.
Simple as that.

>>11290188
came back just to lol at this again

>>11291708
Let me do it for him.
https://www.strawpoll.me/19200725

>>11291723
>someone actually threw in a bot
Absolutely based.

Is Khan Academy's math courses good enough background for university mathematics bachelor degree?

I have many interests and mathematics is what is common between all of them. I do chemical and mechanical engineering as hobby, but do not want to choose either of them as my major because I have bad experience choosing what I like as hobby as my main studies. I did like cars and motorcycles when I was younger but after 2 years in mechanic school I wanted to kill myself and I don't want to have anything to do with them anymore.

I like mathematics by itself and I think it would be great tool for my hobbies. I don't care about being top mathematician. I just want to be able to model world around me and maybe I could get some job where I can live inside my head like I do most of my time now.

>>11291201
i assume you meant A, B disjoint in (iii)
put A=B into (ii), you get that the function [math]\chi(A)[/math] can only have values 0 or 1
So you can write [math]f(A) := \{x \in X : \chi(A)(x) = 1\}[/math], then simply [math]\chi(A) = 1_{f(A)}[/math] (*). The four conditions can be now equivalently stated for f:
(i) [math]f(\emptyset) = \emptyset[/math],
(ii) [math]f(A \cap B) = f(A) \cap f(B)[/math],
(iii) [math]f(A), f(B)[/math] are disjoint and [math]f(A \cup B) = f(A) \cup f(B)[/math]
(iv) f injective
let [math]g: X \rightarrow P(X)[/math] be defined by [math]g(x) = f(\{x\})[/math] (**). So f and g are related by
[math]f(A) = \sum_{x \in A}g(a)[/math]. From (i-iv) it quickly follows that
(a) if [math]x \neq y[/math] then g(x) and g(y) are disjoint
(b) g(x) is nonempty
and vice versa, from any g satysfying (a-b) we obtain f using (*) and then chi using (**) which satisfies the original requirements

>>11291810
oops I meant
[math]f(A) = \bigcup_{x \in A} g(x)[/math]

>>11291810
Literally one entire day ahead of you >>11288882

>>11291810
>>11291830
for all intents and purposes, you're the same weeb

>>11291723
what the fuck is that vote count?

>>11291830
you're right
I didn't read this far back

>>11291688
Yukari seems like late graduate school to me, as someone with early grad standing who knows a good 75% of what yukari talks about. Could be PhD though, not sure what else yukari knows and how it's done in matphys.

Nikolaj ist top >>11289677

>>11291728
>bot
what did you mean by this?

[math] x^x = x \sum_{n=0}^\infty \prod_{k=1}^n (1-x) \left(1-\frac{1}{k} (1+x) \right) = x \sum_{n=0}^\infty \frac{1}{n!}(1-x)_n(1-x)^n [/math]

>>11291728
>bot
what did you mean by this?

You die alone, and you do math alone.

[math] x^x = x \sum_{n=0}^\infty \prod_{k=1}^n (1-x)\left(1-\frac{1}{k}(1+x)\right) [/math]

Is that our fate?

>>11291728
>bot
what did you mean by this?

You die alone, and you do math alone.

[math] x^x = \sum_{n=0}^\infty \prod_{k=1}^n (1-x)\left(1-\frac{1}{k}(1+x)\right) [/math]

Is that our fate?

>>11292053
He's stated before he's doing a PhD, and I don't recall any "It's fucking done fucking finally" posts from him.
>not sure what else yukari knows
He's toned it down a lot lately, but he still goes out of his way to fuck with me sometimes.
>>/sci/thread/S11235344#p11245791
>>/sci/thread/S11250238#p11255762

Choose wisely:
[eqn]\frac{\pi}{9} + \frac{n\pi}{3}[/eqn]
vs
[eqn]\frac{\pi + n\pi}{9}[/eqn]

Choose wisely:
[eqn]\frac{\pi}{9} + \frac{n\pi}{3}[/eqn]
vs
[eqn]\frac{\pi + 3n\pi}{9}[/eqn]

Given
>R and A are square matrices
>x and b are vectors
>A" = RAR
>x" = R^-1x
>b" = Rb
>A"x"=b"
>A", x", and b" are known
>A, x, b, and R are unknown
Find either A, x, b, or R in terms of A", x", and b". The first right answer gets $15 of ethereum.

