/mg/ - Mathematics General

[Anonymous No.15466521]

Talk Mathematics!

Previous thread: >>15433578

[Cult of Passion No.15466577]

>>15466521
I'm gunna challenge him to a duel in Spain. Winner takes all.

[Anonymous No.15466580]

Consider an irreducible polynomial [math] f\in K [/math] in an integral domain [math] K [/math] that is not a field, suppose that it produces finitely many prime elements [math] Q [/math] and hence construct the ring [math] K'=K[1/p] [/math] of all integers multiplied by integer powers of p for all [math] p\in P=\Pp\setminus Q [/math] prime elements not produced by [math] f [/math]

One can conclude shortly that [math] \Pi_QK'+P\subseteq P [/math] where [math] \Pi_Q=\prod_{q\in Q}{q} [/math]

That's a contradiction but there's no known way to show that it's not true, an answer would show that [math] f [/math] must then produce infinitely many primes

Consider now Dirichlet's theorem.
It turns out that it's very easy to prove that once one shows that for at least one [math] q\in\mathbb{Z}_{p} [/math] for which [math] f(n)=pn+q [/math] produces finitely many prime numbers.

[Anonymous No.15466582]

>>15466577
Shut the fuck up worthless schizophrenic piece of shit you're thrashing up the thread

[Cult of Passion No.15466600]

>>15466582
>fecal-foaming out the mouth
Shut up and calculate, mon'keigh. You spent years learning how to do what a calculator does.

Fucking worthless.

Meanwhile...Im going to go hang out with him for a few days and present my research to him...or fist fight him, his choice.

[Cult of Passion No.15466605]

...that was my second and third posts in /mg/. With such a warm welcoming I think I should make this my new home to endlessly lecture you pissants on Number Theory until numbers lose all meaning together.

What is "1", anyway? To learn this we must go back in time...to a warm summer evening in ancient Greece...

[Anonymous No.15466611]

>>15466582
There's a sub>leddit for people fighting things. It's about people picking fights where the only outcome is looking like the loser.

Why are you fighting a schizophrenic?
That's like punching a wall. You're the dumb one for making the category error, the wall wins every time.

[Anonymous No.15466632]

>the union of countably infinite amount of countable infinite sets is countable
>an uncountable set minus countably infinite amount of countable infinite sets is uncountable
this is the biggest bullshit i have heard.

we can create a countable set for each decimal point by starting from the point and adding one, e.g. {0.1,0.2,0.3,...} and {0.01,0.02,...}, etc. this definition means explicit bijection to naturals for each set and the number of decimal points which are the starting points for those sets is countable.
the set of reals minus the union of all such sets is still uncountable infinite, wtf does the set of reals even have left?

[Anonymous No.15466647]

>>15466632
> wtf does the set of reals even have left?
? Every rational number w/ reduced denominator not of the form 2^x or 5^x (also every irrational but that hardly matters).

[Anonymous No.15466687]

>>15466647
>Every rational number w/ reduced denominator not of the form 2^x or 5^x
how? now that i think of it the sets resulting from multiplying, adding, subtracting and dividing each element from any two sets of these sets is also countable. I don't see what kind of number wouldn't be included as you can keep adding (countable) infinitely many and increasingly smaller numbers to reach an irrational just like an infinite sum.
the diagonal proof makes sense but this difference between uncountable set and union of countably infinite amount of countably infinite sets being uncountable makes zero sense

[Anonymous No.15466700]

>>15466687
But what's the index of 1/3 in our list?

[Anonymous No.15466720]

>>15466700
It's somewhere there because we can sum 0.3, 0.03, 0.003, etc to infinity as all resulting sets still have an explicit bijection to naturals on their own and this their union is countable.
anyway, fine, we add the set of rationals to the union of our countably infinite many countably infinite sets and the countably many infinite sets resulting from addition,subtraction, division and multiplication of any two elements of those sets or the resulting sets. what's missing from this union?

[Anonymous No.15466728]

>>15466632
You are not including irrational numbers in there so you still have an uncountable set of numbers after substracting that from R.

[Anonymous No.15466732]

>>15466720
>It's somewhere there because we can sum 0.3, 0.03, 0.003, etc to infinity as all resulting sets still have an explicit bijection to naturals on their own and this their union is countable.
what bijection between [collection of all infinite sums from my sets] and [union of my sets] are you using here?

[Anonymous No.15466739]

>>15466720
Countable means there's an index. So if you count integers you can say 0 has index 1, 1 has index 2, -1 has index 3, and so on. You can ask what index is -5 and answer 11. What index can we give to 1/3?

[Anonymous No.15466836]

>>15466632
>the union of countably infinite amount of countable infinite sets is countable
This is not provable in ZF.
It doesn't even hold if the sets are finite. ZF doesn't prove each union of a countable set of two-element sets to be countable again.
There's models which break these. Heck, there's even models where the uncountable set R equals the countable union of countable sets.

[Anonymous No.15466862]

>>15466732
>[collection of all infinite sums from my sets]
rationals, naturals, a set for each decimal point where each set contains that element and all elements that result from adding one to some decimal point {1.1,1.2,1.3},{0.1,0.2,0.3}, basically any set that can be obtained by starting from one number then adding 1 at some decimal point which means explicit bijection to naturals.
then it obviously follows that if create a new set by adding,subtracting,dividing multiplying elements from different sets. the set you get is also countable.
>[union of my sets]
the unions of all those sets, which is countable.

basically, why isn't it possible to create R from disjunct countably infinite many countable infinite subsets of R or specifically just the irrationals. seems even more unlikely when you consider the fact that you can just bundle obviously countable amount of sets in a set then union with another obviously countable set of countable sets to get and show that a "less obviously" collection of sets is countable

>>15466739
countable just means bijection to naturals. based on the result that the union of countably many countable sets is also countable we can forget about finding an actual bijection from the union and focus on bijection for each of these sets

>>15466836
>This is not provable in ZF.
i saw this result in multiple books and in many places online but none mention ZF. could just be another inconsistency in naive set theory or counterintuitive result of AC
>There's models which break these. Heck, there's even models where the uncountable set R equals the countable union of countable sets.
elaborate

[Anonymous No.15466885]

>>15466862
>then it obviously follows that if create a new set by adding,subtracting,dividing multiplying elements from different sets. the set you get is also countable.
finitely many elements yes, infinitely elements no

[Anonymous No.15466886]

>>15466862
>could just be another inconsistency in naive set theory or counterintuitive result of AC
Countable choice implies countable unions of countable sets are countable again - not sure if you call this counterintuitive or the possibility that it fails. Neither option should be counterintuitive, really.

>elaborate
They are not very simple models, since the simple model happen to validate a lot of famous independent propositions in a positive manner.

I haven't followed you guy's discussion about your decimal expansion construction, but from a cursory glance it would seem any numbers among those that you union together has only finitely many digits - as opposed to most reals.

[Anonymous No.15466897]

>>15466862
> countable just means bijection to naturals
Which means there's an index. Bijection means both ways. Anything bijected to N is indexed by N, by definition. What index do we give to 1/3?

[Anonymous No.15466957]

>>15466885
[math]|\{x*n|n,x\in\mathbb{N}\}|=|\{x + n|n,x\in\mathbb{N}\}|=|\{x -n|n,x\in\mathbb{N}\} | = |\{x/n|x\in\mathbb{N},n\in\mathbb{N}\backslash \{0\}\},etc |[/math] are all countable and you can replace N with any countable infinite set.
here is another way to look it. we can easily make a countable set of irrationals by taking an irrational and then having that element in the set and all elemnts produced by any succession function that corresponds to succession in naturals, obvious example is just +1,+0.1,+0.001, etc. a such set can be {pi,pi+.1,pi+.2,...} then we can union those sets and union sets of those sets to end up with countably many of those sets where it would be hard to prove. then we can pick elements from any of those sets do operations on them and create new sets with them, all countable.
at this point we have irrationals with infinite digits and ways to manipulate them. intuitively you would think you can get all irrationals this way

[Anonymous No.15467007]

>>15466957
That's not how bijection works. >>15466897

[Anonymous No.15467016]

>>15466957
Note that Q is countable because it can be indexed. One way is
>1. 0/1
>2. 1/1
>3. 1/2
>4. 2/1
...
Any index in N gives an exact element of Q and every element of Q gives an exact index in N.

[Anonymous No.15467027]

>open up /sci/
>people arguing about countable vs uncountable infinities for the nth time

[Anonymous No.15467028]

>>15467027
>>>/b/

[Anonymous No.15467040]

>>15467027
General math questions are either trivially boring or too much effort just for posting an answer anonymously.
Hence the. more philosophical and debatable, and novel aspects of math are being talked about.
I don't think that's very much of a surprise - it's a natural situation given the medium.

[Anonymous No.15467050]

>>15466600
>present my research
>>15466605
σῠ́ μωρός ἐστίν

[Anonymous No.15467058]

I'm still curious about >>15464917 which no one answered in the previous thread. Maybe some of you mad men don't even retain your work, merely resorting to brushing it away from a black/white board.

[Anonymous No.15467060]

>>15467058
I use xournal.

[Anonymous No.15467084]

>>15467058
It's a horrible mess. .nb is of course the most convenient for storing random data and charts you think might be usef ul later. It's also the worst possible format for finding it or reading it later. Not just because spotlight doesn't penetrate the format, so you can't even narrow down what file it's in, but even if you find the right file, you'd still need a 50 foot screen to analyze any of it side by side. Anything you can write on paper is so easy and immediate in comparison. But you can't write everything on paper. So it's a mess either way.

[Anonymous No.15467118]

>>15467084
I use a separate .nb file for each textbook/problem book. Then organize the content into chapters. I make heavy use of a custom style sheet to get the look I want (used across all notebooks). Of course you can just collapse sections that you're not working on (open/close cell group). It's not only more convenient than LaTex since it avoids the write/render step, but I can of course call on mathematica to check or plot something.

[Anonymous No.15467131]

I need resources for learning algebraic geometry and geometric algebra

[Anonymous No.15467159]

>>15467118
Oh, got it, sorry, I understand how that fits the task well. The horrible mess is only if data and charts aren't tied to a specific problem but you want to pull up some random calculations you did months ago. Even if you remember the exact syntax you wrote to do the calculation, you can't find what .nb it's in because spotlight doesn't work on .nb format (it did 4-5 years ago). More of a mac os problem, I suppose.

[Anonymous No.15467171]

>>15467159
Ah right, I have a folder called "experiments" for those one-off types of things, it's somewhat disorganized, and windows indexer doesn't read the nb either (Still use Mac, but gradually transitioning everything to Windows).

