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Board
/sci/ - Science & Math

Formerly >>14974666

Talk maths.
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>>14991073
First!
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math isn't even real science..
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what formula do i use to get a girlfriend ?
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>>14991239
$\int \! e^x$
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based
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>>14988114
>>14986282
Linear Algebra is the local slut.
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>>14987175
No, I don't. My computations are correct, and that is without making g=10 like he wants everyone to do. I solve for g as a vector field with a 10 digit approximation instead.
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>>14991370
>I solve for g as a vector field with a 10 digit approximation instead.
So you do 10 times the work to get the same result?
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>>14991370
Anon, I'm not sure you're understanding the issue. Your professor can just add "use $g = 1 m / s^2$" and "give the result with two degrees of precision in radians or you'll fail the question" to question statements and then start zeroing your assignments until you quit acting out.
>>
I missed three tests worth 20% of my grade in each module, I do most of my work from books and rarely check my course materials online or watch lectures so I didn't know we had them..
Is it worth lying about depression or something to see if they'll let me off? I'm devastated
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>>14991357
considering doubling up on applied linear algebra course along with statistics. Just not sure if I can balance those + embedded & dynamical systems, linear systems, and EE lab. I have been doing work on studying linear algebra outside of school so it's not totally foreign to me. Any advise? stick with linear algebra or take it later?
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Can anyone recommend a difficult Linear Programming book for someone well-versed in rigorous Linear Algebra?

>>14991627
I have only ever self-studied so I have no idea about university. All I can say is Linear Algebra is everywhere, especially in Statistics.
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What am I in for?
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>>14991194
that's right bitch it's better
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>>14991638
>difficult Linear Programming book for someone well-versed in rigorous Linear Algebra
I know of many LP books, but you might just need to settle for skipping easy parts, plenty of the theory is quite trivial.
Anyway, Matousek-Gartner is solid.
What is your goal with LP? To me the only interesting applications I've seen are those to combinatorics and discrete optimization.
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>>14991194
If math were a science, then the definition of "science" would be circular, because math is necessary previous component for the definition of science.
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>>14991672
irreversible brain damage
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>>14991680
What makes you say that?
I found his Topology quite good.
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>>14991677
>What is your goal with LP?
Nothing, I just want to self-loorn.
Know any other books on applications of Linear Algebra?
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>>14991921
>any other books on applications of Linear Algebra
I mean, LA is so essential that most math, physics and engineering texts will be building on it.
Again depends on what you want to do, classical machine learning is fun to learn about, or you may look into quantum physics. There are also some direct applications in graph theory.
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>>14991373
No, I do the proper work rather than idiotic physics approximations that might as well be guesses with some math symbols thrown in to try and give it validity.

>>14991388
Sure, but then it wouldn't be the actual physics problem, and you would need to just have an abstracted function and parameters that don't relate to real phenomena.

I only need to finish this modern physics course and another elective in order to graduate, im already accepted into a graduate program for spring 2023, I am not going to lower my standards to appease this clown. Physics is garbage anyhow.
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>>14991682
in general calculus on manifolds is pretty tough to learn (in my experience)
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>>14991959
>There are also some direct applications in graph theory.
Yep matroids and stuff seem real interesting to me.
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>>14991982
No you're just worthless
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>>14992002
kill yourself nigger
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>96% of people fail to understand material implication
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>>14991594
Lol no
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>>14991986
Is matroid theory built to aid graph theory though? I though they were their own field.
>>14992002
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>>14992013
>material implication
I don't think material implication relates a lot to command statements ("If A, then you must do B").
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>>14992122
>then you must do
>do
Illiterate
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>>14992013
>it's another episode of the Wason selection task
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>>14992269
Should be promoted to "the natural selection task"
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>>14991638
>Can anyone recommend a difficult Linear Programming book for someone well-versed in rigorous Linear Algebra?
Look at Sigfried Bosch. IDK if there's an English version though, haven't checked.
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>>14992013
so just enough to verify the conditional? that wouldnt have occured to me if i didnt see it in a math context desu
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>>14992322
And that's the scary part.
How often have you made illogical decisions based on that?
At most 4% of the world are logical. Most likely quite less, because there's way more ways to be illogical (fallacies, not understanding probability, etc.)
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>>14992334
>And that's the scary part.
How is that scary? are you legitimately scared because of this? Doesn't sound very logical to use language so frivolously. But don't let me rain on your parade of huffing your own farts and disparaging most of the world population because they don't care enough to think slowly about your little card trick.
The fact is, probability and formal mathematical logic can be learned and at the level of the problem wouldn't take more than 30 minutes. You're the kind of dweeb that gives those who love math a bad name. Imagine if the plumber made fun of you and implied you were an inferior being because you didn't know some trick of his trade. Grow up kid.
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>>14992352
>trick
If basic understanding of spoken language is a magic "trick" to you, then kill yourself, monkey.

No one needs to understand plumbing because we delegate that to plumbers, and we know they're qualified.
But everyone INSISTS on directly voting on policy and who to delegate to, regardless of qualification.
That's why everyone should learn basic language and logic.
I'm not asking anyone to get a degree in math or even learn algebra, dumbass. Just stay out of decision-making if you're not gonna put the effort to make sure you're not casting retarded votes.

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>>14992394
Its only spoken language in a small set with few implications. Even then the way you're solving it is the same way you would symbolically solve any statement during your intro to proofs course in college. I have a math degree too, I know exactly what you're visualizing when you read those problems, and its not anything an average person is exposed to.

They insist on voting because it directly affects them. You don't own people, and if you disenfranchise them they will literally group up and kill you, read a book.

>Just stay out of decision-making if you're not gonna put the effort to make sure you're not casting retarded votes.
No. I agree with you that I don't want to live around retards and wish we lived in some geniusland utopia, but that is never going to happen. If you want that, just start your own country. But how could you without the retards you despise providing the labor and military force?
Again, grow up. You look even more like a child with this second post.
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>>14992428
>if you disenfranchise them they will literally group up and kill you, read a book.
Im fucking waiting. Do something America.
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>>14992394
Egotistical pseud take.
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>>14992428
>its not anything an average person is exposed to
They ought to be.

>They insist on voting because it directly affects them
Should a child get a vote on whether they ought to take their medicine?
No, and for the same reason: They don't know any better. And until they do, that decision shouldn't be up to them.
It's worse for voting, because it's not only them that it affects, but everyone else. Just look at Americans and their shit country.

>You don't own people, and if you disenfranchise them they will literally group up and kill you
Are you... a westerner?

>wish we lived in some geniusland utopia, but that is never going to happen
Cool, but I didn't say that. I said:
"I'm not asking anyone to get a degree in math or even learn algebra, dumbass"
"stay out of decision-making if you're not gonna put the effort to make sure you're not casting retarded votes"

>Again, grow up. You look even more like a child with this second post.
"Submit to us retards. Stop making us look in the mirror."
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>>14992449
>you're a pseud if you understand magical tricky words
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>>14992428
>I don't even wanna think about doing anything to change the current situation; I'm not gonna entertain the thought on a Vietnamese zoetrope forum that doesn't even affect anything
>it's better to just accept getting dicked by retards for the rest of humanity's history
But of course, things were always changed for the better by people who said "I don't wanna change anything".
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>>14992428
>>14992523
>words words words
>>>/lit/
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>>14992540
>You have to waste your time doing things that benefit me and things I care about, or my opinion of things is the only valid one.
How is this even a good reply? Dude's job isn't to care about your opinion. I mean, if all my neighbors got holocausted I wouldn't care, not my fucking problem. If my country started going to shit I would just run away somewhere else, I don't owe anyone anything as it is, in your fantasy world it'd be even worse.
And to solve both your problems, you can reach a compromise by having your logic courses as part of the k-12 education system and a GED or high school diploma required to get a voter ID. The problems you guys are making up are easy.
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>>14992583
>strawman
No wonder you defend retards with a passion; you're a retard.
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((p - 1) * (p - 1) - 1) / p = p - 2
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>>14991373
>>14991388
>>14991370
Lol, fuck physicstards.