>>11292648
>Find either A, x, b, or R in terms of A", x", and b".
What have you tried?

>>11292648
obviously no unique solution in general. you want the set of all possible solutions? maybe say something more about the problem?

>>11292650
>>11292668
Break my cryptosystem. Raising the stakes to $25.

>>11292682
encryption has to be invertible, and while you havent said how encryption works in your system, the stuff you posted seems to be not invertible (no unique way to get A,x,b from A',x',b'. Also using exclusively linear operations is known to be v bad.

>>11292702
Solving A"x"=b" for x" gives you R^-1x. You decrypt the answer by multiplying by R.

>>11292708
you still havent really explained what ishappening but ok. say R is an nxn matrix. i perform a chosen plaintext attack with a basis of the n-dimensional space. this uniquely determines R^-1, and the system is broken i guess. so it seems that with very few plaintext-ciphertext pairs i can break your system, which makes it insecure.

>>11292648
[math]A''x''=b''[/math] implies that [math]RARR^{-1}x=Rb[/math]
So [math]RAx=Rb[/math] implies [math]Ax=b[/math], since R is invertible.

R could be any matrix tho.

Could somebody please explain to me the order of operations for integrals? Can you simplify? Can you simplify only before or after u-substitution? How much can you simplify? How do you know when to use substitution? What should you assume when there is multiplication or division in an integral? How much of the simplification depends on where the variable is at? Do you want roots in the denominator or no? Do you want negative exponents or over 1? Which is easier normally? Who the fuck thought integration was a good idea?

I am really fucking confused.

>>11292736
>>11292740
Well, I should have specified that R is a one-time pad.

>>11292744
i mean a one time pad with size as large as the message is provably secure, why would you use a one time pad that is much larger? thats not efficient at all.

>>11292613
[math]\frac{k\pi}{9},[/math] [math] k\in 1+3\mathbb{Z} [/math]

>>11292744
I mean, anon. You're essentially taking a random number generator's results, passing it through a linear map, and expecting us to unencrypt it.
It's honestly pretty unreasonable.

>>11292749
>>11292752
I just want a sanity check before I embarrass myself in front of a bunch of people. Okay, what about this? Suppose R is a sparse permutation matrix whose entries are random numbers in the range 0-1. Does that have an effect on the security? (for $20)

>>11292762
Anon, picture the following.
I have chosen a real number a. I then proceed to randomly generate numbers, multiply them by a, and I give the result of the multiplication to you.
I then ask you to unencrypt the results by finding out a.

It's just completely nonsensical lad, do you think I'm a fucking wizard?

>>11292762
the moment you reuse the matrix, the chosen plaintext attack works. its impossible for laymen to come up with secure and even decently efficient cryptosystems. if you have to talk with ppl about it, just read up on snp's or whatever.

>>11292766
>>11292769
I'm concerned because, if R is a permutation matrix, technically it isn't a one time pad. You have m*(m+1) independent values in Ax=b, but only 3*m values in a sparse R (in COO format: row, col, val).

Given [eqn]cos 3t = \frac{1}{2}[/eqn]
[eqn]3t = \frac{\pi}{3}[/eqn] is easy enough to remember/figure out. but what about the other value, [eqn]\frac{5\pi}{3}[/eqn]?

Given [math]cos 3t = \frac{1}{2}[/math]
[math]3t = \frac{\pi}{3}[/math] is easy enough to remember/figure out. but what about the other value, [math]\frac{5\pi}{3}[/math]?

>>11292790
pic related

>>11292790
its just [math] 2\pi - \frac{\pi}{3} [/math]

How much times passes between 5:20pm and 4:35am the next day?

