/mg/ = /math/ general: Genius Edition

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I like Math but depression is killing my brain.

>>9043298
I feel the same way, have not found a way to stop this torment and do what I "enjoy"

>>9043298 >>9043321

Be Positive, not Negative.

Think Positive [math] \mathbb{R}_{>0} = \{ x \in \mathbb{R} | x > 0 \} [/math]

>>9043298
>>9043321

I just call other people brainlets on /sci/ because, deep down, I'm afraid I'm stupid. I've squandered all my opportunities in life because I'm too afraid to try.

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>>9043344
What if I have a topological mindset? How should I orient myself?
>>9043298
>>9043321
Drugs. I'm ordering a chemistry set myself and I'm going to synthesise ketamine (helpful against depression), some amphetamines (for obvious reasons), and LSD.
I just need my first salary first.

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>>9043298

>>9043359
How much would it cost? That sounds like a legit solution to approach math with depression

>>9043369
By my back of the envelope estimation (I haven't ordered anything yet, no funds) a few hundred euros (price of reagents not included, just the tools). I've thought about this a lot in recent weeks and I think the investment is worth it since it'd be much safer than buying from a dealer, and besides narcotics I really see no other means to deal with such issues.

>>9043359

i doubt you'll be able to synthesize LSD mate. amphetamines are fairly straightforward though, as are a number of opiates. ketamine is one of my fave drugs so best of luck on your endeavors

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>>9043298
You just wait until you start getting memory loss. You'll struggle to remember Calculus formulas, and what problem you're even solving. And that's just the beginning.

>>9043384

i combat the fog with stimulants and the depression with opiates, but still doing well in a STEM degree hahah i want to blow my brains out

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Found this cool meme list the other day. I was thinking about following it thoroughly over the next 5 years. What does /mg/ think?

-- -- -- --

>0. Remedial Mathematics
Khan Academy

-- -- -- --

>1. The Prerequisites of University Mathematics
Pre-Calculus - Carl Stitz & Jeff Zeager
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
How to Prove It - D. J. Velleman

-- -- -- --

Pick One Path:

>2a. Introduction to Applied Mathematics (Some Proofs)
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Differential Equations - Shepley Ross
<go do your STEM lol>

>2b. Introduction to Pure Mathematics (Proof-Based)
Calculus Vol. I & II - T. M. Apostol
Principles of Topology - Fred H. Croom
A Book of Abstract Algebra - C. C. Pinter
<go do your pure maths lol>

>2c. The Mixed Approach
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Differential Equations - Shepley Ross
Principles of Topology - Fred H. Croom
A Book of Abstract Algebra - C. C. Pinter
<go do whatever you want lol>

-- -- -- --

>3. Foundations for Advanced Pure Mathematics
Linear Algebra - K. M. Hoffman & Ray Kunze
Analysis I & II - Terence Tao
Visual Complex Analysis - Tristan Needham
Algebra - Michael Artin
<feel free to branch off into any specialization>

>>9043381
My priorities are special K and meth right now. I am already noticing the effects of age-induced reduced mental acuity and it's killing me. My window is closing, and it's closing fast.

>>9043395
elaborate. what's your background, and how exactly are you planning on following it?

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>>9043402
How old are you?

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>>9043413
...28.

>>9043409
>>9043409
I'm a 20 year old chemistry major who've finished up to Calculus II, which I did well in with only a little bit of difficulty with the weird convergence tests. I started to like mathematics after calculus, and I wanted to challenge myself to see how far I could go. I figure if I end up hating it after giving it a fair trial, I could still use the background to gain marketable skills and maybe get a little bit smarter/more disciplined for the effort while my brain is still malleable.

I plan on dedicating ~1 hour minimum per day for at least 5 days a week, probably more on the weekends, with weekly recaps to review methods, theorems, proofs, etc. I would begin with "How to Prove It" by Velleman and then probably continue along the "2b" path in order to avoid overlapping with the linear algebra and multivariable calculus that I will be taking anyway as part of my major requirements. It's all organized in order that I would read it I guess, and it seems like a prudent path, but I'm not sure. All I know is that I can't go wrong with my first choice.

>>9043436
If you're not published by 25 you'll never make it. Your brain is already decaying and there will not be enough time for you to learn. Sorry anon, but you're stuck. The only intellectually productive time is one's 20s.

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>>9043298
Are you me? Ebin :D

I must say, I appreciate the Mitchell-Bénabou language.

>>9043298
>>9043321
>>9043344
>>9043357
>>9043359
>>9043364
>>9043369
>>9043377
>>9043381
>>9043384
>>9043388
>>9043402
>>9043413
>>9043436
Jesus christ anons, what the hell happened to you guys? Do you wanna talk about it or something? Maybe some helpful /mg/ advice can help ya out.

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>>9043451
...b-b-but I did publish (well, only two papers), just not before 25! why are brains so fragile anyway, this is not fair!

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>>9043459
I literally do not wish upon being alive anymore. I have been a disappoint to humanity and the only thing I've found joy in since I've been labelled a disgrace is math. Alcohol has only been my only friend and I am unable to do math because of this depression haunting me like an ghost keeping me distracted from making any progress. I'm terrible at math and it's funny that the only thing you have passion for is the thing you are unable to do

>>9043460
To sort the true winners from the brainlet losers like you, obviously. The truly intelligent succeed effortlessly. The fact that you're having any difficulty or have ever had to try proves you're just an impostor.

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>>9043459
There is nothing to talk about. My whole life is a mistake, my only solace are numbers but now they're fading.

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>>9043459
>what the hell happened to you guys?
When the only communication you have with the outside is via the internet, you begin to manifest the same problems as one involuntarily placed in solitary confinement. And the only way out is to meet people, but you can't do it because your social skills have atrophied through years of shitposting.
Half a decade of laughing at the misfortune of others and ironically telling people to kill themselves has led me to the point of unironically considering suicide myself. The universe is truly ironic.

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>>9043493
...

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>Think you have it hard white boi?
>Why don't we swap places, I do the whining, and you man the gun?

>>9043515
Nice trigger discipline!

>>9043515
>implying I wouldn't take this trade
that kid's job is killing niggers. he's living the dream

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>>9043459
I don't actually know.
>unwanted child
>some kind of attention issue had me struggle to keep up even in early primary school
>parents get me evaluated some years later
>+2 sigma
>no, baby anon - this shows you're just a shitty kid trying to make us look bad.
>never really complete a grade, allowed to move on anyway because +2 sigma
>retreat into vidya
>drop out at 15
>3 years WoW
>4 years alcohol
>accepted into good school anyway by testing in
>breakdown
>DEPRESSION x5 years


I'm an empty shell of a person with no knowledge or skills, or hope.

>>9043515
If killing a baby were to raise my IQ by just one point I'd kill dozens gladly.

I always wonder why these threads start with people talking about suicide and then in the middle people start animeposting in what looks like coping to me.

Aren't we all living the life? Doing mathematics 24/7? Isn't this the literal dream. What happened?

>>9043395
>>9043437
So we have one kid whose life is still ahead of them but you faggots would rather all circlejerk about how you wasted your time like undisciplined niggers instead of preventing another generation reach the same miserable faith. Shame on you, you bunch of narcissistic faggot /r9k/ spawn.

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>>9043539
Math makes the voices silent. The voices tell me I'm good for nothing.

>>9043543
>Math makes the voices silent.

Then do more math dummy. Want a number theory problem?

>>9043545
He's is being ironic dumbass.

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>>9043459

>what the hell happened to you guys?