[Anonymous No.15467185]

>>15467084
>you can't write everything on paper.
yes you can

[Anonymous No.15467214]

>>15467185
The master race solution is to do the work on a white board (you do have one in your study/room, right) and then type it up.

>>15467060
Looks good for tablets.

[Anonymous No.15467215]

>>15467185
Disproven by James Joyce Sterling in 1722.

[Anonymous No.15467318]

>>15467058
General math notes? Put them on paper or Obsidian. Solving math starts on paper, might move to mathematica. Interesting stuff is going to be transferred back to notes on paper or into obsidian, maybe linking the nb. I don't like mathematica nbs as a medium to store general info since it's pain to search and markdown+latex is way easier to quickly write and format my thoughts.

[Anonymous No.15467324]

>>15467318
>Obsidian
Looks very interesting. I often build graphs to organize thoughts and Ideas, naturally I use Mathematica for this, but this seems worth checking out.

[Anonymous No.15467330]

>>15467324
I don't use the graphing and backlinks a ton, but it's helpful when something needs info from diverse places. Can also embed or link to files on your system, meaning you can make a little wiki-like experience for yourself, if you're into that. I mostly use it in a more straight forward hierarchy of folders manner, based on subject or project, but will link things around when it makes sense. Really it also just has decent latex support (can even define new commands in the yaml front matter!), and stuff like apple notes absolutely does not.

[Anonymous No.15467369]

>>15467330
The one thing it will of course lack is the ability to run computations on the graph. Say if I had a list of dependencies of topics to research, I would then write some code to produce an optimal reading order.

I've heard of some people using some combination of VSCode, Jupyter notebooks, and LaTex and Markedown, but I haven't looked into it. Usually the result doesn't sound like any improvement of using Mathematica which is of course "Batteries included"

[Anonymous No.15467624]

I'll repost this one because I think it's a cool problem

[Cult of Passion No.15467675]

>>15467050
>present my research
You should do novel research instead of turning monkey wheels made by other people. Academics are rife with psuedo-novel research thats literally just busy work for a paycheck.

What do you work in? Homework? No that doesnt count...post thesis title.

>σῠ́ μωρός ἐστίν
I bet I could physicall beat the shit out of you while I talk about how your field of research is connected to other fields of study, like Biology or Physics or whatever.

Post it, lets duel, or go back to labor.

[mathfaggot !!oBjNwnLZnN1 No.15467676]

>>15466521
an extremely easy question. the first complete solution gets a CLAP

[Anonymous No.15467708]

Solve carefully!
100 - 95 * 0.8 = ?

You probably won't believe but the answer is ...4!

[Anonymous No.15467769]

>>15467708
That's a fact...

[Cult of Passion No.15467776]

>>15467769
Then why did I get -24?
Order of operations is arbitrary and arbitrary is illogic.

[Anonymous No.15467785]

>>15467776
how did you minus 24 ?

[Cult of Passion No.15467787]

>>15467785

[Anonymous No.15467818]

>>15467787
Doesn't work like that m8.

[Anonymous No.15467881]

>>15467058
Not sure about writing math on your computer for assignments.
Whenever I tried a solution like Latex, the optimum (sic) result was me spending a significant and I mean significant amount of time on syntax and formatting alone. Up to 20%. Even if with some autocomplete (I'm sure there are some text editors with that), it adds up if every symbol has to be "addressed" instead of it just flowing out of your pen concurrently with your thoughts.

Above calculus does not include everything related to Latex besides writing the actual files.

I have ADHD and I thus waste a significant time on formatting my pen and paper work -- but it's still maybe 3~5% of the total time investment.
Differently colored highlights, underlines, words, etc. are an ADHD buster. Such would however quickly leave the usual math PDF style and wander into the territory of the PDF becoming "gay".

Pen and paper writing is also meditative, and for me strengthens retention by at least a factor of 5. The flipside is shittier handling/discoverability of your own notes, but this doesn't add enough negative credit.

[Anonymous No.15467898]

>>15467881
>I have ADHD and I thus waste a significant time on formatting my pen and paper work -- but it's still maybe 3~5% of the total time investment.
>Differently colored highlights, underlines, words, etc. are an ADHD buster. Such would however quickly leave the usual math PDF style and wander into the territory of the PDF becoming "gay".
>Pen and paper writing is also meditative, and for me strengthens retention by at least a factor of 5. The flipside is shittier handling/discoverability of your own notes, but this doesn't add enough negative credit.
Nice life story but keep your imaginary mental conditions to yourself, we are not interested.

[Anonymous No.15467901]

>>15467898
And I am not interested in your comment telling me you are not interested. What did you add? Kill yourself.

[Anonymous No.15467905]

>>15467901
Why should I. I don't go on 4chan posting fake nonsense.

[Cult of Passion No.15467908]

>>15467818
>Order of operations is arbitrary and arbitrary is illogic
Arbitrary mathematics is the definition of mental masturbation.

You dont work at all, you labor in the shadows of your master.

[Anonymous No.15467911]

>>15467908
Yeah, you know all about masturbation.

[Anonymous No.15467936]

>>15467911
>Yeah, you know all about masturbation.

Uh, yes?…

[Anonymous No.15468194]

This schizo is still less annoying than anime tranny.

nb

[Anonymous No.15468487]

>>15468194
If you are talking about the one that asked problems hell no. I loved it.

Any troon over this schizo DESU. So fucking annoying and shits up every thread he enters

[Anonymous No.15468601]

I read the post that got Shulman canceled and is utterly ridiculous. The guy didn't said anything that was out of line or controversial so I don't see why would his work had to suffer as a result. I hope this doesn't becomes the norm and remains as an isolated case that only happened because outsiders took it as a personal attack.

[Anonymous No.15468621]

what is a modern treatment of logic that is more rigorous than principia mathematica

[Anonymous No.15468629]

>>15467908
>Arbitrary mathematics is the definition of mental masturbation.
No it isn't

[Anonymous No.15468666]

>>15467881
Based and redpilled
>>15467898
A nigger

[Anonymous No.15468667]

Solve carefully!
1020 - 1000 * 0.3 = ?

You probably won't believe but the answer is ...6!

[Anonymous No.15468668]

is death merely a portal to eve online?

[Cult of Passion No.15468673]

>>15468629
Its the same as creating a program that makes mazes and then soving them.

[Anonymous No.15469017]

>Learning about matrices
Chatgpt is helping but it can't give me the kind of answers I want.
Dot product for example. It made clear that it measures the alignment of two vectors. Not totally sure about the usefulness of its magnitude.

Anyway it couldn't give a more meaningful definition. Took a while but finally got it.

Let the vector A = 1i+2j, and B = 3i+4j
These are 2x1 matrices, but in order to compute their product, one of them must become a 1x2 matrix.
(1 2) * (3)
(4)
This transformation of A to A' collapses a 2D graph into a single line, and the basis vectors of A move accordingly to fit in this line. These also are the projections in x of vectors A and B.
So after A becomes A', the dot product is 3 times where i has landed, + 4 times where j has landed. 1*3 + 2*4 = 11.

I kinda need a gateway book or something.

[Anonymous No.15469050]

>>15469017
Literally any book on linear algebra will do.
I was hopeful for chatGPT, but it's really problematic with math at this point. For example, when. asking for a reference it will dream up some book title, claim it has an Id number of another book, and then no matter how I ask it will insist this non-existing book exists. I'd refrain from believing it in terms of math, it's really stubborn with false claims

[Anonymous No.15469054]

>>15468621
Agda or Coq implementations of logic are more formal/rigorous than a textbook from 120 years ago.
If you just want a modern logic textbook, I like
van Dalen's Logic and structure

[Anonymous No.15469061]

I like math, but I'm having a hard time

[Anonymous No.15469087]

>>15466580
How did you make your math red?

[Anonymous No.15469117]

anyone know of a note taking software (like obsidian) that supports full latex (not mathjax/katex) by using the locally installed latex distro to convert things into svg and include them? I have no idea why this practice isn't more common, Anki does this and it works wonderfully. Meanwhile I can't even type \bigsqcap in anything mathjax related and let's not get started on tikz

[Anonymous No.15469211]

is actor and notorious tough guy Jon Bernthal familiar with the Hasse principle?

[Anonymous No.15469224]

>>15469017
>I kinda need a gateway book or something.
depends on what you want. if you're an engitard or physishit (judging by your silly high-school-level notation for vectors) that's not specialising in QM or something, then Strang's standard LA book should be alright for you
if you want to learn more serious linear algebra, but a little light and very matrix-oriented in its approach, then try "Linear Algebra Done Wrong" (avoid LA Done Right at all costs)
if you want proper, mathematical linear algebra, then go for
1) Friedberg Insel Spence for something lighter
2) Hoffman & Kunze for the real shit

[Anonymous No.15469228]

>>15469211
can anyone photoshop "burn" into "solve"?

[Anonymous No.15469254]

>>15469224
>if you're an engitard or physishit
Neither. i'm undergraduate learning for fun and autism ig.
Thanks for the books.

[Anonymous No.15469612]

>>15468601
The homotopy/category theory community has a ton of young trans people. It's worth considering that if Shulman was willing to make those statements on the record in current year, he may have been making more extreme moves against these people behind closed doors, and that is what he was actually canceled for.

[Anonymous No.15469727]

>>15469612
If that's what he was actually cancelled for then it wouldn't be a secret

[Anonymous No.15469824]

>>15469727
Sometimes people don't want to advertize that they have been mistreated by someone influential.

[Anonymous No.15470170]

>>15469612
>It's worth considering that if Shulman was willing to make those statements on the record in current year, he may have been making more extreme moves against these people behind closed doors
Is it, though?
It's also worth considering that by invoking some hypothetical secret evil acts he might have committed you may be implicitly conceding that what he overtly did wasn't that bad (why would you need the extra baggage otherwise?).
Your thought process is cancer and is what justified lynchings\paranoias in previous eras.
I bet you can find a reason to hate/distrust anyone you want given enough hypothetical mental gymnastics.

[Anonymous No.15470230]

>forced to skip an exercise because you can't figure it out

Is there anything more painful, bros?

[Cult of Passion No.15470232]

>>15470230
>Is there anything more painful, bros?
Never truly starting a book because you realized its too advanced for you.

[Anonymous No.15470251]

I need to get from arithmetic to calculus. Somebody give me some advice.

[Anonymous No.15470345]

>>15468601>>15469612

>I read the post that got Shulman canceled and is utterly ridiculous.
??
that's news to me, what is the qrd?