How do I calculate this? I used an online calculator and the result is 11hr 5m. But I can't do it myself.
Normally I would convert them both into 24 hour time and find the difference. Eg. 2pm till 8pm
>20.00 — 14.00 = 6 = 6 hours.

If I try and use this method or anything similar I am getting 12.85 or 13.00. I feel like a proper idiot. Please send brain...

>>11292801
Is it [math]2\pi[/math] because that's the period of cosine? So for tangent it would just be [math]\pi - \frac{\pi}{3}[/math]?

>>11292814
You're forgetting the day change.

if midnight this morning was 00:00, then 5:20pm = 17:20 and 4:35am the next day is 28:35.

If you're doing it in a program (like Excel), you can just subtract and add 24 if it's negative. If it's a proper programming language, convert to Unix time (number of seconds that have elapsed since 1970-01-01 00:00:00 UTC) first and you get

1578717300 - 1578676800 = 40500 seconds = 11.25 hours

>>11292814
You're forgetting the day change. If midnight this morning was 00:00, then 5:20pm = 17:20 and 4:35am the next day is 28:35.

If you're doing it in a program (like Excel), you can just subtract and add 24 if it's negative. If it's a proper programming language, convert to Unix time (number of seconds that have elapsed since 1970-01-01 00:00:00 UTC) first and you get
1578717300 - 1578676800 = 40500 seconds = 11.25 hours

>>11292847
This makes sense! You're right I should be accounting for the change of day. Now I know how to adjust my formula thank you. It's strange the website I used to calculate it actually got it wrong. It managed 11hr 5m somehow which is incorrect.

>>11292871
No worries. I had to figure that out when I was creating employee schedules in Excel years ago.

Also, tt calculated the time difference incorrectly because you put in 4:25, not 4:35.

>>11292790
>>11292793
>>11292801
>>11292814
>>11292820
>>11292871
>>11292875
>mg - maths general

>>11288925
It only gets worse, I'm a bit ashamed to admit that a single problem once took me 3 months to crack, and the solution wasn't even all that special, just turns out I was being a complete fucking moron.
>>11289261
One way you can think about it is that it makes the statement "the composition of continuous functions is continuous" manifest while the epsilon delta definition makes it less obvious.
>>11290161
Depends entirely on your aspirations, though if you couple that with some extra skills like>>11290165 mentioned than you should be ready for the 300k starting life.
>>11290238
>>11290265
>>11290272
/sci/ in general is complete and utter fucking trash, /mg/ is the only reason I come to this shitty board. In general I'd the level of /mg/ isn't all that high, but that just might be because I'm comparing it to the average stem student (which is also not at a high level but is above average). There are a few anons who know their shit but don't post as often since they have other obligations or the texing takes too long.
>>11291450
Interesting find anon, I keep forgetting the noncommutative ring theory is a thing. It's weird, none of my algebra inclined friends talk about it.
>>11286076
So I failed at socializing with the other grad students today. Gonna drown my sorrows in pizza and diet coke (no dr. pepper, cream soda, or ginger ale at kroger, the fuckers).

>>11292919
>dr pepper, cream soda, ginger ale
patrician taste

>>11291723
Where is the option for a BA in math?

>>11292919
stop mass replying you fucking faggot
>>11292906
CS is math too don't you know!

Simple question, sharp and sweet:
What's the best connective and quantified? Sort.

[math] \to [/math]

[math] \land[/math]

[math] \or[/math]

[math] \neg [/math]

[math] \Box [/math]

[math] \forall [/math]

[math] \exists [/math]

>>11293420
[math] \lor [/math]

hello b-b-ros
i am just learning about Group Theory and is having trouble understanding partitions or equivalence relations in general
is this in any way similar to std::partition(...) in c++?

>>11293220
>CS is math too don't you know!
Actually, other way around: maths is a strict subcategory of computer science.

