/mg/ – maths general

[Anonymous No.15662730]

Needful edition
formerly >>15608042

[Anonymous No.15662740]

Could you approximate the probability of finding amicable numbers on the number line in a similar way like you can approximate the probability of prime numbers?

[Anonymous No.15662880]

How do I self study from Serge Lang algebra book ? I have always been dependant on teachers and now I want to change that..(too much spoonfeeding isn't good for learning)

[Anonymous No.15662886]

>>15662740
They are working on bounds. It was shown that the amicable counting function A(x) < x/exp(sqrt(log(x))) for large x. Erdos guessed x/x^y < A(x) for some smallish y.

[Anonymous No.15662889]

>>15662880
With these supplements: https://math.berkeley.edu/~gbergman/.C.to.L/ the book is a slapdash hackjob like literally everything Lang wrote.

[Anonymous No.15663215]

>failed PDEs twice
god i hate myself, i'm getting 90+ in my algebra based classes but still making no progress in PDEs

[Anonymous No.15663256]

I don't know much about models and foundations, but a guy in the geometry department said the following to our student groupchat:
>Different foundations choose what can be impredicative, what goes on the ramified hierarchy, and where is the final cut off. If you want to know the specifics, you would have to look into that specific foundation. For example, ZFC (and also NBG, basically) include a couple impredicative things and shove everything else in the "no fun allowed" bucket, avoiding the ramified hierarchy wherever possible, which, IMO, is a shit way to approach classes.
It was pretty interesting and I've done a bit of wiki trawling since and I think I'd like to learn about the stuff he was talking about. How do I get started?

[Anonymous No.15664509]

>>15662730
Did Ramanujan really did the needful?

[Anonymous No.15664528]

Obsessed about finite projective planes lately my babes

[Anonymous No.15664535]

>>15662730

[Anonymous No.15664546]

>>15664528
Wish I was able to connect this to steiner systems, but I'm a dumdum with self-study, leaving academia was the worst decision of my life

[Anonymous No.15664609]

My probability course sucked ass so I didn't learn Bayesian Inference very well.

Do any of you have any Bayesian inference books/courses you would recommend? It seems to important too be stuck with shitty teaching

[Anonymous No.15664619]

>>15664609
>Bayesian inference
That's a white supremacist conspiracy theory

[Anonymous No.15664623]

>>15664619
Is stats the white mans math?

[Anonymous No.15664671]

What a stupid fucking gathering of retards

[Anonymous No.15664676]

Imagine having anything better to do than throw down some boring shit on a niche thread on a niche site.

Live your life but wow

[Anonymous No.15664908]

https://files.catbox.moe/0g3erd.png
Shouldn't this say XOR instead of OR?
Either or statement implies one or the other but not both
Why do they use OR to represent it instead of XOR
Is it a bad example for this or am I retarded?

[Anonymous No.15664928]

>>15663215
I don't get how some people have problems with certain math classes but are fine in others, unless the teacher and provided material are shit of course. It is all just applying arbitrary abstraction, there should be little variance in difficulty for equally complex courses. The only time I feel like it would make sense is if you are comparing a more applied math like statistics, where the work typically involves word problems, or don't have the prerequisite knowledge for a certain topic.

[Anonymous No.15664965]

https://www.youtube.com/watch?v=BipvGD-LCjU
Wanted to post the exceptionally rare math song that's actually at a high level, by grad students
The singing's shitty but by god do they have soul

[Anonymous No.15664968]

>>15664535
And you may find yourself living in a shotgun shack
And you may find yourself in another part of the world
And you may find yourself recalling dreams from a large deity
And you may find yourself in a great university...
With a great advisor...
And you may ask yourself: "Well...how did I get a scholarship here?"

https://www.youtube.com/watch?v=--ejMmgX9iA

[Anonymous No.15664972]

>>15664968
https://www.youtube.com/watch?v=pf2DgSJuUHc

[Anonymous No.15664982]

this shit cannot be serious? I wonder if they purposely sabotaged some of the logic that goes into this to not let middle/high schoolers cheat easily

[Anonymous No.15664993]

https://www.youtube.com/watch?v=fxvkI9MTQw4

lmao, lol even

[Anonymous No.15664998]

>>15664908
It is right, it is just that ors in formal logic are retarded and not consistent with day to day english. So, if you see a either in a propositional logic problem, you need to assume it is not exclusive. On top of that, their decision to have ~p be 'get to work on time' is retarded because it is represents a negation of a negative action which can cause confusion. What they should have done is have p be 'get to work on time' and q be 'you are fired'. You can see in picrel that the two statements are in fact equal, but the xor is not.
You have to think about it, not from an intuitive logical sense, but from whether a conclusion is valid given solely the supplied premises ex:
using ~p and q truth values then 'either'=XOR can't be valid as
you get to work on time: ~p = 1
you are fired: q = 1
then: ~p xor q = 0
while: p -> q = 1
as the validity of conditionals is always true if the antecedent is false as the proposition only indicates a correlation between the two values when it is true.
Rewritten in english:
The only way I can be fired is if:
I either get to work on time or I am fired, but not both
If I don't get to work on time then I am fired
This can't be true because
I got to work on time
yet I was still fired
tldr; you aren't retarded, the problem is correct, but the language of the problem is retarded

[Anonymous No.15665004]

>>15664998
fuck meant to post this one

[Anonymous No.15665006]

Finite fucking projective planes
Eat my fucking ass nerds

[Anonymous No.15665012]

Guys, I'm having problem with picrel.
When I did it, by first converting to (r,theta0, the answer comes to 0.
Then for confirmation, I gave it to symbolab. In symbolab, if its done normall, the answer comes to -128, and if done in (r,theta) the answer comes to 24pi.
idk where I went wrong, I checked and re-checked the whole thing. even asked chatgpt. chatgpt seems to agree the answer will be 0

[Anonymous No.15665013]

>>15665012
sorry forgot the pic

[Anonymous No.15665015]

>>15665012
>>15665013
btw just to make sure, its the area of a full circle right? with radius 4?
so, the limits will be 0 to 4 for r, and 0 to 2pi for theta, right?

[Anonymous No.15665019]

>>15664972
>>15664968
I guess that's my favorite now for this month. Thanks.

[Anonymous No.15665027]

>>15664982
leaving aside the obvious, that they lobotomized the shit out of their models, which reduced their logic capabilities, its not fair to evaluate an LLM eith math. They simply are made for conversations first and formost. any mathematical ability, among others, is emergent from that training, but can also be wrong

[Anonymous No.15665109]

>>15665015
no, it should be a semi circle. Double check the order of variables you are integrating with respect to

[Anonymous No.15665216]

>>15665109
how though? if you draw a graph, its a full circle on the negative side of x, from -4 to 0

[Anonymous No.15665227]

>>15662730
Should I consider maths research as a field?, I don’t perform extremely great on maths tests but I proved that there are infinite primes and derived a formula for finding the sum of n squares on my own when I was about 15. I also proved the Pythagoras theorem on my own a few years before.

[Anonymous No.15665302]

Finite projective planes you fucking cowards

[Anonymous No.15665308]

Eat a fucking dick you absolute cowards
>hurr de durr I don't undersnd finite projective planes
Ask me about it you literal tomato

[Anonymous No.15665311]

Pointless

[Anonymous No.15665321]

>>15665216
>its a full circle on the negative side of x, from -4 to 0
what?

[Anonymous No.15665328]

Finite projective planes are rad as fuck

[Anonymous No.15665333]

>>15665321
ok its on the middle. but why am I supposed to take theta limit as pi/2 to pi? its a full circle, so isn't the limit supposed to be 0 to 2pi?

[Anonymous No.15665339]

>>15665333
>>15665321

hol up I think I got it.
does the limit given to x, -4 to 0 indicate that I'm only supposed to evaluate the area of the left side of the circle? which is why the limit's pi/2 to pi?

[Anonymous No.15665444]

>>15665339
>does the limit given to x, -4 to 0 indicate that I'm only supposed to evaluate the area of the left side of the circle?
Almost, what the double integration and its limits mean is that you are supposed to find the volume of the shape formed by the curve f(x)=3x and the semi-circle R below it, defined by x^2 + y^2 = 16; -4<x<0
>picrel

[Anonymous No.15665465]

>>15662730
Ok lads, im a probability-let so I am kind of stumped by this:

If we have 2 random variables [math]X,Y[/math] then Jensen's inequality quickly gives:
[eqn]E[|E[Y|X]|^2] \leq E[E[|Y|^2|X]] = E[|Y|^2][/eqn]
So that the operator norm of [math]E[( \cdot )|X][/math] is less than or equal to 1.