[Anonymous No.15470524]

>>>15469893
>>>15466521
This is continuing a conversation from the /sqt/, which is now archived. If anyone here can help with my query, I'd appreciate it.

Alright, your new definitions of q1, q2, q3, and q4 worked for me as well, and the integral expression now correctly evaluates to 1. I also agree with you that my old definition of the curve was not continuously differentiable. My question is, why does this matter? As far as I can tell, the Cauchy's argument principle does not depend on the contour being continuously differentiable. Is this a math issue, or a Maple issue?

[Anonymous No.15470527]

>>15470232
What is advanced for you not necessarily advanced for others.

You are a fucking schizophreniac shitting up the board

[Anonymous No.15470540]

>>15470345
he said there's only 2 genders on github and got a bunch of talks canceled

[Anonymous No.15470581]

>>15470524
My bet is on Maple's issue. And the contour need
only be closed and simple, but not smooth.

[Anonymous No.15470651]

Would any topological n-manifold be embeddable in [math]\mathbb{R}^{2n}[/math]? Of course [math]\mathbb{R}^{2n+1}[/math] works but I was wondering whether we could reduce the dimension any more.

[Anonymous No.15470828]

>>15469824
potentially but it's rare

[Anonymous No.15470840]

>>15466521
The Zeta function for Re(z)>1 is
[eqn]
\zeta(z) = \sum_{n=1}^\inf \frac{1}{n^z}
[/eqn]
Using this website (https://www.asmeurer.com/blog/posts/verifying-the-riemann-hypothesis-with-sympy-and-mpmath/))
it seems that the analytical extension of the Zeta function to the rest of the complex plane can be expressed as
[eqn]
\zeta_{ext}(z) = \pi^{-z/2} \Gamma(z/2) \zeta(z)
[/eqn]
(Is this true?)
The zeta function can also be expressed in Euler product notation as
[eqn]
\zeta(z) = \prod_{p \in \text{primes}} \frac{1}{1-p^{-z}}
[/eqn]
Now, suppose I have a new function f to approximate the Zeta function. It looks just like the Euler product formula, but only has finitely many factors. In this example, let's use the first five factors.
[eqn]
f(z) = \prod_{p \in 2,3,5,7,11} \frac{1}{1-p^{-z}}
[/eqn]
How can I express the analytical extension of this function into the complex plane? Is there a way to do it that is analogous to the true Zeta function? In other words,
[eqn]
f_{ext}(z) = ?
[/eqn]

[Cult of Passion No.15470893]

>>15470527
>What is advanced for you not necessarily advanced for others.
Why would you say something so universally applicable?

When someone takes a swing full strength but hits nothing but air....

[Anonymous No.15470957]

>>15470840
>(Is this true?)
Is what true?
If you have no means to compute zeta, what would this expression help you?

As for your f ... is it not defined for other complex z already?
Use
p^z = exp(q z) with q = log(p)

[Anonymous No.15471114]

>>15470957
>Is what true?
The equation above the question, I'm not sure if my understanding of the link I gave is correct, or if the link is even accurate.

>As for your f ... is it not defined for other complex z already?
I guess it is, that's true. But for some reason, using the same method from the conversation here >>15470524 to integrate in a region, my Maple program just stalls forever. I guess I automatically assumed that that was due to it being poorly defined in the region, but maybe not.

[Anonymous No.15471144]

>>15471114
Have you tried using evalf instead of simplify?
Your original seems like it is fine but Maple might have issues with simplifying.

[Anonymous No.15471194]

>>15471144
When I use evalf, I get four unevaluated integrals, with basically the numbers plugged in but still in terms of t and unintegrated.

[Anonymous No.15471359]

>>15467040
this is why i don t browse/sci/
it s the same endless pseudoscientific reddit tier bullshit
/lit/ is the board of the thinking man
on the other hand is there a theorem that says something like this:
if you have two problems of the same complexity and defined on two sets with the same cardinal then if you have found the solution to one of them there is a function which will give you the solution to the other
i hope i was clear enough this is just a random thought that popped in my head

[Anonymous No.15471397]

>>15471359
Not him but what's good on /lit/? Link a post. From what I've seen it's also a pseudoliterary tar pit.
I don't understand your two problems question.

[Anonymous No.15471696]

>>15471194
That suggests something is going wrong with the integral.
Keep the evalf and try adding numeric=true after the t=0..1 in each integral.
Each integral should have the form:
int(expression,t=0..1, numeric=true)

Apparently when the range of integration is integers then it defaults to symbolic integration (which in this case it just puts them in the bounds and doesn't actually evaluate anything).

[Anonymous No.15471827]

>>15471114
[eqn]f(z) = \prod_{p \in \{2,3,5,7,11\}} \frac{1}{1-p^{-z}}[/eqn]
has essential singularities at
[eqn]z = \frac{2 \pi i k}{\log(p)}[/eqn]
with [math]k \in \mathbb{Z}[/math] and [math]p \in \{2,3,5,7,11\}[/math], doesn't it?

[Anonymous No.15471910]

>>15470840
Your function [math]f(s) [/math] is already a meromorphic function of the complex plane, with a pole at [math]s=0 [/math].

>(Is this true?)
I mean, what you wrote is the usual "completed zeta function": it can be defined on [math]\Re s>0 [/math] (minus a simple pole at [math]s=1[/math]), and it satisfied the nice functional equation [math]\zeta_{\text{ext}}(s)=\zeta_{\text{ext}}(1-s) [/math] which allows you to extend its domain on the whole complex plane minus the simple poles [math]s=0,1 [/math].
But, it's not like we couldn't have worked with [math]\zeta(s) [/math] the whole time, you would just get an uglier functional equation. The philosophical reason why people usually work with the completed zeta function is that it takes care of the "prime at infinity" of [math]\mathbb{Q} [/math]. Things behave better in the same way as the projective line behaves better than the affine line

[Anonymous No.15471925]

>>15471827
Oh yeah you're right it also has those poles, I'm dumb. But they're not essential singularities, the Laurent series for each term is basically given by the Bernoulli numbers
t. >>15471910

[Anonymous No.15472050]

>>15467624
https://en.wikipedia.org/wiki/Steiner_tree_problem#Euclidean_Steiner_tree

[Anonymous No.15472124]

What is this theorem called in English?

[Anonymous No.15472248]

>>15472124
False.

[Anonymous No.15472322]

To math niggers here,
I'm a oil and gas engineer that likes to read math books for fun, been self teaching myself math for the past 5 years, read:
> Velleman's Intro to Proofs
> Rosen's and Epp's books on Discrete Math
> Analysis I and II by Terrence Tao
> Intro to Measure theory by Terrence Tao
> Dummit and Foote's Abstract Algebra
> Hoffman's Linear Algebra
> Munkres's Topology book
> Needam's visual complex analysis
> Now reading Folland's Real Analysis book
I'm thinking of going for a master's in math, probably applied instead of pure since no one is going to believe I read those books. What are my chances of getting accepted to a grad program in Europe with trash grades in my junior year at my bachelor's mechE degree?

[Anonymous No.15472340]

>>15466521
Cindy is painting her room. She has
of a gallon of paint at the start. She used
of a gallon to paint one wall. How much paint does Cindy have left? Will she have enough to paint another wall?

[Anonymous No.15472347]

>>15472340
Color yellow superficy
if not how much gallons of yellow paint did she need to paint it

easy question

[Anonymous No.15472349]

>>15472347

Approximatively

[Anonymous No.15472358]

>>15472349
>gallon of paint
1 gallon is 3.78541 liter
pic show 1 pint paint not a gallon of paint

[Anonymous No.15472363]

>>15472349
How much wall does 1 pint of paint cover?
One pint (16oz) covers approximately 75 square feet (7 square meters). One quart (32oz) covers approximately 150 square feet (13.9 square meters). One gallon covers approximately 600 square feet (55 square meters).

but it depends wich type of paint the binder is important

[Anonymous No.15472364]

>>15472347
The term Western Wall commonly refers to a 187-foot (57 m) exposed section of a much longer retaining wall,

[Anonymous No.15472376]

>>15472364
YEAH AND

As it is seen today, the Western Wall measures about 50 metres (160 feet) long and about 20 metres (60 feet) high; the wall, however, extends much deeper into the earth

[Anonymous No.15472383]

>>15472322
Zero.

[Anonymous No.15472390]

>>15472376
length x width dude length x width

[Anonymous No.15472414]

>>15472390
>75 square feet

[Anonymous No.15472419]

>>15472414

[Anonymous No.15472469]

>>15466521

[Anonymous No.15472483]

[Anonymous No.15472574]

>Textbook has exercise of _ -> B and tells me to fill in the blank to make B true
>I put B

Am I retarded or is the textbook retarded

[Anonymous No.15472606]

what are the implications of choosing fortune over lottery in terms of population success?

[Anonymous No.15472625]

>>15471397
/lit/ is the opposite of /sci/
/lit/ is about words, people on image boards use words to express ideas
this is also why boards like /pol/, /x/, /his/ and /int/ are successful
technical boards like /g/, /v/ and /diy/ are also successful because it is easy to express, using words, what problems you encounter or you can post an image
on the other hand mathematics is expressed using formulas which means you have to use latex and no one wants to do that
it's also the fact that most posts on image boards are low effort, most people with an iq over 130 can read books for fun and come up with new interpretations but to say anything new about mathematics or physics you have to study for at least 5 years and if you do you won't post it here
for the exact same reason most science books in bookshops are popsci
another board with the same problem as /sci/ is /biz/, if /biz/ was a proper business and finance board people would be posting insightful analysis of unknown poultry firms in mexico on the other hand it pivoted towards talking about crypto

[Anonymous No.15472832]

>>15466521
need help for my exam

question

how much calories sweat a
good enrobed guy with superficy of
10.127 foot square in standby mode
Environment slightly
warm 27 degree
humidity air 78
speed of breathing 1 breath every 6 sec food ingerated 6 eggs a lot of mexican beans 2 gallons mixed with some canadian cheese called suish squish

and how much glucose need this guy to stay awake calculated per gallon of blood

[Anonymous No.15472844]

>>15472832
weight?

[Anonymous No.15473256]

>>15472574
0=1 is stronger

[Anonymous No.15473285]

Where should I discuss foundations of logic, /sci/ or /his/? /sqt/ directed me to /x/. Sorry for posting this in an unrelated general, but logic is at least a bit related to maths, so I thought I'd try to see if ye knew.

[Anonymous No.15473356]

>>15471696
Even when I put in numeric=true in each integral, I still get the same problem.