>>11293641
>c++
>>>/g/

>>11293641
Your basic example is modular arithmetic. Take the 12 hour clock that you know. Consider only the hours. If I tell you you go to bed at 10, and sleep for 9 hours, and ask when you wake up. You'd tell me you wake up at 7 (unless you're a retard). So 10+9 = 7 ? Well, yes so long as you're in Z/12Z, the 12 hour clock. Elements of Z quotiented by its ideal 12Z (the set of multiples of 12) are equivalent so long as their remainder by Euclidean division by 12 is the same. Here 10+9=19, which modulo 12 is equal to 7, so in this context, 19 and 7 are the same number.

Partitions and equivalence relations are linked in the following way. Every element of Z can be identified with a single element of Z/12Z. So you can divide the elements of Z into 12 non-intersecting subsets (ie, a partition of Z in 12 subsets that unioned together form Z): the subset of those element that are equivalent to 0, noted 12Z; of those that are equivalent to 1, noted 12Z +1; ... of those that are equivalent to 11, noted 12Z + 11. Each of these is called an equivalence class.

For grown-up mathematicians, you also learn about kernels of homomorphisms, basically by taking this "remainder of a division by 12" function (a ring homomorphism), and looking which elements of Z are mapped to 0, you get most of the remaining information needed to build the quotient space Z/12Z.

Has anyone ever tried to implement this before

>>11291723
I'm in a related field (CS)

>>11291723
>https://www.strawpoll.me/19200725
Where is BMath?

>>11291837
>I finish making the poll
>I cast a vote
>open up the results page
>1 vote
>vote count suddenly rising very fast with votes being distributed homogenously
>stops at 101
I was expecting everyone to just vote on the joke options, but this was even better.
>>11294620
>>11293065
I'm not american so I didn't remember that even existed.

>>11294548
Whole book about it.
Computational topology as field

https://geometrica.saclay.inria.fr/team/Fred.Chazal/papers/CGLcourseNotes/main.pdf

>>11294630
>I'm not american so I didn't remember that even existed.
What does America have to do with maths?

>>11294685

I'm talking about the specific program described in that picture.

This isn't *real math* it's just a way to draw a picture of an abstract simplicial complex

>>11294630
>american
*cries in Canadian

I've been out of undergrad for almost a year and I still don't know if I want to go to grad school.
Help me /mg/

>>11293916
No it isn't at all, retard. That doesn't even make any fucking sense, think about what you're trying to say before communicating with others.

>>11287598
Construct the triangle and measure the ratio of sides

>>11295550
>That doesn't even make any fucking sense, think about what you're trying to say before communicating with others.
There's a difference between something not making any sense and you not being intelligent enough to understand it, please think hard before posting such ignorant contributions in my thread.

how do I integrate, from 0 to pi/2, the absolute value of: sin x - cos 2x

if I'm not mistaken, integrating sinx - cos2x would be -cos x - 0.5sin 2x but I'm not sure what I have to do to deal with that absolute value

I'm trying my best to drill this stuff but I haven't taken a math class besides basic stats in 15 years so I'm having to do a lot of review.. but time is limited cause I work 12-13 hours a day, so I'll probably go review the chapter on integration tonight but I figured I'd ask this before work and then refresh it when I get home

I found something about integrating absolute value but then I feel like the sin and cos stuff further complicates that

gonna plan on getting to school real early tomorrow to try to get some tutoring :^)

>>11296280
i would try to figure out where sinx - cos2x >0, and where sinx - cos2x < 0, then just integrate on those intervals

>>11296280
>>>/sci/sqt
But essentially, you just split it into two integrals.

>>11296316
Wrong image.

If you assume (i) and then multiply both sides by Q(x), you get (ii) except the right hand side is P(x) (not zero.)

Why

>>11296378
ANON
P(X) HAS DEGREE LESS THAN D
Q(X) HAS DEGREE D
BUT (i) SAYS THAT THE DIVISION EQUALS A POLYNOMIAL
WHAT DOES THIS TELL YOU?

