/mg/ maths general

[Anonymous No.16062685]

Shrigma male of St Petersburg edition
Talk maths, formerly >>16035182

[Anonymous No.16062693]

>>16062685
If I had his brain, I would dress like 50 cents.
but then... he's only worth about much.

[Anonymous No.16062694]

-farts on you-
-poops on your nose-

[Anonymous No.16062708]

My lecturer said: "Let us define reflection as any isometry of space that changes orientation." Is he stupid? Or is there any deeper meaning in treating point symmetry in 3D as reflection?

[Anonymous No.16062722]

how to get better at modeling

[Cult of Passion No.16062732]

>>16062722
Its all in the hip sway and maintaining eye contact. VERY intense.

[Anonymous No.16062733]

>>16062675
What does, according to you?

[Cult of Passion No.16062741]

>>16062675
Ive been saying for years that there needs to be a restructuring of credentials in academia.

Doctor used to mean 'indisputable source' on whatever subject, now its semi-political and asleep at the wheel. Covid and twitter, everyone sees that now for MDs, but its across the board, virtually all fields.

Most PhDs are technicians, not doctors.

[Anonymous No.16062761]

I'm going to have 2 pets(a marine bird like a swan and a sun cat), 4 plants, some fish and one son.

[Anonymous No.16062768]

>>16062761
they will eat each other

[Anonymous No.16062771]

>>16062768
You animal dumb

[lowercase sage !!IaxlA1xvEP/ No.16062772]

>>16062733
Understanding why (as long as characteristics of field F is not 2) defining determinant as
1. function from (F^n)^n to F that's multilinear and antisymmetric and
2. determinant of identity matrix is equal to 1
is sufficient.

[Anonymous No.16062803]

Was math discovered or invented?
only people with more than 300IQ answer please.

[Anonymous No.16062809]

>>16062803
Mathematics is both invented and discovered.
While mathematical truths, like 1+1=2 or the Pythagorean theorem, are discoveries about reality, the techniques and proofs used to understand them are inventions by mathematicians.
The debate about whether math is invented or discovered continues, with some arguing for Formalism (math as an invention) and others for Platonism (math as a discovery).

[Anonymous No.16062902]

>>16062809
I can accept that some of it is invented but you definitely can't say that none of it is discovered. For example, for a long time people sidn't know what the solution to tbe famous Basel problem was, so did they just invent the answer because tbe problem was too hard? No, they discovered that it is (pi^2)/6. That is something that always existed in nature and it had to be discovered. Or something like what is the most efficient way to fill space with spheres, that is something that exists as a fact of nature and has to be discovered like an archeologist discovering relics. Vast majority of math at least is discovered.

[Anonymous No.16062905]

>>16062809
I can accept that some of it is invented but you definitely can't say that none of it is discovered. For example, for a long time people didn't know what the solution to the famous Basel problem was, so did they just invent the answer because the problem was too hard? No, they discovered that it was (pi^2)/6. That is something that always existed in nature and was waiting to be discovered. Or something like what is the most efficient way to fill space with spheres, that is something that exists as a fact of nature and has to be discovered like an archeologist discovering relics. The vast majority of math is discovered.

[Anonymous No.16062949]

>>16062803
Math is both the study of invented methods and the thing in which the methods help to make discoveries.

[Anonymous No.16063163]

I don't watch math youtube videos because they always make the boldest claims in the name of math that goes against any sort of basic logic and commonsense. I'm sure you know the kind of videos I'm talking about when some low probability example is brought up but then they say "well actually, following this formula, it's actually quite high!" Like they say if you place 30 random people in a room that it's almost certain that there will always be at least two people in that room who share the same birthday. Commonsense just tells me that's bullshit and those sorts of absolute mathematical claims just piss me off.

[Anonymous No.16063174]

>>16062741
I used to think people at the forefront were geniuses. Now I just see them as regular people and everyone else as slackers.

[Anonymous No.16063240]

>>16062803
Discovered.
[math] \textit{Proof.} [/math] Suppose it was discovered. Then we are done.
Suppose it was invented. Then the fact that it was invented
implies that its invention was discovered. Hence, math was
discovered. [math] \hskip7.3cm \square [/math]

[Anonymous No.16063244]

>>16063240
Argos the Discoverer.

[Anonymous No.16063266]

(prime-emirp)%18=0
(9967-7699)%18=0
why?

[Anonymous No.16063270]

What is a good book to self-study probability at around a first year graduate level?

[Anonymous No.16063273]

>>16063163
That claim can be experimentally verified. Survey your peers and run the numbers if you are not convinced of some statistical fact.

[Anonymous No.16063276]

>>16063240
You forgot the third case, divine revelation.

[Anonymous No.16063284]

>>16063163
>Like they say if you place 30 random people in a room
So what do you do? You're clearly not a programmer since then you'd know about the probability of a hash collision. Are you a retarded faggot child?

[Anonymous No.16063324]

>>16063270
Probability Theory: The Logic of Science by E.T. Jaynes (pbuh)

[Anonymous No.16063330]

>>16063324
sorry haha I cant read ayylmao

[Anonymous No.16063377]

>>16062708
What the fuck does he mean by “orientation”?

[Anonymous No.16063379]

>>16062803
Math doesn’t exist.

[Anonymous No.16063389]

>>16063377
The determinant of an isometry is always either 1 or -1. Changing orientation means the determinant is -1.

[Anonymous No.16063392]

>>16063270
Williams, Probability with martingales

[Anonymous No.16063396]

>>16063270
"Measure Theory" by Bogachev.

[Anonymous No.16063492]

>>16063266
the difference between any number in base 10 and the number you get by reversing its digits is a multiple of 9
the difference between any two odd numbers is a multiple of 2
anything that meets these conditions will be a multiple of 18

[lowercase sage !!IaxlA1xvEP/ No.16063506]

>>16063492
>the difference between any two odd numbers
Friendly reminder that 2 is also emirp.

[Anonymous No.16063515]

>>16063506
the difference between 2 and itself is also trivially a multiple of 2, but like most things involving primes, 2 is a number worth addressing on its own.
But, fine. The difference between any two numbers of the same polarity is a multiple of 2. Happy now, generalist?

[Anonymous No.16063633]

>>16062803
Every aspect of human culture has probably been predecided so unless someone comes up with a truly crazy theory of causality its probably just a semantics question

[Anonymous No.16063666]

>>16062803
Both. We discover a lot of math that emanates from nous but I don't think you can say stuff like Wiles's proof of Fermat's last theorem was discovered rather than invented in the same way that there isn't really an ideal metaphysical form for a chair, there are ideal mathematical shapes that can make up the chair which humans used to build it.

[Anonymous No.16063671]

>>16062803
Both because god exists :^)

[Cult of Passion No.16063675]

>>16063174
Very upstairs-pilled archon pilled.

[Anonymous No.16063677]

>>16063633
>unless someone comes up with a truly crazy theory of causality
anyone else got that feeling that there is a crazy one, just that it seems to be pretty fucking insane to figure out? it's like...it's there, I can almost touch it, just that not yet

[lowercase sage !!IaxlA1xvEP/ No.16063790]

>>16062905
>No, they discovered that it was (pi^2)/6. That is something that always existed in nature and was waiting to be discovered.
Very bold claim that requires a proof. Do reciprocals of squares exist in nature? Do infinite series exist in nature? Does π itself exist in nature?

[Anonymous No.16063802]

>>16063790
>Does π itself exist in nature?
no, you'll always get a finite approximation

[Anonymous No.16063816]

>>16062803
discovered. the confusion arises from distinct elements from math which by themselves construct shit different from reality. this universe is all math at the same time, which results in this.

[Anonymous No.16063822]

>>16062803
math is invented but we are not schizos hallucinating insanity into existence so the math we made is grounded in reality and pretty useful

[Anonymous No.16063839]

>>16063790
>Do reciprocals of squares exist in nature?
Well, two physical forces (gravity and electrostatic) are proportional to inverse of square of distance.
>Do infinite series exist in nature?
Hmm... Renormalization in quantum field theory? (Any specialists in QFT around?)

[Anonymous No.16064025]

World's hardest math problem

[Anonymous No.16064093]

Was listening to NPR earlier today and they literally had a segment about some drag queen mathematician talking about both things. The fact that this person described mathematics as being "invented" >>16063822 during the segment is strong evidence in favor of Platonism.

The thing that makes Science Friday such an awful program isn't even that sort of demoralization (which was pretty overt in that instance). If you spend any time listening to the program (I listen for a few minutes at a time), it becomes very clear that the host, the presenter doesn't give a shit about any sort of science and has no passion or interest in any of it. He lobs softballs: "Well, [widely understood popsci notion], how about that?" He's just some juwe in a sinecure who phones it in, pretty much how Larry King made his career.

[Anonymous No.16064101]

>>16063790
I'm using the word "nature" kind of loosely. You definitely can have an illustration of the basel problem in real life or in "nature," this video in fact is a cool example of that:

https://www.youtube.com/watch?v=S26_O2B8h8k

[Anonymous No.16064854]

How hard is it to become an ivy league professor? What percent of people can do that? Are they just somewhat harder working and somewhat smarter so that's why they're ahead of others?

[Anonymous No.16064863]

>>16064101
>calculating π
mf you can never calculate π, you can only approximate it in this reality.

[Cult of Passion No.16064878]

>>16064863
I calculated Pi in its entirety, then I wrote a hudrend pages on the definition of the numeral 1...the results are; We may never know.