When you've lived around social anxiety your whole life so much so that you're too afraid to even go outside anymore, that you're starting to get slightly paranoid and trying your hardest so that no one can tell how your thought-process works, and that you don't talk with anyone all day, and all that you do is post on 4chan about what you would have liked your life to have been like had you not screwed it up by nearly failing high school and no being able to study STEM and not being able to do what you enjoy. When you know you'll never be able to do what you enjoy in life and that at 22 your better years are already behind you, because of mistakes you made when you were 14, because you were too much of a stupid lazy arrogant anxious retard to realize what you were doing. When you feel constantly inferior to everyone on /sci/ because they understand complex problems and can solve them with their intellect, which you can't even understand the basics of calculus, because, hey, you failed high school math like the moron you are. When you try to meme your IQ to grasp on the last thing you might have, but you realize you're actually average and so incompetent that there's no way you'll ever understand anything STEM-related, so you stay at home, jobless, anxious, hating yourself.

God, I'm ashamed of being associated with you people

I have a problem: how many cubes of side [math] c [/math] can you pack inside an elliptic paraboloid truncated at height [math] h [/math] by a plane perpendicular to its axis of symmetry.

>>9043395
add Analysis: With an Introduction to Proof by Lay to option 1

>>9043563
>22 your better years are already behind you

Oh sweet summer child

>>9043567
>goes on /sci/
>superiority complex

pick one

>>9043571
Do you mean like for option 2a)? And why?

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>>9043545
No, I don't do number theory. I haven't found it interesting.

>>9043559
Or was I? I really think I'm shit unless I succeed at math problems.

>>9043290

Did you guys ever have to memorize binomial coefficent identities and simplify sums of binomial coefficients?

I might have to do this but I hear that there is a way around it if you learn how to use a hypergeometric series and learn a couple of identities

but it's confusing af

>>9043590
>No, I don't do number theory. I haven't found it interesting.
any mathematician who disregards a big, core area like this is not a good mathematician

>>9043590
>I haven't found it interesting.

>You learned that there were infinitely many primes
>You did not immediately want to find out more about primes

Shit man I think I found the source of your problems. You were born a brainlet.

Prove that [math] 2^{2^n} + 1 [/math] divides [math] 2^{2^{2^n} + 1} - 2 [/math]

>>9043585
I used to come here to have discussions about math and occasionally see math problems. These days it's either traps or niggers or people talking about how pathetic they are. If I wanted to see pathetic people talk about how pathetic they are and how totally not gay traps are, I'd go to /r9k/.

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>>9043569
>>9043603

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>>9043602
You know, I am not looking for acceptance, at least not online.

>>9043603
The existence itself is enough for me. Primes give some nice proofs like the countability of finite products of countable sets, etc, but they are not relevant to my interests per se.

>>9043610
The /mg/ started at a bad time. The first time the thread was made it had an anime picture and then some faggot started posting about how "animeposters pedophiles need to go back to /a/" and this caused a massive strike of people posting anime girls and traps just so spite him.

The thread lived and died like that, and it became a meme. Then when the second one was made the OP did not have an anime picture, but people quickly followed suit posting anime girls again.

I declare the /mg/ needs to die for its own sake and then in 5 months we re-built and lets hope that this time it all goes right and that it does not turn into an ironic meme.

>>9043618
>The existence itself is enough for me.

But what about curiosity? I mean, perhaps now your research interests are away from number theory but what about when you were a kid/university student. How could you not obsess over prime numbers as a kid?

>>9043620
everything is a meme my friend
we are the memes

>>9043620

Memes aside, the paragraph I posted about my pathetic self is true.

>>9043630
Nobody cares
>>>/r9k/

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>>9043626
I saw the infinity proof in hs, and on the same course we covered stuff like proof by induction and predicate logic. Why does that proof method work? What can be expressed using propositional calculus, quantifiers and relations? These questions were more interesting in my opinion.

>>9043634
Oh so you are into pure logic. I think that is a courageous choice, given that it is a dead field but good luck.

>>9043620
>The first time the thread was made it had an anime picture and then some faggot started posting about how "animeposters pedophiles need to go back to /a/" and this caused a massive strike of people posting anime girls and traps just so spite him.
The anti-anime shitposting only starts because there are maybe 3-4 users here who hijack every thread by circlejerking with anime avatars, who have been doing this longer and far more consistently than anybody bitches about it
There's no "irony" involved other than the millenial defense mechanism of claiming everything is merely ironic so you're at a safe distance from people calling you a faggot

>>9043631

The friendly anon did.

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>>9043636
Logic is what got me into math, but then I ventured into the realm of topology. Topology lead to algebraic topology and pointless topology. To understand pointless topology, I had to get myself familiar with Heyting algebras, which are intuitionistic logic stuff, so I sort of returned back to where it all started. At the moment I'm tackling topos theory to get a firmer grip on what lies ahead.

How about you?

>>9043653
>How about you?

I am a simple man. I like number theory. I originally did not view numbers in a sexualized manner but I was mainly intrigued in how you can easily craft interesting problems in number theory. You know, when you see elementary number theory problems and you can solve them you feel really good about yourself. It is a nice high because solving them genuinely makes you feel like you are at the top 1% of intelligence. I liked to feel like that.

To this day I keep that tradition of solving hard problems. If you were in the last /mg/ I was the one who posted a solution to a Putnam problem.

But that was just the beginning, the more I studied number theory the more I started seeing natural numbers affectionately. I started to really care about them in a personal way, like if they were my friends. So this got me interested in how you prove big theorems like PNT and that got me into analytic number theory, which I study now. I doubt I will move on from this. Number theory just looks like the field I want to contribute to and I happened to be really good at analysis so I am just doing what is convenient. I suck at fucking algebra.

>>9043451

you're dumb as fuck anon

>>9043493

lol. none of this shit matters, if you can't make cool shit with your skills and meet other like minded people then it's all worthless. if you devote a life to academia than a couple years literally means nothing, and outside of academia it doesn't matter. the bulk of interesting research isn't done by fucking 20 year olds. you're trolling but smug posting that just shows your own inexperience is super gay

Use difference of squares:
[math] 2^{2^{2^{n}} +1} - 2 = 2(2^{2^{2^{n}}} - 1) = 2(2^{2^{2^{n}-1}} - 1)(2^{2^{2^{n}-1}} + 1) = \cdots = 2(2^{2^n} - 1)(2^{2^n} + 1)(2^{2^{n+1}} +1)\alpha [/math] with [math] \alpha [/math] being a long sausage of powers of [math] 2 [/math] to which you add [math] 1 [/math].

>>9043689
Meant for
>>9043603

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>>9043668
>To this day I keep that tradition of solving hard problems. If you were in the last /mg/ I was the one who posted a solution to a Putnam problem.
I was pretty sure that was you. It's that brainlet thing of yours, it made me connect the dots. You got a lot of shit in that thread.

>I suck at fucking algebra
But anon, algebra is the easiest field.

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>>9043720
>algebra is the easiest field.
What. (Not that guy by the way.)

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>>9043725
It's the field in which I'm best, so it must be easy.

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>>9043725
Are you implying it isn't?

>>9043692
You are right but more detail is needed. But I'm not your teacher so who cares.

>>9043720
Yeah, people who don't like number theory are mean.

>But anon, algebra is the easiest field.
I thought that but I don't know, I feel like a suck at it. I just don't intuitively "feel" algebra like I do analysis. But well, I have to take like 2 more algebra classes in the future so perhaps my perspective will change.

Anyways, I seem to be good at elementary algebra and I was just able to solve this problem so I give it to both of you and the entire thread to have some good old high school fun:

Let [math] a \in \mathbb{R}_{>1} [/math]. Simplify the expression [math] \sqrt{a + 2\sqrt{a-1}} + \sqrt{a - 2\sqrt{a-1}} [/math]

Tip if you get really lost and end up with something weird: the expression can be simplified to just an integer times a square root with a linear expression in terms of a inside.