>DUDE, you need to use an extremely precise and lengthy taylor series to solve this harmonic motion problem, but also use 10 m/s for gravity
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(3x^5 - 2x^4 + 3x^2 - 2x) / (x^3 + 1) = (3x^2 - 2x)
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(x^4 + x^3 +4x^2 + 3x + 4) / (x^2 + x + 1) = x^2 + 3 + 1 / (x^2 + x + 1)
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What do you think about mathematician Caroline Ellison?
>Get into one of the world's best universities in the world because your dad is a professor there
>Finish your mathematics bachelor's and become a billionaire and ceo of quant trading firm despite having zero mathematical or financial skill or talent
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>>14993075
What problems did you solve in highschool?
>alumnae from Math Prize for Girls:
>Caroline Ellison (Newton North High School, advised byGiorgia Fortuna of MIT, as part of the PRIMES program) discussed her work on a problem originally suggested by MIT Professor Richard Stanley, The number of nonzero coefficients of powers of a polynomial over a finite field.
>Coefficients of polynomials over finite fields often encode information that can be applied in various areas of science; for instance, computer science and representation theory. The purpose of this project is to investigate these coefficients over the finite field Fp. We use Stanley's matrices to find what we conjecture to be an approximation for the sum over n of the number of nonzero coefficients of P(x)nover Fp. This leads to questions in representation theory and combinatorics. We hope for further research in this area to find a relationship between the number of nonzero coefficients in the expansion of a polynomial to the nthpower and the digits of n base p.
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>>14993106
>We use Stanley's matrices to find what we conjecture to be an approximation for the sum over n of the number of nonzero coefficients of P(x)nover Fp.
>We hope for further research in this area to find a relationship between the number of nonzero coefficients in the expansion of a polynomial to the nthpower and the digits of n base p.
She didn't solve anything.
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Is there anything more humiliating than working on a tough math problem for hours and then asking a friend for help and they solve it in like 30 seconds?
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>>14993121
No, I didn't read the quote. I looked what the other alumnae from that year are doing and I am kind of seething that I wasted my highschool years half assing things and playing vidya.
here is that years "math prize for girls" list, all of them are associates professors, postdoc researchers, millionaires, etc
https://mathprizeforgirlscommunity.blogspot.com/2012/01/mpgers-present-their-research-at-joint.html
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>>14993075
Don't care and don't feel anything, women don't have to work for anything and their success or failure is either based on their father/husband's or entirely random.
So cool I guess?
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>>14993075
Guess that's more than anon can claim to have achieved.
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>>14992013
I wonder why the equivalent version >>14977977 is so much simpler for laypeople (including myself, when my brain is having a bad day). Is it because they have some kind of instinct for "detecting trouble" whenever a rule is violated, which they're applying to the problem?
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>>14992290
What's the name of the book?
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>>14993311
I think the difference is that in the alcohol version, they're not actually abstracting and using their brains; they're simply recalling information.
They know that "drinking alcohol or younger than legal = possible rule violation" from experience in life.
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>>14993538
Just 'Linear Algebra'. There's another one from him called just 'Algebra' but that's about abstract algebra and not linear algebra
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Why would we prefer Fourier Transforms over Laplace Transforms to solve differential equations?
It's straight forward in case for solving DEs involving signal processing, but how would a mathematician decide between the two?
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Can /mg/ explain, in layman terms, to an engineer, what is the motivation behind using Jordan canonical form of matrices?

Please explain how are similar matrices, diagonalization, and Jordan form related to each other, and what are the implication of those for the corresponding vector spaces?
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>>14993821
>what is the motivation behind using Jordan canonical form of matrices
It's a way to write the matrix sparsely that reveals a lot of information about it. At most, there are 2 nonzero elements per row.
>explain how are similar matrices, diagonalization, and Jordan form related to each other
>similar
Think of similarity as "these two things are actually the same, but we're looking at them from different perspectives".
Imagine a square in front of you, and you rotate it 90 degrees clockwise. To someone on the other side, they'll see the square rotated 90 degrees counter-clockwise. So both the actions of rotating 90 degrees clockwise and counter-clockwie are actually "the same".
The way to go to this new perspective is to change your basis.
>Jordan form
What I said above about them. And every matrix is similar to a matrix with a Jordan form.
>diagonalization
A special type of Jordan form, where all the nonzero elements are on the diagonal. It's even easier to work with, because when you multiply it by a vector, you're just multiplying each component of the vector by a single number.
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>>14993916
>every matrix is similar to a matrix with a Jordan form
What matrix in Jordan form is similiar to
[eqn] \begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix} \in M_2(\mathbb{F}_2)[/eqn]
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>>14993938
The 2x2 diagonal matrix with v and v+1 in the diagonal, where v and v+1 are the roots of x^2+x+1 in the algebraic closure of F_2.
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>watch standup maths video
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>>14993916
Thanks for the reply, anon. My intuitive understanding of linear algebra is not very good (compared to, say, calculus, DE's or complex analysis), so please give me a rope here.
My understanding is:

If, say hypothetically, there are $N$ dimensions each having a force component $F_i$, and the resultant is $\sum{F_i} = F$. If we were to change the basis to another different set of $N$ bases of components by representing in Jordan form, the resultant will essentially remain the same, but the Jordan form will somehow help in analyzing the force, $F$?
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social norm is the discrete hexagonal lattice metric. because of muhdick and 4 limbs and 1 brain.
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>>14993075
>What do you think about mathematician Caroline Ellison?
Incredibly ugly
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On the real number line, how cringe is getting an outlined square when I finish my undergrad and a filled in black one if I ever get a PhD?
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So a computer checked finitely many graphs to prove the four color theorem and found it applied in every case - what is the proof that they only needed to check a finite number of graphs?
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Spending 11 years becoming a reputable mathematician in high regard and learning stupid logic to subtly sabotage Coq
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What is the prerequisite to reading picrel?

What am I in for?
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>>14994570
Real Analysis and Linear Algebra to a thorough depth. Nothing else is necessary for intro FA, but to go beyond intro FA in FA you need Topology and Measure Theory.
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I think I'm gonna be kicked out of college...
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>>14994790
What happened?
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>>14994790
Fucked several Prof's, or rather they fucked me
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>>14994590
Why is that book recommended in /sci/ wiki's electrical engineering resources? Engineers don't have to take real analysis formally in college. What gives?
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>>14994817
It's been two semesters now that I stop going to classes midway through, didn't even do any tests. I hope they don't mind it, but that's already grounds for expulsion.
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>>14994920
>I hope they don't mind it
ya think?
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>>14991594
this reminds me of recurring nightmares I had about missing exams and forgetting I signed up for a class
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>>14994893
>>14994920
Normally that's a regular Friday night in any other
case but what made you stop coming to class?
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>>14994975
Depression and anxiety, I thought only weak people had those things so I turned a blind eye to my condition for way too long, until the departament head called me to his office and said that I should get my shit together or he would have to kick me out, so I promised I'd go to a psychiatrist.
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>>14994982
>until the departament head called me to his office and said that I should get my shit together
Do americans really?
Here they would just kick you out.
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>>14995019
Here they like to boast about how humane they are, so they gave me several warnings beforehand, of which I ignored all and then he called me to his office to give me an ultimatum.
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>>14994982
No, anyone can have depression and anxiety.
Anxiety by itself isn't so bad if you can work
through it and not like that of a panic attack.
your mood and not as deep as depression.