[Anonymous No.16064909]

>>16064854
Divide the yearly number of new Ivy League hires by the yearly number of PhDs awarded

[Anonymous No.16064924]

>>16064909
Bro forgot the factor of Jewish nepotism

[Anonymous No.16064927]

>>16064878
Another one of CoP's fake stories. He ain't a man, he's a puff peasle. Lol retards listen to him and become more retarded.

What a cuck spoon.

[Anonymous No.16064929]

How to prove Ceva's, Menelaus's and Routh's theorems and not to get into a loop of circular references?

[Anonymous No.16064930]

>>16064929
How to solve the faggot crisis?
Problem: you

[lowercase sage !!IaxlA1xvEP/ No.16064937]

>>16064930
Anon, are you brain-damaged?
>>16064929
Have you tried proving them independently in barycentric coordinates?

[Cult of Passion No.16064947]

>>16064927
What fields do you work in?

[Anonymous No.16065062]

I’ve heard number theory is a fairly self-contained field. Like you can begin studying it without many pre-requisites. Is this true?

[Anonymous No.16065090]

>>16064909
Well I didn't really mean the rarity but how hard is it?

[Anonymous No.16065097]

Good morning sirs.
I was doing some coding and noticed that if x=9, then x squared + 2x will return 99, if x 99, then it will return 9999 and so on felt like huge discovery to my tiny code monkey brain.

[Anonymous No.16065104]

>>16063270
A treatise on probability, by Keynes.

[Anonymous No.16065110]

>>16063666
trips of truth

[Anonymous No.16065397]

>>16065062
Elementary number theory, yes. I suggest reading "Number theory for beginners" by Weil.

[Anonymous No.16065437]

>>16065397
>"Number theory for beginners" by Weil
Thanks. Is it better than Elementary Number Theory by Burton?

[Anonymous No.16065464]

>>16064025
In fact this has been solved. The minimum side of that square is the solution of this equation in picrel.

Source
https://kingbird.myphotos.cc/packing/squares_in_squares.html

[lowercase sage !!IaxlA1xvEP/ No.16065482]

>>16065464
>374x312
How about a file not for ants?

[Anonymous No.16065489]

>>16065464
oh some of these diagrams are so nasty lmao

[Anonymous No.16065496]

>>16065464
Man, the one for 51 is crazy

[lowercase sage !!IaxlA1xvEP/ No.16065505]

>>16065496
>>16065489
Do you want to see something crazy? Seven circles in square. Six are neatly arranged and one is free-floating.

[Anonymous No.16065507]

Is it worth spending time learning abstract algebra? I've got an EE degree and am fairly comfortable with real analysis, measure, probability, and some basics of metric topology but don't have any background in abstract algebra.

Is it worth trying to self teach it?

[Anonymous No.16065512]

>>16065507
I mean sure but why? Just for fun? If you love math and don't know any algebra you basically have blinders on but it's not like group theory will make you a better engineer.

[Anonymous No.16065590]

>>16065512
>it's not like group theory will make you a better engineer.
not him but why not?

[Anonymous No.16065596]

>>16065590
I don't really see any apparent applications is all. Maybe I'm just naive about engineering but it seems like analysis and probability are much more related, I would guess he's better off going further down that route into things like harmonic analysis if he wants math he can use.

[Anonymous No.16065607]

>>16065512
The closest related use for algebra is coding theory. I do some information theoretic research sometimes, and I've heard that algebra and group/galois theory can be very helpful for information theoretic shenanigans.

I've been able to avoid it for the most part, but I've always wondered if knowing some algebra and some galois theory would be helpful.

[Anonymous No.16065789]

>>16065505
Imagine that you were to manufacture the most efficient square container for seven soda cans and then one of them was just free-floating there.

[Anonymous No.16066205]

>>16063270
Probability, Kallenstein

[Anonymous No.16066281]

>>16062772
see Groups, Matrices, ... by James Carrell section 7.5.3 on multilinear maps

[Anonymous No.16066622]

Pls help my online class lectures are useless

Can someone explain to me the steps for simplifying the resulting transformed equation after putting it above the respective LCD’s of x^3 and x^4? Tried to use Photomath to reverse engineer it from the answer but I just don’t understand

[Anonymous No.16066624]

>>16066622
It’s this step right here I need explained in Retard terms. Why does the numerator gain that variable and why does the denominator not change at all? Where did the LCDs even go in this step?

[Anonymous No.16066639]

>>16066624
Multiply both the numerator and denominator by [math]x^4[/math].
That cancels out the x^4 in the denominator's denominator, and the x^3 in the numerator's denominator with another x left over, which is why the x shows up there

[Anonymous No.16066641]

Hello sci.
I am an undergrad student, struggling A LOT with commutative ring theory (the stuff in Artin Algebra chapter 11 12 13 15).

I am struggling with problems of factoring stuff in a ring, finding which two given rings are isomorphic and in general i have been unable to develop intuition for the subject

I studied group theory from Keith Conrad's notes, Rotman an Introduction to the Theory of Groups, Herstein Topics in Algebra, and Martin Isaac finite group theory and liked them a lot

But I have not found similar resources for ring theory. Should i just do Herstein and call it a day?

Any good books /prerequisites/pathways to develop a strong intuitive familiarity and deep understanding of this topic?

[Anonymous No.16066649]

>>16066639
Thankyou kind anon

Math is funny, I do fine at it until I hit a step that just wasn’t explained to me and then it is so painful. Other than that I just cruise right along. Been quarreling with this assignment for days and now I will probably breeze through it wondering how I ever struggled. It makes me wonder though if I’m being filtered for not figuring something like that out on my own and will hit a wall in higher lvl math or if I’m just being taught poorly

[Anonymous No.16066688]

>>16062685
Why isnt the math general not called DMT/daily math general

[Anonymous No.16066692]

>>16066688
Daily math thread

[Anonymous No.16066693]

>>16064854
It's very difficult since everyone and their mother wants those positions just because of "muh brand name". They are usually going to very respected or accomplished mathematicians which in turn has in part to do with luck/nepotism and pumping out good research. There are also a lot of phenomenal faculty that aren't tenured at Ivy League schools which are at other schools. While nepotism/luck will certainly help you you eventually can only hide behind that so long until you actually start making a name for yourself by the caliber of your research output and connections you make along the way. I know a few ivy League Mathers who are dog shit researchers/even employees and just work now in some corporate ho hum job. They were the very best students perhaps but average at best researchers. You'd be amazed at how incompetent a lot of people are even at supposed elite institutions, you'll see it as you age.

[Anonymous No.16066703]

>>16066693
I can give you my perspective as someone who went through a very competitive program at a "public ivy" (though in an applied math discipline rather than pure math).

Being a good student and being a good researcher are not the same thing. Being a great student means you can quickly come to understand how other people's research works, but doesn't tell you much about your abilities with identifying open problems that are solvable with your skill set.

In a certain sense, a lot of the best researchers I met were actually kind of crap students because often their willingness to try new things were directly related to them not understanding how fucked the problem is from other perspectives. If you don't spend a lot of time focusing on what roadblocks other people have run into, you might find yourself stumbling into great ideas that nobody else thought of.

[Anonymous No.16066830]

>>16063666
Btfo by andrew wiles himself at 7:09
https://m.youtube.com/watch?v=KaVytLupxmo&pp=ygUvQW5kcmV3IFdpbGVzIG9uIGlzIG1hdGhzIGludmVudGVkIG9yIGRpc2NvdmVyZWQ%3D

[Anonymous No.16067051]

If I want to show that B isn't derivable from A, can I assume that A is given, and show that in no possible line of proof can B show up without causing a contradiction? If this does work, would such a proof rely on the assumption that the system in question is consistent?

[Anonymous No.16067061]

>>16062809
>1+1=2 is a discovery about reality
It is a tautology. "2" is what we call the result of adding 1 to 1.

[Anonymous No.16067063]

>>16062694
Concern with excretion, probably jewish.

[Anonymous No.16067068]

>>16067051
How would you go about showing that "no possible line of proof" could produce B without showing a contradiction?

I would understand if you are making the claim "B cannot be related to A via X-process," then you could use the definition of the mathematical process and show a contradiction. How would you do this without inherently inclusion some sort of specific structure by which you are claiming B cannot come from A?

[Anonymous No.16067132]

ive stagnated. which is stupid because there is some shit i should write but always put off. i guess when you get no feedback ever its tough to care

[Anonymous No.16067133]

>>16067068
It will turn out that when A is assumed, a certain ~C is inconsistent. And it can further be shown that if under the assumption of A we derive B, ~C is consistent. This leads me to believe that B cannot be derived from A.

[Anonymous No.16067139]

>>16067133
You are being very vague. Are you doing some sort of formal mathematical logic or something?

[Anonymous No.16067205]

>>16067139
how was that vague

[Anonymous No.16067281]

>>16067205
It's vague because "under A we derive B" is ambiguous about the kind of process which relates A to B. If it's possible for B to be derived without being inconsistent with ~C by some other process, then your proof by contradiction won't hold.

It has to be the case that deriving B from A necessitates ~C to be true.

[Anonymous No.16067312]

I don't know anything about math so question about integrals in picture.

So my understanding there is a plane wave in here.

This article here:

https://en.m.wikipedia.org/wiki/Conditional_probability_distribution

has picture example of "bivariate joint distribution" in the second section on "conditional continuous distributions".