Now, what happens if I add another random variable to the mix? As in, whats the operator norm of:
[eqn]F(Y) := E[ZY|X][/eqn]

In general, we can't assume Z is X measurable

[Anonymous No.15665550]

There must exist a computer algorithm that calculates the digits of pi the most efficiently. That is, it outputs the most number of digits in unit of time.

Is it possible to prove mathematically that a certain algorithm is indeed the absolute optimal one in this regard?

[Anonymous No.15665592]

>>15665550
You can't by unit of time, but you can by computational complexity. It doesn't make sense to measure by units of time as that entirely depends on the architecture and speed of the processing computing it. To the point where the implementation of assumed constant time operations like addition and multiplication for arbitrary size integers effect the computation time immensely. There is no objective way to directly convert total operations to time, nor is there even a good way that gives a approximation. This isn't even taking into account differences in hardware specifications like total memory or cache. An algorithm that beats another but uses sufficient memory, could lose to the same algorithm if the memory is lowered. That is why FLOPs haven't been replaced even though they suck dick at actually comparing speed.

[Anonymous No.15665618]

I came up with a random problem.

You have a container, let's say it's one cubic meter and shaped as a cube. You want to fill it with water bottles (the bottles can be any shape you want) such that each bottle is 0.5 liters and they all add up to one cubic meter of water. So there's no empty space in the container. But you want to optimize the container in such a way that the material that has to be used in the water bottles is minimum. The problem is as follows. What is the total amount of material used in the water bottles in terms of surface area?

In other words, how do you divide a cube into 2000 sub-regions each of which have equal volume such that the total surface area of all the subregions is minimized?

A bonus problem is to solve the average surface area of one water bottle if the container is just infinice 3D space.

[Anonymous No.15665621]

I came up with a random problem.

You have a container, let's say it's one cubic meter and shaped as a cube. You want to fill it with water bottles (the bottles can be any shape you want) such that each bottle is 0.5 liters and they all add up to one cubic meter of water. So there's no empty space in the container. But you want to optimize the container in such a way that the material that has to be used in the water bottles is minimum. The problem is as follows. What is the total amount of material used in the water bottles in terms of surface area?

In other words, how do you divide a cube into 2000 sub-regions each of which have equal volume such that the total surface area of all the subregions is minimized?

A bonus problem is to solve the average surface area of one water bottle if the container is infinite 3D space.

[Anonymous No.15665792]

>>15665444
isn't a double integral for finding area? I don't think there's any volume business in this integral.

[Anonymous No.15665828]

I have a math-adjacent problem for the compsci students I'm TAing. It's a fun one and I want to give it to them as homework but I can't figure out how to rephrase it in a nice formal way.
Is there a good guide for making word problems formal?

[Anonymous No.15665853]

how to become good at visualizing?

https://www.youtube.com/playlist?list=PLOxODW9vlVLRpXYW1iMEjMJ0Xy2F0d4Q_

[Anonymous No.15665945]

>>15665828
I've never seen a word problem writing guide anywhere because most problems are easy for anybody who is familiar with the respective topic to describe. Post your draft problem and we'll see if it needs rewriting.

[Anonymous No.15666222]

>>15665945
Here goes:
>A p by q square lattice is randomly two-colored. On this lattice, a solid box is any set of nodes from x_i,y_j to x_k,y_l (a rectangle) that are all of the same color.
>A hollow box is any set of nodes from x_i,y_j to x_k,y_l (a rectangle) where all of the outermost nodes of the rectangle are the same color, but the interior nodes may be the other color.
>It's obvious that all solid boxes are a subset of the hollow boxes.
>Devise two search algorithms, one for finding the largest solid box and the other for finding the largest hollow box. Show that these two algorithms have the same time complexity.
It took me about 20 minutes to do it myself so I figure it'll take the median students 2-3 hours, but I don't like the way I've described it at all.

[Anonymous No.15666264]

What's the trick to factorize quadratic forms? Guess and check isn't very efficient

[Anonymous No.15666464]

If I have a data set that shows a somewhat sine curve, can I transform the data by taking the sine function, so I can "straighten" it out for a linear model? Not homework btw, just a little personal project

[Anonymous No.15666489]

Guys i have a question regarding the critical points for a function of 2 variables.
They say for the function z = f(x, y), the point (a, b) is a critical point if:
1- both partial derivatives are zero on that point
or
2- one or both of the partial derivatives are undefined in that point, right?

Now the function z = x^(2/3) + y^(2/3)
if you take the first partial derivatives with respect to x and y, you'd have
dz/dx = (2/3) x^(-1/3)
and
dz/dy = (2/3) y^(-1/3)
clearly (0, 0) is a critical point because x and y are in the denominator of partial derivatives and can't be zero, so both partial derivatives are nonexistent in that point.
but other points like (0, 1), (3, 0), or any point with one coordinate 0 should also be a critical point because in that case one of the partial derivatives is nonexistent and it satisfies the second condition for the critical point.
So does this function has infinity many critical points?

[Anonymous No.15666939]

I feel like this should be very basic but somehow I'm stuck. How do I show that the tangent bundle of a smooth affine variety is itself an affine variety? I suspect it should be explicitly constructible from the defining polynomials f1,...,fk. I just don't see how.

[Anonymous No.15666953]

>>15665792
the first integrals taught in class are area under a curve. other than that I dunno how much you can generalize from just the number of integrations

[Anonymous No.15666956]

>>15666939
Ok nvm, I figured it out. Sorry for my low IQ.

[Anonymous No.15667053]

How is the standard deviation a square root of the variance (it's claimed as one)? And how is the variance calculated in this risk + risk free portfolio situation? T. brainlet who didn't go to highschool

[Anonymous No.15667356]

Geometric algebra extends linear algebra by defining and manipulating multivectors, such as a A+3B-C, where A is a vector, B is a 2x2 square matrix and C is a 3x4 matrix.
.
In the most basic type systems, 2 is a valid expression and false is a valid expression but 3x^2+4xfalse-true+3false^2 is not a valid expression. Is there a similar kind of extension and does it contain anything interesting?

[Anonymous No.15667420]

>>15662740
What does amicable numbers mean?

[Anonymous No.15667481]

>>15667420
A and B are amicable if A's proper divisors sum to B, and B's sum to A
the smallest such pair is 220 and 284:
1+2+4+71+142=220
1+2+4+5+10+11+20+22+44+55+110=284

[Anonymous No.15667485]

>>15664982
LLMs don't work that way. There's no actual thinking being done. They work by token prediction; they "understand" language extraordinarily well, but they don't actually "understand" math (unless they've seen the specific problem before)

[Anonymous No.15667614]

>>15667356
>In the most basic type systems, 2 is a valid expression and false is a valid expression but 3x^2+4xfalse-true+3false^2 is not a valid expression.
Adding in the multiplication for you and determining a type for x,
>console.log(3*'x'^2+4*'x'*false-true+3*false^2)
> 2
If you want to go far in math, you'll want to move past those "basic" type systems (eg category theoretic or HoTT-based) pretty quickly. Javascript is what really advanced mathematicians prefer.

[Anonymous No.15667781]

>>15667614
>JavaScript
HAHA

[Anonymous No.15667862]

>>15667781
Javascript is a functional language that supports church encoding.

[Anonymous No.15667903]

Anyone know any textbooks/lecture notes on 2-categories

[Anonymous No.15668062]

>>15665853
sorry bud not much improvement you can do
either born with it or not

[Anonymous No.15668235]

>>15662730
Baboon here:
about the Riemman's proposed refutal shilled so often every now and then (kek):
>Evaluation of Riemann’s equation is undefined due to the product ∞ · 0.
>There is no contradiction
>robust character of Riemann’s func-
tional equation in the neighborhood of infinity.
>The theorem of Hadamard and de la Vallée-Poussin (((should))) fail along the
portions of that line lying in the neighborhood of infinity due becausd of (((reasons))) like the arithmetic of numbers in the neighborhood of infinity
Could someone clarify this part or provide a reference/example/formal/intiutive representation
Thanks

[Anonymous No.15668554]

>>15667862
I'd use Python or R over GoodMorningSirs

[Anonymous No.15668957]

>>15665853
practice

[Anonymous No.15668999]

>>15663256
>Different foundations choose what can be impredicative
You probably mean primitive instead of impredicative. The primitives of your theory are like undefined terms (e.g. the points and lines in Euclid's Elements; don't let his attempt at defining them fool you!), whereas a definition is called impredicative if it is self-referential (more precisely, see e.g. https://iep.utm.edu/predicative-and-impredicative-definitions/).). You don't really design your theories with the goal of picking and choosing which definitions will be impredicative, you just choose whether you want to allow them or not.