In a way, there is something you feel you lack
or that you're facing a large wall...you don't
know how it got there or why it's happening
now of all times, but you must address it as
ugly as it is.
>>
Proof that P = NP:

Assume that this is a P != NP universe (call it RU for real universe)
Then there exists a problem (call it %) which is NP but not P
Simulate a universe (call it SU) in which P = NP
Use your simulation to find a polynomial algorithm for %
Copy the algorithm from SU to RU
This contradicts the claim that RU is a P != NP universe

QED
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>>14995081
P=NP if and only if N=1.
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You do play a classical instrument and read classical literature, right? You're not just a math drone who thinks everything in life can be reduced to theorems and propositions, right?
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>>14995102
>play a classical instrument
yes, several. music has a close relationship to mathematics.
no, and I don't really intend to start.
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>>14994443
you'd thinl that would be part of the proof they published
>>14994375
0.99999...
>>14995102
>muh classical this and that
i play with my cock and read the weather
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>>14995206
cringe, and yet unfathomly based
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>>14995081
and hence the diagram commutes
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>>14994443
That's why the proof consists of two parts. One showing the seeming infinite number of maps / graphs can be reduced to a finite number of configurations. Then all of those configurations had to be verified by computer and back in the 1970's that was something like a 4-5 weeks of cpu time for each one.
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>>14995102
Literature is cool, but instruments are a huge time sink. I’d rather listen to a symphony than replicate it
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>>14995300
math is also a huge time sink in this regard. playing music is incomparable to only listening to it, and composing is completely unlike either of them. nearly anyone can read a book, many can analyze them. these things are not of the same order of sophistication.
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good anons of /mg/, join the discussion on algebra textbooks in this thread >>14995223
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>>14995359
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how do you ploot a sinc function without the divide by zero condition?
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>>14995468
Piecewise
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>>14995102
>You do play a classical instrument and read classical literature, right?
Yes, because I am one flesh with my wife, that does all of those things for us.
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Are there any particular math books you own with high quality binding and covers you love? Colorful glossy plastic designs and yellow paperbacks just seem insulting for the content in most books.
Can only thing of an old copy of Elements of modern abstract algebra by Miller, that really captures the class and formality math textbooks deserve.
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Why does the sci wiki recommend functional analysis for EEng?
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>>14995564
No they cost like \$500.
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Is X correct? Is there a way to simplify that last statement? Sorry for the shitty paint sketch.
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>>14996149
fuck I just realized I could've used the law of cosine
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>>14996149
sin(90° - arcsin(S)) = cos(arcsin(S)) = sqrt(1 - (sin(arcsin(S)))^2) = sqrt(1 - S^2)

as you would have also gotten quicker if you just used Pythagoras from the start.
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>>14996163
Thanks! I completely forgot about Pythagoras.
why do I never see the simplest solutions first ffs
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>>14996124
I have the same question. I'm guessing it's an elaborate troll attempt from some /mg/ fags
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>>14996175
It's best if you don't use inverse sine/cosine in your solutions.
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Man Calc 3 is so kino once you get to vector fields and beyond. I can't wait to take differential geometry bros.
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>>14996278
Why?
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Doing babby Galois theory. Sure, fine, you can't solve general quintics in radicals, what the fuck is "radicals"? I want an exact definition. Is it just $(x+c_{1})*(x+c_{2})* (x+c_{3}) *\cdots *(x+c_{n}), \; c_{i} \in \mathbb{Z}$? Is x+pi a radical?
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>>14996593
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>>14996603
Thanks, I cannot believe my book doesn't have a rigorous definition of them
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>>14996348
Im also studying multi calc, its much more interesting than real analysis.
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>>14996646
Wait till you find out about analysis on manifolds
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>>14996646
principles of mathematical analysis (baby rudin) chapter 9 covers everything important in a standard vector calc class and significantly more.
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>>14996654
He just read the first chapter and decided Analysis is boring and fake, like rest of the board.
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>>14996575
There aren't many identities with them.
Most of the identities you learn involve sines and cosines directly, e.g. law of sines/cosine, angle sum formulas, etc.

This stems from something more important, and I feel like I should discuss it because it's a way of thinking different from what you're used to (and perhaps others would like to read this as well).

Normally when you're presented with a problem in school, you throw all the tools you know at it, without stopping to think through and see if there's an easier way. What do I mean? Imagine if I gave you a quadratic polynomial p(x) = x^2 - 3x + 17, and I asked you to find the sum of its zeros, how would you do it? You (the general reader, not OP specifically) would first solve the equation p(x) = 0, because the question wants you to do something with the zeros, so naturally you'd start there. Then after you're done you sum the two solutions.

What's the faster way of doing it? If the roots were r and s, then p(x) = (x-r)(x-s). Expand this, and you get x^2 - (r+s)x +rs. The answer drops right out: r+s is just minus the coefficient of x. So you get 3.

The difference between this approach and the first approach, is that the first one is the "backwards" approach, and the second one is the "forwards" approach. In the backwards approach, you start with something and you want to undo it. In the forwards approach, you assume you have it already, then do the operation.

In the polynomial example, the first approach wanted to essentially factor the polynomial to find the roots. But the question doesn't ask for the roots anyways, so you're doing more work. But in the second, you assume you have it already factored, then you multiply. Factoring is the undoing of multiplication, hence why it's backwards, while multiplication is forwards.

The reason brought all this up is: arcsin is the "backwards" of sin, so it's more work to deal with it, and it's best to avoid it.
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>>14996673
Interesting. I would have proceeded with the second approach to the polynomial problem too, but that's because I was taught explicitly how to do it (for generally a polynomial of degree 'n').

But how do I develop this kind of thinking even if I am not explicitly taught the techniques? Any good reads?
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>>14996762
>But how do I develop this kind of thinking even if I am not explicitly taught the techniques? Any good reads?
I don't have any specific resource that I used. For me, it's just intuition built through experience.

Though I'm not gonna send you off empty-handed. There's a YouTube channel called SyberMath, and he solves math problems daily (more challenging than what you'd see in school/undergrad). What's different about him is that for every problem, he solves it with 2 or 3 different ways, and I do notice that he starts with the backwards most of the time, then does the forwards. Maybe you'll start seeing how this way of thinking goes?
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>>14993160
without further proof its safe to assume anyone in a "women in stem" program who does research had her hand held the entire time
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How do I prove that every subset of the irrationals is closed?
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>>14997051
Why would you want to do that?
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>>14997058
Willard's Topology:
>A subset A of a topological space X is dense in X only if the union of all open subsets in the complement of A is empty.
If there are non-empty open subsets of the irrationals then the rationals must not be dense in the reals.
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>>14997051
This doesn't seem to be true consider
[eqn] \left\{ \pi^{-n} | n\in \mathbb{N} \right\}[/eqn]
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>>14997067
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>>14997075
>Munkres
American trash.
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>>14993138
yes.
> Solving it after hours of hard work
> show it to a friend
> he spots an error in 30 seconds
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>>14995102
I used to play piano, then I got into maths
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>>14996648
I already know a bit about that. Im pretty hyped for smooth manifolds, they seem so interesting to study.
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>>14997097
This is why I hated self studying math. I could never trust my own proofs.
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>>14996662
Nah, I read spivak's, and yes it was boring as fuck. But I also completed it
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>>14997104
All my proofs are correct if i dont check them
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>>14997097
I gotta stop acting like I have friends who like math
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Why is differential geometry so full of indices
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>>14997311
Because it's full of dimensions
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I finally got a break for a few days after weeks of stressful deadlines.