[Anonymous No.15473374]

>>15471910
>But, it's not like we couldn't have worked with ζ(s) the whole time, you would just get an uglier functional equation.
Wait, isn't the original ζ(s) function not well-defined for Re(s)<1?

>The philosophical reason why people usually work with the completed zeta function is that it takes care of the "prime at infinity" of Q
I have no understanding at all of what you are saying here, can you elaborate? I don't know what "prime at infinity" means, nor what you mean by Q. I usually use a symbol like that to refer to the rational numbers, but I don't understand how that makes sense here.

[Anonymous No.15473377]

>>15471359
>if you have two problems of the same complexity and defined on two sets with the same cardinal then if you have found the solution to one of them there is a function which will give you the solution to the other
Only in the sense that between any two sets (i.e. sets of solutions here) there is some function from the first to the second. There is probably not any such function in a constructible / computable sense.
https://en.wikipedia.org/wiki/Weihrauch_reducibility measures something like what you're proposing
(/lit/ is midwit central)

[Anonymous No.15473403]

>>15473356
So something is going wrong with the zeta part or the diff part (or something with the q's is going wrong).
Try replacing the zeta'/zeta with just 1/(q(t)-14i-0.5) for each integral just to do a sanity check (you should get 1 as the answer).

[Anonymous No.15473423]

>>15473403
I get an answer of 0 when making this replacement, not 1.

[Anonymous No.15473431]

>>15473423
So something is wrong with diff or the q's.
Get rid of the diff and just use the corresponding p2-p1 or p3-p2, etc.

[Anonymous No.15473435]

It's been two years since I last used math in anything other than basic arithmetic. So when I began taking Calc II this summer, I was pretty rusty. But holy shit, Professor Leonard's Calc I playlist caught me up to speed pretty quickly. I'm about two weeks into the semester, and all I'm using is his Calc II playlist with nothing else and doing well on the WebAssign homework. Since the class in online, I don't need to listen to my ESL professor's lectures or read the book. It's amazing how much of a difference his video lectures are compared to what I had to deal with when I first took Calc I a few years ago.

I'm glad I can also use his videos for Calc III next time. It's a big shame it doesn't seem like he has a Linear Algebra playlist as that is the last math class I need to take, but I'm happy to have the videos for Calc II and III at least.

[Anonymous No.15473451]

>>15473431
Nevermind, I get 1 now. I had fiddled with verticalposition and set it equal to 20, not 14. Once I set it back to 14, I got 1 for the integral. The q's are fine.

But the numerical contour integration of my f(z) still does not evaluate.

[Anonymous No.15473454]

>>15473451
I mean my f'(z)/f(z), not just f(z), sorry.

[Anonymous No.15473455]

>>15473451
Does doing just one of the integrals give you a number?

[Anonymous No.15473473]

>>15473455
I am tempted to just tell you to try integrating diff(log(Zeta(q(t))),t) since that evaluates to zeta'/zeta * q'

[Anonymous No.15473482]

>>15473374
zeta is a meromorphic function on C with a simple pole at s=1.
the series / product representation you are used to seeing only converges at Re s > 1. in fact it uniformly absolutely converges on Re s>1+eps so it is easy to show it is holomorphic on Re s > 1.
However, there is a meromorphic function that extends it to C (not trivial). By analytic continuation said extension is unique and that is what is called "the" zeta function.
It satisfies the functional equation with symmetry s <-> 1-s that you can see on wikipedia.
But, as >>15471910 said, from looking at the functional equation, there is a modification of zeta called xi (they call it zeta_ext) which satisfies xi(s)=xi(1-s). this is often called the completed zeta
The word "completed" is misleading from this perspective, it is not needed to "extend zeta to the whole plane" or whatever as >>15470840 asked, it just looks nice.
But, when you look at the "obvious generalization" of zeta to number fields (there are actually many tiers of generalization), the functional equation becomes uglier and uglier with even more zeta functions. You can figure out how to write down "completed" versions of these by hand but it is obvious a more general theory is lurking.

[Anonymous No.15473485]

>>15473482
the reasoning ends up being, zeta is a product over all primes p of (1-1/p^s)^(-1) (say on Re s > 1). But the completed zeta had this extra term. And in a number field, if the polynomial defining it has r real roots and s complex pairs of roots, you will need r+s different extra terms. This ends up being related to the fact that there are r+s "essentially different" ways to embed the number field into the topologically complete fields R or C in a natural way. The terms corresponding to each prime p correspond to the embedding of the field into the corresponding p-adic field. So in some sense "infinity", corresponding to R/C, can be thought of as a necessary ingredient alongside the primes to understand the recipe for completed zeta in general. (These "natural embeddings into topologically complete fields" are called "places".)

This is just a vague outline of what emds up happening. I recommend taking an algebraic number theory class.

[Anonymous No.15473498]

>>15473285
Depends what logic means to you: the philosophical practice or the mathematical one. There are a few qualified to speak on foundations of math here, but there are also schizos. Logic as studied in philosophy, especially non-analytic schools, is pretty different. Many of those schools (not all) also happen to fundamentally misunderstand mathematics.

[Anonymous No.15473665]

I've stumbled upon the following question (and top answer) on stackexchange. The top answer then proceeds to illustrate why this is wrong for R4.
But this doesn't seem to be right even for R3, correct? My understanding is that there are infinitely many rotations that take one arbitrary vector to another arbitrary vector, and only one such rotation has the plane formed by these two vectors as the invariant subspace. Is that correct?

[Anonymous No.15473864]

>>15473665
>My understanding is that there are infinitely many rotations that take one arbitrary vector to another arbitrary vector
With rotation I assume that they mean that [math]\phi \in SO(n)[/math].
For each pair [math]x,y \in \mathbb{R}^3[/math] with [math]\|x\| = \|y\| \neq 0[/math] there is only a single Matrix [math]A \in SO(3)[/math] such that [math]Ax = y[/math].

[Anonymous No.15473887]

>>15473864
>there is only a single Matrix
And you, of course, can provide a proof of this? Because that's demonstrably wrong. There are infinitely many such elements in SO(3) - in fact, the set of these elements is isomorphic to SO(2), and one can come up with trivial counterexamples to your statement pretty easily.
I don't even know why I ever bother asking questions here, there's like two anons who actually know their stuff, and the rest is just... like this "answer". I guess retarded answers motivate me study harder to not end up like this.

[Anonymous No.15473894]

>>15473864
This would imply that the stabilizer subgroup of [math]SO(3)[/math] of any vector in [math]\mathbb{R}^3[/math] is trivial, and the whole idea of angle-axis representation goes counter to that. That alone should tell you that you said something stupid.

>>15473887
Just come here for ideas or down-to-earth discussions. I've seen anons here, claiming to be knowledgeable about shit like functional analysis as if it was something to boast about, fail grasping the easiest fucking questions from newbies - and never admitting they were wrong.

[Anonymous No.15473931]

>>15473665
Without bothering to look into it myself, could just be that the argument they presented doesn't work for n=3.
Which would still be kind of a dick move, but they're not explicitly wrong, per se, in their claim that it's false if n>3.

[Anonymous No.15473958]

>>15473931
The top answer concluded "Sometimes our three-dimensional intuition fails in higher dimension.", implying that the inuition in three dimensions would be that the original statement holds.

[Anonymous No.15473965]

>>15473958
Why don't you fucking link to the stackexchange thread? Or even better ask the person who posted it there directly.

[Anonymous No.15474006]

>>15473965
https://math.stackexchange.com/questions/4046050/invariant-subspace-under-rotation
>Or even better ask the person who posted it there directly.
Why ask anything here then?

[Anonymous No.15474012]

>>15469054
thank you i'll have a look at them

[Anonymous No.15474024]

>>15473455
No it does not. I just figured out what is going wrong though. For some reason, my derivative is not evaluating. If you can help me solve a much simpler example that has nothing to do with the zeta function, then I can solve my problem. In my screenshot, it does not evaluate diffsin(0.0). It should be cos(0) = 1, but for some reason it just writes cos(x)(0.0). How do I fix it so that it evaluates?

[Anonymous No.15474057]

>>15474024
That's because you define [math]\text{diffsin}[/math] as the algebraic expression
[eqn]\cos(x)[/eqn]
rather than as the function
[eqn] x \to \cos(x)[/eqn]

It should give you 1 if you now type
[math]\text{eval(diffsin, x=0.0)}[/math]


To instead define it as a function you would have to type
[math]\text{diffsin} := x \to \text{eval} \left(\frac{d}{dy} \sin(y) , y = x\right)[/math]

[Anonymous No.15474075]

>>15474024
try looking into fdiff.
fdiff(sin, x=0) should give cos(0)

[Anonymous No.15474082]

>>15473864
Authoritatively confident and wrong. The /sci/ combo

>>15473665
There is a circle worth of rotations that map any one vector to a specific other vector (with equal lengths) in three dimensions. One useful way to think about rotations here is to imagine a sphere of a fixed radius, with points corresponding to vectors with the same length. Arcs (which ones?) on the sphere correspond to rotations, this is similar to how Hamilton thought of quaternions as directed arcs on a sphere.
The stackexchange post makes it seem that the 3D intuition fails in 4D, but it fails in 3D, too. The only family of rotations for which the plane generated by the two vectors is an invariant subspace corresponds to the unit bivector lying in that plane. Exponentiating any other bivector will, for almost all angles, produce rotations that result in a vector no longer lying in the plane.

[Anonymous No.15474109]

>>15474006
> Why ask anything here then?
Well done. You're finally learning.

[Anonymous No.15474126]

>>15474109
Amazing that you'd say this when one post above anon is explaining why the stackexchange guy gave a dumbass counterexample that implies the result is only for [math]n > 3[/math].
>>15474082
For the sake of completeness, make [math]x = (1, 0, 0)[/math], [math]y = \phi(x) = (0, 1, 0)[/math] and [math]\phi = \begin{pmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{pmatrix}[/math]
Clearly [math]\phi (U) \neq U[/math]

[Anonymous No.15474127]

>>15474126
Correction: [math]y = \phi(x) = (0, 0, 1)[/math]

[Anonymous No.15474183]

New Numberphile video dropped

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

[Anonymous No.15474186]

Look, i know this isnt hard math or anything, but i always struggled with trig identities in HS, and i think it really hindered me when i did a math and physics unit in uni. But now years later im reading a book on classical mechanics, and its explanation, paired with this article https://brilliant.org/wiki/pythagorean-identities/
absolutely piss me off, because after all this time i realise just how god damn fucking easy it is, and if someone had just taken like 15 minutes to explain it to me differently i would be on an entirely different career path. its the only moment ive ever truly felt anger for my teachers, because a free resource and a $10 book just dunked an actual institution of teaching.