>How do I get started with models and foundationss?
For the more philosophical side you could turn to the following:
- 'Oxford Handbook of Philosophy of Mathematics' (if I remember correctly it covers hierarchies but not predicativity nor Poincaré's philosophy of conventionalism)
- I remember enjoying the intro to 'Set Theory and its Philosophy' a lot, introducing some of the philosohpical problems with set theory.
- 'What do we want our foundations to do' comes at the problem of foundations from a practical angle and also discusses various foundational systems.
I am personally very excited about Blasjo's thesis about operationalism (a kind of constructivism) in which he also attacks purely verbal modes of logic.

I don't know any model theory beyond the basics; enough to proof the transfer principle for hyper products. I also haven't studied ZFC in any real depth. Maybe this MO question can help you tho: https://mathoverflow.net/questions/76641/a-book-about-model-theory

[Anonymous No.15669141]

Is set theory just a type theory with only one type?

[Anonymous No.15669336]

>>15666464
Answer pls?

[Anonymous No.15669727]

>>15669141
No, you need a type for booleans too, and function types. But if you have those then yeah, any theory can be turned into a type theory.

[Anonymous No.15669845]

>>15664609
Just read the Bayesian sections of All of Statistics by Wasserman and Statistical Inference by Casella & Berger. It'll get you mostly there.

I explain to normies that it's a series of useful Statistical methods we can utilize if we have some prior information about the problem. If not just don't worry about it. For undergrads, it's typically just modifying* the Likelihood function and accounting for constant parameters becoming random variables.

In general Bayesian Methods you have to be careful with, they're more I guess robust in a lot of ways, and truly are the generalization of frequentist inference, but also rarely are they computationally beautiful and they truly are a product of probabilistic math (where a lot of frequentist methods are trivially described in terms of linear algebra and basic optimization)

[Anonymous No.15669848]

>>15664982
They did. It's pretty well documented. Some of the compute resources are going to them trying to build out GPT 5, but it's hard now with so many competitors.

Try seeing what Bing and Bard give as contrast. The future though will be opensource bots, especially as the government, medical industry, etc. starts to stick their fingers in the pot more.

[Anonymous No.15669849]

How far along are you?

[Anonymous No.15669851]

>>15667614
Not using LISP but it's bastard web browser offspring. Do parenthesis scare you?

[Anonymous No.15669857]

>>15666464
Yes. But it also depends on what you're doing. If you're building a statistical model, you'll run into additive vs multiplicative error issues.

Basically if your data is:
y = bsin(ax) + noise
Then the transformation will 'bucket' the noise with sin(ax) making the noise nonlinear (this doesn't always happen btw so you need to investigate residuals).

A lot of times, for problems like this, statisticians will find TWO simple models. One by transforming and linearizing the relationship and fitting a simple linear model to, then another (the actual model) using nonlinear regression with the parameters of the simple model as starting points (since they should be approximately similar). Does this all make sense? The statistician may also employ a general method, like kernel regressions or something which let's them REALLY ignore the shape of data relationships, but those models aren't as informative.

[Anonymous No.15669862]

>>15669849
>All theory and pure math
>Nothing actually useful
>Not even useful theory like measures
Lmao.

If there were a global digital Holocaust and mass burning of all books at once, what math do you think would survive?

[Anonymous No.15669868]

>>15667862
Mathematicians use like R or Matlab in my experience for their simple shit, and then C++ or Fortran for anything serious. You might ask why Matlab, I don't know, i think there was a lot of focus on it in the 90s and some just got hooked? Personally, the only thing of value on that proprietary piece of shit is simulink. I don't know why literally just the open source clone (Scilab) is the only other software that does anything close to that.

[Anonymous No.15669893]

does mathematics attract just as many cranks as philosophy and computer science do? and which field if mathematics attracts the most cranks?

[Anonymous No.15669897]

>>15669893
>does mathematics attract just as many cranks as philosophy and computer science do?
no

>and which field if mathematics attracts the most cranks?
millennium prize problems

[Anonymous No.15669898]

Is every square number greater than 1 the sum of two primes?

[Anonymous No.15669905]

>>15669898
no

[Anonymous No.15669921]

>>15669905
Yes I realised since a lot of them are odd and the only even prime is 2 so the sums wouldn't make the differences.

[Anonymous No.15669922]

how do you stay interested in mathematics for so long
The last time I had fun with it was when I was in high school and hanging out with math frens. It's just so pointless and unfulfilling. I like math, it's just that it has no large purpose in society and it's a lonely as fuck field

[Anonymous No.15669929]

>>15669922
Its interesting cause its nature for your mind.
Modern society wouldn't exist without the developments of math.

[Anonymous No.15669948]

>>15669929
but modern society just made us more miserable
sure refrigerators and showers are nice but all that did was make struggle pointless and living unfulfilling

[Anonymous No.15669950]

[math]\int _{-4}^0\:\int _{-\sqrt{16\:-x^2}}^{\sqrt{16-x^2}}\:3x\:dy\:dx[/math]

I've evaluated this a gorillion times, used both desmos and symbolab but the answer doesn't match up. Doing it both in normal form and r,theta gives me 64 answer, but symbolab and desmos says its -128 in both cases. I don't know which line exactly I'm going wrong. I can't be this retarded.

[Anonymous No.15669985]

>>15669922
I work only on applied problems that are real issues. That's how I stay motivated.

[Anonymous No.15670013]

>>15669950
The 'normal' way gives me, starting with the inner integral:
[eqn]\begin{align}
\int_{-\sqrt{16-x^2}}^{\sqrt{16-x^2}}\ 3x\ dy &= 3x \left[ y \right]_{y=-\sqrt{16-x^2}}^{y=\sqrt{16-x^2}} \\
&= 3x(\sqrt{16-x^2} + \sqrt{16-x^2}) \\
&= 6x \sqrt{16-x^2}
\end{align}[/eqn]
Then do a u-sub for the remaining integral. [math]u = 16 - x^2 \implies du = - 2x\ dx[/math]
[eqn]\begin{align}
\int_{-4}^{0} 6x \sqrt{16-x^2}\ dx &= -3 \int_{0}^{16} \sqrt{u}\ du \\
&= -3 \left[ \frac{2}{3} u^{3/2} \right]_{u=0}^{u=16} \\
&= -2 (64) = -128
\end{align}[/eqn]

[Anonymous No.15670017]

>>15665109
why is the limit of radius, r, -4 to 4? radius can't be negative. shouldn't it be 0 to 4?

[Anonymous No.15670064]

>>15670013
nvm I rechecked, and I got -128 in cartesian form.
But in polar form, I keep getting -64. Aren't the cartesian and polar forms give same result?
It seems to be a question of r's limits
>>15665321
>>15670017
but shouldn't r's limits be (-4, 0) instead of (-4, 4) since radius can't be negative?

[Anonymous No.15670158]

>>15670064
The radius should be from 0 to 4. The -4 is
basically "doubling up" the answer.

[Anonymous No.15670272]

>>15669857
Thank you handsome anon

[Anonymous No.15670315]

>>15669857
I pulled a race vs crime data set from the US feds and also population census data. When I plotted the violent crime of one group over time it appeared nonlinear, like a sine wave. The diagnostic plots werent normal and I thought to normalize the data it would be a decent idea to use the sine function for transforming the data `plot(lm(sin(crime_group)~time))`. I tried using spearman's correlation but that didn't clean the data up. Since the data is from 1981-2019 I think I would have to make a few different models, more than the two you suggested. I think the model is violating independence assumptions because of law maker interference, so itd make sense why the linear model sucks. Since theres interference from people, does this make prediction impossible? Here's my graphs. Also it seems I made the QQ plot worse with the sine transformation, but the residuals vs fitted appears more centered around zero.

[Anonymous No.15670561]

>>15669922
i like trying to uncover the inner workings of numbers
there are so many patters, it's mysterious

[Anonymous No.15670612]

>>15669893
anyone is allowed to do anything and shouldn't be stigmatised as long as the work is rigorous.

[Anonymous No.15670746]

>>15670612
If it's rigorous they're not a crank. Cranks are the ones with bullshit proofs that ZFC is inconsistent or the RH is true, or the RH is false, or the same for the goldbach conjecture or any of the problens with a big prize.

[Anonymous No.15670901]

What are some good textbooks to learn vanilla geometric algebra and projective geometric algebra? Preferably something that builds them from the ground up, like for example starting from the geometric product and from that define the dot and wedge product, insteas of the other way around.

[Anonymous No.15670905]

>>15670901
>Look at me, I watch a schizo math youtube channel

[Anonymous No.15670910]

>>15670905
>schizo is when thing i don't like

[Anonymous No.15670915]

Using already dead animals to make products is more moral than using live plants to do so.

[Anonymous No.15670930]

I'm going to a psychiatric hospital and want to take some small math book with me to stay fit while in there. Do you have any recommendations? Assume that I have a good math undergrad education.

[Anonymous No.15670958]

can someone explain to me multiplication in a galois field? addition was easy enough to understand, but i am struggling somewhat to fully grok multiplication and then modulo
ty

[Anonymous No.15670984]

>>15669893
Dont speak poorly about Terry Davis, or Uncle Ted.