Now I know that the image in this post is not about probabilities, but my question is whether the plane wave is analogous to how they talk about conditional probability distribution in the picture in the link (yes, they use word plane there which is unrelated and coincidental).

Then this integral thing in image is telling you to sum all of the plane waves from all different points it is conditioned on (which not same as probability sum yes but the plane wave itself is going to be related to conditional probability since all the points on it are equal like equal probability distribution?)

So just question is if my intuition here is correct or way off.

[Anonymous No.16067351]

>>16062685

Are there infinitely many integers n such that [math]n^2 + 1[/math] is prime?

[Anonymous No.16067357]

>>16067139
Yes I am, sorry about the vagueness. How about this instead. We want to show that B cannot be derived from A. We assume the opposite, that B can be derived from A. This means that given A, by applying rules R1-R5, we can derive B. But given A, we have ~C. But from ~C and our assumption that B can be derived from A, we can obtain C. Does this contradiction mean that B cannot be derived from A, or does it mean that under the assumption that B is derivable from A, A is not true?

[Anonymous No.16067367]

>>16062803
Its both.
Math exists in platonic realm and we invent the language - equations and other symbols that let us approximate it and building on itself get another glimpse into that platonic realm entity thus discovering it in our physical realm

[Anonymous No.16067377]

>>16067357
If I'm understanding you correctly, whether or not there is a contradiction would depend on whether or not B and C are related.

It could be the case that from A you could derive C or ~C regardless of whether B is true (and vice versa). You need to establish that B being derived from A is what is directly resulting in the problem with C. Otherwise, it could be the case that you have this contradiction in C/~C from A regardless of whether A -> B.

Do you know what I'm saying?

[Anonymous No.16067379]

>>16067357
convoluted and vague, you want to use induction, only truth can be infered from truth, proof by contradiction uses this fact like so:
> want to prove that property P(a) is false for all chosen objects a
> flip it on its head and say
> if P(a) was true for chosen objects a then some other property Q(a) must also necesairly be true
> show that Q(a) is false
> since false cannot be infered from truth it the proposition that P(a) is true must be false
your proposed proof is
IF (B derivable from A AND ~C) THEN C
left side is false if at least one preposition is false, which doesnt disproves B derivable from A
you need to structure your proof so that you get
IF B derivable from A THEN (Z and ~Z)

[Anonymous No.16067397]

>>16067377
>>16067379
I don't quite get it, sorry. Why exactly does it not work? And how come ~C is a separate premise? In my understanding we are doing this:
Assume that B is derivable from A. So there is some proof that begins by assuming A and obtains B in a finite amount of steps. We take that proof under which we already have A as an assumption. We know that A gives ~C, and ~C together with A|=B gives C. So such a proof would yield ~C and C.

[Anonymous No.16067407]

>>16064025
Still an open problem
>>16065464
Has never been proven to be the minimum, it's just the smallest we know of

[Anonymous No.16067418]

>>16067397
Does B modify A? This is your process if I'm understanding correctly.

1) Assume A -> B
2) Assume A -> ~C
3) If (A -> B) then A -> C
4) Thus A !-> B

The issue is that you need to establish clearly why A -> B results in A -> C rather than A -> ~C. Is it that B modifies A in some fashion?

It could also be that your assumption for A is wrong if A -> C is happening.

What would be the meaningful difference between your procedure and the following?
1) Assume A -> B
2) Assume A -> ~C
3) If (A -> B) then A -> C
4) Thus A ! -> ~C

You have more assumptions than you have contradictions with an unclear chain connecting which assumption is violated to your contradiction.

[Anonymous No.16067465]

>>16067418
I'm sorry, I'm not quite sure what you mean by B modifying A. But we can prove elsewhere that ~C is true given A. We can also prove that given ~C, and given that A|=B, then C is true.
>1) Assume A -> B
>2) Assume A -> ~C
>3) If (A -> B) then A -> C
>4) Thus A ! -> ~C
I want to only have one assumption, that A|=B, and then extrapolate to a scenario under which A is true and B is true, and then show that such a scenario gives a contradiction. So in step 4) I'd hopefully get A ! -> B only.

[Anonymous No.16067488]

i came up with an interesting practical use for a rational function, but I could use some help implementing it.

looking at pic related, it's pretty easy for me to set a y-intercept and a horizontal asymptote which is useful, but I have found other transformations to be quite hard. I'm wondering if there is a clever way to fit a rational function to a limited set of co-ordinates...I'm sure there's a way but I don't know what such a technique would be called.

[Anonymous No.16067491]

>>16067465
So you have

1) By definition: If A then ~C
2) Assumption: A -> B
3) If (A & B) then (A & B) -> C
4) Thus A ! -> B

By B modifying A, are you certain that it is the case that A -> ~C requires (A & B) -> ~ C?

What if the truth behind A -> C is that it's truly the case that (A & ~B) -> ~C, and (A & B) -> C?

I'm not a logician, and most of proof experience comes in the background of analysis, measure and probability, but I'll try to give you a counter example.

Let A be the event {Alarm is going off}, B is the event {House is on fire} and C is the event {No burglar}.

Your assumption from previous work is that A -> ~C, meaning if the alarm is going off, there is a burglar. However, if the alarm is going off and the house is on fire, you could have {No burglar} be the truth.

This is because your statement A -> ~ C was improperly specified, and in truth it needs to be (A & ~B) -> ~C.

Obviously, I don't know your specific use case, but it reminds me of the kinds of digital logic problems we have for probabilistic graphs/behavior trees.

[Anonymous No.16067501]

>>16067061
based visionairy

[Anonymous No.16067540]

>>16067051
The question you are asking extends to decidability.
https://en.wikipedia.org/wiki/Decidability_(logic)
It's nontrivial

[Anonymous No.16067549]

I started relearning/finishing calculus since I never finished college. Reading elementary calculus by Klein from the wiki. It's actually really great to be able to understand and care about why things work. I never did that before.

I thought i'd just blow through it so I could get calculus out of the way, but it's pretty enjoyable being able to say to yourself in plain English the what and the why of what is happening in the equation (well so far, I'm only 3 chapters in). Just sitting here and taking a break to think about what I read instead of just closing the book since I did the problems required for homework.

[Anonymous No.16067637]

>>16067051
Yes, if you show B iff ~A, then supposing A: A -> ~B.

>>16067133
A -> ~~C, (A & B) -> ~C;
C, C -> A
hmmm not a correct approach here.
(A & B) -> ~C == ~(A v B) -> ~C ==
~(AB v A~B v (~A)B) -> ~C =>
AB v A~B v (~A)B -> C
Given A, we see: B v ~B -> C. C is independent of B.

>>16067465
A could be an invalid assumption if A -> (C & ~C)

[Anonymous No.16067647]

>>16067549
Godspeed, anon

[Anonymous No.16067655]

>>16067549
That's how mathematics should be taught and that is the right way to learn real mathematics. Sadly we're still stuck in the stone ages of half-assed training people to be human calculators instead of mathematicians/logicians, succeeding in creating the bulk of students who can do neither. The country that gets this right first and stops using it as elitist gatekeeping, or halfassedly carrying human-calculator pedagogical baggage from ages past, is going to blow the rest of the world out of the water.

[Anonymous No.16067699]

>>16067655
Agreed. Never understood why problem-solving and logical/mathematical reasoning in general plays such a small role in school.

[Anonymous No.16067721]

>>16067699
Historically it's a matter of pragmatism. I kind of want to rant on this for a bit because it bothers me to no end and it holds us back when we worship the past for the pasts sake. There have always been calculating tools, but people operationally better at being "human calculator" were generally more useful at doing more of the brute force calculations more efficiently and double-checking tool assisted calculations faster. I believe nearly every country has some history of mass employment of such people, from China, India, the western world used these too including the USA where "computers" used to be people employed in mass teams hammering numbers into machines whether analog or electrical.

Maybe I'm from enough of a backwater country the history of this is recent enough that I know of it by cultural memory. I'm not sure, but I am sure that's the reason for it. A combination of elitist gatekeeping where only the "gentry" or elites would be afforded the real education, while aptitudes among others were used as mass employed "skilled" labor that amounted to little more than number crunching. Modern computers, or even devices making this easier like tyepwriters or mechanical calculators, these are but a blip on the overall history where for much of it people had to slave away on analog devices combined with crunching numbers in their heads.

Pedagogy just hasn't caught up. It just hasn't realized that era, despite dominating almost all human history, that era is gone and its vestiges need to die. That's why the pedagogy is all wrong, because it's tradition for tradition's sake without realizing why that tradition existed and how it's no longer relevant. The same as learning weird cursive scripts made for fountain pens nobody uses anymore, or memorizing times tables, etc. It's all behind for a tradition whose purpose is long gone.

[Anonymous No.16067739]

>>16067721
>Pedagogy just hasn't caught up. It just hasn't realized that era, despite dominating almost all human history, that era is gone and its vestiges need to die. That's why the pedagogy is all wrong, because it's tradition for tradition's sake without realizing why that tradition existed and how it's no longer relevant. The same as learning weird cursive scripts made for fountain pens nobody uses anymore, or memorizing times tables, etc. It's all behind for a tradition whose purpose is long gone.
The truth is that the civil servants viewing themselves as teachers is an abnormality on historical scales. And the civil servants don't know nor are interested in pedagogy nor in the primary topics of educations in the first place.