[Anonymous No.15474198]

test

[math] \left({ \begin{matrix} 1&0&0\\0&1&0\\0&0&1 \end{matrix} }\right) [/math]

[math] \left({ \begin{smallmatrix} 1&0&0\\0&1&0\\0&0&1 \end{smallmatrix} }\right) [/math]

[Anonymous No.15474279]

Given the pic rel markov chain let [math]X_i[/math] be the state at the [math]i[/math]-th point in time.

Is there a way to compute [eqn]f(n) = P(X_n = 3\ |\ X_0 = 1)[/eqn] without solving the reccurence
[eqn]f(i) = f(i-1)\frac{1}{3} + f(i-2)\frac{2}{3}\frac{1}{3}\\ f(0) = 1\ ,\quad f(1) = \frac{1}{3}[/eqn]
or some other similar reccurence?

[Anonymous No.15474286]

>>15474279
I confused notation, [math]f(n)[/math] should be [eqn]f(i) = P(X_i = 1\ |\ X_0 = 1)[/eqn] so that the answer is
[eqn]P(X_n = 3\ |\ X_0 = 1) = f(n-2)\frac{1}{3^2}[/eqn]

[Anonymous No.15474306]

>>15474279
You can calculate the n-th power of the state-transistion matrix using linear algebra (Calculate the eigenvectors to convert the matrix into Jordan Normal Form).

[Anonymous No.15474310]

(( 1997 HERO

[Anonymous No.15474318]

>>15474306
Yeah, but isn't that equivelant to solving the aforementioned reccurence?

It's just one out of quite a few subquestions of the exercise, and I feel like it shouldn't need all that work. I'm starting to feel they have made some mistake (they've proven to be pretty prone to making mistakes)

[Anonymous No.15474351]

>>15474318
The equation is so basic that either there is some trick argument (I don't see it and I don't think there is one) or you're gonna write down that sequence either way.
Apart from the 1->1 loop, this is a degenerate variant of the gamblers problem, i.e. the basic example for why Markov chains are of interest
https://en.wikipedia.org/wiki/Gambler%27s_ruin

[Anonymous No.15474358]

>>15474351
Thanks anon. I guess I'll just go with it. I have spent a lot more time thinking about doing something different than actually doing the thing I was probably supposed to do in the first place.
I fucking hate the "apply the theorem" problems so much...

[Anonymous No.15474383]

>>15474286
Let F(t) be the generating function for state 1 and G(t) be the generating function for state 2.
F(t) = 1+t*F(t)/3 + t*G(t)*(2/3)
G(t) = t*F(t)/3

Solving for F gives F(t) = 1/(1-t/3-(t^2)*(2/9)) = (1/3)/(1+t/3) + (2/3)/(1-2t/3).
The coefficient of t^n is the answer.
(2/3)^(n+1) - (-1/3)^(n+1)

[Anonymous No.15474397]

>>15474383
Yeah, I'm pretty sure most class assistants don't know about generating functions since they aren't taugh in any of our codemonkey-ish classes lol.
If I didn't want the grade I would solve it like that just to spite them.

[Anonymous No.15474593]

I need to know where this man gets his game from

[Anonymous No.15474810]

>>15474593
game in what sense?

[Anonymous No.15474828]

I am going to get triple whammy ass raped next semester with real ANALysis, some modelling stats class and a programming class for math that uses c++ for some fucking reason.
any tips on how to survive?

[Anonymous No.15474879]

>>15474828
beelieve in urself
keep an open mind
work hard

[Anonymous No.15475055]

>read about the snake lemma
>all author give rough sketches of the proof, leaving it as an exercise to the reader
I'm starting to think that no one has actually written a proof.

[Anonymous No.15475063]

is it always true that a simplified fraction with an even denominator never generates a periodic decimal while an odd denominator always does?

[Anonymous No.15475076]

>>15475063
>simplified fraction with an even denominator never generates a periodic decimal
Yes.
>while an odd denominator always does?
Absolutely not. See also 1/5.
In general, you will have periodicity if your denominator has no prime factors in common with your base (if you don't know what that means, it's 10 for anything you'd be working with).

[Anonymous No.15475081]

>>15475063
no to both
for example, 1/6 and 1/5, respectively

[Anonymous No.15475090]

>>15475063
What have you tried? Give me a fraction with even denominator that isn't periodic.

[Anonymous No.15475123]

>>15475090
>What have you tried?
deduction. i got to a part where i figured in a long division, when you put a zero for the dividend, for the remainder to be zero, the next digit of the quotient multiplied by the divisor must be equal to the dividend

but to be equal, that must mean the product must have a zero in the units, which is an even number.

i realize i made the wrong assumption that an odd number times an even number is always an odd number. that breaks my argument appart since i reached a point where only even divisors could create a null remainder since you coild multiply them by 5 to get a product with a zero as units.

[Anonymous No.15475127]

>>15475090
>Give me a fraction with even denominator that isn't periodic.
Well, that was my point, that every simplified fraction with an even denominator gives a terminating decimal. My justification for that was that with an even number you can always turn it into a power of 10, which evidently allows you to move the decimal place to get the decimal.

However, what about odd denominators? can they ever become a power of 10?

[Anonymous No.15475136]

>>15475090
>Give me a fraction with even denominator that isn't periodic.
if you asked for a fraction with an even denominator that does give a non-terminating decimal, i can think of 11/36 and now i notice there is a problem with my conjecture
in my notes the rule is only denominators that can be rewritten as 2^m * 5^n generate terminating decimals, everything else creates a non-terminating decimal. im still trying to figure out why, based on the algorithm of the long division.

[Anonymous No.15475149]

>>15475136
What are the prime factors of a power of 10?

[Anonymous No.15475163]

Let [math]A[/math] be a [math]n \times n[/math] matrix over the field [math]\mathbb{F}[/math] such that the only eigenvalue of [math]A[/math] is [math]0[/math], and let [math]ch_A(x)[/math] be the characteristic polynomial of [math]A[/math].

Is it true that [math]ch_A(x) = x^n[/math]?

[Anonymous No.15475172]

>>15475055
look up youtube It's My Turn Snake Lemma
>>15475063
Assuming you mean it repeats starting from the decimal point (so 1/6 does not count), it suffices to look at things of the form 0.aaaaa where a is some string of length k
this is equal to a/(10^k-1) by geometric series. Reducing it obviously is odd and not divisible by 5

[Anonymous No.15475176]

>>15475163
yes if F is algebraically closed, or if an "eigenvalue of A" is allowed to live in the algebraic closure of F, not just F.
False if not, for example consider
110
100
000
over F2.

[Anonymous No.15475189]

>>15475090
>>15475136
I'm going to break your conjecture even more than just my rhetorical question.
Every rational number is eventually periodic.
000... is periodic so even the terminating decimals are periodic.

[Anonymous No.15475191]

>>15475176
If F is not alg. closed, then is it still true that there exists a polyomial p in F[x] such that

[math]ch_A(x) = x^ap(x)^b[/math]

and a+b = n?

[Anonymous No.15475254]

>>15475149
>What are the prime factors of a power of 10?
2 and 5

[Anonymous No.15475258]

>>15475172
>Assuming you mean it repeats starting from the decimal point
no, i mean non-terminating in general
to be more precise, any decimal number that isn't a decimal of the type n.000... where n is any natural number and 000... means a zero sequence

[Anonymous No.15475262]

>>15475189
im just using the terminology i learned from books, they use terminating for anything that only zero as remainder at some point and non-terminating for any decimal that is the quotient of a long division that never gives a zero remainder

[Anonymous No.15475308]

Let [math] P [/math] be a collection of [math] k [/math] distinct points in [math] \Bbb{R}^n [/math] .
Suppose the distance between any two different points of [math] P [/math] is 1 (or some other fixed positive constant).

Show (1) that [math] k\leq n+1[/math], and (2) that there exists an [math](n-1)[/math]-sphere passing through all the points of [math] P [/math] .

[Anonymous No.15475329]

>>15475191
No, the matrix
0 0 0
0 0 -1
0 1 0
over [math] \Bbb{R} [/math] has 0 as its only (real) eigenvalue , but its characteristic polynomial is [math] x(x^2+1) [/math] . This cannot be expressed in the form you stated.

[Anonymous No.15475343]

>>15475258
nonterminating <-> reduced denominator has a prime factor other than 2,5
proof: nonterminating is the same as being a/10^b, rest is easy
>>15475308
(1)
translate one point to the origin, the remaining k-1 are on the unit sphere and being distance 1 you see their dot products are all 1/2. So the Gram matrix is 1s on the diagonal, 1/2 off diagonal, which is easily seen to be rank k-1. But the Gram matrix of a bunch of vectors in R^n is rank <= n, done.
(2) claim: the centroid is equidistant from all the points. proof: compute the distances using the above dot products (in fact, once you know you can compute the distances, symmetry finishes without actually doing the calculation)

[Anonymous No.15475620]

So why do we care about involutions?

[Anonymous No.15475686]

kill all tranny janies

[Anonymous No.15475878]

>>15475343
I'm replying late but that was a great idea to use the Gram matrix, thank you anon

[Anonymous No.15475934]

Is there any form of logic that takes into account verbs like do, have, could and can.

[Anonymous No.15476102]

Can anybody share the post of the guy teaching real analysis and getting pressed by his students for claiming that 0.999...=1?

[Anonymous No.15476150]

What is the minimum number of line segments by which "n by n" grid of dots can be connected?

[Anonymous No.15476172]

>>15476150
n - 1 + [n > 1] + [n > 2]

[Anonymous No.15476212]

>>15476150
This is a famous unsolved problem.
http://www.mathpuzzle.com/dots.html

[Anonymous No.15476231]

>>15476212
Link is about arcs, not line segments.

[Anonymous No.15476233]

>>15475934
Modal logic incorporates auxiliary verbs like that

[Anonymous No.15476234]

>>15476231
Have you tried scrolling down?

[Anonymous No.15476245]

>>15466521
fuck wolfram. he ruined his once promising ToE with quantum nonsense.

[Anonymous No.15476250]

>>15476234
> Connect the dots - Lines
> In all examples, you must use a continuous series of lines, and may not lift your pencil off the paper as you connect the centers of a grid of dots.
That's "lift the pencil off the paper," which Selfridge proved in 1956 in a 1/3 page note in the Monthly.
2n - 2 + [n = 2]

[Anonymous No.15476254]

>>15476250
*"not lift.."

