Alright, reading a paper, and I witness this
>F : R → C
Now I wouldn't go bother you to figure out what does this mean, however google does not work for these things. I only need a phrase or something to google to look it up. Any help ?
>Pic related: It's the context
>>8169154
F is a function from the real numbers R to the complex numbers C
>>8169156
I am thankful
>>8169154
https://en.wikipedia.org/wiki/Function_(mathematics)#Notation
>>8169160
Oh that's even better
I love you
>>8169154
why the fuck are you even reading a paper in the first place ?
>>8169236
Need to write an essay of 4000 words that would include some of my "research" (It can be weak, it's high school). Began reading about the Goldbach conjecture, found out maths I hadn't learned yet and began reading up on them. All in hopes that I'll get some ideas for the essay.
>>8169261
Began reading about the Goldbach conjecture, found out maths I hadn't learned yet and began reading up on them. All in hopes that I'll get some ideas for the essay
lol
>>8169316
Basically
>>8169261
Why would anyone care about some conjectures when we have an enormous problem of changing climate.
>>8169323
Ok gee please refrain from shitposting
>>8169261
You're going to want to pop open a low level textbook, not a goddamn research paper.
>>8169323
lel
>>8169154
Ask in the sqt or qtddtot
It means F is a function that goes from the reals to the complex numbers (maybe to the class of smooth functions, I'm not reading the context)
>>8169325
Thanks
Any suggessions ? I have no clue of the "cyllabus" , so I have no clue in what order should I learn things.
>>8169332
Spivak - Calculus
Pugh - Analysis if you're feeling ambitious
>>8169334
Very thankful
Will it help me with the conjecture though ? I really don't want to invest time in things that may not prove useful for the essay.
Even though I can change the topic, still..
>>8169346
have you read the wikipedia article for the goldbach conjecture and also all the links at the bottom of the page?
have you gone to the library and got one of the many popsci books written on the goldbach conjecture?
> I really don't want to invest time in things that may not prove useful for the essay.
you're not gonna make it kid.
>>8169346
you can NOT understand any paper on the conjecture at all
you're wasting your time
read popsci explanations or wiki articles instead
>>8169377
>have you read the wikipedia article for the goldbach conjecture and also all the links at the bottom of the page?
Yeah that's where I got the paper from. Working on stuff.
>have you gone to the library and got one of the many popsci books written on the goldbach conjecture?
Local libraries suck I'm afraid
Well I'm really only concerned for the essay. Given that I have nothing I'm investing time anywhere I can.
>>8169382
Yeah done the popsci things, they're not enough for the essay. This is the issue that things worthy of a good mark in the essay are often way above our league.
>>8169393
>Local libraries suck I'm afraid
There isn't any college or university in your town or city?
>>8169397
The town is dying, no books published later than 1980's. All the mathematics books are either high school mathematics or statistics.
>>8169154
4000 word essay in high school on the goldbach conjecture?
The fuck?
>>8169405
Well not necessarily on goldbach, anything related to maths.
The reason why I chose it is because there was another essay that got max grades, and it was on the collatz conjecture. He used different approaches, did maths of his own. I'm hoping I'll manage to do something like that, so I looked for some unsolved conjectures to ramble about for 4k words.
>>8169154
If you can change your project, why not write an essay about the real numbers or calculus?
>>8169405
too easy for high schoolers, right?
write 1500 words about the history of number theory leading up to the conjecture while you're stoned, then write 750 words on the conjecture itself, have a few beers, write 750 words on modern attempts even though you don't understand them, get more stoned, and write 1000 words about how "we can't know nothing teach"
then get your mom or big sister to proofread it
>>8169407
it's easy to fool people into believing you're doing math when you're actually spouting nonsense
that's what the collatz guy did. do you want to do something similar? you don't seem like a liar.
>>8169409
If the topic is that wide the essay will be unfocused. There has to be a research question and mathematical working out in the middle of the fluff.
>>8169410
Yeah way too much on the history. The conjecture and modern attempts was one of my plans.