[Anonymous No.15671198]

>>15669948
That's more of an issue with the governing ideology e.g. capitalism. There certainly is a class of people who live without worry and misery.
Also you won't dodge this predicament if you go back any number of years. you'll be shitposting to your 8 year old friend while you clean a chimney rather than an internet forum that is only possible via the advancements in math.

[Anonymous No.15671205]

>>15670930
Mathematics in everyday things - WC Vergara

Best of luck

[Anonymous No.15671257]

>>15670958
I'm not an expert, but some things:
1) Try the Wikipedia page? Just going through it carefully https://en.wikipedia.org/wiki/Finite_field
The definition for q=p^n of GF(q) = Zp[X]/(P) for some irreducible P in Zp[X] (which allegedly there always exists some P). Try working this out for some concrete values of p,q, and a choice of P.
2) Try working out GF(4) just from bare principles, ignoring the above. There must exist 0,1 from the field definition, some third element a, and then 1+a by closure under addition; etc, and use field axioms to determine what the multiplication must be.

[Anonymous No.15671360]

Does he still post here?

[Anonymous No.15671666]

>>15670930
Probability by Jim Pittman. Download the answer guide too and work through the problems.

[Anonymous No.15672344]

How exactly do I get started on this problem? I can't determine the volume when there's two shapes involved.

[Anonymous No.15672642]

>>15672344
To get started, your three constraints are:
1) "within the sphere x^2+y^2+z^2 = 9"
2) "outside the cone z=sqrt(x^2+y^2)"
3) "above the xy-plane"
You want to convert these to spherical coordinates -- rho, theta, phi. Some thoughts:
a) All three constraints are radially symmetric, so this implies what about the bounds of one of your coordinates?
b) Which of the three place a maximum limit on rho?
c) What do these three figures look like?
d) If you graphed restriction #2 side-on, to a 2D plane marked with an 'r' axis and a 'z' axis, what would it look like? What about the throwing the other figures on? (An 'r-z' graph is often a useful trick for these problems -- especially when they're radially symmetric, or somewhat so.)

[Anonymous No.15673227]

How to prove this for independent events?

[Anonymous No.15673288]

I've been posting here for four years and there have been more type theory questions in the last three months than all of the previous months.
Is there a meme and/or normie youtube video that is responsible?

[Anonymous No.15673502]

>>15669898
121 is a counterexample

[Anonymous No.15673512]

>>15673502
bruh 2+ 119

[Anonymous No.15673521]

>>15673512
>He thinks 119 is prime

[Anonymous No.15673782]

>>15673502
yes I remembered that a few minutes after I posted the question. I admit I didn't think much before posting.

[Anonymous No.15673790]

>>15673521
119 = 1* 119 = 119 * 1 therefore 119 is a prime.

[Anonymous No.15674066]

>>15673790
119 = 7*17 retard

[Anonymous No.15675377]

>>15671360
I think the search probably petered out since that video.
Who knows if he comes around here?

[Anonymous No.15675556]

>>15671257
i was just being silly and misreading something, ty though

[Anonymous No.15675560]

\[ \alpha a b c x \]

[Anonymous No.15675566]

>>15673227
P(S) = P(A)P(B) + P(A)P(!B) + P(!A)P(B) + P(!A)P(!B)

flip two coins. your potential outcomes are HH HT TH TT
the probability of heads and heads is 1 - the probability of every other outcome

[Anonymous No.15675594]

I took a quotient of the quaternions (using the commutator) and got:
{ {+1, -1} , {+i, -i} , {+j, -j} , {+k, -k} }
How do I demonstrate that this group is abelian under addition when looking at the quotient again? Do I multiply any two elements from any two cosets and then see what coset that result "lands" in? That's what chatgpt suggested, but I'm unsure if that's correct. Any anon that knows please verify.

[Anonymous No.15675851]

Does anyone know the answer to this >>15674132 ?

[Anonymous No.15676097]

An n-omino is like a tetris tile made up of n squares. For example, for n=5 they are called pentominos and there are 18 distinct such tiles.

How many distinct n-omino tiles are there for a given n?

[Anonymous No.15676171]

>>15675377
Once youre here, youre here forever. He must still come here.

[Anonymous No.15676173]

>>15676097
what the fuck dude give us the answer

[Anonymous No.15676178]

>>15665621
I think the solution is kind of a foam, bubbles following Plateau's laws

[Anonymous No.15676263]

What should a theoretical mathematician read to get into higher physics?

[Anonymous No.15676382]

>>15676173
https://oeis.org/A000988

[Anonymous No.15676429]

>>15673227
I was wondering the same question lately and it's pretty easy to figure out.

What does probability mean? The number of wanted outcomes divided by the number of all possible outcomes. That's why the probability of rolling a six with a dice is 1/6 because there's only one six and six possible outcomes overall.

Now what is the probability of rolling a six and a one by rolling the dice two times? Now the number of possible outcomes is six squared (for every outcome from one dice, there are six from the other dice. So it's six times six).

So the probability then is 1/(6*6) which is equal to (1/6)*(1/6). So notice how we just did the multiplication rule without even knowing about it. The probability of rolling a six and a one is P(six) multiplied by P(one).

[Anonymous No.15676449]

For people in research: How much progress do you make each day on average?

[Anonymous No.15676488]

>>15676382
There's no general formula except in terms of other integer sequences which themselves have their own formulas in terms of other sequences and so on. No simple formula where you could just plug in n=51 and get the number of different 51-ominoes.

[Anonymous No.15676948]

>>15673227
You can either take rule 1 as the definition of "independent events", and then combine with rule 2 to show P(B)=P(B|A) for A,B independent; or say "independent events" A and B is defined as P(B)=P(B|A) (and vice versa), and combine with rule 2 to prove rule 1.
To prove rule 2... yeah idk, not a probability person, just wanted to point out that proving one of these might be tricky but the 'independent' one is really just a subset of the second one.
Maybe something like, in a discrete case: Out of a set M of objects, where X is the set (subset of M) of 'A' objects, Y the set (subset of M) of 'B' objects, and Z the set (subset of X and Y, and thus M) of 'A and B' objects -- then P(A and B) = |Z|/|M|, P(A) = |X|/|M|, P(B) = |Y|/|M|, P(B|A) = |Z|/|X| ("given A is true, what subset is also B"), and so P(A&B) = |Z|/M| = (|Z|/|X|)*(|X|/|M|) = P(B|A)*P(A)? That mirrors my intuition, though idk the formal definition of probability used for more advanced stuff.

[Anonymous No.15676992]

>>15673227
Experiments

[Anonymous No.15676993]

>>15675594
...quaternions are abelian under *addition*, yes? They're a ring. (And so their quotient would too.)
If you mean abelian under multiplication... idk, I'm a ringslet, but if your four cosets really are +-1, +-i, +-j, +-k, can't you just say that, like, in the quaternions in general ab = -ba; and for any z in one of your cosets, -z is also in that coset; so for any two elements a,b, (using <x> to indicate 'the coset of x'), <ab> = <-ba> = <ba>?
idk what you're doing exactly but "write out every possible multiple" is basically never good advice if you have any way to avoid it... I'm guessing chatgpt was pulling from a lot of the "intro to group theory" websites out there, which do it for demonstrative purposes at first but then quickly move onto better methods later

[Anonymous No.15676999]

>>15676449
actually bumping this for anyone who sees it, I'm also interested in the answer

[Anonymous No.15677478]

Can somebody help me find a proof that steiner symmetrisation preserves compactness? Boundedness is trivial, but I don't know how to prove it is closed

[Anonymous No.15678589]

>>15675594
Yes! You've created the coset group of representatives. You have to check the group axioms on cosets - it suffices to check these on *some* representatives of the cosets, not *all* elements in the coset.

[Anonymous No.15678610]

>>15662730
Hi, /mg/. I'm approximately on the counting-apples-on-my-fingers level of mathematical education and I need your professional opinion on something. You know how you can express a phase-shifted sinusoid as the sum of sin and cos functions without the phase shift? Can I do something like that if instead of a sinusoid I have some funny periodic squiggle, something like picrel (e.g. gradient noise)? I realize there's no way I'm getting a shifted version of the exact same waveform, and that it'd probably take more than scaling and adding a shifted copy, but can I somehow get something with a similar frequency content and shifted peaks?

[Anonymous No.15678920]

>>15678610
would a simple Fourier series suffice?

[Anonymous No.15678949]

>>15678920
> a simple Fourier series
You mean working with a Fourier transform of the waveform? No. Maybe I shouldn't be talking about phase shifts. I guess I just need the cheapest, simplest way to combine the original waveform with itself to produce variants of it with similar frequency content and the peaks shifted to wherever I want along the X axis.