[Anonymous No.16067758]

>>16067739
>The truth is that the civil servants viewing themselves as teachers is an abnormality on historical scales.
I'm not sure what you mean. Government education historically has primarily been for civil service of numerous kinds, in the west you see examples of this even in ancient Rome and of course you see this throughout different kingdoms in China and India. There has always been a kind of contrast between "service oriented" education versus what was often navel gazing affordable by elites, very few of which ever amounted to anything. I'm not arguing for a completely detached educational system either.

In terms of quantity and duration I'd argue the civil service style oriented training that still anchors us to the past is the most typical of education historically. Both in quantity of persons and time scale of history. That's exactly what the problem is because what civil service needs is vastly different from what it used to be and pedagogy is flailing about completely confused as to its purpose while accomplishing nothing useful to anybody in the meanwhile.

Far from dismissing it I'd argue what we need is a new concept of civil service oriented pedagogy because that gives it standardization and a mission. That mission should be, rather than what amounts to training people wrong as a joke, training people to be the best citizens they can be. Hence logic, mathematics, history, probably functional societal legalistic and moral training too. Less training people to be machines thrown into the gears (I am reminded of the movie Snowpiercer) and more training people to be the best people they can be instead. IDK in my country this kind of thing everyone seems to feel but can't say because it's weird.

[Anonymous No.16067760]

>>16067758
Sorry I meant gears thrown into the machine. Got the grammar backward.

[Anonymous No.16067959]

>>16067655
>>16067721
History may not be a hard science, but what did the USSR do with their math education Didn't they have a lot of people in math olympiads?

[Anonymous No.16067990]

>>16067959
The people in math olympiads were genuinely good at math, so good that even shitty ussr math education could not stop them progressing further in math. The rest average and above average people were taught simple priciples to solve simple and advanced algebra problems (same repeating problems with little variations over and over again), that's why most people who finished school were pretty good at solving known problems, good at doing those math operations on paper but also in their head, the better one, generally considered above average (white) westerner, however they stagnated at the introduction of calculus, there was just too much variation for them, and they cometely failed at any kind of (mathematical) creative thinking, sime creative problems that middle school kids (in non retards western schools) do would completely baffle and confuse average ("normal") ussr person with high school diploma.

[Anonymous No.16068032]

>>16067990
What surprises me is I would say the same thing you have said about the USSR, but about the USA and its backward mathematics education that is stuck between worlds. It is not as bad as that, but it is caught "in-between" where it is not allowed to progress because of people worshiping tradition for its own sake. The USA still has you memorize things pointlessly for memory sake, and still roots its mathematics in memorizing for ultimately testing rote memorization of rules and operations rather than working on logic or being introduced to real mathematics (e.g. propositional calculus, proof theory, etc). So it is caught between worlds in the worst way where it is terrible at all of them.
>>16067959
Olympiads are that kind of "training for being human calculator" people talk about but on steroids. Unless they've radically changed them since my youth. It's as the other anon said, you're functioning more on rote memorization and mental math tricks without thinking about the logic.

Mathematical logic, propositional calculus, etc, these things matter more and will especially matter a lot more as automation lets people simply use abstract logic to build and navigate systems without requiring rote drudgery. We're not there yet, but we're getting there by steps, and we'll be there a lot sooner than people think. What matters most in that world is not whether you've memorized some arbitrary praxis, but learned how to craft theory to design a praxis. I think we're already there, but we're going to hit a real wall as the zeitgeist shifts to utilize that.

Yes, you're still going to know how to calculate solutions of course, but who cares if you've gotten it beaten into you over 900 homework problems until you blurt out answers in a couple seconds? That's the problem. Emphasis on the wrong skillset. Testing the wrong things.

[Anonymous No.16068266]

>>16068032
>Olympiads are that kind of "training for being human calculator" people talk about but on steroids.
I thought they would be the opposite

[Anonymous No.16068278]

>>16068266
Here? Far as I know and I've seen it's "human calculator olympics" for K-12. I think there are college competitions but they don't really exist. It's entirely about solving calculator problems as quickly as possible without a calculator using mental math tricks and shortcuts.

So yeah, "human calculator on steroids". What did you think it was? Maybe this is a translation or culture issue? I'm not sure what you thought they were but I've never seen them be anything but that.

[Anonymous No.16068361]

Four-Variable Jacobian Conjecture in a Topological Quantum Model of Intersecting Fields

[Anonymous No.16068365]

Maths thread.

Tagline influences talking over maths.

>Mathematicians

GET OUT

[Anonymous No.16068904]

>>16068278
If you can find a calculator that can do this sort of thing I'll be impressed

[Anonymous No.16068913]

I have a few week break between quarters, and I'm hoping to catch up on math a little. This is my daily goal:

2 hours on Tao's Analysis 1&2 (already familiar with peano arithmetic and analysis, just reading Analysis 1 to fill any gaps)
2 hours on Munkres topology
2 hours on some graph theory textbooks

Do I have any chance of covering a decent amount of material in each of those areas in a couple weeks with that schedule? Should I just cut out graph theory and focus on topology and analysis?

[Anonymous No.16068938]

>>16065097
You're looking at numbers of the form x = 10^n -1
Then, compute
(10^n-1)^2 + 2(10^n-1) = 10^2n - 1 and that explains what you observed.

[lowercase sage !!IaxlA1xvEP/ No.16068958]

>>16065097
Now check what happens when you multiply 12345679 by 9. And then check what happens when you multiply 12345679 by 9n.

[Anonymous No.16068963]

>>16067351
It's a consequence of Hilbert's irreducibility theorem.

[Anonymous No.16068968]

How the fuck do I construct a discrete dynamical system f(x;r) with a fixed point at 1/2 for all parameter r values? Needs to go up until 1/2 and then down on 0<=x<=1.

[Anonymous No.16069171]

>>16066830
>in some sense perhaps the proofs are created
did you even watch the video or read my reply?

[Anonymous No.16069460]

>>16062693
I see the joke you were trying to make, ESL. I appreciate it.

[Anonymous No.16069574]

>>16068913
Munkres topology isn't too bad, and depending on the book, graph theory isn't terrible either.

I was able to mostly self-teach Munkres topology as a braindead EE grad student, so I have faith in you.

[Anonymous No.16069637]

My sister is about to start her Masters. I'm just a dumb engineer but she's asking me for help. What texts are good for babbys first maths masters? I've recommended Rudin and Lang, is that a good start?

[Anonymous No.16069654]

Does anyone have the meme where the mug morphs into a torus and it's captioned "this might not be normal, but on math it is"?

[Anonymous No.16069757]

>>16062708
What bothers you about that definition?

[Anonymous No.16069758]

>>16063270
Shiryev.

[Anonymous No.16069940]

>>16068968
How about [math]f(x;r) = 2^{2r-1}x^r(1-x)^r[/math]?

[Anonymous No.16070094]

>>16062803
Math is human thought.
We have evolved to think in a specific way, and this is reflected in math.

It is discovered in the sense that the environment has influenced the way we think, and it is invented in the sense that it is a product of our thoughts.

[Anonymous No.16070096]

>>16065507
Sure, it's not that hard or time consuming to learn the basics.

[Anonymous No.16070208]

Is Metamath the best formal proof system?

[Anonymous No.16070270]

Mathematically speaking, how do you cope with having 120 IQ instead of 140 IQ?

[Anonymous No.16070305]

>>16070270
It's not about superficial properties like your IQ, what matters is what's on the inside, that is, your homotopy type.

[Anonymous No.16070313]

>>16068968
>>16069940
here's another one: [math]f(x;r)=2^{r-1}\min(x^r,(1-x)^r)[/math]
I'm assuming you want [math]f : [0, 1] \rightarrow [0,1] [/math], these work with any [math]r > 0[/math]

[Anonymous No.16070441]

>>16069940
>>16070313
These work for all the conditions except he wants a stable periodic orbit for some value of r (also 0<= r<=1). I can find functions that fit all the criteria always except 1 condition gets broken.

[Anonymous No.16070459]

>>16070441
In that case I think it's not possible to get a periodic orbit if you interpret
>Needs to go up until 1/2 and then down on 0<=x<=1.
as requiring that the sign of [math]\partial_x f(x)[/math] changes only at [math]x=1/2[/math]
If you relax that it should be possible for at least some [math]x_0[/math], not sure if you can get a periodic orbit for every starting value

[Anonymous No.16070522]

>>16070305
If your brain is smooth and convex, you'll never make it.

[Anonymous No.16070656]

>>16070459
Actually I misinterpreted one of the conditions. It requires that f(x) <= x for x > 1/2 and f(x) >= x for x < 1/2

[Anonymous No.16070776]

When does point-set topology get interesting? This feels like the driest math course I've ever taken

[Anonymous No.16070783]

How do I solve this inequality?

[Anonymous No.16070785]

>>16070783
Welfare checks.

[Anonymous No.16070825]

If from the assumption of some A it follows that A is a theorem, then under threat of inconsistency of the system ¬A is not derivable from A. Is this statement true?

[Anonymous No.16071171]

>>16070776
It doesn't, just slog through it so you can get to algebraic topology

[Anonymous No.16071509]

You ever think about the fact that a greater % of integers start with 3 than end with 3?

[Anonymous No.16071570]

>>16071509
Not really because that has to do with base 10

[Anonymous No.16071582]

Where does e come from?

[Anonymous No.16071584]

>>16071570
No. The same is true in base 9.

[Anonymous No.16071602]

>>16071582
Compound interest calculations.