>>11296381

> EQUALS A POLYNOMIAL

An infinite power series is not really a polynomial

>>11296378
Multiply (i) by Q(x), then take nth derivative

>>11296386

That would change the left hand side

>>11296386
*d-th derivative, and then you probably evaluate at zero.
>>11296391
Would it tho?

>>11296386
>>11296381
>>11296378

This isn't very intuitive, but I think this is what the book says:

The complex vector space of functions f where (i) holds, V_1, has dimension d because the polynomials p=x^i are a basis.

The complex vector space where (ii) holds, V_2 has dimension d because it's a homogeneous linear recurrence.

[math]V_2 \in V_1[/math] because [math]V_2[/math] is the special case where [math]P(x)=0[/math]. Therefore [math]V_1 = V_2[/math]

>>11296396
>the solutions of (i) form a vector space
Do they? Are you sure? 100% assured?

>>11296401

Yes, it is very clear that this is a vector space.

The vectors of this vector space are the set of functions f where this (i) holds.

So, the vector space is literally just rational functions with denominator Q(x) and numerator at most degree d.

I think this 3rd condition which is also supposed to be equivalent to the first two is just saying "you can find a partial fraction expansion"

So the theorem basically says:

1. The "literal defintion"; rational functions with denominator Q(x).
2. the space of solutions to the corresponding homogenous linear recurrance
3. The partial fraction expansion

are all equivalent

>>11296385
Read again the screenshot

>sheaf
>stalk
>germ
why are they called like that?

>>11296317
Oh. Right. Thanks. Ill try it when i get home and i think ill get it

>>11296704
Grothendieck was a hippie, he felt cool naming stuff after farming terms

>>11289261
Well for one, the proof just works. If you understand the proof you should be pretty convinced. Geometrically it makes a lot of sense if you swap open with closed in the defn cuz limit points.

>>11296704
if you understand how holomorphic function is uniquely defined by its values at a neigbourhood, or its power series at a single point, the words >stalk >germ feel pretty natural, at least that was my impression
then, a collection of stalks is obviously a "sheaf" just like collection of maps is an atlas

>>11286076
hello my friends
Does anybody have a copy of Donald McQuarrie's Mathematical Methods for Scientists and Engineers from 2003. I have scoured library genesis and torrent sites for it and I need it to begin one of my math classes soon and the cheapest options are $81 and by god I am so poor. Any help would be greatly appreciated, even if it's just a referral. Thank you anons

I've been playing with the function f(x)={x:x>0, 0 otherwise}.
I found that f(a*b)=ab/ (d/dx(ab)) * d/dx(f(ab)). Rearranging this and integrating, you get f(ab)=ab*exp(C). But this makes no fucking sense

>>11296887
This is a thread for mathematics, not for "mathematics for scientists and engineers".

>>11296889
Wow, it turns out that functions which aren't differentiable.... aren't differentiable! What a surprise!

>>11296909
Sorry, I thought it was kind of cool.

>>11296910
Are you new here? You're supposed to reply in vitriol and call me an idiot.

>>11296907
I know. I'm a pure mathematics students but this is a prereq for partial differential equations

>>11296968
I'm not new, I'm just not as good at math as you guys are and I understand that

>>11296887
libgen.is bro

>>11296969
Perhaps you should just download Evans and read that then? I'm sure it's a much better introduction than whatever book you're talking about. Your book doesn't seem related to functional analysis of unbounded operators on Sobolev spaces.

>>11296969
>maths for engineers is a prerequisite for PDEs in the pure maths course

>>11297490
blame the u of a dude I didn't make this shit up. honestly math here could be a lot better but at least my professors care for the most part
>>11297256
I need that specific book for a class, I'd definitely pick something else for self study

>>11296969
>pure math
>partial differential equations
fuck off back to >>>/lgbt/ with that weak bait.

>>11297565
No, you don't "need" any specific book for any given class. Is this what you've been led to believe? You need someone to have the book who will let you take pictures of the problems (if necessary, which it shouldn't be but that's not realistic) and you need an ounce of maturity to figure out what is going on from lecture and problems without a garbage superfluous textbook. All "math for engineers and scientists" books are the same, find another. It probably just needs fourier series and linear algebra stuff for your purposes.