[Anonymous No.15678973]

>>15678949
no, I mean a Fourier series
https://en.wikipedia.org/wiki/Fourier_series

[Anonymous No.15678975]

>>15678949
No, I mean breaking down the waveform into a Fourier series and manipulating copies of those

[Anonymous No.15679003]

>>15678975
>breaking down the waveform into a Fourier series
Not an option for my case, unless it's just to precompute something that can be reused cheaply. Maybe I could use the Fourier series to find a function orthogonal to my waveform and use some linear combinations of the two like with sin and cos? (Sorry if this is nonsensical babble.)

[Anonymous No.15679037]

why is all the interesting logic stuff happening in CS departments these days? how easy is it to ingratiate my way into one with a pure maths background?

[Anonymous No.15679258]

>textbook says something is easy to verify
>it isn't

[Anonymous No.15679273]

>>15678939
math general is this true

[Anonymous No.15679307]

There exists a well-ordering of the reals.

[Anonymous No.15679473]

>>15679307
oh yeah? show us this well-order then why don't you?

[Anonymous No.15679541]

>>15676449
I finish a publishable paper every couple days, but a big theorem could take me as long as a week.

[Anonymous No.15679693]

newb here

does the fraction 70y/80y simplify to 7y/8y or just 7/8?
please explain if possible
thannks

[Anonymous No.15679849]

>>15679693
>7/8
whatever value y is can be factored out of both the numerator and the denominator. unless y=0, but in that case your entire expression is invalid anyway

[Anonymous No.15680145]

>>15679541
I hope to be in a published paper some day.
t. low iq casual

[Anonymous No.15680487]

what have been the biggest breakthroughs in maths so far this year?

[Anonymous No.15680769]

Does this prove [math](-a)(-b) = ab[/math] correctly?

[math]ab - ab = 0[/math]
[math](-a) (-b) - ab = 0[/math]

By distributive property
[math](-b + b)(-a - a) = 0(-2a) = 0[/math]

Probably messing up by stating something unproven in line two and then backing it up after.

[Anonymous No.15680789]

>>15680769
That hasn't proven anything especially your distributive property is wrong. It should be [math](-a)(b - b) = 0[/math]. All that proves is b = b and/or a = 0.

You need to start from [math](-a)(-b)[/math] and then show it is equal to [math]ab[/math].

[Anonymous No.15681045]

>>15679473
Why don't you show your le big bang?

[Anonymous No.15681269]

>>15677478
Help pls

[Anonymous No.15681448]

>>15678975
So here's what I ended up doing:
1. Compute the DFT of the sampled waveform
2. Swap the real and imaginary parts of the output
3. Negate the real parts for the first half of the resulting and the imaginary parts for the second half
4. Compute an inverse DFT from that to get a new waveform
5. Use linear combinations of the two waveforms scaled by the sin and cos of the desired phase shift
This preserves the frequency content and slides the peaks like I wanted. Of course, the higher the frequency the more the corresponding component slides, but gradient noise contains mostly low frequencies, anyway, so it works out well enough. Your suggestion put me on the right track, so thanks.

[Anonymous No.15681484]

>>15681045
>how about this other blatantly false thing?
this is the type of L i expect from axiom of chuds

[Anonymous No.15681551]

>>15681484
Why don't you show your le God then?

[Anonymous No.15681846]

Kurt Godel (1956): we can automate math proofs!

[Anonymous No.15681861]

>>15681846
>after all, one would simply have to choose the natural number n so large that when the machine does not deliver a result, it makes no sense to think more about the problem
Applied mathematics bros, we won.

[Anonymous No.15681864]

>>15679307
The axiom of determinacy is better than the axiom of choice.

[Anonymous No.15681872]

>>15681846
Huh didn't know Godel was a midwit.

[Anonymous No.15682443]

>>15680487
If Mochizuki can tidy up his proof of the ABC conjecture that'll probably be the biggest of math news of the year.
You can also look at who their handing fields medals out to, to figure out what area of math is highly praised but those are usually given to people for their contributions from several years ago.

[Anonymous No.15682883]

There was an IAS talk that suggested that everything is a function.
Is ZFC just a function?
Is the primitive notion of composition a function?

[Anonymous No.15682920]

x

[Anonymous No.15682930]

>>15681872
he was actually the first shitposter

[Anonymous No.15682946]

>>15681846
Godel's idea of taking human verification out of the process that produces mathematical literature was famously applied against Western journalism by krauts. The resulting debacle came to be known as a "non-surveyable proof," i.e. garbage produced by a charlatan who claims to have a proof but does not provide one.
https://en.wikipedia.org/wiki/Four_color_theorem
https://en.wikipedia.org/wiki/Non-surveyable_proof
it's really just about krauts abusing the Western press and getting Western idiots to irritate & annoy mathematicians.
There's also a bogus modernism involved in the process, essentially misapplying Darwinian (bottom-up) to mathematics. This is like forgetting the first half of the hermetic axiom "as above, so below; as below, so above"
A criticism of the socio-political background of the early 20th century: https://www.youtube.com/watch?v=6_9G95Ozonw "Tradition betrayed ; the false prophets of modernism by Professor Harry Oldmeadow"

[Anonymous No.15682960]

>>15681861
...obviously...
...simply...
Gödel didn't really do the work he claimed he did; he just insulted anyone intelligent enough to understand or partially understand him

[Anonymous No.15682962]

>>15682946
GPT-2-tier schizobabble.

[Anonymous No.15682967]

>Closed unit disc is compact
>X is compact if it is sequentially compact
I have a counterexample:
e^i, e^2i, e^3i, e^4i, e^5i, e^6i, e^7i...
Since pi is irrational, no subsequence of this converges to any point.

[Anonymous No.15682986]

>>15682883
This is true. Everything is just a function.
Def. A function is a rule that takes another function and outputs T or F.
Here are my axioms for it.
1. If two functions F,G have the same values for all arguments, then F=G
2. For every function F, there exists a function G such that F(G)=T and there is no function H such that F(H)=G(H)=T
3. If F is a function, then for any predicate phi there exists a function G such that G(x) = T iff F(x) and phi.
4. If F,G are functions, there exists a function H such that H(x)=T iff x = F or x=G
5. If F is a function, there exists a function G such that G(x)=T iff there exists a y such that F(Y)=T and Y(x)=T
and so on

[Anonymous No.15683004]

>>15682962
there are multiple aspects of this post that mimic Gödel's eristic [1] style of argumentation
- first, it's vague, and the informal remark can't be formalized
- second, there is no way to refine the remark to a precise statement
- third, it makes use of a put down such as "obviously" or "simply"
- fourth, it makes no attempt to find the truth, merely settling for disputing what another says
- fifth, it makes use of Freudian psychoanalytic manipulation, encouraging prejudice against the speaker without regard to what has been spoken
So, in short, you're transmitting the poor habits of a Freudian charlatan who exploited destabilization prior to World War II by publishing fraudulent mathematical literature; he was a German Nazi and German idealist to the core, and he was also an anti-authoritarian who tirelessly worked to subvert the work of anyone capable of understanding him. He spread disorder, confusion, and anti-intellectualism. Germans should apologize to the West for Gödel's idiocy, but instead they multiply it like so many spoiled brats.
[1] https://en.wikipedia.org/wiki/Eristic

[Anonymous No.15683009]

>>15675566
>>15676429
>>15676948
>>15676992

Thanks, chads. I love this board.
As I figured ,more formal aprouch would be to take
conditional probability formula P(A|B)=P(A∩B)P(B) => rule for dependent events.
P(B|A) = P(B) => rule for independent events.

[Anonymous No.15683011]

How do you prove this intuitively?

[Anonymous No.15683015]

>>15682986
what's a rule??

[Anonymous No.15683021]

>>15683011
that's the definition of center of mass
it isn't a theorem
as such, there is no proof

[Anonymous No.15683564]

>>15682967
That sequence does have convergent subsequences. Why would pi being irrational imply it doesn't? Pi is rational iff that sequence has no eventually constant subsequences, but not all convergent sequences are eventually constant.

[Anonymous No.15683909]

>>15683011
Think of it as simply an average. The amount of mass as point 1 + the amount of mass at point 2 + .... all divided by the total mass.

>>15683021
It may be a definition but it's not an arbitrary one. You can prove fields like gravity produced by a body of any shape and composition is equivalent to one made by a point-like mass located at the center of mass.

[Anonymous No.15683910]

>Impossible to attain higher than Magna Cum Laude because of faggot physics professor giving me a C in modern physics
Over or Joever?
I just want a sweet government job with a title as mathematician.