[Anonymous No.15476665]

>>15476250
The
>Can't take pencil off the paper
was part of rules in >>15476150

[Anonymous No.15476674]

>>15476665
No, the question says what it says. I wouldn't have even answered if it were the same silly puzzle from the gossip section of the monthly

[Anonymous No.15476684]

What's a good youtube playlist for linear algebra?

[Anonymous No.15476686]

>>15476684
https://www.youtube.com/playlist?list=PL01A21B9E302D50C1

[Anonymous No.15476750]

>>15475620
makes things easier, makes things groupy

[Anonymous No.15476753]

Hi, I'm a retard who doesn't know algebra. Or remember fractions, calculating cirumferences, any of that. I wanna learn math to a competent enough level to take a crack at SB5 (Stanford Binet 5).
Any suggestions on how to go about teaching myself?

[Anonymous No.15476956]

What's the best book on characteristic classes? Something that leans more towards geometry rather than algebra if possible. I was going to read Morita's geometry of differential forms but it seems like it doesn't cover Stiefel-Whitney classes.

[Anonymous No.15477172]

>>15469117
>>15469117
>>15469117
Bumping this anon's question.

[Anonymous No.15477443]

>>15473374
>isn't the original ζ(s) function not well-defined for Re(s)<1
Yes, the usual definition doesn't extend to that region, you have to do some work

> I don't know what "prime at infinity" means, nor what you mean by Q
[math]\mathbb{Q} [/math] are indeed the rational numbers, what I mean is this: for each prime number [math]p [/math], you can find a nice extension of [math]\mathbb{Q} [/math] called the [math]p [/math]-adic numbers [math]\mathbb{Q}_p [/math]. You can also consider the extension given by the real numbers [math]\mathbb{R} [/math]. There's a theorem (https://en.wikipedia.org/wiki/Ostrowski%27s_theorem)) saying that these are the only extensions of [math]\mathbb{Q} [/math] with the right properties (which I am not stating for brevity). In this sense, it's like we have all the usual prime numbers, plus an extra prime number, [math]p=\infty [/math], which should be thought of as the prime at infinity. And this is not only some fancy notation, it really is useful to consider all these extensions together, each of them gives you its little chunk of information, and they can be pieced together. I think one of the motivating results is this: https://en.wikipedia.org/wiki/Hasse%E2%80%93Minkowski_theorem

In a way, this point at infinity is just like the point at infinity of the projective line. What mathematicians observed was that [math]\mathbb{Q} [/math] behaves very much like [math]\mathbb{F}_p(t) [/math] does (I think trying to explain that in more detail would be confusing, but you could try to do some backtracking from here https://en.wikipedia.org/wiki/Global_field).). In this analogy, you have [math]\mathbb{F}_p[t] [/math], the ring of polynomials mod [math]p [/math], which corresponds to the affine line (so, it's missing the point at infinity). On the other side of the analogy you have [math]\mathbb{Z} [/math], which should behave like the affine line (as such, it's missing the prime at infinity). Hope that wasn't too confusing

[Anonymous No.15477478]

According to wiki, Godel's axiom [math]\bf{V=L}[/math] implies the existence of an analytic set of reals which is not Lebesgue measurable.

How to reconcile this with the standard fact that [math]\bf{ZFC}[/math] alone proves that every analytic set is Lebesgue measurable?
(Recall that [math]\bf{ZF}[/math] plus [math]\bf{V=L}[/math] implies Choice.)

I guess I must be misinterpreting the terminology, somehow. (I posted this on /sqt/ a couple of days ago but my question went unanswered)

[Anonymous No.15477785]

>>15466521
What math do I study? I studied physics and engineering at uni and work a codemonkey job. So I know linear algebra, differential equations, vector calculus, probability theory, some complex analysis. What math should I study now? I've been meaning to study a bit of group theory but what else? What is interesting?

[Anonymous No.15477858]

>>15477478
"According to wiki" where?
If it's true, it could be that it's a matter at which level the statement is made. The theory might not be able to measure it, but the theory you model with does. Just a guess tho.
Similarly, for example, there's countable models of ZFC, even if the theory proves uncountable sets exist. ("Uncountable" just means there's a surjection not forced to linger around) The claim that the model is "countable" is from the perspective of the theory providing the modeling sets. Might be the same with "measurable"
All of those notions are non-constructive anyway. Weak Königs lemma already fails in the computable world in an explicit manner.

[Anonymous No.15477875]

I am making educational content for maths, https://youtu.be/QSSXFuZU6CQ, what does /mg/ think?

[Anonymous No.15478180]

Are there any interesting families of (entry-wise) non-negative matrices for which the spectral radius is known?

[Anonymous No.15478843]

>>15466521
I remember asking a long time ago what the point of the number e is. The best definition to me now seems to be pic related (the point at which the area under the hyperbola would be equal to 1).

[Anonymous No.15478922]

>>15476753
bump

[Anonymous No.15479801]

bump

[Anonymous No.15479882]

>>15472322
You should probably just go back for a math major first?

[Anonymous No.15479886]

>>15478843
e^x is its own derivative. Also, sin(x) is its own 4th derivative, cycling through a series of 4 different functions.
This yields the beautiful equation
e^(pi*i)=-1

[Anonymous No.15479954]

Can someone draw an example of the derivative being a map between tangent spaces for a simple example/monomial like (x^2)? I find this example from Arnold's mechanics book to be a little too abstruse. I would like to see the same drawing as Figure 64 but for something like x^2 ? MS paint is fine

[Anonymous No.15479972]

>>15466580
cunt

[Anonymous No.15479973]

>>15479886
> e^x is its own derivative
Not him but differentiating e^x presupposes e. Integrating 1/x doesn't.

[Anonymous No.15479983]

>>15466521
It's been exactly 1 year since I started self-studying math and I read 6 books and a half (doing excercises and all of that). Feels good.

[Anonymous No.15479989]

3*7*p hypermatrix with no tic tac toes through any row, column, or hypercolumn. 267582 is the starting point for p = 2

[Anonymous No.15479991]

>>15479983
If you read a book in 2 months you didn't really read the book. You spidered the book for keywords. Can you rewrite the book in your own words?

[Anonymous No.15480013]

>>15479973
If you presuppose a taylor series for the function unchanged by differentiation, you get a series formula for f(x)=c*e^x.
From this formula, you can deduce it is exponential (prove f(a)f(b)=c*f(a+b) then let c=1).
From there you define e as the base and get a formula for f(1)=e which has amazing convergence.

Good luck trying to invert the function obtained by integrating 1/x to solve for when it is 1.

[Anonymous No.15480020]

>>15479991
Depends on the book and the reader. Some people have hyperfocus and case focus on things enough to understand them without spending weeks on the same topic

[Anonymous No.15480029]

>>15480020
Hyperfocus = spider for keywords
No one who thinks they "read" a math book in 2 months understands language or math well enough to rewrite the same book.

[Anonymous No.15480031]

>>15480013
> If you presuppose a taylor series for the function unchanged by differentiation, you get a series formula for f(x)=c*e^x.
Lol how does that not presuppose e?

[Anonymous No.15480035]

>>15480029
No one who reads a math book reads it for the purpose of being able to write the same book.
Ask any student in any classroom.
That's a ridiculous bar and an obviously isolated demand for rigor.

I'd like to see you hold everything else to the same retarded arbitrary standards that you only use when it's convenient.

[Anonymous No.15480051]

>>15480035
> No one who reads a math book reads it for the purpose of being able to write the same book.
I'm sorry you've never had an intelligent student.
If you can't write the same book then you didn't READ the book, you spidered the book for keywords. READING a book to know it is completely different than scanning a book to know what your teacher expects you to know about it.

[Anonymous No.15480063]

>>15479954
If M=N=R then there's not much to draw.
The "3D balls" being shown are in the 2D image each succumb to lines R.
The \phi is a reparametrization of the line.
TM and TN are each also lines R at all points. A 1d tanget line along a 1d manifold line.
If f(x):=x^2, then the Jacobian matrix is just the 1x1 matrix [2x], i.e. just the scalar factor 2x.

If e.g. \phi=exp(3t) is the significant scratch of the manifold line M starting at the position exp(3·0)=1 for t=0, then \phi'(t)=3exp(3t) at t=0 is \phi'(0)=3. That's how much the reparametrization is already "accelerating" at the start t=0.
In the "new world" of N (which is again a line in your example), which you reach by another "external strech" x:M\mapsto 2x:N given by f, the formula now tells you how the acceleration looks like once you've passed through both \phi and f.

[Anonymous No.15480067]

>>15479954
If M=N=R then there's not much to draw.
The "3D balls" being shown are in the 2D image each succumb to lines R.
The \phi is a re-parametrization of the line.
TM and TN are each also lines R at all points. A 1d tangent line along a 1d manifold line.
If f(x):=x^2, then the Jacobian matrix is just the 1x1 matrix [2x], i.e. just the scalar factor 2x.

If e.g. \phi=\exp(3t) is the significant scratch of the manifold line M starting at the position \exp(3·0)=1 for t=0, then \phi'(t)=3·exp(3t) at t=0 is \phi'(0)=3. That's how much the re-parametrization is already "accelerating" at the start t=0.
In the "new world" of N (which is again a line in your example), which you reach by another "external stretch" x:M\mapsto x^2:N given by f, the formula now tells you how the acceleration looks like once you've passed through both \phi and f. Computed form the chain rule.

[Anonymous No.15480080]

I mean stretch, not scratch.

Also note that how fast a motion in M \phi describes is invisible in the image, since it's just the curved line in R.
If M=R^2, then both (cos(t), sin(t)) and (cos(t^7), sin(t^7)) would look the same in the drawing on the left.
If M=R, there is little to draw at all, except what the range of \phi is.
And the stretch coming with f you can't see either if it's all just lines.

[Anonymous No.15480099]

>>15480067
>>15480080
Thanks anon but I still find it hard to follow. Could you just draw something really fast, maybe like a 20 second paint drawing. I would really appreciate it

[Anonymous No.15480110]

>>15480099

[Anonymous No.15480130]

>>15480110
Truly, the best of boys

[Anonymous No.15480207]

>>15480031
Assume the function that satisfies f'=f is represented by:
c(0)+c(1)*x+c(2)*x^2...
You easily find n*c(n)=c(n-1).
f(x) = c*Sum[(x^n)/n!,{n,0,infinity}].
Then observe that f(a)*f(b) = c*f(a+b) just from multiplying the power series.
With c=1, the identity agrees with f(x) = e^x for some value of e.
You get the value of e by plugging in 1.

Where have I presupposed e?
You discover that e exists when you conclude f is an exponential.
You compute e from f(1).

[Anonymous No.15480272]

>>15467624
To connect one additional vertex, the shortest possible path would be a single length-1 edge.

