/mg/ = /math/ general: Genius Edition

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.

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

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

>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

>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

-- -- -- --

>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

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.

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

How old are you?

...28.

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.

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 user, but you're stuck. The only intellectually productive time is one's 20s.

Are you me? Ebin :D

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

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.

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

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

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.

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

>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.

...

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

Nice trigger discipline!

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

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 user - 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.

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?

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.

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

>Math makes the voices silent.

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

He's is being ironic dumbass.

>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 Veeky Forums 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 Veeky Forums 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.

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

>22 your better years are already behind you

Oh sweet summer child

>goes on Veeky Forums
>superiority complex

pick one

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

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

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

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

>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

>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]

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/.

...

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

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.

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.

>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?

everything is a meme my friend
we are the memes

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

Nobody cares

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.

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

>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

The friendly user did.

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?

>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.

you're dumb as fuck user

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].

Meant for

>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 user, algebra is the easiest field.

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

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

Are you implying it isn't?

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

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

>But user, 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.

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

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

wait, that's only if a > 2, otherwise it's just 2
No, I did it in my head

What? It was quick by your standards maybe.

Explain reasoning.

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

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]

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

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.

Very elegant, I like it.

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

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

fmf.uni-lj.si/~lavric/Santos - Number Theory for Mathematical Contests.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.

>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.

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].

>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.

>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.

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

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

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

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

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

you czech ?

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

nope, french

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

Extraterrestrials in skin-suits don't count.

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.

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

Je parle aussi français. Merci pour les suggestions!