[Anonymous No.15684115]

>>15683910
Having honors like that already gives credence to
the level of work that you do--it's not a stumbling
block. And it's entirely possible to improve on
your expertise that your issue of not having S.C.L.
is well behind you. You'll get that job yet, but build
yourself to where you want to be first.

t. another graduated M.C.L. (2015)

[Anonymous No.15684432]

>>15683564
The limit of any convergent sequence is a single element of the set. No subsequence of e^i, e^2i, e^3i... converges to any single element of C.

[Anonymous No.15684437]

>>15684432
>The limit of any convergent sequence is a single element of the set.
false right out of the gate but okay

[Anonymous No.15684450]

>>15683011
It might help to study the arithmetic mean. If we have the mean M=(x1+...+xn)/n then by subtracting 0=(x1+...+xn) - Mn = (x1-M)+...+(xn-M).

So the sum of (xi-M) is zero. Thinking about it this shows that M is the value such that the sum of distances to xi<M balances with the sum of distances to xi>M.

center of mass is a weighted mean

[Anonymous No.15684677]

>>15684437
That's what I got from Tao's analysis books, did he teach me wrong?

[Anonymous No.15684681]

>>15684432
Bro, you can make a converging subsequence from your sequence for any point on the unit circle that is not an integer number of radians around the circle.
Example: e^8.5i
>e^i is pretty close
>e^2i is a bit closer
>throw away all of the terms until you get an even closer term (e^43i, I would guess)
>repeat
>your subsequence converges to e^8.5i

[Anonymous No.15684686]

>>15684677
Consider as an example the sequence 1, 1/2, 1/3, ..., wherein every element of the sequence is in the set {1/n} for positive integral n.
Does this sequence converge?
If so, does it converge to some element within the set that, by definition, contains every element of the sequence?

[Anonymous No.15684692]

How to prove this?

[Anonymous No.15684727]

>>15684692
What is the coefficient of x in (x-r1)*(x-r2)?

[Anonymous No.15684791]

>>15684727
Could you elaborate on that?

[Anonymous No.15684897]

>>15684791
No

[Anonymous No.15685552]

>>15684692
Trace is independent of choice of basis. First prove that tr(AB) = tr(BA), then it would follow that tr(C^-1AC)=tr(ACC^-1)=tr(A). Choose the eigenvector basis and your equality follows.

[Anonymous No.15685729]

Taking a history of mathematics course, and it only takes a few minutes to understand egyptian or babylonian methods. Its rudimentary, yet this is what their high priests were devoting their lives to. If aliens came to visit us, they'd surely think all of our math is trivial. Our grandchildren would grow up learning their math and make fun of us.

[Anonymous No.15685826]

How do you guys take notes from books by self studying ? Is it just writing definitions in points or something else ? And how to understand stuff like calc 2-3 by self learning ? ( the college maths is extremely proof based...something I never did in my life and was always dependant on lecturer to teach me stuff.

T. Engineering major

[Anonymous No.15686010]

How do I learn to think. I've gotten through calculus by having a good memory and doing a lot of problems whose general frameworks/approaches are replicated on the exams, but I quickly forget pretty much everything I've learnt. Even when I learn how to derive equations or demonstrate why something works, I don't really "get" how it works, and I lose the information quickly.
I guess what I'm asking is how to become the type of person who understands math and problem solving enough that I can go through a problem I've never seen before, get the right answer, and KNOW it's the right answer instead of guessing and checking.
If I can't do this, then math definitely isn't for me, so I'm desperate for answers.

[Anonymous No.15686014]

>>15686010
Kicking myself for not putting a question mark in the very first sentence. Maybe the problem is that I don't pay attention.

[Anonymous No.15686019]

https://www.youtube.com/watch?v=A2IAyXc0LuE

[Anonymous No.15686142]

>>15684686
He means a convergent sequence of members of set C converges to an element in set C. The set he refers to is not the sequence.

[Anonymous No.15686286]

>>15685826
Experience and continually learning topics. Your brain is a muscle if you don't use it, it will become weak. There are maybe a thousand types of problems in American Calculus I,II,III you can learn the general approach to all of them or learn analysis (Baby Rudin) and apply the underlying math to solve them, which the general approaches start to hint at but are not gonna have you do limits all the time.

[Anonymous No.15686311]

>>15685826
My "notes" consist of working things out until I feel like I understand what they mean, through examples or analogies or filling in details or things like that.
IMO, there's no point in sitting there mindlessly transcribing a book; if you read something and go "ok, I get it" then just move on. You can just check the book if you need a refresher, not your notes.
It's when you don't understand that you need to write out something which isn't in the book to explain in a way that you personally understand what it means

[Anonymous No.15686312]

>>15683909
>You can prove fields like gravity produced by a body of any shape and composition is equivalent to one made by a point-like mass located at the center of mass.
That's not true lol.

[Anonymous No.15686333]

>>15686142
So, he means that a convergent sequence of members of a given set, such as the set of all numbers of the form 1/n with n a positive integer, converges to an element in the set? So if 1, 1/2, 1/3, etc., converges, it converges to an element in the set in question?

[Anonymous No.15686372]

>>15686333
Not in that case, because the set of all numbers of the form 1/n with n a positive integer is not compact.

[Anonymous No.15686400]

>>15686312
What makes you think its not?

[Anonymous No.15686439]

Are you skilled at simplifying complicated expressions?

[Anonymous No.15686807]

>>15686439
Yes, of course.

The simplification is left to the reader.

[Anonymous No.15687116]

>>15686400
dialectic fraud: falsely assuming at least one party is capable of thought in order to drag the discussion into an eristic tailspin
https://en.wikipedia.org/wiki/Eristic
it's preposterous to drag metaphysical concepts like thought into a mathematical discussion; the only possible motive is disputing what another says rather than attempting to find the truth
by accusing the other side of being capable of thought, you're ignoring the truth of the matter
bringing up thought is a red herring; it misleads the discussion and distracts from the matter at hand
regardless, it's clear that thought is controversial and eristically arguing about thought is a pastime of armchair philosophers, so it's also an attempt to hijack a math conversation and inject metaphysical discussion, which should be confined to /lit/ and /his/, into /sci/

[Anonymous No.15687261]

>>15662730
guys, this should be easy enough for you.

I am about to calculate a ratio between two averages.

((x+y)/2)/((a+b+c)/3)

the problem is, x is ten times as big as y, a is 200 times smaller than b etc.
it gives a skewed picture.

I tried adding weights
((x+(y*10)) and ((a*200)+b etc.

the problem with that is that the numbers change so the weighing changes over time and a fixed weight does not reflect those changes.

how can I make the weighing more dynamic?

[Anonymous No.15687262]

>>15687261
Protip: you could probably solve your problem on your own if you had any solid idea of what you were even trying to accomplish.

[Anonymous No.15687263]

>>15687262
i know very well what i would like to achieve. i just suck at math if that is what you need to hear.
should my question be more clear?

[Anonymous No.15687266]

>>15687263
>should my question be more clear?
Yes. What are you trying to accomplish? What you did was to tell everyone how you were trying to accomplish something, not what you were trying to accomplish.

[Anonymous No.15687267]

>>15687262
i think I solved it.
basically,
I can just divide x by y to find out the ratio. and multiply y by that ratio.

it was actually pretty easy
that should make it dynamic

I just need to structure that so that it works when there are more than two numbers like in the case of a, b and c.

this is elementary school math, I am just really far behind in my life on math.

[Anonymous No.15687269]

>>15687266
its about prices.
say a costs 5 today
b costs 100 today
c costs 150 today

in a few months those prices have change in random directions.

I need to make an average of the a b and c so that neither of the three weighs more than the rest.

[Anonymous No.15687271]

>>15687267
>I can just divide x by y to find out the ratio. and multiply y by that ratio.
>divide x by y to find out the ratio. and multiply y by that ratio.
>(x/y)*y
>it was actually pretty easy
Nice science board.

[Anonymous No.15687272]

>>15687269
>I need to make an average of the a b and c
Why? That doesn't make sense.

[Anonymous No.15687279]

>>15687272
say a is 5
b is 100
c is 150

I want a number based on the three that goes up when either of the three goes up.
I want the number to go down when either of the tree goes down.
problem is, the number does not go up as much if a goes up 5% as when b goes up 5%.

is there a way to transform the three individually in some way to make the number change as much regardless if its a, b or c that changes by 5%

[Anonymous No.15687282]

>>15687279
Just calculate the growth percentage for each one and average those? I just can't comprehend why you'd want that. If a costs 5 cents and b costs $500, do you really want one to affect your metric as much as the other?

[Anonymous No.15687284]

>>15687282
yes I want it to affect as much.
its deliberate
i only care about percentage change not absolute change.

[Anonymous No.15687287]

>>15687284
That's retarded, but there, I gave you the solution.

[Anonymous No.15687288]

>>15687282
a is not fixed, its a time series which changes.
it changes over time.
like stock prices.