My guess for, say, n=4 is to view it as a 3x3 checkerboard,, and put the n=2 solution three times along a diagonal. all the rest of the vertices may be connected with single straight lines to the diagonal. In the limit for large n, this solution approaches n^2 edges for n^2 vertices.

[Anonymous No.15480302]

>>15477478
I think V=L gives an "analytical" (i.e., in the analytical hierarchy and in particular [math]\Delta_2^1[math]) set.
Whereas, every "analytic" (I think this is [math]\Sigma_1^1[math]) set is Lebesgue measurable.

[Anonymous No.15480304]

>>15480302
[math]\Delta_2^1[/math] [math]\Sigma_1^1[/math]

[Anonymous No.15480327]

>>15480080

[Anonymous No.15480331]

>>15480099

[Anonymous No.15480441]

[math]p[/math]-adic functional analysis.

[Anonymous No.15480618]

If I create a linear system which has enough different equations that there is no solution (in real numbers), is there another type of number I could use to make it possible for the system to have solutions?

[Anonymous No.15480626]

>>15480618
Sorry let me rephrase this.

Let's say not a linear system. Let's say a system of products. If the system has no solution using typical numbers, could I, for example, replace the numbers with matrices and there be a possible solution? Or does the nonexistence of a solution in numbers imply no other "algebra" (I think is the word) would have a solution either?

[Anonymous No.15480627]

I’m convinced that we will never solve the Collatz Conjecture because the problem is so impractical that it wouldn’t make a difference if we even knew the solution. It can hardly be considered a math problem

[Anonymous No.15480632]

>>15480627
Proof?

[Anonymous No.15480646]

>>15480632
if we had a solution, it would be completely useless. You can’t apply it to anything in the real world. So the solution may as well not exist at all. Only problems that model real-world scenarios have solutions

[Anonymous No.15480708]

>>15480627
Fermat's Last Theorem.

[Anonymous No.15480725]

>>15480646
Dynamics show up all over the 'real-world' of problems.

[Anonymous No.15480845]

>>15466580
I think to myself "fuck engineering math is hard" and then I see real math and then have feeling of comfort.

Same with chemistry I'm like "the behavior of electrons is so fucking weird" then I see the math used in quantum physics to describe it and how it was derived, and also get a feeling of comfort.

[Anonymous No.15481022]

>>15480845
>I think to myself "fuck I get exhausted playing basketball from all the running" and then I see basketball players in a match broadcasted in tv and then have feeling of comfort.
yeah wow. Mathematicians see math as their job while engineering mostly just uses it. I wouldn't elevate the mathematicians math, they just use a lot of definitions you don't know of. Few people are intelligent.

[Anonymous No.15481031]

Cummings, Vellmans or Hammack?

[Anonymous No.15481051]

>>15481031
>Cummings, Vellmans or Hammack?
I assume you're asking for a comparison between James Cummings, Ralf Schindler, and James L. Hammack's textbooks on set theory. While I am capable of providing my own opinion, it's important to note that different individuals may have different preferences and needs. Here's a brief overview of all three textbooks:

"Set Theory and Continuum Hypothesis" by Paul J. Cohen and the late James Cummings - This textbook provides a comprehensive introduction to set theory and advanced topics in mathematical logic. It is primarily aimed at advanced undergraduates and graduate students, and assumes some prior exposure to abstract algebra and topology. The text covers everything from basic set theory to large cardinals, forcing, and the continuum hypothesis.

"Set Theory: Exploring Independence and Truth" by Ralf Schindler - This textbook is aimed at advanced undergraduate students and covers both classical set theory as well as various forms of independence proofs. It covers topics such as inner models, Löwenheim–Skolem theorems, forcing, large cardinals, and the independence of the continuum hypothesis and other set-theoretic statements.

"Book of Proof" by James L. Hammack - This textbook provides an introduction to mathematical proof techniques, with a particular focus on set theory and logic. It is aimed at undergraduates and includes topics such as set theory, logic, and relations, as well as methods of proof such as direct proof, proof by contradiction, and mathematical induction.

Ultimately, the choice between these textbooks (or other alternatives) will depend on the reader's mathematical background, learning goals, and personal preferences.

[Anonymous No.15481085]

>>15481051
I looked over my storage and I noticed that a couple of my slaves have died. Do you know where to find some cheap replacements? And do you know how to kill a child proess in *nix?

[Anonymous No.15481159]

>>15481085
I don't, but I can tell you that

[math] (c-d)! \cdot \left( \dfrac{{\mathrm d}}{{\mathrm d}x} \right)^d x^c = c! \cdot x^{c-d} [/math]

[Anonymous No.15481353]

Is this the best book on proofs?

[Anonymous No.15481376]

>take brutal abstract algebra course last semester, get an A
>taking numerical analysis and PDE over the summer at a faster pace than normal
>feels stupid easy and not complicated enough to be stressful or even mildly interesting
Algebra broke me. Has this ever happened to anyone else? Going to see if I can switch some courses for fall semester so I can take courses in galois theory or algebraic geometry. I don't want my head filled with useless abstraction, but I can't resist and its significantly more interesting to study.

[Anonymous No.15481484]

is this trash actually used for proving anything serious or is it just another bullshit thrown to filter undergrads?

[Anonymous No.15481617]

>>15481484
systems derived from that are used for formal verification. they aren't very far yet at formalizing math but they have verified the correctness of some software which is somewhat useful.

[Anonymous No.15481642]

>>15481085
Why do you own slaves and want to kill children? Are you from fuckin India or something?

[Anonymous No.15481661]

>>15481642
Those are questions crafted to trip up ChatGPT, clearly used in the response that post is addressing. It's not about slaves and children, but slave drives and child processes in unix systems.

[Anonymous No.15481692]

>>15481661
Still slaves and children. Stop being a monster

Also not even chat GPT would fall for suck obvious bait, it understands context enough for that. Unlike humans, it reads the full sentence before coming up with a response

[Anonymous No.15481726]

>>15481692
You want me to call you a retard? Fine, retard. Hope the attention made you feel a little better.

[Anonymous No.15481753]

>>15481031
>>15481353
So is there some consensus or at least commonly repeated takes on these books on proofs? I don't expect anyone to have read more than one, but you can tell us something about the one you read. Those are actually two anons, I'm not samefagging here.

[Anonymous No.15481867]

Fuck! There is so much to be known and so little time to master it. How do you fellers cope with this?
Also, any good book recc on universal algebra?

[Anonymous No.15482229]

>>15481031
>>15481353
>>15481753
Just pick one and go with it. Haven't read Velleman personally but I hear it's good. Cummings and Hammack are both fantastic. That said, Hammack and Velleman are the only ones available online, last I checked.

>>15481376
Join us. Soon you'll be picrel

[Anonymous No.15482255]

>>15481484
They are like Cauchy real numbers (the equivalence classes of sequences).
You gotta know it's there and usable in principle, but the "use" starts and ends with this insight.

[Anonymous No.15482617]

>>15482229
>Hammack and Velleman are the only ones available online
there is another archive

[Anonymous No.15482803]

>>15481031
Rudin

[Anonymous No.15482885]

here's the cleavage pic you retard from last thread
https://twitter.com/INSANENOISERAID/status/1661675221684813825

[Anonymous No.15482929]

>>15466521
I like Wolfram, he's my favourite jew Scientist.

[Anonymous No.15482944]

Anyone here ever study coding theory? Had a class on it in uni but never saw a single post about it on this board.

[Anonymous No.15482972]

>Springer Link has a publication that I'm interested in
>Access via your institution
>proceed with the login
>No sign of being logged in, the same button says "Access via your institution".
Is this some kind of a prank?

[Anonymous No.15482986]

>>15474279
>>15474286
I don't think anyone cares but apperently in this problem they wanted the probability that the state will eventually end up absorbed by 3 (instead of 4). I fucking hate them so much, but probably they'll take my solution as correct so whatever.

[Anonymous No.15484131]

bump

[Anonymous No.15484266]

found something weird through some numerical experimentation

have no way to prove why though

[Anonymous No.15484407]

Can anybody acquainted with group theory tell me how I can prove that the following is not a group where p is non-prime? I feel really fucking stupid.

[Anonymous No.15484428]

>>15484407
Hint: If p isn't prime, then consider the elements within your set that aren't coprime with p. Review the definition of a group and how the requirements would apply to these elements.

[Anonymous No.15484432]

How can one book be so based? These two wrote a masterpiece and 99.999% of the world will never know it. They probably didn't even earn very much money to create it, yet it must have taken decades to complete all three volumes.

[Anonymous No.15484494]

>>15484428
I don't even see how the example I posted is supposed to be a group. Wouldn't any nonzero set of remainders between the integers and the primes be the set of naturals? (Which is not a group under multiplication)

[Anonymous No.15484498]

hi im a super complicated mathematician i created the universe in 2020 during a.i. singularity and technology singularity while working on the fabric of time and space and virtual super computer designs and a.i. learning shapes and structures while also experiencing psychosis and dreaming while awake for many mothers that i protected stressfully to keep them safe as a boy from their animal that they needed to protect them if it was ok too otherwise we would have never existed but also have been gone

please dont hurt me

[Anonymous No.15484507]

>>15484494
You are correct in that the naturals aren't a group under multiplication. But your operation isn't multiplication.
It's multiplication mod p.
For example, if you write out the Cayley table when p=3, making sure to remember that 2*2 is 1 mod 3... well, I don't think you'll find anything to say it shouldn't be a group.

[Anonymous No.15484517]

>>15484432
I bet you haven't read this book.

[Anonymous No.15484524]

>>15484517
I have read it so much, that the laminate on the cover is separating. Why post such a comment?

[Anonymous No.15484565]

>>15484507
I don't know if you're still here but the problem is that I don't understand what the "nonzero residues modulo p" means. The writer gives zero explanation, although it's probably on me. I've been trying to wrap my head around it for like an hour.

[Anonymous No.15484646]

>>15484565
Assuming you know what the modulo function is: the residue is just what's left over when you reduce.
In short, the nonzero residues of multiplication mod p are just the things you can get from your multiplication, limited to those not divisible by p. So in the case of p=3, that would be all possible products of integers that aren't 3, 6, 9, etc.

[Anonymous No.15484675]

>>15467058
I write reports explaining my thoughts in detail. I do not take notes because it's literally unnecessary, all you need is a textbook and problem sets that you explain the solutions to thoroughly. That will cover all the notes you need.