>>9043753
[math]2\sqrt{a-1}[/math]

>>9043757
Shit how did you do it so quickly? Did you already know it?

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>>9043760
What? It was quick by your standards maybe.

>>9043757
Explain reasoning.

>>9043769
[math]a \pm 2 \sqrt{a-1} = (\sqrt{a-1}\pm 1)^2[/math]

>>9043763
>>9043764

No way you can do all of this in your head:

[math] k = \sqrt{a + 2\sqrt{a-1}} + \sqrt{a - 2\sqrt{a-1}} \\
k^2 = a + 2\sqrt{a-1} + a - 2\sqrt{a-1} + 2\sqrt{a + 2\sqrt{a-1}}\sqrt{a - 2\sqrt{a-1}} \\
k^2 = 2a + 2\sqrt{a^2 - 2a\sqrt{a-1} + 2a\sqrt{a-1} -4a + 4} \\
k^2 = 2a + 2 \sqrt{a^2 -4a + 4} = 2a + 2\sqrt{(a-2)^2} \\
k^2= 2a + 2(a-2) = 2a + 2a - 4 = 4a - 4 = 4(a-1) \\
k = 2\sqrt{a-1}
[/math]

>>9043772
You don't have to, you just need to be a studious person and solve enough exercises.

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>>9043753
I suck at elementary stuff, but I'm decent in abstract algebra. Maybe you'll do some homological stuff and that will make you like it more.

>>9043771
Very elegant, I like it.

>>9043772
That's because I did it by noticing this >>9043771
instead of expanding like a caveman, also I'm not >>9043764

>>9043775
Meh, knowing an identity like that just takes the fun out of the problem but I guess it works.

Anyways, if anyone cares the problems are all from

http://www.fmf.uni-lj.si/~lavric/Santos%20-%20Number%20Theory%20for%20Mathematical%20Contests.pdf

I found this book months ago when I was given a homework problem in number theory and I couldn't do it, I panicked and then I started googling for the problem. It was nowhere to be found so I then went on stackexchange. There the problem had not been asked either, so then I googled for all the number theory problem compilations I could find online and I went looked problem by problem.

I never found the problem like this... but I did find a lot of good problem compilations like this, and I particularly like this one as it adds not only problems but a short list of theorems I can quickly refer to, so I don't need to look elsewhere for theorems and lemmas. And now I'm on vacation so I decided I will do all the problems in the book in the 3 weeks I have free from university.

>>9043784
>instead of expanding like a caveman

Why is /mg/ so mean? I am not a caveman. I just haven't memorized all the algebra identities :(. And I think my proof is better as it is more creative. It is trivial to apply a known identity, but it is non-trivial to square the entire thing and start seeing where that takes you.

>>9043791
You don't need to memorise that. All you need to 'memorise' is that [math] (a \pm b)^2 = a^2 \pm 2ab + b^2 [/math] and [math] (\sqrt{a})^2 = a [/math].

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>>9043791
>why are you pointing out i'm retarded?
>i'm just retarded!
You need to fuck off and come back when you have a basic understanding of mathematics.

>>9043791
>Why is /mg/ so mean?
Okay that wasn't very nice, granted.

> It is trivial to apply a known identity
Yes, but it is non trivial to recognize known identities (here (a+b)^2 = ...) in non-obvious situations. That's why integration problems are troublesome (everyone knows fubini, u-sub and integration by parts, but it's another thing to know when and how to do these things).
That being said, in any other situation, I would have done what you did, because it's the natural thing to do.

>>9043800

How do I acquire that basic understanding of mathematics? :c I wanna be like you guys.

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Stop ganging up on the guy he made a minor oversight. It happens to everyone sometimes. (R-right?)

>>9043812
Natsuki is the only decent girl in the whole series, and she probably smells like a stinky NEET!

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>>9043812
>It happens to everyone sometimes. (R-right?)
*Blocks your path*
You wanna bet on that?

>>9043810
Read equations and inequalities by Kucera, Herman and Simsa. That's where I learned everything I know about basic stuff

>>9043817
you czech ?

>>9043817

Is that accessible to someone who only has knowledge of precalculus? I forgot a lot of it too.

>>9043820
nope, french

>>9043603
https://math.stackexchange.com/questions/2176998/show-that-every-composite-fermat-number-is-a-pseudoprime-base-2

>>9043814
Extraterrestrials in skin-suits don't count.

>>9043821
Yes, that's what I liked about it. Basically, as long as you know what a variable is and are familiar with basic algebra, you should be good to go.
Also, it doesn't try to be clever, doesn't skip steps etc. Really a great book for a beginner.

>>9043822
too bad. kucera and simsa are from my university, kucera is problably the best lecturer I've had so far

>>9043822
>>9043825

Je parle aussi français. Merci pour les suggestions!

>>9043826
No way haha this is crazy ! Well I'm indebted to him, I probably wouldn't be where I am today if it weren't for this book. It was just what I needed to read before college.

What is the largest number of points that can be distributed in a unit disk
such that the distance between any two of them is greater than 1?

What is the minimum number of planes required to cut a given cube into at least [math] n [/math] pieces?

>>9043854
6 ?

>>9043866
Nope.

>>9043854
[math] n \gt 1 [/math] or [math] n \ge 1 [/math]

>>9043359
Go read the buyer bible on /r/dnms
You'll save yourself a lot of trouble and be safer.
Don't go synthesizing psychoactive substances yourself.

>>9043882
Strictly greater than 1.

>>9043878
Really ? 5 then ?

Show that [math] 1 + 2 + 3 + 4 [/math] divides [math] 1^n + 2^n + 3^n + 4^n [/math], [math] \forall n \in \mathbb{N} \setminus 4 \mathbb{N} [/math].

>>9043892
Anon, are you actually even trying to solve this problem or just throwing guesses around?

Let [math] a < b < c [/math].
If they are consecutive odd integers, what is the value of [math] a^2 - 2b^2 + c^2 [/math]? What about when they are consecutive even integers?

What subfields of math have applications in manufacturing and finance? The only one i came up with is Operations Research

>>9043899
It is enough to show that it is divisible by 10=2*5

It is trivially always divisible by 2 so it only needs to be checked that 5 divides it.

When n is odd the problem is trivial as modulo 5, 3 = -1 and 4 = -2 so the sum will always add up to 0 modulo 5.

If n is of the form 4k + 2 then 4k + 2 is -2 modulo 5 so the resulting sum would be 1 + 2 + 3 + 4 = 10 = 0 modulo 5. (Calculate the inverses mod 5 of the numbers).

So it has been proven for numbers of the form 4k+1, 4k+2 and 4k+3 and that completes the proof.

>>9043899
I'm not. Here's my thinking: If I have n > 5 points on the unit circle, then at least two of them, say p and q are such that [math]\theta = \widehat{pOq} \le \frac{2\pi}{n}[/math]. Then, [eqn]|p-q| = |1- e^{i\theta}| = 2\left|\sin\left(\frac{\theta}{2}\right)\right| = 2\sin\left(\frac{\theta}{2}\right) \le 2\sin\left(\frac{\pi}{n}\right) \le 2\sin\left(\frac{\pi}{6}\right) = 1[/eqn]

>>9043907
either way, it's [math](b-2)^2 -2b^2 + (b+2)^2 = 8[/math]

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assume you have the the normal distribution where the mean is 0 and standard deviation is 1. shown as N(0, 1). N(0, 1) will, with a 50% chance give you a negative value and 50% positive. N(0, 1) will also give 0 as the mean and median.