In the coming weeks I have:
>presentation
>report
>paper
>project
>exam
All due soon before finals.

I just wanna play a bit more. I'm suffocating.
>>
>>14997097
There's nothing wrong with another pair of eyes...

...eviscerating, critiquing, tearing you proof down...
>>
>>14997589
Well, you can play with yourself first.
Best to get it out before the semester-end
academic slamfest and the pity afterparty.
>>
I want to teach myself maths from the ground up. Is khanacademy still the best starting point?
>>
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>>14997589
>I just wanna play a bit more. I'm suffocating.
do you mean work on your own math projects? or just fuck off and play vidya

if you have the motivation you should do it. because eventually that wanes and it just feels like work again
>>
So, I was studying today metrics in this online course and i saw something that had no explanation (neither searching the internet i could find something)

Why Liters = Dm^3? I know volume is used when we are speaking about how much we can fill something, but I couldn't find a explanation for something so basic.

Sorry for the stupid question, math isn't my thing and I'm studying the basics for this important test to college.
>>
>>14997936
Along with the conveniences of using the metric
system, one of them is the direct connection
between volume (dm^3) and fluid measure (L).

When the meter was defined and used to make
dimensional measurements, it's natural to think
about what amount of liquid can fit in a box (or cup, etc.)
from the measurements. But, the liter initially started
as the amount of water that weighs 1kg under
standard temperature and pressure.
Since 1964, the liter definition changed to be 1 dm^3.
>https://edu.rsc.org/endpoint/a-plea-for-litres/4011076.article

There might be a slight difference in water in the change
of definition, but I figured that amount is close
enough to the volume (dm^3) measure anyway. In chemistry,
the use of dm^3 is even preferred than the fluid measure (L).
>https://www.quora.com/Why-is-Dm3-preferred-over-litre
>https://goldbook.iupac.org/

Finally, here's an awkward video of a guy showing
the connection between 1 liter and 1 cubic decimeter
with a paperclip thrown in.

(*This is very familiar if you hear of an engine
with 6.7 L [or 6700 cm^3] of air displacement,
or a nurse requiring 10cc [10 cm^3] of medicine,
for example)
>>
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you dumbasses don't just become mathematicians.. you first have to investigate mysteries.. and if you investigate the greatest of mysteries, your honest dedication to finding the answer is what makes you a mathematician.. you don't just pick up this book or that.. there has to be something you want to know.. but more importantly, it has to be something that others have failed at, preferably for generations or even millenia.. if you want to be great, do what it takes to be great.. and be willing to put aside prestige.. for if you are correct, and if you do indeed find something.. then you will be hated and rejected by those who were unwilling to embark on the journey
>>
>>14998074
sure thing frobenius, I'll drop out and start working on whatever that means right away
>>
>>14998121
>>
>>14998136
i'll watch this but I gotta warn you my expectations are very low
>>
>>14998144
props to steve youngs what a pass
still not sure what you wanted me to take from this
>>
>https://en.wikipedia.org/wiki/Longest_common_subsequence_problem#Second_property
can someone explain this to a brainlet? is this help in eliminating the last character in the case that they are different?
>>
Currently applying to PhD programs. Is the expectation that you should have published research already as an undergrad? Because that's the impression that I'm getting, but this seems virtually impossible if your interest is something like algebraic geometry/topology or representation theory, where you only dip your toes in during undergrad. Can anyone clarify this stuff for me?
>>
>>14998402
it's true that graduate programs tend to expect some research to be done as an undergrad, but they won't expect you to have done it in your intended area of study. they're mostly just looking to see that you have the potential to perform well in a research environment. you could have a strong resume without doing any sort of research on graduate math topics, like for example helping out with cross-discipline research that needs a math person. if you're feeling up to it, reaching out to one of your professors to see if you can get onto one of their active projects would be a great option. and nice list of intended areas of study! algebraic topology and representation theory are some of my favorites as well.
>>
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>>14996779
Thanks anon.
>>
>>14998417
I mean, part of my degree involves a "research" project which is more or less going in depth on a particular topic and/or doing examples, but it's not really anything publishable.
I have plenty to write about on my statement of purpose, but it's just tripping up that they have a specific section in the application to include your published work. Also, even if what I'm doing in my undergrad research project did get published by some miracle, it wouldn't be until after I had sent out my applications.
>>
>>14998458
though it's definitely helpful undergrad research assuredly isn't a prereq to a graduate program. a strong letter of recommendation and references to things you've studied or worked on that would indicate potential for research will be very attractive to admissions readers. you might want to consider reaching out to professors at the schools you're applying to that share your interests and could help you craft a more specific letter for individual programs.
>>
Suppose weekdays of birthdays and genders are unifomly distributed among Babies.

Suppose a family has two kids and one of them is a boy. Then the probability that the family has two sons is 1/3.

Suppose a family has two kids and one of them is a boy Born on a monday. Then the probability of the family having two sons is 13/27.

This is really fucking with my head. If we now also know that the boys name is anon will the probabilitx of two sons change again?
>>
>>14998475
Thanks for the advice. I'll see how I go.
>>
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Is duality related to dual spaces?
>>
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I was watching "A Beautiful Mind" the other night. In one scene, John Nash gives this problem to his students of his multivariable calculus class. At first glance it seems like it has something to do with vectors spaces of vector fields with zero curl, but that's about all I can make out. Anyone know what the question is or want to try solving the problem?
>>
>>14998839
http://www.personal.psu.edu/jwh6013/Math21aF09/LECTURE24WS.PDF
it's actually a fairly nice problem for a vector calc class.
>>
>>14998839
He's defining a set V (I don't understand the whole definition where does the 'X' and 'V' come from) and W as gradient of some 'g'. Then he's asking for the solution for the divergence of (V/W).
>>
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>>14998858
I think it's "dim" not "div". Besides, v and w seemed to be sets and not vector fields.
>>
>>14998773
What kind of duality?
>>
>>14998839
he's basically asking them to calculate $H^1(\mathbb R^3\setminus X)$ (first de Rham cohomology)
>>
>>14998888
I don't know. I hear that thing all the time in context of optimisation.
>>
>>14998839
How do people write like this and not get repulsed by their handwriting?
>>
>>14999027
why do retards like you care about handwriting?
>>
>>14999034
Not who you replied to, but I worked as a grader, and I saw the most atrocious handwritings.
I used to send pics of what I saw to friends and ask them what they thought the student's writing said. I'd know what they mean because I know the correct answers, but no one knew what was written.