[Anonymous No.15687289]

>>15687288
And? Do you understand what "growth percentage" means? Jesus, I hope you bet all your pocket money on this and your mom refuses to give you more.

[Anonymous No.15687290]

>>15687287
dont worry, its not retarded.
you just dont see why.

its about allocation. there is as much money in a as there is in b.
say $100 in a and $100 in b
number of shares in position of stock A is $100/a.
same for b,
$100/b

I am not sure if I understand by "just calculate growth percentage".
its not explicit enough for my brain.

anyway, thats alot for taking the time

[Anonymous No.15687291]

>>15687289
i'm probably older than you, i am just a mathlet

[Anonymous No.15687292]

>>15687290
((a1/a0)+(b1/b0)+(c1/c0))/3*100

[Anonymous No.15687293]

>>15685826
whqt do you want the number to do if
A goes up 5%
B goes up 11%
C stays
should the number go up 5%, 11%, 16%?

[Anonymous No.15687297]

>>15687292
>>15687293

ill be back in 10 minutes or so.

[Anonymous No.15687362]

>>15687292
not sure if I understand the 1 and 0 part.

>>15687293
in that scenario, the number would definitely not go up by 16. neither by 11. more like 5 or a little bit more like 5.1% or 5.2%
thats just how I see it instinctively just by looking.

[Anonymous No.15687366]

>>15687292
i think I get it, you mean a1 is the previous a? and a0 is the current a?

[Anonymous No.15687368]

>>15687362
>not sure if I understand the 1 and 0 part.
Jesus. You're hopeless. Unironically find something else to do with your life.

[Anonymous No.15687371]

>>15687366
The other way around. a0 doesn't even have to be the previous value. It can be some windowed running average or any other baseline value.

[Anonymous No.15687421]

>>15687368
>>15687371
i dont even know if its the same person or not.
what a snobby board.

I am already running a strategy.
it is a spread strategy.
you take good assets, (stocks, currencies, crypto) you bet on their rise.
you take bad assets, and bet on their fall.
its more about fundamental analysis than it is about technical mathematical analysis.

I just wanted to make my chart more precise. that is all.
here is the faulty formula:
example 1
(long1+long2)/2 / (short1+short2+short3)/3

it is way more precise if I have the same number of assets on both sides because then I can use a simple ratio calculation instead
example 2:
(long1/short1)/(short2/long2)

this ratio will rise if long1 and long2 rise more than short1 and short2.

the point is to stay hedged in case of general market downturn.

now, if I instead have 3 assets on the short side. like in example 1 it changes the calculation.
obviously, the allocation would change.
long1 and long2 have 1/4 of the money each. meanwhile short1, short2 and short3 would have 1/6 each.

[Anonymous No.15687426]

problem is, in example 1 in post just above i would need weighing or else I get skewed charts.

now, I can weigh them but only based on the recent prices which is good enough for whats happening now. but obviously will not take into account the past, nor the future.

[Anonymous No.15687428]

honestly, its not a big deal.
if I have to deal with superiority complex guys, its not worth the trouble. I already have a workaround which kind of works.

thanks.

[Anonymous No.15687442]

>>15687421
obviously, i dont mix currencies and crypto. its by asset class.

[Anonymous No.15687461]

its like as if I needed a pc.
I go to a computer shot.
now, imagine I have no idea how a pc works. but I need to do this and this and this.

then the guy at the counter starts talking to me about l3 cache, about ram speed.
I say:
look, I dont know what youre talking about. I just need my software to run.
then the guy says:
you might want to stop what you are doing because you obviously dont know how computers work.

its the first time coming here and I already have this impression.
but whatever. its just funny. have fun circlejerking math

[Anonymous No.15687520]

>>15687269
Geometric mean

[Anonymous No.15687530]

>>15687269
Build a portfolio with equal amounts of money in each item at the start

[Anonymous No.15687572]

>>15687530
that is not possible if I have three assets that are supposed to fall and only two that are supposed to rise.

it needs to be net 0 exposure.
say its $1000 total
500 goes to the longs and 500 goes to the shorts.
in the shorts i happen to have 3 things to short.
in the longs there are 2.
shorts = 500/3 per asset
longs = 500/2 per asset

[Anonymous No.15687633]

>>15687520
this is it!
thank you!

[Anonymous No.15687656]

>>15687520
now I can do the geometric mean of one set of longs (arbitrary amount of longs) divided by an arbitrary amount of shorts and get a ratio between the two sets.
this is perfect.

[Anonymous No.15687716]

>>15687656
i meant to say one geometric mean of x number of numbers divided by a geometric mean of y number of numbers.

[Anonymous No.15687881]

>>15687362
To every anon who mocked financebro, just know that by pure intuition he computed the geometric mean of 1, 1.05 and 1.11 almost to the 2nd decimal place (correct value 1.0524...) without even knowing what he was computing.
Bow to your natural superior, intuitionlets.

[Anonymous No.15687893]

Is there established notation for the left side of the equation? I just used a stand-in symbol [math]\otimes [/math] to make it clear what I'm on about.
[math]A\otimes B:=\left( A\subset B \right)\leftrightarrow \neg \left( B\subset A \right)[/math]

[Anonymous No.15687915]

>>15687893
Oh and inside the brackets are strict subsets not truth functions just to make it clear since some people use the subset symbol for truth functions

[Anonymous No.15687972]

>>15687881
the retard doesn't even know what a geometric mean is or what he's trying to do. here's the extent of his "intuition":

>>15687267
>I can just divide x by y to find out the ratio. and multiply y by that ratio.
>it was actually pretty easy

[Anonymous No.15688116]

>>15667481
Why are we interested in those numbers?

[Anonymous No.15688124]

>>15688116
Like 90% of number theory, there aren't really any practical applications or anything. It's just neat.

[Anonymous No.15688134]

>>15688124
Is there a way to enumerate every "neat" property in number theory? Never mind finding the numbers that have those properties, just finding the properties.

[Anonymous No.15688191]

>>15688124
It is strange that a number can have different properties. They all come from the same building block 1

[Anonymous No.15688379]

What is the condition that three sides can form a triangle?

[Anonymous No.15688399]

>>15662730
What's a good app for improving the speed/accuracy of your mental math? I keep making silly calculation errors that I don't catch without wasting so much time.

[Anonymous No.15688546]

>>15688379
The triangle inequality: the sum of two sides must be greater than the third side

[Anonymous No.15688552]

>>15688546
Why?

[Anonymous No.15688555]

What should I choose Ergodic theory, or Percolation theory? Which has purer math?

[Anonymous No.15688573]

>>15688552
otherwise it doesn't close, or just makes a line

[Anonymous No.15688667]

>>15686400
Common sense and grade school math. You must be severely mentally handicapped.

>>You can prove fields like gravity produced by a body of any shape and composition is equivalent to one made by a point-like mass located at the center of mass.
Go on, show us your proof. I love a good laugh.

[Anonymous No.15688728]

How many hours outside of class per day do you spend on your math degree.
3 hours a day even on weekends with 4 courses a sem seems to be it
Completely doable too.

[Anonymous No.15688740]

For a prime [math]p[\math], find the cardinality of [math]GL_n(\mahtbb{F}_p)[\math].

I've already solved this by considering the combinations of linearly independent columns, but I'm looking for alternate solutions.

[Anonymous No.15688757]

>>15688740
ah fucking backslashes !!

For a prime [math]p[/math], find the cardinality of [math]GL_n(\mathbb{F}_p)[/math].

I've already solved this by considering the combinations of linearly independent columns, but I'm looking for alternate solutions.

[Anonymous No.15688764]

>>15688573
But what's the proof?

[Anonymous No.15688779]

>>15688764
uh... it is known. (don't ask me, i'm a tourist ITT). off the top of my head, if you have a triangle and you project the sides onto the base, the sum of the projections would be obviously equal to the length of the base, so two sides equal to the third is the lower bound (that gives a degenerate triangle with three collinear vertices).

[Anonymous No.15688782]

>>15688764
easiest done geometrically.

Construct an arbitary triangle ABC.
Draw a circle of radius AC around point A, and one of radius BC around point B. Denote the length of the line AB as |AB| and likewise.
Call the point at which the former intersects the line AB D, and the point at which the latter intersects the line AB E.
Then it follows that |BE|=|BC|, and |AD|=|AC| (since they lie on circles of those radii).
But |AB|=|AD|+|DE|+|BE|. Since distance is strictly nonnegative, the triangle inequality follows, with equality iff DE=0 (i.e. if ABC are colinear)

[Anonymous No.15688817]

>>15688782
hmm. plot twist: the circle with radius AC does not intersect AB. how do i into your proof?

[Anonymous No.15688820]

>>15688817
Post a diagram of your situation.