Now we want to create the "absolute normal distribution", which would work in the same way as the normal distribution, except that this distribution calculates the absolute value of all outputs, so the absolute normal distribution would be simply | N(0, 1) |

Now, what is the 1) mean and 2) median of the absolute normal distribution, if we give it the 'normal' mean of 0 and the 'normal' standard deviation of 1.

Hint: question 1) is much easier than question 2)

>>9043854
Geometrically isn't this the maximum number of sides an inscribed polygon may have such as side length > 1? So using the side length formula [math]d = 2 sin(π/n) > 1 \Rightarrow sin(π/n) > 1/2 = sin(π/6) \Rightarrow n < 6[/math]. That is the max possible integer is [math]n = 5[/math].

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>>9043886
I disagree. If I do it myself I can control all the variables.

>>9043919
All this does is prove that [math] n \leq 5 [/math].
You still have to prove that [math] n = 5 [/math].
>>9043939
No. The points must be in the interior of the disc.

>>9043948
Doesn't it follow from my calculations ? If I take the regular pentagon [math]\{e^{ik\pi/5}, 1 \le k \le 5\}[/math], then the distance between any two points is at least [math]2\sin(\pi/5) > 1[/math].

>>9043937
Without any computation:
I'd put mean value around 1, in our case.
Median value will not be the same of the mean. It is definitely minor compared to the mean.

>>9043948
No to the
>isn't this the maximum number of sides an inscribed polygon
part only. The proof that n < 6 is correct, modulo a minor detail (shift the points in the interior along the radius).

>>9043941
You really don't know what you're getting into.
Just buy the purest shit you can find and pay the €50 to have it analyzed by Energy Control to remove any doubts about adulterants if that's what you're worried about.

>>9043964
No anon, because the points in your calculations lie on the boundary of the disc, not its interior.

>>9043990
Actually, never mind. Let's say just say you both solved it since I already mentioned the missing detail. >>9043972

>>9043990
Hmm okay, so I just need to make it smaller no ? If I apply a homothety of center O and a ratio r s.t. 1/2sin(pi/5) < r < 1, then I get five points in the interior such that the property still holds

>>9043974
When I say "control all the variables" I'm not referring only to the ones pertaining to the synthesis process itself.

>>9044002
Yes.
>>9043995

>>9043937
Let X be a random variable with normal distribution. We want to compute 1)
[math]\mathfrak E[|X|][/math] and 2) [math]\sigma(|X|)[/math]
1) [math]\displaystyle \mathfrak E[|X|]= \int_{\mathbb R}|x|e^{-x^2/2} \frac{dx}{\sqrt{2\pi}} = \sqrt{\frac{2}{\pi}}\int_0^{\infty}xe^{-x^2/2} dx = \sqrt{\frac{2}{\pi}}[/math]
2) We need only compute [math]\sigma(|X|)^2 = \mathfrak E[X^2] - (\mathfrak E[|X|])^2[/math].
But, we already know that [math]\sigma(X)^2 = \mathfrak E[X^2] - (\mathfrak E[X])^2 = \mathfrak E[X^2] = 1[/math].
Finally, [math]\sigma(|X|)^2 = 1 - \frac{2}{\pi}[/math]

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How do I do this? No hôpital/cauchy

>>9044008
Why the obsession with control when a couple days of research is all that's necessary to be able to judge who to trust. You'll also find out your risk analysis is way off.

If your end-game is acquiring psychoactive substances for self-medication, you're much better off putting trust in people that know what they're doing rather than going about it yourself.
Can you trust yourself to not fuck it up?

>>9044077
[math]\lim\limits_{x\rightarrow \infty} \frac{\ln(2e^x-e^4)}{x}=\lim\limits_{x\rightarrow\infty}\frac{\ln(e^{2x})}{\ln(e^4)x} = \frac{1}{2}[/math]

>>9044091
>being this wrong
just stop

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>>9044077
This might work, don't shoot me it's late

>>9044091
holy shit ur dumb

>>9044077
[math]\frac{\ln(2e^x-e^4)}{x} \geq \frac{\ln(e^x)}{x} = 1[/math] for all [math]x \geq 4[/math].
Further, [math]\frac{\ln(2e^x-e^4)}{x} \leq \frac{\ln(2e^x)}{x} \overset{x \rightarrow \infty}{\longrightarrow} 1[/math]
Therefore: [math]\lim_{x\rightarrow \infty} \frac{\ln(2e^x-e^4)}{x} = 1[/math]

>>9043502
>The universe is truly ironic.
The universe was merely set up by "him" as a kind of joke. Too bad you're retarded enough to fall for its most primitive tricks.

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I'm going to head to the gym soon so I'll just drop this here: https://arxiv.org/abs/1303.1202.
This article seems to be describing the kind of correspondence I'm interested in, although it focuses on the fusion (operator) algebra instead of the KZ connection. In certain cases (e.g. under assumptions of unitarity and metaplecticity) the two concepts are equivalent, I feel that by constructing an analogue of the KZ connection from a more general form of TQFT would allow us to look at TQFT/CFT in a more general perspective. And since the fusion algebra doesn't tell us anything about the geometry, it isn't useful when I want to look at AdS/CFT.
Overall the article feels like it is limiting itself to a class of very special UMC's so that it could make an 100% accurate and understood correspondence between it and CFT, and we all know being safe and conservative isn't my style when it comes to developing new things.

>>9043603
>You learned that there were infinitely many primes
What you """learned""" is wrong.

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>>9043653
Almost the same here, anon. But I'm just starting out.

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>>9044249
Let your journey be pleasant, little one.

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*enters your finite thread, which will never even have more than 10^1000 posts*

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Do any of you mathfags regret learning math?

Was investing all of this time worth it?

Did you become enlightened in any meaningful way?

>>9044429
>reddit frogs
>>>/b/

>>9044429
No regrets. It was Worthy. I'm enlightened.

If you were a librarian and had a wizard ask you to self learn as much math as possible with no background on anything beyond highschool math, but could use only one book, what book would you give to the wizard?

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>>9044691

>>9044691
the bourbaki collection :^)

>>9044712
>one book

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>>9044691
Fuck off Marisa.

>>9044437
>It was Worthy.
>I'm enlightened.

In what way?

>>9043298
I got depression from falling in love with some I can't have (since I have a gf already). Glad my math alumni anons going through the same thing.

>>9044691
a panorama of pure mathematics or mathematics made difficult

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>>9043502
>tfw my social skills are going to shit
>tfw I laugh at all the depressed people on this site, thinking that could never happen to me
>tfw I ironically tell people to kill themselves constantly

Fuck man... how do I get off this ride before it's too late?

Rate this brainlet realization:

http://0xbeef.coffee/posts/post9.html

>>9044776
>>9044776
Meetup.com for just literally any event that forced you to interact with humans.

Start practicing empathy - when you want to tell someone kys ask yourself first what is your true opinion against them? And is it even about them or is it about your feelings of the world at large? How does the person feel, why are they acting in a way that makes you want to call for their death?

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>>9044795
>http://0xbeef.coffee/posts/post9.html

>>9044816

ight, NIGGA

>>9044776
Be careful. At 16 I was banging bitches and started doing math on the side. After a year of pretty much being stuck in a room studying analysis my social skills were non existent. I'm now back to normal and finishing my undergrad, no bitches though.

>>9043460
You faggots with the need to publish papers amuse me. I'm here to study math for pleasure and the comfy teaching job.

Why do so many people on /sci/ pretend to be black

>>9044894
>Why do so many people on /sci/ pretend to be black
it almost always triggers some insecure whiteys

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>>9044883
>studying math for pleasure

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>>9044900
> not getting a boner after every new idea for a problem

>>9044090
>Can you trust yourself to not fuck it up?
Yes. Also, to add, the DIY element has a certain appeal to itself too.