Examples:
>student writes what looks like "11111", but is actually "144"
>student writes what looks like "1c75c", with the last c below the 5. It's "10750"
>student writes "pre-j", then an "o" above the "j", and a "b" above the "o". He meant "per-job"
>student writes "t", then a mix between an "r" and a "v", then a mix between a "4" and a "u", and another "t". He meant to write "that"

Like Jesus Christ, do you understand that what you write is meant to be read by others?
>>
>>14995102
I used to play Piano but I'm not very good sadly
>>
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>>14999010
Oh that. Yes, that's exactly what is meant. See pic related.
Dual problems are often easier to solve because of greatly reduced dimensionality, and it's nice to know exactly when this also solves the primal.
>>
>>14994375
You mean as a tattoo?
>>
>>14999080
from my experience, in the most severe cases, it's not even meant as disrespect toward the teacher more than it is just minor dysgraphia (especially if it's not consistently ugly, as in letters are written in wildly different (ugly) ways if that makes sense) probably coupled with stress.
One thing that annoys me, though, is that many people seem to confuse cursive with illegible/ugly handwriting. My guess is that it's not taught anymore at a lot of schools.
>>
>>14995102
It's not reprehensible in the slightest to be especially interested in math. Especially if one considers the sheer time investment that is needed to really be proficient in anything, it's not surprising at all that humans tend to specialize.
I'm sure if we all had infinite time, we'd eventually study everything that interests us to a satisfactory degree but that's simply not the case.
Not to mention, mathematicians are usually the most humble people with regard to that I've come across. Outside of the Sokal affair, I'm not aware of any attacks by them on anything non-mathematical.
>>
>>14999160
Yeah
>>
>>14999034
Because if I am attending a lecture, I expect to be able to read what's written on the board.
>>
My brain keeps getting ahead of itself when writing/typing.

Like I'd write a letter before one it's supposed to come after.
>>
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>>14999080
as a lefty ive come to the conclusion that my handwriting will never be beautiful. something about having to push the pen and hand into your words really makes it more difficult. kind of a cart before the horse situation.

and as a plooter ive also come to the conclusion that my work will never be taken seriously by academia or even industry like a quant house or whatever. too bad for me
>>
>>14999289
>something about having to push the pen and hand into your words really makes it more difficult
My language is written from right to left and I'm right-handed, so I know what you mean.
I just stick to English for writing.
>>
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How do I get matrix A without counting S^-1?

if I know S and D

I see you get A*S=S*D when you multiply both sides by S but what then? You can't do a gaussian elimination from there because it's A*S and not S*A, right? What should I do from there
>>
Academia is too stressful. Everyone is always talking about grades and exams and I don’t have time to study other stuff I like.
More than one professor have told me I have very good intuition/insights and asked if I’m interested in a PhD. I don’t think I could finish it, I would just kill myself.
I kinda want to just tell them that “I would kill myself if I were to do a PhD” but I don’t want to be rude.
>>
>>14999165
I've noticed zoomers are bad at cursive handwriting. Maybe too much typing and less writing
>>
>>14999345
Hey anon I'd be happy to help you with this but I'm a little confused about the question. If you're looking for A (assuming diagonalizable) and have it in terms of a matrix of eigenvectors S and and a diagonal matrix D, $S^{-1}$ should exist because S must be invertible. could you say a little more about what you mean by not counting $S^{-1}$?
>>
>>14999354
Grades and exams are not really a problem at grad schools as much as in undergrad though. You have to take less courses and do more research.
>>
>>14999361
They say in the assignment, that there are 2 ways to solve for A, one is the longer way (wich I of course can do) of just taking the inverse matrix of S by gauss elimination.
But they say that there is a shorter way to do it where you do not have to determine inverse matrix of S.

The ultimate question is to solve all solutions for Ax=7x, but I am stuck at how to calculate A.

Thanks for helping me fren.
>>
>>14999371
I don’t know if that makes much difference. Just replace “grades and exams” with “do research and publish”. If anything I will have even less time to spend with my gf and build a family, and the pay (grant) is terrible.
I wish I could tell my professor how I feel because I really want to share this thoughts with someone but it feels rude.
>>
So what's a *typical* PhD like in the US?

Do you take courses? Or is it only research?
How many years is it?
Do you have to teach?
What's the financial situation like? Do they pay you or what? Do they house you?
Are there "entrance exams" or something like that?

I wanna get a PhD, but I basically know nothing.
>>
>>14999402
Well, that’s a choice you have to make. If you really prioritize family over the pursuit of knowledge, you do you.
>>
>be me
>study math
>get into argument with professor about the non-sense of real numbers
>quintessential religious disagreement
>want to switch majors
>applied math rejects me
>CS accepts me
>have to take math for CS class
>lmaothiswillbeeasy.webp
>professor and TA barely understand math
>constantly get marks taken away despite being right
>try to argue my points
>obvious unawareness of math leads to them refusing to accept my points
at least I'll be passing right?
was it a mistake to have left math? should I have just sucked it up and accepted the status quo of reals?
This whole time I thought CS was a very mathematical subfield of math, but it turns out they're all mathematical retards.
When we went over graphs when I was in math it felt like i was being bent over, but when we went over graphs in CS it felt like I was sitting in a preschool school class learning to count.
I can't stop feeling like I made a huge mistake. I had the assumption it was going to be like applied math but for computers.
I've been rejected by the applied college like 8 times already. I think they're just asshole.
>>
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How do you remember everything? I think if I had to retake a calc 3 test over flux equations I wouldn't be able to do it now.

I've taken a couple classes since calc 3 and have only really used derivatives and multivariate integration. But it feels uncomfortable to know that knowledge is just slipping away.

Should I download an an anki deck and just review it every now and again?
>>
>>14991672
A meme book, do Lee instead if you know (very) basic algebraic topology.
>>
>>14999289
>my work will never be taken seriously by academia or even industry like a quant house or whatever

Hey, don't doubt yourself. Your ploots would make it in any
professor's office as a new form of mathematical art. Maybe
clad in bronze for the lobby of a quant house.
>>
>>14999553
You never forget concepts. You may forget some nitty gritty details or formulas, but not the concepts (assuming you actually understood the big picture while learning the topic)
>>
>>14999560
yeah, I guess I just worry I'm NGMI if I don't keep every derivation in my head. It also kinda sucks to but all that time into problems just to forget them later
>>
>>14999546
Anything free from contradictions is not nonsense, including the reals.
If you don't like any specific axiom that leads to the reals, or you don't like working with them (and maybe in the future you'll work in a field where you can avoid them), then that's all fine. But that's no grounds to dismiss anything and implicitly shit on people who work with them. These are all constructs of the mind, whether they have real life application/counterpart or not.

If you're acting like this at the first bump in your road, then math isn't for you.
>>
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>>14998839
Essentially, if you take the vectorfields on $\mathbb{R^3}/{x}$ that have zero curl they form a vectorspace over the reals, and since the curl of the gradient is zero, the gradient of functions form a subspace. He's asking you to compute the dimension of the qoutient of the two spaces. In the given space the qoutient is zero dimensional, i.e every curl-free field is the gradient a scalar field. As a hint, use stokes theorem to show path independence of line integrals and use that to define a scalar field.
As a bonus, try to find a curl-free vectorfield on $\mathbb{R^3}/{(0,0,z)}$ that isn't the gradient of a scalarfield. Why does the previous argument break down in this case?
>>
>>14999657
The last set was meant to be 3d euclidean space with the z-axis removed.
>>
>>14999373
I'm tempted to give what feels like a trivial answer to this. The solutions x for $Ax=7x$ are the eigenvectors of A that correspond to an eigenvalue of 7. I've gotten a bit distracted sorry, but I hope this resource will be helpful for you.

I just saw your other posts
>>>14999483
and
>>>14999550

again, not to border on being too trivial, but if it's a single vector you're looking for, it's probably just the eigenvector associated with eigenvalue 7. To find what this should be, simply look for the value 7 in your matrix D, and the column in S of the same index will be the associated eigenvector. The problem may or may not want you to include a scalar in front of the eigenvector. Hope this helps a little.
>>
>>14999718
another quick note on this I didn't mention, I'm assuming here that D is a diagonal matrix.
>>
>>14999546
>is it me who is wrong?
>no, it's everyone else
crank classic
>>
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Are the parts of discrete mathematics that can't be reduced to matrix operations useful?
>>
I'm given the algebraic number

$x = \sqrt{2} + \sqrt{3} + \sqrt{5}$.