>>11297770
your gatekeeping will guarantee you no friends in life and only serves to dispel your own insecurity for a moment bitch

>>11297770
t. hasn't taken functional analysis

>>11297866
I mean I realized I just needed the problems in such but this was my way of accomplishing that. Also not that it matters but I've never been able to learn from lecture and I benefit from a good text but I'm sorry I hurt your feelings so much

Any body knows a good complex number book?

>>11297872
Kreyszig's Engineering Mathematics has been recommended to me before (by people in real life) and should cover the same topics (wild guessing tbqh).

>>11297891
That's actually the additional text for the course so thanks that is helpful!

>>11297879
Ahlfors Complex Analysis, obviously.

>>11297770
holy shit you're fucking dumb

>>11297235
Piracy is a crime.

>>11298354
I remember while fishing on RuneScape some Venezuelan guy who explained to me that his monthly salary as a doctor in training was roughly the equivalent of 20 USD, and wouldn't be much higher (in absolute) after his education was over. Given that renting a pubmed article over a few days (you don't even know if it'll answer your question) was roughly 30-40$ per article, and buying it was around 80$; also, all his textbooks, in English or Spanish, ran over 200$; the situation was kind of mathematically, hence economically, fucked.
He explained that without piracy, there would be neither medecine nor science in Venezuela. It really put things into perspective for the shitty know-it-all teenage brat that I was.

Then you learn that the Springers and Elseviers of the world obtain private distribution rights over publicly funded research as the rule rather than the exception, and you go "what ? that can't be true". But it is.

And finally, you realize that everyone remotely interested in pirating that doesn't have access to a university library (or just don't have the book in their non-English library), even poor ass fuckers like myself, would pay for a Netflix-like subscription to universal scientific publishing (even State-run) that allows you to keep track of what you've read, take notes and whatnot. A "service problem", as GabeN puts it. Can't argue with the money he's raking in over games people don't even play. Never mind the fake "right to an education" we're supposed to be given; fuck, I'd rather my taxes pay for libgen than for the fucking soul-crushing indoctrination that tries to masquerade as education nowadays.

Until predatory business practices using exclusive licensing disappear, piracy will remain the superior option. Whether it's anime or science.

Those who criticize libgen or sci-hub as "criminal" can suck on the fat nuts of a Venezuelan donkey, and take a closer look at the legal mafias which rule over us in this corpocratic world.

>>11298398
>fucking soul-crushing indoctrination that tries to masquerade as education nowadays
Who will vote for the dumb party if people aren't dumb?

Can you show me an example of elementary function that is not continuous?

>>11298398
Great post. If anything, publishing your work to these big private journals should be the crime. You're stealing it from millions and millions of other people. It doesn't belong to you.

How far is plagiatorism from deducing same things independently in same universe, which is possible. To avoid plagiatorism, we have to read all works done before and avoid them, which is literally impossible.

>>11298457
sin(1/x)

>>11298532
That makes no sense. If you come to a result, you should be able to explain how you came to it significantly better than if you'd just seen it in a paper. Differentiating plagiarism and circumstance is very easy.

>>11298457
Do you mean not continuous everywhere?

>>11298398

that's all well and good, and i firmly believe we should have a good public education system, but don't you think this causes a bit of a problem?

the amish make money with furniture. monks in europe make cheese, bread and beer to make ends meet. what do academics make? they mostly get research money from the government.

what reason does the government have to fund quality, economically relevant public research? they pick and choose who gets money and the sort of research that gets done.