>>9044691
Bourbaki.
>>9044708
>Gowers
Kill yourself.
>>9044727
It's one book spread over several volumes.

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>>9045118
>It's one book spread over several volumes.

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>>9045118
What's wrong with based Gowers?

>>9045123
owl-sowa.blogspot.com

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>>9045127
>owl-sowa.blogspot.com

>>9045131
Read the blog, it's short, only a couple dozen posts.

>>9045134
I'm talking about the entries from 2012, forgot to add. That's where he's explaining just how cancerous Growers is.

>>9044894
I am black tho

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This is a such a comfy book on differential equations.

>>9044729
That image really triggers my autism. English is read from left to right. The stem of the book should be to the left of the on the first cover.

>>9045308
I usually read from right to left. Maybe she does something similar.

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>>9045310
In English? How?

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Why did I get involved into this? I am retard and not able to finish single calculus book. My life is over

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>>9045322
"It is better to have tried and failed than never to have tried at all."

>>9045319
Weeaboos and custom printing. I can see it happening.

>>9045339
wrong, it's just as bad plus you wasted time

>>9045319
>In English?
Yes.
>How?
What do you mean by how? I just read from right to left.

>>9045322
Break everything down into small pieces.
identify the pieces you don't understand.
Work to understand them intuitively.
Bring everything together again.
You now understand it.

That's how I (brainlet) do it.

Not understanding something is not an option. Work on it until you get it. It's a slow process, but it's the only way.

After that it's just doing loads of exercises till it sticks.

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>>9044691

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>>9045433
Excellent choice! Also, Stillwell's Numbers and Geometry. I wish someone had given me these books in high-school (or earlier). My mathematical development would have been very different.

I have come to the realisation that if you are handsome you're a better mathematician.

>>9045499
If that was true I'd be able to solve basic permutation problems and end up with a consistent method :^(

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>>9045538
It is true. I didn't say that looks alone matter, only that looks matter too, so all else equal, a handsome mathematician is a better mathematician. A healthy mathematician with a beautiful face can more easily build rapport with others and collaborate to achieve results that an ugly mathematician with the same intellectual potential is secluded from by virtue of his unappealing features.

Remember how they said Grothendieck had this charisma about him? It was staring everyone in the face: he was handsome! Pic related, Grothendieck's manly, smug, symmetrical mug.

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How would I go about doing this type of question? I'm a brainlet with stats :(

>>9045499
I wouldn't say that, but I have also noticed that the best students tend to also be attractive.

>>9045539
Why is this image so sexual?

>>9043388
oh my god stop being a whiny piece of shit and just finish your degree.
I had a friend like you and all he did was bring me down.
That's how you are. To everyone.

I recommend the rope.

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Is there a typo in this problem? Shouldn't it be [math]\varphi : G \rightarrow G[/math]?
Because otherwise it seems really simple: [math]H \cap N[/math] must be trivial, which means that [math]\varphi[/math] is injective, so [math]G = H, N = \{1\}[/math], which makes the product map in the question very uninsteresting.
This is from Artin's algebra.

>>9045669
>Is there a typo in this problem?
Nope.

>>9045558
I would imagine that each student has the same chance of getting in (since they don't give you enough information if that's not true) so you'd have a binomial distribution with p = .3 and n = 10

The second one is just plugging one number into the distribution

The third you're best off doing by calculating 1 - P(n = 1) - P(n = 0), which is just a more convenient rephrasing of "at least 2" as "not 0 and not 1"

>>9045546
I wouldn't say Grothendieck was especially handsome desu, I think it's much more likely that he had a strong character because of his biography (if you don't know about it, I recommend you and everyone else look it up in mactutor, it's fascinating).

>>9045558
If I'm interpreting it correctly, the first sentence means "if you're Australian, you have a 30% of being accepted." So X represents the number, out of 10, of trials with a chance of success of 30% that succeeded. Which is the definition of a binomial distribution. Once you have that, the rest is just plugging into the equations for Binom.

>>9045683
Is my solution correct then?

>>9045573
>The guy has very obvious mental and drug problems
>"Don't be so whiny bro, just do it!!!!!" (while I whine about a friend bringing me down)
You could at least try to be consistent.

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>>9045134
>>9045137
>go waste an hour reading dozens of blog posts so you can explain to me why my unsubstantiated opinion is right

>>9045698
Not even close.

>>9043569

The volume of the paraboloid is (if I haven't messed it up) [math]\frac{\pi h^3}{3\sqrt{ab}}[/math], so it will fit [math][\frac{\pi h^3}{3c^3\sqrt{ab}}][/math] cubes.

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>>9045669
That's a retraction.

>>9043603
https://en.wikipedia.org/wiki/Fermat%27s_little_theorem

>>9045702
I've read them and he's right, the guy's cancerous AIDS.

>>9045669
it's an injective map

>>9045573

no one knows about this shit except myself and i don't talk about my depression to other people.

>>9045727
It's a homomorphism.
>>9045709
>>9045669
Since [math] {\varphi}_{\mid H} = 1_H[/math], you're right that [math] \text{ker }\varphi \cap H = 0 [/math] (if [math] H = 0 [/math] this is trivially true, if [math] H \neq 0 [/math] assuming there is some [math] H \ni h \in \text{ker }\varphi [/math] we get the contradiction [math] h = 0 [/math]) but it does not follow that [math] G = H [/math].
What you have to conclude is that [math] H \times \text{ker }\varphi \rightarrow G [/math] is a coproduct decomposition of G, i.e. every element in [math] G [/math] is of the form [math] h + n [/math].

>>9045737
It's more than injective.

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>>9045743
The "typo" is a retraction. If [math]i\colon H\to G[/math] is the inclusion map, then [math]\varphi\circ i=1_H[/math], and this means it is a retraction. A consequence of this is that [math]G\congH\oplus N[/math] (or, some people denote that by = in this case). It's a real thing.

>>9045749
[math]G\cong H\oplus N[/math]
I could have sworn there was a space.

>>9043395
>>9043409
>>9043587

>>9043571
>>9043437

Could I have some advice please? Seems like I got left hanging after people started talking about depression.

>>9045743
Here's an example
[math] \varphi (g) = \begin{cases} g\text{, }g \in H\\ 0\text{, }g \not\in H \end{cases}[/math]
>>9045749
Oh, misread. Yeah, [math] H [/math] is a retracted subgroup.

>>9045737
>>9045743
Thanks guys. Yeah, I realized my mistake - the trivial intersection only means the product map is injective, not [math]\varphi[/math].
I was thinking that I need to look at cosets, but didn't really get anywhere.

>>9045757
Nvm that example, I am retarded.

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>>9045766
Very retarded.

>>9043436
There's no loss in mental acuity for another decade and a half at least. You don't need to worry until you're in your forties.

You are worrying and stressed, this accounts for your mental fog and loss of capability. Sort out your stressors and your mind will be better equipped to deal with the more important things you want it to consider.

>>9043395

you need to read a discrete math book at some point

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why is this general full of cucks?

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>>9045772
>le sort yourself out meme
God I wish it were that easy. It's such a beautiful lie. My room is in perfect condition and yet I still make silly mistakes like this >>9045757

>>9043480
I can relate somewhat, which you might be able to relate to animeposter. My only joy in college was learning Japanese so I used it as a minor in an IB degree to work as a translator. I was excellent at it throughout my school life, but it was after I left and tried to use it in a job environment that I found they were not up to snuff. Every day I found myself wanting to use the language and study, but I was intimidated as I was expected to be wholly fluent before I open my mouth, and instead just found I was average.