How can I find the a polynomial $f$ such that $f(x) \in \mathbb{Z}$? How do you search for such a polynominal?
>>
>>14999892
power of mind
>>
>>14999906
so there's no textbook solution for this?
>>
>>14999999
>>15000000
>>
>>14999892
One easy way is to get all its Galois conjugates r (including itself), then multiply all the factors (z-r), z being an indeterminate (using z instead of x to avoid confusion).

In the case of square roots, that's east because the conjugate of sqrt(n) is just -sqrt(n) (for squarefree n).

So there are 8 conjugates in your case (writing s3 for sqrt(3) for brevity):
s2+s3+s5, s2+s3-s5, s2-s3+s5, etc.
You get the idea.

>>14999911
This is the textbook solution ^
>>
>>14999629
>>14999746
>count number of reals
>run out of natural numbers
lmao realtards are literally deranged
>>
>run out of money
lmao poortards are deranged, how can you run out of money?
>>
>>14999916
thank you
>>
>>14999919
all of mathematics is abstraction and none of it is "actual", but it's valid in as far as it yields results and nothing else matters
>>
>>14998054
Thanks, anon. You more than answered my doubts!

Such question has no answers in Portuguese, only mediocre things like " Liters = dm^3 because of volume" yes, I understand this, but how that was developed? And you just gave me everything i wanted. Thanks again, bro. May God bless you.
>>
>>14999953
>>14998054
Of course! Any other questions you have on the
metric system?

Two pairs of new units have been recently approved
for small and large units, if you want to ask on that...
>>
Brainlet, here. I think I'm being filtered by precalc. There is so much shit to remember. This might be where my math career ends. Sorry bros, go on without me...
>>
>>14999999
>>15000000
>>
>>15000011
fear not precalc is extremely fake. depending on how you could choose to continue, algebraic manipulations could be the only relevant part of that class. precalc is an algebra 2 dlc with trig bloat.
>>
>>15000019
brilliant i was just going to look for these
>>
>>14999919
contemplating how close this was to a seasonal get pains me
>>
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>>14999892
You can just use Maple.
>>
>>15000151
>only even terms
Why?
>>
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>>15000165
Because it's a bunch of square roots?
If you use third roots the terms all have exponents divisible by 3.
>>
>>14999553
this is one of the funniest images i've seen on /sci/, thanks
>>
>>14999951
schizo babble
>>
>>15000257
This is why they won't accept you.
>>
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why did math suddenly become fun i never liked it before
>>
>>14999915
:D
>>
>>14999981
Not for now... My test will be today and i will have another in 4th of December, perhaps I will come back in the meantime and ask something else, hope to see you around to help me!
>>
>>15000696
>>14999981
Good luck!
>>
We have the vector space of dimension n of the integer numbers.
We have the vector space of dimension n of the rational numbers.

Let A be a subset of Z^n so that all integer linear combinations of A generate Z^n. Does A also generate Q^n?

I think the standard basis is the only basis that can generate Z^n with integer linear combinations.
The standard basis then also generates Q^n.
And A has to be of the form: "Standardbasis + any amount of vectors from Z^n" to generate Z^n and also Q^n.

But what is the underlying reason or how can I justify that the standard basis is the only basis?

What makes me think that it has to be the standard basis is that for any other linearly Independent family you require rational coefficients to generate Z^n.

Im not sure how to prove this though. On mathstackexchsnge a similar question got asked and it was answered with a proof with determinants, which we havent covered in class.
(Only vector stuff related topics in class we covered where vector spaces, sub spaces, linear (in)dependence, generating sets, basis, dimensions).
>>
>>15000780
There is no vector space of integers unless you mean integers modulo.
>>
>>15000783
My bad yeah Z^n is Just supposed to be a subset of Q^n
Are my other assumptions wrong too?
>>
>>14991073
any professional mathematicians working in Uni here? What kind of pc build do you have for your work? Or is it just a pencil and papers?
>>
>>15000375
Computers do not recognize the validity of ""real"" number
>>
>>15000788
I don't understand your question. For any vector space with a basis you can generate infinitely many other basis if you have infinitely many scalars.
There can be no vector space of only integers, nor could there be an vector space over integers. Integers are not a field, (except residue integers)
>>
>>15000850
>go to Iran
>try to pay with British Pound
>they won't accept it because it's not valid
"Therefore Britain doesn't exist, QED."
See how much of a schizo you sound like?

And why are you complaining anyway? You're basing your arguments on computers anyway; you're where you belong, with the plebs.
>>
So I've got a fun problem related to Euler Maclaurin summation.
Basically, I want to find L,R so that I integrate x^m from n+L to n+R and get n^m for m=0,1,...
This essentially will mean integrating over the interval will agree with simply sampling at n.
The best you can conventionally do is R=1/2 and L=-1/2 which is correct for m=0,1.
Then I tried to be more clever by using complex R,L to see if I could squeeze more power out of doing a single integral.
I wanted to integrate x^m from n+L to n+R and get n^m for the real part.
R = 1/2 +i/sqrt(12), L = -1/2 + i/sqrt(12) makes this work for m=0,1,2,3.

Now I'm considering R and L to be dxd matrices and I want the trace of the integral to be d*n^m
The system of equations I get remind me of the systems in:
Basically I want tr(R-L) = d and tr(R^k - L^k) = 0 for k>1.
I expect it to be able get the correct answer for m < 2d since there are 2d free parameters (the eigenvalues).
I could probably go up to 4d if I allow complex numbers and take the real part of the trace instead.

It might also be worth only using some of the parameters to satisfy the n^m requirement and choosing the rest of them to control the error terms you get from repeatedly integrating by parts (these terms would be analogous to the bernoulli numbers in the usual E-M summation).
This is some black magic and wouldn't even know where to look for information on the topic.
>>
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>>15000859
I will translate the exact wording of the exercise.

"Let n>=1 be a natural number and Z^n the subset of Q^n consisting of all vectors with integer entries

a) Let A be a subset of Z^n such that every element of Z^n can be described as a integer linear combination of the elements of A.
Show that A is a generating system of the Q-Vectorspace Q^n."

So as of yet im thinking, that A has to, atleast, contain the standard vectors.

Because my guess is that not every vector of Z^n can be described as a integer linear combination of a Basis that is different from the standard basis.

And then, since any A has to contain the standard basis, it will generate Q^n too.

First of all is this true? Second of all how do I prove this for the general case of n dimensions?

When I google integer linear combinations, the results are something about greatest common divisor and such. Is this a way to show it?
Along the lines of, with the standard basis 1 is always the gcd so I can find a integer linear combination for any element of Z^n?
>>
>>15000912
You know that every vector in $\mathbb{Q}^n$ can be multiplied with an integer to get an element of $\mathbb{Z}^n$? (By multiplying the the lcm of all the denomominators)
Use that.
>>
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>>
>>15000912
>Because my guess is that not every vector of Z^n can be described as a integer linear combination of a Basis that is different from the standard basis.
$\{(-1,0), (0,-1) \}$ is an obvious counterexample, and so is $\mathbb Z^n$ itself. But whatever the set maybe, since the standard basis vectors belong in $\mathbb Z^n$, it must be in the integral span and hence the rational span of the set. And since the standard basis vectors are included in the span, their span must also be included in the span and hence $\mathbb Q^n$ must also be in the span.
>>15000924
You could also just go for a more constructive proof like this.
>>
>>15000947
I think your example is wrong. But I agree that my hypothesis is wrong too.