>>11298398
>>11298583

and yes, your venezuelan buddy got a leg up because he did not respect intellectual property laws. if none of that material was worth reading, he would not have bothered. but it was worth reading.


i don't really care so much about people who download media, games, or whatever. fuck the man, etc., etc.

but people will always have more real, financial incentive to work privately, especially if they're good. defense and private interests, along with their cronies in the government, have no reason to favor impactful public research. so who will be attracted to public research? people who like fame, notoriety, and recognition.

i guess my concern is that the quality of public research will be hurt by this in the long run. if it isn't self-sustaining to some degree, and depends entirely on outside groups for funding.

university courses are so expensive, fucking professors why do they need all these money for? all they ever need is a pen and paper
what the fuck?

>>11298583
>>11298595
That only works if people who publish research in private, big corporate journals receive more compensation than those who don't, which is the precise model so many people are trying to overturn.

>>11298604
They don't get the money. That's all going to administrative bloat.

>>11298607
anything similar to this but for math?
https://functionalcs.github.io/curriculum/#org7d4129d
no i dont trust any bloke in this anime board to tell what to read

>>11298605

hardly seems like the greatest corporate evil. your venezuelan commie friend will still opt for the five finger discount anyway if it's valuable work.

i don't get why you're so gleeful about it though. it's no wonder academia attracts narcissistic leftists.

>>11298618
Bootlicking scum, 150 springercredits have been deposited into your account. No one in academia has even the least bit of respect for those hacks.

>>11298639
>Bootlicking scum

not at all. if it's just behind a paywall then eventually it will fall into the hands of ingrates and foreigners who can use it to improve their lives. if it's a trade secret it may never see the light of day.

good public/semi-public research conflicts with monied interests. not everyone's playing the same commie ballgame.

and i'd rather that academia not be the domain of frauds, cointelpro operatives, and witless progressives.

but i guess that's just how it's going to go. it's a bleak picture.

here's something i just thought up off the top of my head. might be off base, but it's just an example:

afaik, there are no "open source" gmo vegetables. if a public researcher developed gmo corn on par with products offered by monsanto, wouldn't that help to feed a lot of people? wouldn't that help farmers? wouldn't it net the college a solid profit for a while? so why is that not a priority?

For those that have read Qing Liu, when he says that an affine variety over k is the scheme associated to a f.g. generated algebra over k, does he mean Spec B with the usual sheaf and topology, where B is the f.g. k algebra?

Is a mathematician expected to be able to perform all sorts of algebraic manipulations by hand?
Obviously you need to know about them, and when to use.

>>11298667
>so why is that not a priority?
cont

certainly it could be for any number of reasons, but how can we say that colleges do valuable research if they don't make at least a little bit of money from the work that they do?

i guess you're damned if you do, damned if you don't. if you do public research then people may use that knowledge against your best interests.

>>11298678
What do you mean by "algebraic operations"? Like the stuff you're doing in your college algebra class?
Your question is more or less equivalent to asking if an English professor is expected to be able to write words.

>>11298695
Possibly even simpler things. Imagine you want to factor a big polynomial, with big coefficients. You could probably do it, theoretically, you know what it is.
But perhaps it's better to put it in a CAS or in WolframAlpha and forget about it.

>>11298674
yes

>>11298700
Algebraic Geometers dedicate their entire lives to factoring polynomials, and you can't really make it anywhere nowadays without some knowledge of algebraic geometry.

>>11298700

> You could probably do it, theoretically, you know what it is.

Ummmmm sweetie

>>11298869
awesome, thanks!

>>11298700
In most rings factoring polynomials is hard (like factoring primes). Even in the reals where you can find solutions analytically there is no reason to expect them to be nice.

You should be able to recognise basic factorisations and apply common tricks. Beyond that mathematicians will (and should) absolutely use computer algebra systems.

More of a physics question but since it involves math can someone please explain inertial moments to me? How would I find it for a ladder given its size and mass?

>>11298354
ok bootlicker

whats the point of calculus in the real world?

new thred >>11300155

>>11300129
Calculus does not have one single application. In a sense this question in mindblowing because Calculus has so many applications: https://en.wikipedia.org/wiki/Calculus#Applications

Basically the point is that we are very often interested in instant rate of change and area/volume.

Real new thread:
>>11300167