My advice would be to either ignite another fire in your heart, or find something that will re-ignite your passion in math.

>>9045791
Your room is not you. You are clearly suffering from several stressors that are inhibiting your ability to think. It's quite simple, if difficult. Find the things that are ailing your mind, and solve them. Then you can return to what you were doing.

>>9045803
Ok Mr. Jordan Peterson, how do I find those stressors? (You know, I appreciate the intention but you're platitudes aren't helping.)

>>9045743
>>9045764
Ok, I think I showed your claim (that [math]HK = G[/math]):
The cosets of [math]N[/math] partition [math]G[/math] and the elements of [math]H[/math] are representatives of these cosets, since [math]\varphi(g) = \varphi(g') \implies gN = g'N[/math]. That means that every [math]g \in G[/math] is of the form [math]hn, h \in H, n \in N[/math].
I don't see how this proves that the product map is a homomorphism. It's bijective, but we still need the commutativity of [math]N[/math] with [math]H[/math[ or the normality of [math]H[/math].

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I'm creating a genetic algorithm and there's a couple of questions I'd like to ask.

However, first some background information:
if I have 2N individuals I'd always want to kick out the N worst performing. However, that wouldn't be realistic and might cause some hindrances to calculations so I created a selection method where the better you were, the smaller the chance is that you are kicked and vice versa.

In this picture, I have 1000 individuals ordered in how good they were at a task. the Y-axis tells the chance that an individual is kicked out. The selection algorithm I've made ensures that exactly have of the individuals are selected, while also maintaining the 'randomness of getting selected' (as in, it's still completely random whether individual C gets kicked out or not).

Here are my questions:
1) Is that curve some known function? It starts at (0,0) and ends at (0.8,1) with a total area of 0.5 (duh!)
2) Does there exist an algorithm that would create a straight line from (0,0) to (1,1) while always maintaining the 'randomness of getting selected'
3) I'm reinventing the wheel, aren't I?

>>9045842
starts at (0,0) and ends at (1, 0.8), darned matrices making me confused

>>9045837
both H and N are normal subgroups of G with a trivial intersection, so their elements commute.

>>9045720
This is incorrect. When you do straightforward divisions like this you're implicitly assuming that you can cut up the cubes into pieces and rearrange them inside the paraboloid so that they fill every cranny (or alternatively, that you can melt the cubes and pour them inside the paraboloid).

>>9045791
>le
>>>/r/eddit/

>>9045782
>reddit frogs
>>>/r/eddit/

>>9045863
[math]N[/math] is normal because it's the kernel of a homomorphism. Where are you getting [math]H[/math]'s normality from?

>>9045782
The same reason why every other thread is.

>>9043395
you're going to want an introduction to discrete math/set theory book and a book on probability theory.

>>9045895
apply the initial homomorphism on g*h*(1/g)
.

>>9043395
>cool meme
see >>9045877

>>9045756
>Could I have some advice please?
Okay, here's some advice; nobody in the history of 4chan has ever actually followed through with one of those giant meme curriculums and you aren't going to either. They're just a nice way to feel good about studying while sitting on your ass collecting pdfs.
If you actually want to self-study something, find one, MAYBE two subjects you want/need to learn, spend 5 minutes looking at books on Amazon, pick one and start reading. When you are on the last chapter you can start looking for what to do next.
Right now the most pragmatic thing you could do is read some introductions to analysis and linear algebra (you will need both almost everywhere) but ultimately you should try to read what you find interesting and fill in prerequisites as you go.

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>>9045901
Still not seing how that gives us normality or commutativity.

>>9045954
>Okay, here's some advice; nobody in the history of 4chan has ever actually followed through with one of those giant meme curriculums.
Then I'll be the first. Not all of us are here to whine about depression while posting obscure cartoons.

>Right now the most pragmatic thing you could do is read some introductions to analysis and linear algebra (you will need both almost everywhere) but ultimately you should try to read what you find interesting and fill in prerequisites as you go.
Okay, so I did that, and came across this list which seemed to suit the purpose. Is it a good idea?

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>>9046007
>Then I'll be the first.

how science can explain my anime girls love?

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>>9046007
>Then I'll be the first.

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>>9045954
>sitting on your ass collecting pdfs.
right
in
the
feels

>>9046013
>>9046015
07/18/2017. Write this post down. I'll return within 5 years if this board is still up and if this general is still running with math notes up to analysis & algebra.

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>>9046013
>>9046015
>tfw I have to prove myself to a bunch of autistic, depressed weebs
But a promise is a promise. The time for shitposting is over for me lads.

>>9046024
>I'll return within 5 years when* this board is still up and when* this general is still running
ftfy

>>9045991
>>9045901
>>9045895
Normality of N is enough.

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Why can't you dickheads give me advice? I thought you guys knew math!

>>9045991
let f be the homomorphism from G to H
consider f[g*h'*(1/g)]
and you proved the fact that every g is of the form hn, so just write g = hn and expand it out.

>>9046033
This thread doesn't revolve around you, asshole. You've gotten plenty of advice as is.

>>9046024
>>9046025
>>9046028
nigger the people in this thread are telling you the right thing. you don'tneed a fucking library to start.

>>9046038
>>9046043
I wasn't told anything of value. Just the same negative shit from a bunch of depressed "mathemaricians" who would rather be shitposting about how much they wasted their life.

Not all of us lack discipline, and many people like to plan ahead. I'm starting this list tomorrow from where I said I would earlier. I'd just like the piece of mind that it "makes sense" and doesn't have any obvious issues.

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>>9046053
>I'm starting this list tomorrow
>starting tomorrow

>>9046057
I'm phone-posting away from home. I actually can't start until tomorrow. Again, for some people, their word matters.

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>>9046059
>phoneposter

>>9046053
Just go to some university's math department's website and see what the curriculum for undergrads and the recommended bibliography for each subject are. Virtually every fucking faculty on the planet has something like this.

Either ask something specific or fuck off. Your question is too general and boring clerical crap.

>Reminder: /sci/ is for discussing topics pertaining to science and mathematics, not for helping you with your homework or helping you figure out your career path.

>If you want advice regarding college/university or your career path, go to /adv/ - Advice.

>If you want help with your homework, go to /wsr/ - Worksafe Requests.

>>9046053
lol i'm not depressed or shit. i come here to solve problems because i can't be arsed to open a book.
even the most hardworking students in my undergrad programs would give you the smae advice if they saw that list, jesus.
are you in highschool?

>>9046059
Here you go: https://www.maths.cam.ac.uk/undergrad/course
Now fuck off.

>>9046063
They're going to tell me to take Math 55 and that'll be hell. I'm not ready for that. I don't go to a university where people don't follow up on what they say they'll do, anon.

None of my requests are career or homework related. They pertain to mathematics, as in, would this be a solid core.

>>9046066
I already said I'm a rising junior chemistry major who wants to do more math earlier.

>>9046076
You've received more help than you deserve.
You're fucking annoying. Piss of already.

>>9045127
>Now we can hardly say that mathematics is a useless science in the sense of G.H. Hardy. It contributes to the exploitation in various ways. For example, the theory of stochastic differential equations, a highly sophisticated branch of mathematics, is essential for the financial manipulations leading to a redistribution of wealth from the middle class to the top 1% of the population. The encryption schemes, designed by mathematicians and implemented by software engineers, prevent access of the general public to all sorts of artistic and intellectual goods. This is a new phenomenon, a result of the development of the Internet.
Is this guy/girl the ultimate SJW?

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>>9043290
How do I into fractals? Completed the first year of my maths degree, but every online paper I find is either too advanced or pop-math shit.