>>15000954
Yeah i found the same counter example, my bad.
Your explanation is very nice and makes sense. I tried to come up with something like this.

Thanks for the help to everyone that replied
>>
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Jesus Christ, Linear Algebra is so dull.
>>
How do I proof that the conjugacy class of the kernel of a morphism is equals to the kernel of the kernel of morphism again (without using homomorphism)?
Let
[eqn]
c_{x}: G \to G, c_{x}(g) = xgx^{-1} \\
f: G \to G
[/eqn]
be morphism. Show
[eqn]
c_{x}(Ker\ f) = Ker\ f.
[/eqn]
>>
>>15000965
The fuck do you mean "without using homomorphism"? That doesn't even make sense.
>>
I mean I am not allowed to assume that
[eqn]
f(g') \star f(g) = f(g' \cdot g)
[/eqn]
is, for the groups $(G, \codt), (H, \star)[\math]. >> However I would be happy about any proof idea or hint. >> >>14999892 the polynomial will have degree 8 just find any degree 8 poly with that as a root. >> >>15000011 fuck trigonometry. Pay no mind. You'll memorize as much as you need to do the problems. >> >>15001089 Okay, I guess it follows from the fact that for each [math] x\in G,$ the conjugation morphism $c_x$ is an isomorphism and so this induces an isomorphism of short exact sequences [eqn] 0\to\ker f\hookrightarrow G\xrightarrow{f} H\to 0 [/eqn] and [eqn] 0\to c_x(\ker f)\hookrightarrow G\xrightarrow{f} H\to0, [/eqn] where $H=\operatorname{im} f.$
I'm not actually sure about how to go about showing that the vertical arrow $H\to H$ makes the diagram commute without using the homomorphism identity though. I think maybe since the category of groups has (co)kernels and (co)products, then something like the Five lemma can be worked for the category of groups, but I'd imagine this would still implicitly use the fact that $f$ is a group homomorphism.
Honestly, I feel like the question is ill-formed. I struggle to believe there is a way to prove this without using the fact that $f$ is a group morphism, since if you took any old function which was not a group morphism, then the claim would fail.
>>
Thanks you very much
>>
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How much trigonometry should I know before diving into calculus?

basic identit(t)ies, what polar coordinates are, how rotation works is enough?
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I will also ask the scientific assistant, who writes the exercise sheets. She has already messed a few exercises up, so the probability is not that low that there is a mistake.
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>>15001222
None.
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>>15001222
honestly anon trig is really only relevant to calculus because calculus happens to be applied to trig functions a lot due to how common they are. you'd probably only use it in the context of simplifying integration and changing coordinate/variables of integration. the most important one is $\sin^2(\theta)+\cos^2(\theta)=1$. It's useful enough that it's worth just remembering it. The others can usually just be looked up or derived as needed.
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>>15001222
Understanding unit circles and polar coordinates is enough. Identities are not important especially when you move to complex analysis and derive Euler's formula.
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WOWZERS I JUST LE HECKING LOVE PSEUDOCODE, SO MUCH MORE INTUITIVE THAN JUST WRITING DOWN WHAT TO DO
Fucking CSfags ruined math.
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>>15001299
Make a language based on mathematical syntax
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>>15001307
The English language
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>>15001299
honestly I prefer algorithmic processes to be written in pseudocode, but pic related doesn't actually contain any of it. This is just a list of ordered steps anon for sweeping a matrix, no?
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>>15001336
That was a bad example because it uses algorithms contained in other chapter.
Picrel to find a basis from a generating set is best example. This shit could be explained in one line, but no, the author needs to be a pretentious pseud.
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>>15001359
Ah I see. Yeah you're right this sucks lol. I'm guessing a prof is making you read this, I'd also be very annoyed by it. cringe
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>>15001375
>I'm guessing a prof is making you read this
No, I am self loorning
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>>15001389
oh good stuff anon. self loorning is a sophisticated skill. I read Friedberg's linear algebra when I was loorning, you might give that one a try if you're looking for better books. I could also drop you a pdf somehow if you'd one, but I'm sure it's still up on the libgen directory and such
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>>15001400
I have skimmed through a lot of books including Friedberg, Hoffman, Axler, Halmos, etc., but none of them is as comprehensive (and has difficult exercises) as the one I am following. I am preparing for an exam, so I can't choose the topics I want, otherwise I wouldn't have given a shit about number crunching chapters like solving linear equations.
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>>15001410
huh well that does make sense then. some of those other authors are pretty based as well but I didn't really start consulting multiple books on the same subject til abstract algebra so I'm really only familiar with Friedburger's linear alg. hope the number crunching doesn't get too tedious, good luck with your exam!
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>>15001418
Thanks.
>huh well that does make sense then
It does make sense because they are all pure theory books, but I also have to study some numerical methods. But all the applied undergraduate math books are made for braindead retards. This is the only theoretical book I found which also talks a fair bit about applied theory.
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What books should I read to learn about stuff like Pick's theorem and Euler's formula (for polyhedrons). What subject is it?
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>>15001515
Ah right right, yeah I was kinda wondering why the one you're using would have the sweeping algorithm or even one to find generators for that matter, but generally disliked the book I had for my first linear algebra class so it didn't seem worth recommending. I'm not sure if it's the same everywhere but my program had linear algebra 1, which was mostly numerical (though more basic), and then linear algebra 2. the algorithms is your book didn't look like whatever was in my "Linear algebra with Applications" text, I don't think there was any discussion of the sweep operator at all in that course. But, it was garbage as one would expect. I'm not aware of any others like yours that would be grounded in theory with much emphasis on numerical methods, but I at least understand why the author might be writing this way since it seems it would have a relevant use case to career SWEs looking to implement things more complicated that what would appear in the standard books on applications. I did both cs and math in undergrad so I at least know the pain of reading from those sorts of comp sci adjacent textbooks. Never touched anything that tried to cover theory alongside the other stuff though, closest ones would've been on ai or analyzing algorithms and even those could hardly be said to contain much of it to speak of.
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>>15001571
I'd imagine pick's and euler's formula for polyhedrons would generally be discussed in most books on analytic geometry
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>>15001585
What book though? When I look up analytical geometry, I find kiddie precalculus stuff, but Euler's formula seems way too involved to be treated well in books like those.
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>>15001615
Coxeter happened to have one that might be what you're looking for. I'm not sure if it contains a discussion of Pick's theorem, but
https://archive.org/details/introductiontogeometry2ndedcoxeter1969/page/n169/mode/2up
on page 153 of the text and page 170 of the website e-reader, there's some more detailed discussion on Euler's formula.
some of his other books, namely Non-Euclidean Geometry and Projective Geometry, are more well known and held in high regard. most of the stuff in part 4 probably won't be of use for you at the moment, but parts 1-3 are supposedly quite nice.
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>>15001573
This book (Rao, R.A., & Bhimasankaram, P. ) is definitely more theory than applications. It's written by pure statisticians, so the focus on rigour is not surprising. I could never read those applied books because they would just give an algorithm and you'd pretty much have to believe it works. While here, first the theory is developed (which is done very well, no problem there) then the an algorithm is shown. For example, picrel shows how the $\rho$ank of a submatrix of the original matrix corresponds to the corresponding submatrix of the echelon matrix, and is used to find $\mathscr C$olumn basis. While an applied book would have just told you what to do and believe it works. Wish there were more books like this. I'll probably be in this positing again scouring libgen for rigorous applied books when I decide to study differential equations.
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>>15001634
Nice thanks
>315.5mb
What the fuck?
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>>15001652
there's bigger out there
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>>15001634
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>>15001659
>there's bigger out there
For you.
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>>15001660
lol. lmao even
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>>15001222
Also inverse trig including conversions, basic identities like atan(x)+atan(1/x) = sgn(x)*pi/2 etc
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>>15001635
If I get a chance, I'll ask a prof I had a good relationship with in undergrad about rigorous diff eq books with applications. their focus was geometric measure theory and most of the stuff they're interested in involves more complicated approaches to PDEs in $R^3$. the deepest I've explored in this direction is on the subject of minimal surfaces, which are an interesting thing to read about (lightly) even if not from a rigorous perspective if you're ever looking for a distraction from numerical stuff
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>>15001721
Nice. Thanks.
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>>15001738
no problem, I'll probably be able to get an answer from them by the time you'll be looking for one
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>>15000165
To get an feel for why, try to build the minimal polynomial by yourself