[Anonymous No.16071725]

>>16071509
Huh, really?

[lowercase sage !!IaxlA1xvEP/ No.16071737]

>>16071725
>>16071509
Elementary logic suggests that 1/9 of integers start with 3, but only 1/10 of integers ends with 3.

[Anonymous No.16071821]

I'm trying to determine the continuity of the function [math]f(x,y)=\begin{cases} x \quad\text{if}\quad |x|>|y|\\ y \quad\text{if}\quad |x|<|y|\\ 0 \quad\text{if}\quad |x|=|y|\end{cases} [/math]
It seems obvious to me that for the cases [math] |x|<|y| [/math] and [math] |x|>|y| [/math] there is some open ball in the usual norm around the point [math] (x,y) [/math] such that for any point [math] (u,v) [/math] in the ball, [math] |u|<|v| [/math] and [math] |u|>|v| [/math] repectively.
For the first case, say I take some [math] \epsilon>0 [/math], then I choose my radius to be this epsilon. Then [math] \sqrt{(x-u)^{2}+(y-v)^{2}}<\epsilon\implies |x-u|<\sqrt{\epsilon^{2}-(y-v)^{2}}<\epsilon [/math] and [math] |y-v|<\sqrt{\epsilon^{2}-(x-u)^{2}}<\epsilon [/math], so I can get [math]u[/math] and [math]v[/math] arbitarily close to [math]x[/math] and [math]y[/math], I'm just struggling to show that [math] |u|<|v|[/math], I'm assuming I need to choose my radius to be smaller than some value, however I can't pinpoint it. Any pointers?

[Anonymous No.16071831]

What is the strongest axiom? Has anyone used an axiom and tried to see what percentage of statements it makes true?

[Anonymous No.16071833]

>>16071831
axiom of set existence

[Anonymous No.16071864]

>>16071831
Cogito, ergo sum.

[Anonymous No.16071883]

>>16071831
Reflection principles are pretty strong, but maybe there are stronger things
https://en.wikipedia.org/wiki/Reflection_principle

[Anonymous No.16071885]

>>16071509
Also, a greater number of integers doesn't start with 3 than ends with 3.

[Anonymous No.16071923]

>>16071509
>>16071885
Also, if an integer contains a 3, the probability it starts with a 3 is 100%.

[Anonymous No.16071979]

>>16071864
stole my line
jerkface

[Anonymous No.16072625]

>>16070825
This seems to be false in case A itself is not consistent

[Anonymous No.16072671]

>>16071821
epsilon = (|y|-|x|)/4
|u|<|x|+epsilon
|v|>|y|-epsilon
by triangle inequality

[Anonymous No.16072672]

>>16071821
I didn't read what you're doing, but why should [math]f[/math] be continuous?
If you have a sequence [math]x_n \downarrow 1[/math], then [math]f(x_n,1)=x_n\to1\neq f(1,1)=0[/math].

[Anonymous No.16072818]

>>16071831
axiom of choice

[Anonymous No.16072977]

>>16071831
Axiom of every statement I need is true always

[Anonymous No.16073116]

bourbaki is cringe

[Anonymous No.16073231]

[Anonymous No.16073672]

>>16069654
Nobody?

[Anonymous No.16073687]

>>16073231
A bit over 6

[Anonymous No.16073693]

>>16072671
It's always the most obvious thing in the end, cheers.

[Anonymous No.16073694]

>>16062772
I guess I don't know linear algebra, then. Would you kindly enlighten me?

[Anonymous No.16074298]

>>16071831
identity?

[Anonymous No.16075548]

>>16072672
Just looking for continuous regions.

[Anonymous No.16075732]

>>16070776
Elementary topology is the shittiest course most people ever take in undergrad. Nobody likes it and if you claim you do you probably have some kind of mental deformity
It's medicine, you take it because you have to if you want to do cooler stuff later

[Anonymous No.16076540]

I'll be taking measure theory but I haven't taken real analysis yet. How fucked am I?

[Anonymous No.16077076]

>>16076540
Severely, you're basically me 6 years ago. Better get real comfortable with the big inequalities and convergence theorems real fast.

[Anonymous No.16077206]

How many mathematicians actually discover anything?
I was working (at the same time learning) on some problem that I basically made up and then later when taking a break and casually browsing the net ( just random math stuff) I clicked on one of google seach results and it basically had a solution to what I working on before.

[Anonymous No.16077264]

>>16077206
This is (part of) why grad students spend the first few years of their PhD working on stuff their advisor tells them to work on
Coming up with a problem that seems like it's probably answerable but is not yet answered takes expertise. Anything you're likely to come up with casually is either well-known or wide open because it's a really good question that happens to be totally unapproachable

[Anonymous No.16077667]

>>16075732
My undergrad topology was awesome and we used Munkres. Fite me.

[lowercase sage !!IaxlA1xvEP/ No.16077693]

>>16077667
>Fite me.
Would you kindly tell us something interesting about "fractional" topological spaces? (T2½ and T3½ spaces.)

[Anonymous No.16077705]

>>16076540
Yeah dude, you're in rough shape. I'm taking measure theory now and if I didn't have a relatively strong background in the first 4 chapters of baby Rudin I'd probably not even be able to hang on.

[Anonymous No.16077882]

Is there any rule about using complex numbers for normal xy coordinates? Like are the values real numbers along axes or are they functionally vectors oriented by specific axes which could have imaginary components.

As an example, could you represent the point (0, 1) as (i, 0)?

[Anonymous No.16077910]

Which of the remaining Millenium Prize problems do you think is most likely to be solved next?

[Anonymous No.16077985]

just spent 10 hours doing exercises and now i think i am going to have a well deserved wank

[Anonymous No.16077986]

>>16077882
You would just write it as i. It is common to treat the complex numbers like the real plane with a+bi corresponding to (a,b). Useful for expressing things like harmonic motion concisely.

[Anonymous No.16078601]

>>16077910
I refuse to believe turbulent flow is actually that complicated

[Anonymous No.16079551]

>>16077910
Hodge Conjecture.

[Anonymous No.16079576]

>>16079551
Nah I bet P NP with how many technology nerds and cs is trending

[Anonymous No.16079629]

>>16062685

Let [math]C[/math] be the category whose objects are vector spaces (over some field) and whose morphisms are only the linear *isomorphisms*. View [math] \mathbb{R}[/math] with its usual ordering as a poset category.

Is there a functor [math] F : \mathbb{R} \rightarrow C[/math] which is non-continuous and/or non-cocontinuous?

[Anonymous No.16079901]

>"oh my science math is so BEAUTIFUL"

Despise this NPC statement. Math is power, it has nothing to do with beauty. Most of the time its actually crude, messy, unintuitive, and treacherous. I'm return for spent effective lifespan, stress, and anguish, you gain powerful tools.

[Anonymous No.16079910]

is it true that to truly learn math you need to start with the scrolls?

[Anonymous No.16079913]

>>16079901
Retarded perspective. Math is beautiful.

[Anonymous No.16079916]

>>16079910
yeah lol scrolls through 4chan /sci/ board catalog

[Anonymous No.16079949]

>>16079913
It isn't. There isn't anything special about it. We are simply abstracting things by removal. Aristotle was right, Plato was a clown overly concerned with magical thinking.

[Anonymous No.16079983]

>>16079949
Sounds like you got the wrong type of autism. Sucks to be you I guess.

[Anonymous No.16080204]

>>16079916
>click on a bunch of vaccine and IQ threads
Now I'm ready to take on the millennium prize problems

[Anonymous No.16080310]

>>16079910
you start with a pack of cigarettes and espresso, then you grind problems for 12 hours straight before going to bed and repeating it all again the next day (you're still on the same set of problems from yesterday and will probably be for the next 3 weeks).

[Anonymous No.16080316]

>>16062685
how low are the chances I can get to be taught by that lil nigga?

[Anonymous No.16080324]

>>16080316
you ended up here, so zero.

[Anonymous No.16080715]

Anyone have an invite to /sci/ is math?

[Anonymous No.16080752]

>>16076540
After a certain point, “prerequisites” are just suggestions. Depends on your maturity.

[Anonymous No.16080847]

>>16077986
I know how it would ordinarily be written. What I'm asking is would the other way be still technically correct or a violation of what coordinates are allowed to be as mathematical objects.

Does an (x, y) coordinate mean (some vector in an x-ward direction, some vector in a y-ward direction) or does it mean (the real value along an x-axis, the real value along a y-axis)?

As they are ordinarily used, there wouldn't be a meaningful difference that I can think of as long as either way the coordinates lead to a unique point, and I don't know enough about the development of coordinate systems to tell one way or the other.

[Anonymous No.16081214]

https://www.reddit.com/r/math/comments/1bfres1/there_should_be_or_is_there_international/

Why did this post get downvoted/disagreed with on reddit? Is it correlated to it being on reddit?

[Anonymous No.16081286]

how hard could it be to get myself to do the mathematical tripos exam being an spic?
I need to fix my life

[Anonymous No.16081299]

>>16080847
>technically correct or a violation of what coordinates are allowed to be as mathematical objects.
Coordinates are just notation. There aren't rules about what they're "allowed" to be the same way there aren't rules about what the addition symbol is "allowed" to represent, there are just conventions that make it easier to communicate. You can introduce new notation if you want.