How do I properly immerse myself into deep work /sci/?

I like math, but If I'm not engaging into something mentally distracting and unengaging like a stream video, I either get really depressed or really sleepy.

Should I pick up meditation again?

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>>9046081
That's not how things work. I'll never piss off until I get useful advice.

>>9046084
No. Read on.

>>9046084
>not recognising that copyright and general economic fuckery are stifling human advancement, and these restraints cannot be overcome without mathematical literacy, for reasons including the specific examples offered

Any Putnam Exam anons out there? How'd you do?

>>9046086
Unless it's causing big productivity problems, who cares? I do my best work while watching autists play video games.

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What's the fundamental ethical distinction between accepting a mathematical prize and accepting a salary/grant for doing mathematical research?

>>9046116
The salary and grant are explicitly transactional.

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Sorry to bother you guys with this probably simple problem. I haven't done math in years and I'm as confused as the girl.

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>>9046037
So we have [math]\varphi(gh'g^{-1}) = hh'h^{-1}[/math] for some [math]h \in H[/math]. So sure, [math]\varphi(gh'g^{-1}) \in H[/math], but we already knew that. Why does considering this tell us anything about [math]gh'g^{-1}[/math] being in [math]H[/math]?

>>9046029
Is it? Artin's proof uses the normality of both (pic related).

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>>9046148
Extend via red line. You know the long portion of the red line by congruency, and you can get the short bit because the little triangle at the bottom is similar to the original.
Then the right triangle with height A and red hypotenuse is similar to the circled one.

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>>9043395
>Meme Lists
If you have 5 years to spare then follow the Cambridge Mathematical Tripos list of books.

>Introduction
https://www.maths.cam.ac.uk/sites/www.maths.cam.ac.uk/files/pre2014/undergrad/admissions/readinglist.pdf


>Full Mathematical Tripos book/lecture list:
https://www.maths.cam.ac.uk/undergrad/course/schedules.pdf

For each lecture topic, type into youtube "Lectures Higher-order linear differential equation" or w/e the subj is.

When you're done, get the previous exams for the tripos they are avail public and test your knowledge. See you in 5 years, forget meme lists get a university list.

>>9046258
Your first list is fucking terrible unless I want to read meandering bullshit for 5 years, and the second list goes way beyond the scope of what I want to do in a way that's really unhelpful. You rejected one meme list and replaced it with something 5 times as worse. God, why are you people so obtuse?

>>9046273
>God, why are you people so obtuse?
either way you're willingly falling for a memelist, it doesn't matter which one you pick

>>9046278
>either way you're willingly falling for a memelist, it doesn't matter which one you pick
The list I just posted seemed very reasonable, far more reasonable than the crap you gave me.

>>9046283
>The list I just posted seemed very reasonable
which?

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>>9046283
>Cambridge university
>Crap

>>9046273
Did you just call A Concise Introduction to Pure Mathematics by Martin Liebeck, and Solving Mathematical Problems byTerence Tao... bullshit?

Are you 13yrs old?

>>9046291
Yeah dude, because I totally want to read a long list of books that are too busy talking about doing math to actually do math. Good joke, anon.

>Did you just call A Concise Introduction to Pure Mathematics by Martin Liebeck, and Solving Mathematical Problems byTerence Tao... bullshit?
Tao's book is not what I'm looking for. I don't want to spend my time doing algebra and geometry IMO problems because they're not what I want to do.

Again, it's meandering bullshit, and I'm appalled that any of you thought it was a good idea given what I said I wanted to do. It's a total meme list.

>>9046288
This list: >>9043395. Just trying to get the basics of pure mathematics down as efficiently but thoroughly as possible.

--

Also, I didn't realize that I got some responses.
>>9045899
>>9045774
Thank you all for the input. I was under the impression that How to Prove It was a light introduction to mathematical logic and set theory. I guess if I want to do probability and more logic, I can do the introductions by Tsitsiklis and Tarski which I see namedropped around here. I might look around for more set theory later on, too. But I'm not going to worry about that until later. Just looking to find a fast track to the foundational stuff first.

--

Since the original list I posted didn't seem to disgust anybody enough to complain about the choices present, only recommending breadth for me to consider later, I'm going to assume that it's a fine list. Thanks for those who were helpful.

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>>9046148
A = [math]\frac{183}{28}[/math]

Protip: stare really hard at every single angle. If the problem isn't immediately solvable via Pythagorus' Theorem it's probably got some hidden bullshit with similar triangles, or it's flat-out impossible.

>>9043493
>>9043493

This Ian unequivocally false.

The true masters spent hours and hours, days, weeks, years honing their craft. A spark of talent is all it takes, but any person, given enough drive and focus can contribute meaningfully to the VAST field of mathematics. I want the talent meme to end.

Do you guys really think that people like Einstein, Godel, Newton, even Green had never studied? That they were just born with knowledge of maths? Get the fuck out of here. They had talent but they had to study to learn, just like everyone else

>>9046158
http://at.yorku.ca/cgi-bin/bbqa?forum=ask_an_algebraist_2008&task=show_msg&msg=2300.0002

>>9043359
Make sure you're getting the right isomer...it is why some drugs have side effects or fuck up on occasion

>>9046314
>just trying to get the basics of pure mathematics

>calls A Concise Intro to Pure Mathematics bullshit
>doesn't want to learn strategies for solving problems in Number Theory or Algebra, thinks Tao is a waste of time.
>posts a dozen books on Algebra

You're such a whiny little kid.

>>9046314
>Yeah dude, because I totally want to read a long list of books that are too busy talking about doing math to actually do math. Good joke, anon.
>Tao's book is not what I'm looking for. I don't want to spend my time doing algebra and geometry IMO problems because they're not what I want to do.
>Again, it's meandering bullshit, and I'm appalled that any of you thought it was a good idea given what I said I wanted to do. It's a total meme list.
>Just trying to get the basics of pure mathematics down as efficiently but thoroughly as possible.
With this attitude it doesn't matter which memelist you pick you'll get the same end result, just pick any of them

>>9046349
So for arbitrary [math]G[/math], meaning that it's not necessarily abelian as in the link you posted, we don't know more about the product map, other than that it's bijective. In particular, we don't know if it's a homomorphism, unlike what >>9045743 claimed.

>>9046370
>posts a dozen books on Algebra
I didn't know 2 books is now "1 dozen".

>calls A Concise Intro to Pure Mathematics bullshit
I didn't call it bullshit. But 90% of the books on the list is bullshit and fucking memery at its purist.

A Concise Introduction to Pure Mathematics is probably one of the only relevant books on that list, but it's a condensed survey book, which is what I don't want.

>doesn't want to learn strategies for solving problems in Number Theory or Algebra, thinks Tao is a waste of time.
I don't want to learn it because it's a diversion from what I want to do right now. I already have two books by Tao, anyway, so no he's not a waste of time. I'd rather do analysis and algebra than number theory, especially since advanced number theory seems to require algebra. Everything seems to require algebra once it gets advanced enough.

I guarantee if I had a list with all sorts of random topics on graph theory and number theory when I said "how to start doing pure mathematics", you faggots would have laughed at me for not beelining straight to real analysis and abstract algebra. You elitist faggots are un-fucking believable.

>>9046389
Lang - Basic Math
Lang - Linear Algebra
Lang - Real Analysis I
Artin - Algebra

You're now good to go learn whatever you want

>>9046395
Looks like my list anyway. I'll take it as a sign that I'm on the right track. Thanks for the input.

>>9046314
What part of "fuck off!" is so hard to understand?

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>>9046207
>>9046320
Thanks for helping me with my weeb problem but how do you get (12/7), if I may ask.