\begin{align} x^{2}&=\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)^{2}\\&=10+2\left(\sqrt{6}+\sqrt{15}+\sqrt{10}\right) \\ x^{2}-10&=2\left(\sqrt{2}\left(\sqrt{3}+\sqrt{5}\right)+\sqrt{15}\right)\\&=2\left(\sqrt{2}\left(x-\sqrt{2}\right)+\sqrt{15}\right)\\&=2\left(\sqrt{2}x-2+\sqrt{15} \right) \\ \left(x^{2}-6\right)^{2}&=4\left(\sqrt{2}x+\sqrt{15}\right)^{2} \\ ... \end{align}

For this one you'll get a 8-degree poly with even powers but for some others like $\sqrt{2}+\sqrt{3}+\sqrt{6}$ the minimal poly will be a degree-4, why?
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Rudin, Abbot or Amann?
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>>15001802
$\sqrt{2}+\sqrt{3}+\sqrt{6}$
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>>15000926
Linear Programming feel.
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>>15000454
Are you actually doing math or thinking about doing math?
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If you sum the first N natural numbers and then take the last digit, the sequence for N = 1, 2, 3.. is: 0 1 3 6 0 5 1 8 6 5 5 6 8 1 5 0 6 3 1 0 and repeats. That's also the same forward and backward. What else is there to say about this?
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>>15002356
The sum of the first n numbers equals N*(N+1)/2.
If you look at the last digit in base 10, you look at N*(N+1)/2 mod 10.
That's zero when n*(n+1) is a multiple of 20, e.g. 4*5=20 or 15*16=240, which explain the two zero's around N=4 and and N=15, and of course 19*20 and 20*21.
If you're at the number M and count from there, you get the difference (M+N)*((M+N)+1)/2-N*(N+1)/2 = M*N+N*(N+1)/2 so if you let M be the multiples of 20 and N go from 1 to 19, the zeros must be periodic.
I'm not gonna do all the work for you but I'm sure fixing K a multiple of 20 and going backwards gives you a polinomial which mod 10 is the same as. going forward from K-20, etc.
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>>15001515
>This is the only theoretical book I found which also talks a fair bit about applied theory.
Trefethen and Bau III say hi.
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>>15000892
>Therefore Britain doesn't exist
Correct
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>>15002426
PS by the same logic we can predict the periodic zeors for
$\sum_{n=0}^N n^d$
for any d, given

https://en.wikipedia.org/wiki/Faulhaber%27s_formula

Pic related for $\sum_{n=0}^N n^2$, where we get a 6 in the formula and hence a period 60
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>>15002442
>I'm desperate to win
Keep taking L's, you're not getting back in, crankoid
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>>15002426
just so you know, i don't really understand
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Dear group theory autists,

I'm trying to figure out how to construct a partition P = {P_1, P_2, ..., P_k} of the set {1, -1, 2, -2, 3, ..., n, -n} into q-tuples, where n = qk, in such a way that no sub-collection of P with any number of parts is closed with respect to inverses, except the whole partition.

I've tried using cosets of the group Z_2n, and the primitive element theorem (suggested by another anon), to construct the partition, but neither of those worked. Any other ideas?
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>>14999892
What is the definition of $\sqrt{2}, \sqrt{3}, \sqrt{5}$ ?
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>>15002088
Abbott is an introductory book, it's nothing like the rest. It's by far the most pedagogically sound book I have read though.

>>15002435
Do you mean Numerical Linear Algebra? This doesn't seem to be a book on theory of Linear Algebra but more on its applications.
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>>15002831
>Do you mean Numerical Linear Algebra? This doesn't seem to be a book on theory of Linear Algebra but more on its applications.
I might have misunderstood what you were after, but nonetheless I still hold that this book contains more theory than might be expected at first glance (the authors say as much in the Preface).

In any case, it's an eminently readable book compared to Golub and van Loan (which is probably a better resemblance to the applications book you seem to have in mind), so you have little excuse not to at least leaf through a couple of topics and form your own judgment. Though my personal opinion is that for anyone who needs to go beyond blindly calling linear algebra routines from their software package (and has the mathematical chops for it), this book should be required reading.
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$\sqrt{2} = \left[ {\begin{array}{cc} 1 & 1 \\ 1 & -1 \\ \end{array} } \right] >> >>15002948 [math] \sqrt 2 = \begin{vmatrix} 1 & 1 \\ 1 & -1 \\ \end{vmatrix}$
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>>15002920
Yes I did notice it has a lot of theory, but I am mainly looking for a standard LA book with some applications, mainly solving system of equations. This is a nice find though, and I intend to read it, thanks.
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>>15002973
Basically Gilbert Strang combined with Hoffman.
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>>14997051
>How do I prove that every subset of the irrationals is closed?
>>14997067
>If there are non-empty open subsets of the irrationals then the rationals must not be dense in the reals.
You have missed an important detail, “closed” is not the same as “not open”. Not every subset of the irrationals is closed. Now, how do you prove every subset of the irrationals is not open? I would need to look at how Willard chooses to define the irrationals, but the expected way is to show that whenever $x < y$ are irrationals, there is a rational q such that $x < q < y$.
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>efficient algorithm for solving linear equations
>it was made by a person named Doolittle
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>>15001635
imo, there's just something really ugly about linear algebra. Could also just be because I never read these pure theory books. How is Rao compared to, say, Roman's Advanced Linear Algebra?
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>>15003120
Rao is an undergraduate book, albeit very terse.
>imo, there's just something really ugly about linear algebra
I agree. I think LA can get very boring, as it deals a lot with very abstract identities, and Rao does not shy away from the boring parts. I definitely do not recommend it if you want a fun read, it's more so for those who really want to get into LA. I think Axler is a much more enjoyable read, lots of graphs, and he pretty much ignores all the boring parts. He barely talks about matrices and completely skips linear equations. Linear Algebra shines when it's applied to geometry and calculus.
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Why are they like this?
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>>14991073
Im having some trouble understanding the definition of product sigma algebras as introduced by Folland (picrel).

Specifically I am having trouble seeing what $\pi_{\alpha}^{-1}(E_{\alpha})$ is supposed to be, Specially since he claims that if $E_{\alpha} \in \mathcal{M}_{\alpha}$ then $\pi_{\alpha}^{-1}(E_{\alpha}) = \prod_{\beta \in A} E_{\beta}$ with $E_{\beta} = X$ for $\beta \neq \alpha$ this last statement really baffles me.
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>>15003323
fuck forgot pic
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>>15003308
>find out it's not meant for you