>>8169420
I need a good grade :l I'd prefer it to be of good quality but if the only means are rubbish then I'll have to stoop to the collatz guy's level.
>IB was a mistake
>>8169346
It'll help, but a wiki page would be faster.
You need a couple textbooks under your belt to fully understand what's going on here.
>>8169409
>real numbers
>real
>>8169425
don't. you need a different topic.
what about an informal exposition on galois theory? the 2nd, 3rd and 4th degree formulas with full proofs and derivation, along with an informal talk about why 5th+ degree polynomials don't have formulas
>>8169425
>Yeah way too much on the history. The conjecture and modern attempts was one of my plans.
The conjecture can be stated in two sentences and the modern attempts (few as they are) are above your head.
Have you ever written a fucking paper in high school before dude? It's all about the context and exposition.
>>8169426
Any to suggest ? I'm currently reading Spivak Calculus, I hope it'll help.
>>8169429
You might just saved my ass. If I can make this work I'll name my firstborn son after you.
>>8169432
Yeah I could write that in a paragraph, but I need 4000 words. But the majority of those words should be on the conjecture, and there's penalties on going to wild on the history. Believe me, if it were a viable plan I would be cruisin'.
>>8169435
>Yeah I could write that in a paragraph,
then you picked a shitty topic dude holy cajoles.
pick something more broad like "graph theory" where the history is in the form of problems you can state and explain and the modern theory is diverse and chock full of definitions, simple examples, and applications.
>>8169164
why the fuck are you reading a paper if you're obviously still at kindergarden level maths?
>>8169439
Naw here they want concentrated fluff. You can sum up anything in a paragraph, thus any topic is shitty. And if the topic is really wide I'll get roasted. Life's hard
>>8169446
graph theory is a good suggestion though
you can pick a couple of classic problems and make an exposition on that
>>8169445
I need a good grade and to sound smart
>>8169435
Spivak is worthless to you on this essay. Don't waste your time on it.
>>8169452
Thank you
>>8169446
>You can sum up anything in a paragraph, thus any topic is shitty.
No, that's not what this is about. You can state the goldbach conjecture in a sentence but there's not much else to say. It's funny that we haven't solved it huhuhuh
You can define a graph in a sentence and then write 4000 words about things people do with graphs quite easily.
>>8169472
Ok yeah you have a point, thanks.
I hope galois theory has things to talk about.
>>8169495
it does but they are more technical than graph theory.
>>8169498
I like that, interests me more.
>>8169504
ok, please don't come back and make another thread when you don't understand basic notation that appears on the first page of some galois theory text you downloaded.
>>8169507
I'll try but can't promise that, dear
You should really try to do something on at most first year university level.
Some stuff you could do:
- Construction of real numbers from peano axioms
- Countable vs uncoutable infinity (Cantor's diagonal proof)
- Eigenvalues/eigenvectors
- Elementary differential equations like exponential growth / logistic growth and lotka volterra
>>8169429
that might be an idea, but galois theory needs to have a solid foundation of abstract algebra
>>8169554
Oh, another really helpful reply
You're guys are actually not that bad
>>8169565
>You're guys are actually not that bad
Yeah, hold on a second. Why aren't we telling this high schooler to fuck off and do his own homework?
>>8169581
I'm surprised myself
>>8169581
We like math
>>8169589
We got that in common
>>8169554
My vote for you would be the countable vs uncountable infinity thing. You could even talk about the unsolved continuum hypothesis. There's not a "whole lot" of math involved (it's fairly standard to mention in any discrete math course) and there's a wide range of involved topics you can mention (cardinality of sets (some infinities bigger than others), cardinal numbers vs ordinal numbers, completeness in real analysis (this is a very important and fundamental consequence of the properties of real numbers) etc).
>>8169677
I should add, basically, the integers and rational numbers are countable but the real numbers are not. What this means: the interval [0,1] (of real numbers) is the same size as the whole set of real numbers and the natural numbers, integers, and rationals are the same size.
>>8169681
Ay, thanks