>>9046412
The part where I said "that's not how shit works." Why would I leave because some random person told me to?

>>9046329
>Godel, Newton, even Green had never studied?
Literally no one said. Take your strawman, shove it up your ass, and light it on fire.
Idiot.

>>9046416
if you call the smaller section of the big red line "x" you'll find that [math]\frac{x}{4} = \frac{3}{7}[/math]

>>9046417
Fuck off you fucking shitstain.
Why the fuck are you not banned yet.

>>9046389
>rejects swaths of books as 'bullshit'
>makes sweeping claims about mathematics

Protip: You're the elitist

>I didn't know 2 books is now "1 dozen".
Almost everything you posted is filled with algebra.

>Pre-Calculus
>How to Prove it - Velleman
>Linear Algebra and Its Applications - David C. Lay
>A Book of Abstract Algebra - C. C. Pinter
>Algebra - Michael Artin
>Differential Eq - Ross (eigenfunctions)
>Principles of Topology - Croom (algebraic topology)
>Analaysis by Tao (Banach Algebra proof of prime number theorem)
>Visual Complex Analysis (Polynomials)

Go away kid, stop larping as a "chemistry major" you're summer time cancer.

>>9046437
>>expecting a ban on /sci/ for asking math questions
There's a difference between math questions and 'spoonfeed me books to read' questions. You're nowhere near asking a math question.

>>9046439
He's not an elitist. He's a clueless moron. If he knew what he was talking about about he wouldn't need to ask for a fucking list in the first place.

>Protip: You're the elitist

Because reading 30 books of math apologetics is the same as doing mathematics, right? Fuck off with your stupid attempt to reverse the tables. You know EXACTLY that you're being a disingenuous retard right now, and I'll make an extra effort to stay because of it, since I know you know better.

>Almost everything you posted is filled with algebra.
>hurr durr everything that builds up to real analysis and abstract algebra is basically abstract algebra
>hurr durr its a bad thing when most relevant mathematics today uses abstract algebra
Increasingly insightful, anon. I bet you're going to ask me to read Rosen to get a full dose of that algebra-reliant number theory, right?

>booklist
I don't even plan on reading half of those books because it would overlap with my major requirements. I wanted to do Velleman --> Apostol --> Intro Topology/Algebra --> Kunze --> Tao --> Artin, and I wanted to know if that was a good idea.

>Go away kid, stop larping as a "chemistry major" you're summer time cancer.
Says the conceited Redditor. Go back to memeing about Rick and Morty you insufferable maggot.

>>9046442
I provided the books for you. That's not spoonfeeding by any measure. I wanted to know if it's a good list for the purposes I stated. Didn't ask for recommendations.

Jesus Christ, all I asked was a simple question and instead I get a bunch of arrogant weeaboo neckbeards telling me to read Hardy's Apology and the History of Mathematics as if it's a fucking good use of my time, and then bitching when I call it out for being nothing but a meme. Goddamn you people. Seriously. Don't you have nothing better to do? I would have been gone a long time ago if you had looked at the list for 3 seconds, gave me some quick tips that aren't some bullshit like "hurr durr don't even try" or "read all of these mathematics history books and start doing IMO problem books", and then sent me on my way. Is /mg/ where they keep the antisocial virgins contained?

>>9046466
>this much cringe in one post
jesus i'll take 10 more animeposters over this guy

>>9046466
You're not supposed to read the whole list, its recommended books university professors have read/audited to choose from. You may want to learn how to read before you try math as that is clearly in the intro.

>>9046478
Cry me a river. You're wasting your time bitching over what was a simple, innocent question.

>>9046482
>You're not supposed to read the whole list, its recommended books university professors have read/audited to choose from. You may want to learn how to read before you try math as that is clearly in the intro.
Most of the books are totally irrelevant towards what I want to do. If they actually have the slightest bit of relevance, they're only watered-down survey versions of what I want to do. I don't get how difficult it is to get this point across. If I asked for a list for an introduction to modern european history, for example, why would anybody think it's a good idea to recommend me Oswald Spengler's Decline of the West or a book on Chinese history?

>>9046484
>You're wasting your time bitching over what was a simple, innocent question.
your question 'What does /mg/ think? ' has nothing to do with math, you just want some validation for this list for whatever reason

if you want to read the books go read, but I doubt you'll even get past the first chapter of two of those books based on your posts in this thread

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>a fifth of the thread wasted by an abject moron who posts a meme list and whines when people give him a thoroughly detailed academic guideline which he can use as a base

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>>9046491
>a thread ruined by people that would rather reply to his retarded ass than discussing actual math

>>9046487
Please be trolling, no one should be this much of an imbecile. Did you even read the intro of the fucking link to the Cambridge math curriculum you stupid ape? Watered-down survey version? Are you this retarded?

Your question was asked exactly on point several times already. Go find the nearest tree and hang yourself.
Waste of oxygen.

>>9046502
answered*

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>>9046490
>beginner asking mathematically knowledgeable people about whether a list of 6-7 books is a good start for getting grounded
>not relevant to mathematics.
You can't be serious.

>>9046491
>here, read some books about why mathematics is so great, the biography of Erdos, how to do IMO problems, a watered-down survey, a "whoa dude" book on fractals, etc.
>thoroughly detailed academic guideline that can be used as a base
You can't be serious.

>>9046495
>thread ruined by retards not giving simple advice and instead whining about their depression and posting obscure Japanese cartoons
You can't be serious.

>>9046502
>Did you even read the intro of the fucking link to the Cambridge math curriculum you stupid ape?
I did, and like I said earlier, I saw many of the books on my planned reading list on there, so it confirmed my decision to do what I planned on doing. Apostol, Artin, etc. I was railing against others here for focusing on the other list recommended because it was obvious they hadn't read it.

Anyway, I live for the tears of aggressive neckbeards with no sense of reality, so keep swinging for the fences. Seriously. Wasting your damn time complaining instead of being helpful. If you didn't focus so hard on trolling me, I would have left a long time ago.

>>9046514
>You can't be serious.
I am, very.

>>9046514
Your list sucks.
Fuck off.

>>9046517
The only thing you're serious about is your commitment to troll if you're any one of those posters I mentioned holding that belief.

>>9046519
Why does it suck? Is it because it's all "algebra"? If my eyes rolled any harder, they'd pop out of my skull.

>>9046382
he's retarded.

>>9045872
but doesnt a linearly deformed cube share the same area as a normal cube?

>>9045809
look for god, hea everywhere around you

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>>9046532
Can confirm.
>>9046538
It's a packing problem. The only allowed transformations are isometries.
>>9046553
God is my stressor?? Well, damn...
He is isn't he? He's making my brain rot.

>>9045872
>>9046590
what about dividing each cube into an infinite number of smaller cubes.

or a number of smaller paraboloids, like a space filling sequence?

>>9046624
Cutting anything up is not an isometric transformation so no. But feel free to play around with stuff anon. Just keep in mind that you're no longer trying to solve the original problem.

What fields of math should I study in undergrad that would have the most relevance towards AI?

>>9047019
simplical complexes and maybe algebraic number theory. as well as a shit ton of linear algebra/matrix algebra.

im an economist by trade and I wonder if you could use this to simulate 'flavor' in an analysis. giving a way to quantify general qualitative aspects. being able to handle using different matrices to categorize the 'weight' of variables. im a newbie myself, but that is quite the skill to have

>>9046085
The larger area fractal maths is related to is called complex dynamics. I don't know shit about the topic, but you could look for some standard textbook on the subject, look at the prereqs and start working.

>>9046491
>>9046514
>reddit garbage
>>>/r/eddit/