[Anonymous No.16081388]

>>16081299
>There aren't rules about what they're "allowed" to be the same way there aren't rules about what the addition symbol is "allowed" to represent
But there are? Certain symbols have base meanings within particular fields and subfields (and institutions/organizations/books/etc) and if you are going to use or overload a symbol with some particular meaning, it can't contradict those base meanings without some warning. Likewise a symbol can't contradict any other meanings you've given it in an established context.

As an example, you wouldn't want to have + mean subtraction without establishing a ground rule that basic arithmetical notation isn't going to be used as is.

So, sure, I'm aware I could change the rules to whatever the fuck I want. I'm asking if I *have to in the first place*. What technically is a coordinate in conventional use? Do (0, 0) and (i, -1) represent the same point in common convention or is (i, -1) gibberish without clarification?

[Anonymous No.16081550]

consider this problem
https://walkccc.me/CLRS/Chap03/3.2/#32-4-star
my solution is
[math
lgn! \leq n! \in Theta(n^n)
[/math]
and then i say that there doesn't a costant a such that
[math]
n^n \in Theta(n^a)
[/math]
which is obvious (?) for [math] n \to \infty [\math].

was this a good dimonstration? i find all my solutions differ from that guy's websites even though they look right to me. is my method too sloppy?

[Anonymous No.16081553]

consider this problem
https://walkccc.me/CLRS/Chap03/3.2/#32-4-star
my solution is
[math]
lgn! \leq n! \in Theta(n^n)
[/math]
and then i say that there doesn't a costant a such that
nn∈Theta(na)
which is obvious (?) for [math] n \to \infty [\math].

was this a good dimonstration? i find all my solutions differ from that guy's websites even though they look right to me. is my method too sloppy?

[Anonymous No.16081556]

consider this problem
https://walkccc.me/CLRS/Chap03/3.2/#32-4-star
my solution is
[math]
lgn! \leq n! \in \Theta(n^n)
[/math]
and then i say that there doesn't a costant [math]a[\math] such that
[math]
n^n \in \Theta(na)
[\math]
which is obvious (?) for [math] n \to \infty [\math].

was this a good dimonstration? i find that all my solutions differ from that guy's websites even though they look right to me. is my method too sloppy?

[Anonymous No.16081572]

consider this problem
https://walkccc.me/CLRS/Chap03/3.2/#32-4-star
my solution is
[math]
\log n! \leq n! \in \Theta(n^n)
[/math]
and then i conclude by saying there doesn't exist a costant [math]b[/math] such that
[math]
\Theta(n^n) = \Theta(n^b)
[/math]
which is obvious (?).

is my dimonstration good? i find that my solutions differ from that guy's websites but the logics seems good to me. is my method too sloppy?

[Anonymous No.16081577]

>>16081550
>>16081553
>>16081556
>>16081572
I still haven't considered the problem, please post it again

[Anonymous No.16081581]

>>16081577
latex got me confused and i used \math to close the tag lmao

[Anonymous No.16081586]

>>16081388
>What technically is a coordinate in conventional use?
I believe proper English word is "tuple" (ordered pair).
>Do (0, 0) and (i, -1) represent the same point in common convention
Troll or autist? (It's 4chan. I need to ask.) Complex number a+b*i can be interpeted as a tuple of *real* numbers (a, b). Nobody sane would use notation (i, -1). (Well, technically it might represent quaternion (0, 1, -1, 0), but I digress.)

>>16073694
Bump? Would anyone enlighten me why >>16062772 is a legit definition of determinant?

[Anonymous No.16081592]

>>16081581
NTA but we've all been there. I haven't with latex, but I've had days with other things just as bad if not worse.

[Anonymous No.16081611]

>>16081592
my brain is fried. i spent 5 hours studying CLRS and i'm not really sure what i did. i just read 50 pages and did all the exercises but i feel even stupider than before i began.
i just don't know how to study

[Anonymous No.16081631]

>>16066624
when you divide by a fraction it is actually the fraction flipped and muliplied

(1/2 / 4/5) <==> 1/2 * 5/4

[Anonymous No.16081645]

>>16066641
say you have a matrix A that permits operation +, * and you have a second matrix B with operations +, *. Does AB = BA if yes? then its a commutative ring lmfao

[Anonymous No.16081664]

Are there good math books series for physicists, engineers or applied mathematicians? Something like "Cambridge Texts in Applied Mathematics", but more organized for progressive learning? I take the first volume, read it, then I take the second volume, etc.

[Anonymous No.16081676]

i solved physiques most easy matz on my live ama answeres for free...

[Anonymous No.16081708]

>>16081611
Have you tried a knowledge management system, such as Obsidian and a Zettelkasten-style inter reference system? If you need rote memorization you can do that plus make flash cards for spaced repetition. Even basics such as marking out time on a calendar and schedule to study daily, so you don't have to cram, can help so long as you can stick to it.

People use a lot of things for notebooks these days, there are many besides Obsidian I just consider it a kind of "entry level" to the concept. Jupyter is of course one and would be far more powerful depending on what kind of notes you're seeking to store, but as with all open source projects suffers severely from shit documentation and bugs galore. Would any of those suggestions help?

[Anonymous No.16081741]

>>16081286
erm
any anon in cambridge?

[Anonymous No.16081760]

>>16081708
first of all thanks for you help.
i will say that i'm a pen and paper person and i like it this way, i just have a problem with CLRS: i don't like how it's written, the solutions of the exercises on the internet sucks and i'm a serial procrastinator. i re-read the first 3 chapters and still feel like i don't really know what they are all about.
no bragging, but i think i'm pretty good at programming and i like coming up with interesting algorithms on my own but this book is really humbling me, i don't know how to approach it.

[Anonymous No.16081787]

>>16081760
I suppose I did jump in making suggestions without first asking if you wanted any. Forgive the faux pas it was a lapse on my part. Capping off the suggestion you can of course do that in addition to written notes and materials, the added immersive elements probably couldn't hurt.

Either way I forgot to ask first. Need more coffee.

[Anonymous No.16081791]

>>16081787
you're so kind i think i'm talking with a bot.

[Anonymous No.16081800]

>>16081586
>Nobody sane would use notation (i, -1)
Assume I'm insane. I am aware this is akin to asking if you could write 0 as 4087-4087, although probably less useful.

>Complex number a+b*i can be interpeted as a tuple of *real* numbers (a, b)
I wasn't asking if they can be interpreted as a tuple of real numbers. I was asking if they can't be interpreted as a tuple of complex numbers. i+(-1)i and 0+0i return the same result. Could you technically then use (i, -1) and (0, 0) interchangeably?

This isn't about practicality. This is about consistency.

[Anonymous No.16081804]

>>16081791
Hahahaha oh no it's come around full circle

[Anonymous No.16081815]

>>16081572
anybody?

[Anonymous No.16081817]

>>16081572
You are trying to argue that [math]\log n![/math] is not bounded by some polynomial, and your argument is that some other larger function is not bounded by a polynomial. That doesn't imply anything about your original, smaller function (there might be a polynomial bound in between).

[Anonymous No.16081826]

>>16081817
oh yeah, if i used a function smaller than my original would the proof be okay?

[Anonymous No.16081827]

>>16081826
yes

[Anonymous No.16081898]

>>16081800
No, that isn't how you would write it. If you wrote it how you want to, you would write i+(-1)i as (0, 1-1).

[Anonymous No.16081909]

>Cantor: there is no set of all sets.
>me(big dick): take the inverse of the null set.
>cantor: *dies of heart attack.*


Weyl bros, we fucking won.

[Anonymous No.16081926]

>>16081909
https://en.wikipedia.org/wiki/Principle_of_explosion
But do go on

[Anonymous No.16082099]

>>16081898
>If you wrote it how you want to, you would write i+(-1)i as (0, 1-1).
I don't want to write it any particular way. I'm asking it if other ways of writing it would be considered correct.

(0, 0), (1, i), (i, -1), (-2+i, -1-2i). Is it all the same shit?

I feel like I'm just asking if 1+1=2 and I'm not getting a straight answer.

To reiterate
1. I am not trying to write coordinates any particular way.
2. I understand that if it's not correct, I could define shit to make it correct.
3. I understand this would almost definitely be useless/pointless/insane/impractical to do.

If nobody's ever asked this particular dumb question before so math literally doesn't have an answer, that's fine. If the answer is yes or no, that's also fine.

[Anonymous No.16082104]

>>16081909
The set of all sets is defined as not a set for convenience. What now?

[Anonymous No.16082115]

>>16082099
The issue is that you are not asking about any established framework, so I cannot tell you if it is correct or incorrect because you really haven't asked a question yet. I have never seen anyone use a coordinate system like the one you are describing and the examples you are giving seem completely inconsistent. It would not be considered correct or incorrect, it would be considered incoherent.

[Anonymous No.16082177]

>>16082104
Isn't that the real issue? ZFC is consistent until it isn't, and the inconsistencies are rules we set as a sort of counter axiom, thereby simply undermining the philosophical underpinnings of set theory, and thereby subscribing to a crude copy of formalism a la Hilbert. If I'm wrong I'd appreciate a through explanation(free lecture) , I promise I will read it throughly and appreciate your words.

[Anonymous No.16082202]

>>16082177
Since you didn't get the hint from >>16081926 the problem is your reasoning leads to a contradiction https://en.wikipedia.org/wiki/Russell%27s_paradox
Which follows from https://en.wikipedia.org/wiki/Cantor%27s_theorem
>ZFC is consistent until it isn't
This I am confused by. In what sense? That particular contradiction only arises if one asserts there is, on the same order logic as other axioms, a set containing all sets. It is therefore not an example of what you're referring to, as it is perfectly consistent to discover a binary relation of that sort leads to a contradiction without higher-order logic to account for its complex nature (e.g. nonbinary connectives).