[Anonymous No.15688829]

>>15688820
i think i have a case of bad triangle

[Anonymous No.15688841]

>>15688782
That just shows every triangle satisfies the triangle inequality, not that any triplet of line satisfying triangle inequality can be made into a triangle.

[Anonymous No.15688880]

>>15688841
I mean, at that point I don't think there could be said to actually be a proof outside of "just give it a shot". Certainly none I've ever heard of.
>>15688829
right, right. Well, in this case, you've successfully proven that AB is not the longest side of the triangle even on its own, so it is obviously not longer than the sum of the other two lengths. Which is a start.
To show that |BC| is less than |AC|+|AB|, do the same method, but with a circle of radius BA centred at B and a circle of radius CA centred at C

[Anonymous No.15688897]

>>15688880
i don't understand. can you just give a proof that works no matter how i label the vertices?

[Anonymous No.15688919]

>>15688897
The triangle inequality says that the length of one side of a triangle cannot be greater than the sum of the lengths of the other two sides:
[math]|AB| + |AC| \geq |BC|[/math]
[math]|AB| + |BC| \geq |AC|[/math]
[math]|AC| + |BC| \geq |AB|[/math]

You only need to demonstrate this is true for the longest side(s).
If the side you're looking at individually isn't the longest side, then the inequality holds even when you consider the longest side on its own on the left, without needing to think about the third side at all.

So to show it for the longest side, you use the method I mentioned with your circles constructed around the endpoints of the longest side and their radii enough to reach the vertex opposite the longest side. If you have multiple sides of equal length, you apply that method multiple times with each one.

[Anonymous No.15688935]

>>15688919
now you get a pass

[Anonymous No.15689657]

>>15688667
They probably mean center of gravity, not center of mass. However in many cases they are identical.

[Anonymous No.15690814]

Are there logic books that deal with substructural logics and discuss structural rules more in-depth?

[Anonymous No.15691417]

>>15689657
>They probably mean center of gravity
No such thing. Doesn't exist.
> However in many cases they are identical.
Absolutely wrong.
/mg/ has really become retarded. I suggest you both leave before you embarrass yourself even more. This isn't even complicated, this is grade school math.

[Anonymous No.15691491]

[Anonymous No.15691545]

>>15691491
lol

[Anonymous No.15691684]

>>15691417
https://en.wikipedia.org/wiki/Center_of_mass#Center_of_gravity

[Anonymous No.15691794]

HyperoperationGODS, when are we revolutionizing mathematics?

[Anonymous No.15691818]

>>15691684
>You can prove fields like gravity produced by a body of any shape and composition is equivalent to one made by a point-like mass located at
Can you read?

[Anonymous No.15691896]

>>15691818
Can you? Even Newton's Law works that way.

[Anonymous No.15691915]

>>15691896
Don't forget to breathe.

[Anonymous No.15692251]

Wouldn't a much simpler formula be just

>pi = 4*arctan(1)

[Anonymous No.15692565]

>>15692251
the arctan series at x=1 does not converge quickly

[Anonymous No.15693301]

>>15684432
>import cmath
>def convergent_sequence(N, L):
> indices = range(1,N)
> values = [abs(L-cmath.exp(k*1j)) for k in indices]
> # fuck
> output = []
> for j in indices:
> if len(output) == 0 or values[j-1] < output[-1][1]:
> output.append( (j, values[j-1]) )
> return output
>
>print(convergent_sequence(100000, 1))

>[(1, 0.9588510772084059), (6, 0.2822400161197344), (19, 0.15030224092361863), (25, 0.13264379470240137), (44, 0.017702618580807752), (333, 0.008821251916950467), (710, 6.0288706718976894e-05), (103993, 1.9129335779298754e-05), (312689, 2.900699389335162e-06)]

The subsequence with indices beginning with [1,6,19,25,44,333,710,...] approaches 1, rather quickly

[Anonymous No.15693674]

I want to create a sheet of exercises on LATEX. How do I manage to number the exercises automatically (Exercise 1, Exercise 2, ...) ?

[Anonymous No.15693751]

>>15693674
look up how to typeset theorems in latex (the same packages and commands are also used for exercises, lemmas, definitions, etc)

[Anonymous No.15693889]

>>15666489
Gentlemen
Before this thread dies, can you please answer it?!

[Anonymous No.15693919]

i want to get into mathematics, im a beginner with some experience in calculus etc, what books should i read

[Anonymous No.15693953]

>>15693919
Measure, integration and real analysis by axler

[Anonymous No.15694019]

Bros, I derived a cool solution to cubic equations.
[math]Let\ p\ be\ a\ cubic\ polynomial.\\
Let\ X,Y\ be\ the\ roots\ of\ 3pp''-2p'^2.\\
The\ roots\ of\ p\ are:\ {Y-X(p(Y)/p(X))^{1/3} \over 1 - (p(Y)/p(X))^{1/3}}.[/math]

I'm still trying to work out what happens for the pathological cases of 3pp''-2p'^2.
It is at most quadratic (even though it looks quartic).
Things work as desired with 2 distinct roots.
For a double root, idk.
If it is linear then let the other root be infinity.
For 3pp''-2p'^2 = const, idk.

I like this solution because it uses the polynomial, p, itself with no reference to coefficients.

[Anonymous No.15694067]

>>15693919
Rudin.

[Anonymous No.15694316]

>>15694019
3pp''-2p'^2 has a double root when p has a double root (it is the same double root)
3pp''-2p'^2 is linear if p = (x+a)^3 + c
3pp''-2p'^2 is constant if p = (x+a)^3

All of these can be resolved by perturbing p to p+εx, solving the quadratic for the distinct roots X(ε), Y(ε), plugging things in and taking the limit ε 0.

[Anonymous No.15694357]

Retard here
I understand by now what a derivative is, but I still don't really get what a differential is, how they're different and what I need it for, how it really fits into the whole picture and what it represents on a graph
The related terms like differentiable, differentiate just confuse me even more since I can't grasp the difference between a differential and a derivate
I've solved problems without any real understanding of what it is

[Anonymous No.15694377]

>>15694357
Write out the definitions you were given of both notions.

[Anonymous No.15694384]

bump

[Anonymous No.15694470]

>>15694384
There was absolutely no need for the bump

[Anonymous No.15695587]

>>15666489
If [math] z=x^{2/3}+y^{2/3} [/math], then...
[math] z_x={2 \over 3x^{1/3}} [/math] and
[math] z_y={2 \over 3y^{1/3}} [/math].

Since both partials are undefined where x,y=0,
The x-axis OR the y-axis are the critical points.
The second derivative discriminant won't help
out much in terms of undefined values, but one
critical point (0,0) actually gives the minimum
when you evaluate z--any other critical point
gives values of z>0.

[Anonymous No.15695668]

>>15695587
Thank you

[Anonymous No.15696793]

>>15695668
>>15695587
Of course.

[Anonymous No.15697123]

any news?

[Anonymous No.15697237]

>>15697123
Some current news:

>new method to predict the next school shooting
>9th Dedekind number just dropped
>Maynard takes the Fields, number theory's new kid on the block
>aperiodic monotiles, enough said--get yours today
>slow rotating black holes proven (mathematically) stable
>media founder's bounty on abc conjecture; up to $100,000/yr alive, $1 mil. dead

...more to come at 11 PM

[Anonymous No.15697850]

Help a turbo brainlet out. This should be easy, I can't wrap my head around it.
My coworkers and I all earn the same ($22 an hour) and work a fixed schedule, 40 hours a week. We're supposed to stick to a certain time for break (paid and lunch (unpaid) and outside of those hours we are "available". If I'm available all the time that I should be, I feel like I'm really earning my $22 an hour. But if someone else is only available for 50% of the day - maybe he's on extended breaks or fucking off somewhere - he's committing time theft. So how much is he REALLY getting per hour of being available? So how can I formulate this?
In my mind, there are two options:
pay period (80 hours) × wage ($22 an hour) = 1760 before taxes.
A) if he's available only 50% of the time, it's 1760 / 50 to get a
"true wage" of $35.2 an hour.
B) work week (80) x available time 50% = 40. 1760/40 = $44
an hour

I’m planning to quit next week and just want to call out some people

[Anonymous No.15698586]

Is there a way to make a bijection between F(a,b) and N where a,b are prime and F(a,b) is not equal to F(b,a) unless a=b?

[Anonymous No.15698656]

>>15697850
>My coworkers and I all earn the same ($22 an hour)
I'm sorry.

[Anonymous No.15698687]

>>15698586
What's F(a,b)?

[Anonymous No.15698970]

>>15697850
A makes no sense. You can't just drop the % like that. B is correct.

[Anonymous No.15698973]

become an independent researcher

[Anonymous No.15699156]

new >>15699155

[Anonymous No.15699257]

>>15698586
F is a function and N is a set.
Do you want the domain of F or the range of F?