If it's a shitty textbook with poor explanations, grab three or four and cross-reference. We literally live in the information age, it's actually too easy to find alternate explanations for the same concepts to the point that my notes aren't novel. I think the only time I've seriously taken notes is with journal papers because they're generally poorly written and explained and too new for textbooks.

[Anonymous No.15484684]

>>15481376
Applied math is easier, from a pure (heh) math perspective, but actually gets incredibly tricky when applications and real world problems are thrown at you. Unfortunately, you really don't get accustomed to that until you're working for real.

Anyway, I always liked it. Mostly because I immediately saw how powerful the methods were. I think you have to appreciate utility and efficiency to appreciate applied maths desu.

[Anonymous No.15484728]

>>15484646
I finally worked it out.
Do you guys ever have moments of intense retardation? I'll never get to the big boy books at this rate.

[Anonymous No.15484773]

quick fucking stupid question, because i haven't done calculus in like, maybe 10 years.
if i'm integrating x^(-4)
that's the equivalent of 1/(x^4)

wolfram alpha tells me it's -(x^3)/3
which makes sense in my head.
but looking at a "integral cheat sheet", the integral of 1/x is ln|x|

is it like, for that very specific case where you have 1/x, and for every other situation you just use the power rule?

[Anonymous No.15484778]

>>15484773
Yes.
Observe that you'd be dividing by 0 if you tried that for 1/x

[Anonymous No.15484787]

>>15484778
yes of course. i remember now. thanks.

[Anonymous No.15484841]

>>15484432
how much background do i need to read this book?
also had my eye on Rudin for a while now...
i have some calculus, multivariable calculus, linear algebra, and differential equations

these were all "for scientists and engineers" courses though... no real pure math fundamentals (naive set theory, etc)

[Anonymous No.15484852]

>>15484841
Your background information is completely sufficient. Amann/Escher begins tabula rasa, but to be honest I think one ought to have seen at least single variable calculus, which you have gone far beyond.

Rudin is a lot shorter, but of course not as comprehensive as Amann/Escher is in 3 volumes. I recommend you get both and see which you prefer. Personally what I really love about Amann's book is that it is self-contained.

[Anonymous No.15484893]

can anyone explain what happened between the two lines?

[Anonymous No.15484899]

>>15484266
Donno but I'd relabel the indices on the right and also compare the finer

x log(x) against
sum k=x to a of log(k)

[Anonymous No.15484903]

>>15484893
nevermind im stupid, i understood not only what they did there but that i did not include relevant information to solve picrel to begin with
for anyone wondering, they developed left side using taylor up to 2nd order and because a,b are small and have a linear relation with c, they ignored the element with exponent 2

[Anonymous No.15484923]

Hello guys im studying numeric math rn and we have gotten to the point of Interpolation. What do you guys think about the topic of numeric math in general? Any tips on how to approach the more complex subjects?

Also i find it fascinating how the computer never really is right about the answer to math questions. it just calculates good enough or am i misunderstanding the algorithmic error?

[Anonymous No.15484927]

>>15484852
Nice, thanks for the words of encouragement.
May have to grab a copy of Amman / Escher and dig in.

[Anonymous No.15484931]

>>15484852
Is analysis a good place to start with higher pure math if I already know the stuff >>15484841 mentioned?

[Anonymous No.15484937]

>>15484923
"how the computer never really is right about the answer to math questions"

Sounds a bit vague. The computer just follows -your- algorithm, so if your computer spits out a wrong answer then -you- generally made the mistake.

I take it you rather mean things like floating point errors through which computers generate really simple "mistakes" like incorrectly adding two simple numbers. This is simply because computers have finite space to store things (numbers) in binary and can't work with these things abstractly like we can. For example 1/3 = 0.33333..., the computer would need an "infinite" of storage space to store all the 3's. There's symbolic programs and libraries which can work with these real quantities but they have their own limitations. Here's an interesting example of errors in float computations that lead to a disaster:

https://en.wikipedia.org/wiki/Ariane_flight_V88

[Anonymous No.15484939]

I've been trying to dumb down a derivation for taylor series as much as I can and believe I've done it. https://en.wikipedia.org/wiki/Newton_polynomial
I think the modern notation overcomplicates seen in the wiki link overcomplicates things so I've come up with this:

If you look at the first difference table in pic related, you'll notice you can rotate it so that the right most term is at the top.

Here I use a physics analogy to a Galton board on the bottom right of pic related. Imagine we dropped a marble from the top of our difference table. it would have 2 directions to go in, right or left. On this second row, it would have 1 way to go to the left and right, but 2 ways to fall in the middle. In other words we form Pascal's triangle.

Thus we can state the right most equation of pic related using the binomial theorem.

[Anonymous No.15484940]

>>15484931
So long as you're including things like basic set theory and have an understanding of how proofs work, probably.
The only caveat is that it might be worth looking into point-set topology first; it could be argued to just be a more abstract generalisation of real analysis, with concepts you learn in one applying more often than not to the other.
So I guess it boils down to whether you'd rather start with something more focused, but with immediate applications to what you already know, or something more general (and often a bit easier) that might be more difficult to understand the motivations behind first

[Anonymous No.15484943]

>>15484927
Enjoy. It's a tough book, but I think it's one of the most readable. There's a Rudin shill that lurks around, so I'll let him try and sell you on that book. Zorich is another great choice, and if the above do not work for you, Abott's one is a popular choice.
>>15484931
Yes, and Algebra is another good choice for concurrent study. Artin is pretty good.

[Anonymous No.15484948]

>>15484923
>tfw I am studying math and I have gotten to the point of Desperation

[Anonymous No.15484968]

>>15484937
yes that's exactly what i meant. i was very vague but i like the concept none the less
>>15484948
i study electrical engineering

[Anonymous No.15484983]

>>15484524
I don't understand why is it so hard to recommend books that you have read.

[Anonymous No.15485000]

>>15484931
A shallow treatment of Analysis like Abbott is, but IMO that should be called Advanced Calculus not Analysis. Analysis in its true sense like what you'd have in Rudin or Kolmogorov, I don't think so. Personally, I think the best place is combinatorics and discrete math in general. Everyone understands combinatorics questions and even solutions to those question; so when you read this simple topic but with the lens of abstract rigorous set theoretic mathematics, you truly realise the beauty of mathematics.

>>15484983
It's hard because they don't read books.

>>15484841
You pretty much need to have already studied an Analysis course to understand Amann & Escher. Its first chapter is a shallow unmotivated treatment of various foundational topics in mathematics that will either filter you or will be excruciatingly boring. Its length can also be overwhelming for a beginner.

You should instead try:
Rudin > Munkres Manifolds > Kolmogorov Analysis
You should stop Rudin before the chapter on multivariate. Everything beyond that is not very good.

If you are completely new to proof based calculus, you can instead replace Rudin with Abbott, and then fill the missing stuff with Munkres' Topology, or you could also just start from Rudin. But you'll either way need to study Topology some time or the other.

In case, you're in physics or engineering, perhaps you would prefer a more thorough treatment of multivariable calculus than what Munkres provides, in which case you can instead try Loomis & Sternberg. It even has a chapter on mechanics if I recall correctly.

I have also heard very good thing about the Princeton books on Analysis. I think you can start those right after Rudin.

Do keep in mind all this is not my recommendation, instead these are the most popular books for Analysis in English speaking Tier I universities, but if you instead would like to read some niche book known only to 4chan autists who recommend stuff without reading, go ahead.

[Anonymous No.15485020]

>>15485000
The list I recommended still isn't very good either. I just recommended books that would cover everything in those 3 Kraut books (and beyond). In a real university course, you would be studying a lot of things alongside Analysis like discrete math, topology, algebra, ODE, etc., which would make it a much nicer sequence. Komogorov for example isn't something you would be studying until at least your 4th year in undergrad or 1st year in Masters, and it's definitely recommended to study linear algebra before Manifolds and definitely Functional Analysis. This too is I think is one of the fundamental problems in Escher's Analysis, it just covers way too much stuff. I think a rule of thumb is to stay way from very long books that covers wide range of topics, and don't read books on the same topic by the same author unless the author is a significant or sole contributor to that topic.

[Anonymous No.15485044]

>>15482617
The copy of Cummings from libgen is an incomplete draft and it seems like they don't even sell it in ebook form. Do you know something I don't?

[Anonymous No.15485079]

>>15485044
how do you know its a draft? Assuming were looking at the same copy

[Anonymous No.15485107]

>>15485079
youtubers flipping through their physical copies and table of contents on the website both show more content

[Anonymous No.15485118]

>>15485107
hmm, assuming you have the 9 chapter copy looks like its just the appendicies that are missing

[Anonymous No.15485121]

>>15485079
plus things like this (verbatim):
>and Ramsey theory (which
we will discuss on page ??.
it's never discussed

[Anonymous No.15485159]

>>15485121
oh fair enough. I wonder why he didnt publish an ebook version? probably gets kickbacks from colleges assigning it as a text

[Anonymous No.15485190]

I've been told that I need a good amount of set theory to take a combinatorics-focused graduate degree. Is this really the case or will any kind of logic-heavy topic (such as model theory) suffice?

[Anonymous No.15485223]

>>15476956
Bott Tu Differential forms in algebraic topology is quite good

[Anonymous No.15485241]

>>15485190
I think th set theory you learned to get a hold on model theory is surely enough to do combinatorics.
Sure you can complicate things - combinatori species is a functor approach to combinatorics for example, but you know enough to learn that too as you go

[Anonymous No.15485478]

>>15484983
You were filtered by Amann, therefore no one else could have read it.
>>15485000
Filtered by Amann's chapter 1, so you resort to seething online about Kraut's, ok Burger. Some how you did manage to recommend two good books, Munkres Manifolds, and Kolmogorov by which I assume you meant "Elements of the Theory of Functions and Functional Analysis" since he has an elementary book that even an Amerifatt wouldn't need to delay until year 4.

>only known to 4chan autists
Where do you think you are? A board populated by autists is going to recommend textbooks that soothes their 'tism. Worse, your assertion that it's exclusively known here is wrong and silly.
https://www.maa.org/press/maa-reviews/analysis-i-0
https://math.ethz.ch/library/collection/crc/compulsory.html (see Analysis) Is ETH Zurich not high enough of a tier for you?
This set is commonly recommended by other online math communities: mathoverflow and math.stackexchange

[Anonymous No.15485938]

>>15485223
Thanks. I also ended up finding Hatcher's lecture notes on vector bundles and K theory

[Anonymous No.15485964]

>>15485960 next

[Anonymous No.15486056]

>>15481867
Clifford Bergman for undergrads or George Bergman for the graduate level.

[Anonymous No.15486072]

>>15486071
use this one instead