For example, if we analogize first-order logic to something akin to a binary state that must be true or false, of course it cannot be both larger and the same as the subsets therein as that violates identity. However, by analogy if you allow something akin to a temporal dimension you have a non-contradictory answer in that such a set must be "infinitely becoming" in that it is infinitely expanding. In such a logic, the set of all sets could be described as such an infinitely expanding perpetuity without contradiction conceptually.

Just to demonstrate some different ways and orders that one can think about problems. Contradictions that result from the nature of first order logic do not imply the whole system is wrong, inherently, only a potential incompleteness due to limitations of the logic employed.

Hopefully the analogy makes sense because as a general rule metalogic stuff is best alluded to indirectly a la "call of cthulu" lest insanity result and cthulu hear his names. Either way the point is you need a way better example because that really isn't an example.

[Anonymous No.16082210]

Can someone explain in undergrad terms how one generally proves axioms are independent?

[Anonymous No.16082234]

>>16082210
https://en.wikipedia.org/wiki/Independence_(mathematical_logic)

[Anonymous No.16082237]

>>16082115
>The issue is that you are not asking about any established framework
I think I probably am and I'm so out of my depth I don't even begin to have the vocabulary to describe it.

Vector spaces were about as close as I got after too much wiki reading.

[Anonymous No.16082253]

Perelman? he hasnt been seen in the public sphere in over a decade. it is a shame we never got to hear him explain the proof in a more digestible format but im sure he is very busy with other things. his mother is quite old now as i understand it. well since im here i may as well give a short proof. let D9x be a sequence of balls with radii. obviously this space is disconnected. now we attach a deformation principle to each such that principle fiber bundle connection has the double ehorn. in finding ancient solutions to the ricci flow there is an exact sequence that splits. now each ball has associated ring structure so it is a scheme. now choose zariski topology so that the germ is isotopic to the soliton. since the soliton has a fibration with the 3 sphere space it is therefore diffeomorphic

[Anonymous No.16082266]

>>16082237
Well the issue is just that coordinates are something you choose, there are common choices but it's still a choice. You're asking about coordinates on the complex numbers, but I've never seen anyone use 2-tuples for that in the way you're doing so I can't really tell you if you're using them correctly or not because you haven't described your coordinate system.

[Anonymous No.16082287]

>>16082237
>Vector spaces were about as close as I got after too much wiki reading
read a book

[Anonymous No.16082288]

>>16082237
>I think I probably am and I'm so out of my depth I don't even begin to have the vocabulary to describe it.
I've been there. I often feel like I exist there as a perpetual state. It's great I fucking hate it. Anyway, I'm an elephant and I'm here to help.
>>16077882
>Is there any rule about using complex numbers for normal xy coordinates?
To review, complex numbers are of the form "a+b*i" where "a" and "b" are real numbers and "i" is effectively changing (operating on) the quadrant of "b". This has all manner of analogies, including rotation. In effect,
>Like are the values real numbers along axes or are they functionally vectors oriented by specific axes which could have imaginary components.
You can think of it like a function that changes the quadrant, and so merely "operating on" or representing some alteration, rather than carrying some value. "i" may as well be another symbol like the other operators. So in any ordinary meaning it wouldn't be like "values" any more than any operator could be said to have "a value" in the ordinary numerical sense on its own.
>As an example, could you represent the point (0, 1) as (i, 0)?
In the sense described, not meaningfully. It would be akin to (+, 0) and therefore meaningless.

Granted you could make some designated coordinate map such that either the "x" or "y" axis represents operators but I've no idea what you'd have the number represent on such a map.

However that headache has given me an absolute migraine in fathoming combinations of such, and contemplating the implications of such a coordinate space of operators such as (i,/) or (i,+) and (i,i).
Ow my fucking brain
You monster

[Anonymous No.16082301]

>>16081286
erm
hewoooo
also what do anons listen while stuyding?

[Anonymous No.16082341]

What is the most elegant or simplest way to prove that if the volume of an object is multplied by X (assuming it's still the same shape), any length between any two points on the object must be multiplied by cube root of X?

[Anonymous No.16082373]

>>16082210
Read John M. Lee's Axiomatic Geometry. Second chapter.

[Anonymous No.16082401]

>>16082373
Thanks, will do

[Anonymous No.16082908]

>>16082341
break your object of volume V into N arbitrarily small cubes, each of volume V/N and side length cbrt(V/N)
scale the volume by X, so now each cube is of volume VX/N and of side length cbrt(VX/N)=cbrt(V/N)cbrt(X)
thus all lengths are scaled by a factor of the cube root of X, including the length between any two points

[Anonymous No.16082992]

>>16063270
that one book by Laplace

[Anonymous No.16083033]

>>16082341
>Volumes can be expressed as integrals of 2D areas over a distance
>2D areas can be expressed as integrals of 1D lines over a distance
>1D lines are distances between points
>multiplying each of those distances by some scaling factor k means that the volume will be multiplied by k^3
>If you assume k^3=X then k=X^(1/3)
>ergo scaling a volume by X means scaling the distances between points by X^(1/3)
>orientation is arbitrary to volume and length so this holds true for all pairs of points on the object

[Anonymous No.16083081]

>>16062685
Just wondering. Does anyone here suffer from severe mental illness and see signs in the post numbers, like dubs, trips, etc?
Are you so mentally ill that you think that God is trying to give you a sign? Get help. Check ‘em though!

[Anonymous No.16084168]

scholzesisters?
https://arxiv.org/abs/2403.10430

[Anonymous No.16084186]

>>16062708
Are you the stupid one?

[Anonymous No.16084208]

>>16068266
They are. I used to do Olympiads in high school and have no idea how you’d make it far with just memorisation

[Anonymous No.16084285]

>>16068904
>>16084208
There are only so many such types of problems that can reasonably be solved without advanced techniques. If you drill them all the time you will readily solve them, but this is not very similar to what mathematicians would consider "doing mathematics" to be.

[Anonymous No.16084407]

Is there a better math AI than thetawise? Just asking before I throw money at them.

[Anonymous No.16084470]

>>16069654

[Anonymous No.16084598]

Would working through all problems in axler's linear algebra done right be enough experience for working through real and complex analysis by rudin?

I plan on just finishing the linear algebra text and then working through "real and complex analysis" and ending the math there. Do I really need to go through another analysis text prior to working through real and complex analysis by rudin?

[Anonymous No.16084622]

>>16084598
You clearly have no idea what you're talking about

[Anonymous No.16084714]

>>16062685
Everything is interesting bros. Years ago I decided to branch out from my initially narrow interests and try looking at other fields of math and I've never stopped. It's all interesting. Pure math is gorgeous. Applied math is everywhere in the world and lets you take a simple idea and actually do something with it. Algebraic geometry felt like diving deep into an ocean trench and seeing all sorts of mysterious structures appear and suddenly make sense and combinatorics felt so simple you feel like a kid again playing games and coming up with creative solutions with hardly any limits on your creativity because you don't have the right background. Some days I wish I could do this forever.

[Anonymous No.16084846]

I've been fucking around after work on the traveling salesman problem because I seemingly can't resist setting myself impossible tasks. Didn't expect to get very far, but it seems like the method I've been developing is actually quite good and I've been able to find the optimal path in O(n^2) at worst for the graphs I've tried. I can prove why it works for a subset of graphs (which are generally n<20) but the general case still evades me. I would like to find counterexamples where my algorithm doesn't work, but for obvious reasons, I can't get a solution to compare to for anything of a meaningful size. What should I do lol

[Anonymous No.16085057]

Let [math]G[/math] be a closed subgroup of [math]\mathbb{R}[/math]. Then [math]G[/math] is either (I) the trivial group, (II) a dilation of [math]\mathbb{Z}[/math], or (III) all of [math]\mathbb{R}[/math].

What are some analytic or algebraic conditions that one can check to exclude the possibility of (II)? For example, if [math]G[/math] is convex, or connected, then this excludes (II). Or, if [math]G[/math] is bounded then this excludes both (II) and (III). I'm looking for more conditions of this form.

[Anonymous No.16085130]

prove that if f:[a,b]->R is uniformly continuous at [a,c] and [c,b] then it's also uniformly continous on [a,b]

[Anonymous No.16085200]

>>16062685
Let p_n denote the nth prime number, starting with p_1 = 2 .

Then does [math] \sum_{n=1}^{\infty} \frac{1}{p_n} [/math] converge?

[Anonymous No.16085206]

>>16085057
>if G is bounded then this excludes both (II) and (III).
Could you explain what you mean by G being "bounded"? As in, compact? A compact group can certainly have discrete closed subgroups, like for example the group of nth roots of unity in the complex unit circle

[Anonymous No.16085208]

>>16085200
Sorry, just found an answer: https://en.wikipedia.org/wiki/Divergence_of_the_sum_of_the_reciprocals_of_the_primes

[Anonymous No.16085222]

>>16085130
f is continuous on [a,c] and [c,b] so its continuous on [a,b] too which is a compact set.
A continuous function defined on a compact set is always uniformly continuous.

[Anonymous No.16085253]

>>16084846
This website has a lot of examples
https://www.math.uwaterloo.ca/tsp/data/index.html
You probably even get money if you beat the best known solutions

[Anonymous No.16085256]

>>16062685
Letting p_n denote the nth prime number,
is there a way to show [math] \lim_{n\to\infty} p_n /n^2 = 0[/math] without using the prime number theorem?

[Anonymous No.16085316]

>>16085256
Euler proved there were more primes than squares so I think that would mean squares of ordinals of primes would have to grow faster than the primes themselves.

Right? I feel like I'm right. Like there must be a square number representing an ordinal of a prime, but there are finitely many primes and finitely many squares less than a given prime and if there are more primes than squares that means for a given prime the squares representing their ordinal eventually have to be more than the primes themselves if the primes out number the squares.

[Anonymous No.16085339]

>>16085256
Bertrand's postulate

[Anonymous No.16085610]

>>16085339
Maybe I'm being dumb, but how does Bertrand's postulate prove this limit: >>16085256
?

[Anonymous No.16085643]

>>16085610
There are more even numbers than squares

[Anonymous No.16085671]

>>16085643
This is wrong. Take any even number [math]n[/math] and map it to [math](2 n + 1)^2[/math] and you get a different square number. But there are square numbers that can't be produced like this like [math]4[/math].

[Anonymous No.16085699]

>>16085671
If n gets sufficiently large you can easily say (n, n^2)=(n, 2n] U (2n, 4n] U ... [2^xn, n^2) via induction, and assuming bertrands postulate this would prove lim p(n)/n^2 -> 0

[Anonymous No.16085703]

>>16085671

[lowercase sage !!IaxlA1xvEP/ No.16085708]

>>16085316
>Euler proved there were more primes than squares
The last time I checked sets of primes and squares were infinite. Was there any breakthrough in numver theory since?

[Anonymous No.16085861]

>>16085253
this is helpful thank you anon

[Anonymous No.16085884]

>>16083081
Hey, making fun of mentally ill people is a serious offence. I like that you’re trying to help them tho. Maybe just say it with a different tone, jackass.
You wouldn’t want to return to Earth to be mentally ill, would you? Maybe you already are, who knows.

[Anonymous No.16085989]

Kind of a dumb LaTeX question from me, but if I want to write "[math]x,y[/math] and [math]z[/math]", then should it be:

$x,y$ and $z$

...or...

$x$, $y$ and $z$

???????
Any strong preference between these two?

[Anonymous No.16086081]

>>16085206
Simply a bounded subset of [math]\mathbb{R}[/math]

[Anonymous No.16086168]

Which is the better overall analysis textbook? understanding analysis by abbot or analysis by Ross?

[Anonymous No.16086176]

>>16077910
imho
1. Navier-Stokes: apparently they're close to showing it's false (singular solutions exist)
2. BSD: we don't know how to extend current methods for special cases. Much of what modern number theory studies helps, so it's more of a collective effort
3. RH: what's sad about this one is that every single analytic number theorist has tried to tackle it to no avail. An analytic proof is decades away, if we're lucky we will have an "algebraic" proof (best possible scenario: condensed mathematics is the right framework for compactifying [math] \mathrm{Spec}\ \mathcal{O}_K [/math], and we follow the steps of the Weil conjectures to prove GRH). But historically analytical proofs come before algebraic proofs, so it's unlikely
4. Hodge: we have a lot of special cases, but nothing substantial; it feels like current GAGA results are in their infancy wrt the Hodge conjecture
5. Yang-Mills: I haven't heard many opinions on this one, but to my understanding we don't have a promising program to attack it
6. P vs NP: experts from the field tend to agree that it's incredibly hard, solving this one would probably require such advancements in theoretical CS as to make almost every other problem solved as well. I'm always baffled by this, because I can imagine someone coming up with a sort of Gödel encoding to separate NP from P; but I'll trust the experts

1 >> 2,3,4 > 5 >> 6
I can't overstate how difficult 2,3,4 are already, I've put them side to side but there's probably a power gap somewhere, it's hard to evaluate them (maybe swap RH and Hodge as well, again it's hard to say)

[Anonymous No.16086269]

>>16085708
Uh, I should say he proved primes occur more frequently than squares.

Uh...he proved the infinite product of 1/(1-1/p) for all primes p diverges to infinity while the infinite product for 1/(1-1/n^2) for all squares of all natural numbers n>1 converges to 2.

[Anonymous No.16086350]

>>16086176
Yang Mills isn’t going to be near because there’s no will to do it. It’s frankly not as interesting as a lot of people think it is and there’s too much work you’d need to do to get close to a proof. This would mean a decade or so of work on stuff that people aren’t interested in.

[Anonymous No.16086390]

>>16083081
I use my “signs from God” for evil.

[Anonymous No.16086393]

>>16086176
P vs NP feels unsolvable without rebuilding math and/or logic. Not saying a solution consistent with current systems doesn't exist, but I don't think we could reach a solution with our current first principles.

Like you would legitimately be better off trying to build a work-around for the principle of explosion or self-reference.

[Anonymous No.16086458]

Is there a good website to do math problems thats kind of like mathlab? I know i can check most answers in the back of the book but i like being able to see a breakdown if i get stuck. Going back to the text is helpful sometimes but not always.

[Anonymous No.16086460]

>>16086269
>>16086350
>>16086390
>>16086393
>>16086458
You are all worthless children on 4chan and you scientific discussions are worthless

[lowercase sage !!IaxlA1xvEP/ No.16086542]

>>16086269
You could simply say "sum of reciprocals of the primes is infinite while sum of reciprocals of the squares is finite therefore primes are a large set and squares are a small set."

[Anonymous No.16086973]

>>16086542
>primes are a large set and squares are a small set
I thought all countably infinite sets had the same cardinality. Can any /math/ematicians clear this up for me?

[lowercase sage !!IaxlA1xvEP/ No.16086982]

>>16086973
>I thought all countably infinite sets had the same cardinality.
Yes, they do.
>Can any /math/ematicians clear this up for me?
However, in combinatrics terms 'large set' and 'small set' have a special meaning https://en.wikipedia.org/wiki/Large_set_(combinatorics)

[Anonymous No.16087351]

axiom = self evident fact.
>'axioms' in set theory
>aren't self evident
damn

[Anonymous No.16087494]

>>16087351
Read Intuitive Axiomatic Set Theory by Jose L Garcia to clear up that misconception. Although J. R. Shoenfield wrote some arguments explaining why the axioms are "self evident" under some interpatation of the universe. This can be found in the first chapter on set theory, Handbook of Mathematical Logic edited by John Barwise

[Anonymous No.16087517]

I'm getting back into math. Gonna start with a problem generator and some mental math in the morning and evening

[Anonymous No.16087853]

theoretically speaking, the set of all things that exist physically is countable, right?

[Barkon !otRmkgvx22 No.16087855]

>>16087853
There are only 3 billion stars (less) and quadrillions of insects. There's be 1R+ things in existence where R is a system of a quadrillion.

[Anonymous No.16087921]

new Abel prize laureate just dropped

[Anonymous No.16087922]

>>16087855
what about infinite universe or multiverse?
me thinks there is no way to have an uncountable amount of things in a one universe.
multiverse is a bit tricky because a universe can just be a copy of another universe where some physical constant is different by an infinitesimal amount thus creating an uncountable amount of universes

[Barkon !otRmkgvx22 No.16087946]

>>16087922
It's just a system of units.

[Barkon !otRmkgvx22 No.16087947]

>>16087946
Or rather, systems of units where some of those units are other systems in repeating matrix of systems, which in itself is a system.

[Anonymous No.16087998]

>>16085989
The latter will justify the space after the comma if need arises, reducing the chances of overfull hboxes.

[Anonymous No.16088031]

>>16087921
literal who

[Anonymous No.16088051]

>>16088031
unknown to undergrad category theorists maybe

[Anonymous No.16088083]

>>16087998
Thank you very much!

[Anonymous No.16088158]

a - a^2 = x
How do I go about making this as simple as possible? Should I go back and try to remove the squared?

[Anonymous No.16088202]

>>16088158
Hard to say without knowing the specific conditions, but breaking down polynomials into degree-1 terms ([math]a-a^2=(1-a)(a)[/math]) is rarely a bad idea when trying to work through them more easily

[Anonymous No.16088204]

>>16087921
I'm happy for him :)

[Anonymous No.16088244]

>>16087921
Honestly really deserved, his work on concentration of measure is giga useful.

[Anonymous No.16088588]

Is it true that the brightest sudents tend to go into algebraic geometry?

[Anonymous No.16088653]

Is there a more straightforward way to do this?

[Anonymous No.16088676]

>>16088653
Well, it's not true, for starters.
(-4,10) is also a valid solution. As is (10,-6).
In fact, given that (x,y) is a solution with x and y as integers, (x-7r,y+8r) is also a solution for any integer r

[Anonymous No.16088711]

>>16088653
There's one linear equality on R^2, it's probably quite straightforward to that there's a countably infinite # of solutions (a line)

Also holy shit, I knew chatgpt was bad at math and logic but that's taking things to a whole new level

[Anonymous No.16088718]

>>16088711
quite straightforward to prove that there's an uncountably infinite*
I should sleep more

[Anonymous No.16088808]

I just noticed that a plane's (ax+by+cz=d) normal line (a,b,c) can be interpreted as the gradient of a linear three-variable function, with the gradient being the normal curve and the function's level plane being the plane, which are always perpendicular to each other. I thought that was neat.

[Anonymous No.16089120]

new >>16089119