/sci/ - Science & Math

2

is this a magic card?

>>5868464
You must be a genius

Perhaps at 15~18 (For normal people, of course). If you know elementary math and algebra, you can easily learn calculus. Calculus is just another topic. You just need to study for understand. Myself for example, when i was arround 13yo i used to take calculus book and get fascinated by that lot unknow symbols and shit. Then i used the tatic to forget for sometime and try learn again later. Arround 16yo i already know lims and derivates and some integral rules.

>>5868483
Thanks :)
You motivated me to learn

>>5868486

Sorry my english, i am from Brazil. I Advice you to first get a solid theory on basic math, don't ignore any content, then everything will gonna be easy later. The best way to learn math its : don't spend so much time on theory, then go do exercises, a LOT.

Good Luck

>>5868499
>from Brazil
Go outside and throw a bottle full of fire, monkey

>>5868543
look at this tripfaggot who's too big for his britches

>>5868581
I'm Carl! I'm practically royalty on here. Check your faggot mouth before I have my mod friends ban you.
I have a degree in computer science and will backtrack your IP

>>5868543
Says the superior being called tripfag.

>>5868594
That's it. You're gonna get it, buddy.

>>5868581
>>5868594
>2013
>Not knowing the "Carl" troll
Welcome to /sci/

>>5868483
tfw in my country calculus is only taught to h.s. senors and in college...herp derp.

>>5868595
>>5868543
>>5868591
Worst new trip

>>5868468
Progenitus

>>5868460

>>5868460
Knew it? High school
perfected? maybe junior year of college.
Not too good at path integrals though.

Well I finished the calculus sequence (through analysis-intensive Green's/Stokes' theorem) when I was a Junior in high school, so I guess 17? I don't think that I'll truly master calculus until I take a differential manifolds class, which is what I'm taking in the Fall! Plus I still need to take a gander at tensor calculus, but I've never really gotten around to it.

>>5869149
Have you ran into triple integrals?

>>5869185
Hahaha triple integrals, that's cute. I was done with those when I was 16, I studied analysis of multivariable calculus through baby Rudin after that. So let me explain. It usually goes like this. Calc I, Calc II, Calc III (triple integrals), Differential Equations, Linear Algebra, Real Analysis I, Abstract Algebra I, Intro to Number Theory, Real Analysis II, Abstract Algebra II, Topology, Complex Analysis, Algebraic Topology, Mathematical Logic, and then on to graduate math, with probability theory and stochastic processes thrown in there somewhere. Now, I was at the Real Analysis II level when I was 17, so at the tail end of a degree in mathematics, doing analysis in the multivariable calculus arena.

TL;DR - Yes, I have run into triple integrals.

>>5869237
>I was done with AP Calc by the age of 18.

Fixed that for you.

I saw a book on calculus and learned how to do a derivative and an intergral when I was 12. I thought I was the top shit until I found out that calculus was only babby math.

>>5869251

No, I took the AP Calc BC test (for credit in Calc 1 and 2) when I had just turned 16, got a 5, took Calc III (triple integrals/divergence/curl/Green's Theorem/Stokes' Theorem) the first semester of my Junior year, took discrete math in the spring, took diff eq in the fall of my senior year, then linear algebra the spring of my senior year. But I worked through Rudin's Principle of Mathematical Analysis independently for a year, focusing mainly on the multivariable calculus part. I also dabbled a bit in Spivak's Calculus on Manifolds my senior year, but I never really put too much time into it.

>>5869251

But way to be a presumptuous ass and assume that I meant "I was done with AP Calc by the age of 18" by Calc 1-3 and Real Analysis 1-3. If I had to sit through another second of high school math I would have died of the "No Child Left Behind", dumbed-down, low-as-fuck-standards and slow-as-fuck-curriculum classes.

Gonna hijack this thread for a second. What exactly does Real Analysis cover? I heard its like calculus but proof-y, but what kind of proofs are we talking about?

>>5868483
You should've picked up a fucking grammar book.

>>5869287
http://boards.4chan.org/lit/

>>5869282
>but what kind of proofs are we talking about
Proofs of calculus theorems.

>>5869282
It covers stuff that you've seen before in calculus classes, such as series, limits, continuity of functions, differentiation, integration, etc. but with a lot more formalism, abstraction, and in a theorem-proof type of format. Usually convergence of series and sequences is extensively covered, with a lot of focus on continuity of a single function, and eventually continuity of a sequence or series of functions. Things like the mean value theorem, the extreme value theorem, series tests, all of those type of things will be revisited, but this time you will see the actual mathematical proofs and derivation behind said theorems. Real Analysis is more about proving propositions rather than finding answers to problems. So instead of finding the limit of something, you may be asked to prove that the limit of something is M, or to prove that a function is continuous or differentiable or integrable or bounded. In other words, you learn how to analyze instead of just computing.

New things that you will be introduced to, besides the sequences and series of functions, would be topology and a more abstract view of the real numbers. You learn some basic set theory, along with things like compactness, connectedness, open sets, closed sets, limit points, closures, metric spaces, complete spaces, etc. And you finally learn how to prove that a number is irrational.

In other words, real analysis is calculus abstracted and formalized, plus more insights into the space and sets that you're working with, instead of just assuming that you're working with the real numbers in the standard topology with the standard metric as you've always assumed throughout all of prior mathematics.

Good/common course textbooks are: Principles of Mathematical Analysis, Rudin; Mathematical Analysis, Pugh; quick amazon search will return more results.

>>5868543
shitty summerfriend detected

you're not safe from the legendary rule!

I haven't yet perfected in integral calculus because I didn't find the time to go deeper into differential Galois theory.

>>5868714

So pirate a calculus textbook you idiot. Do you really need school to hold your hand?

>>5869307
What's the final boss of Mathematics?

14. 15 year old bro who already knew it taught it to me a year earlier than school intended to do it.

>>5869237
>Calc I, Calc II, Calc III (triple integrals), Differential Equations, Linear Algebra, Real Analysis I, Abstract Algebra I, Intro to Number Theory, Real Analysis II, Abstract Algebra II, Topology, Complex Analysis, Algebraic Topology, Mathematical Logic, and then on to graduate math, with probability theory and stochastic processes thrown in there somewhere
Triple integrals are part of research-level mathematics. Not everyone can be as smart as you are.

>implying theories of integration are anywhere near complete or consisten
>loled

>>5868483
Doing calculations and understanding whats happening is different.

You can tell by how far ahead you can jump into calculus without having to have been taught or read.

If you learn at the same rate you are reading, you are not learning well enough.

>>5869237
How do you feel about integrating hyperreal operators like integral (2x^3)(dx)^2

>>5871479
>please respond

can someone please help me integrate 2x^3(dx)^2

>>5869237

Wait, so hang on, how does one do "calculus" without "real analysis"? What is "calculus" without analysis?

Just computation and memorisation or what?

>>5871503
Yea. You can sort of figure out real analysis by yourself if you really get into calculus by yourself. Make up problems and try to solve/disprove them.

>>5871505
Of course the formalism is a little lost as you sort of become an intuitionist.

>>5868460
When I realized what a slope/sum was (circa 7-8th grade)

>>5869276
How much do you get payed
>implying this isn't the real question

>>5868460

some flaw in your question is that people can easily think they perfected calculus without doing it.

i thought i knew algebra. but i didn't perfect algebra before i learned calculus. (especially if you include all the trig identities and log rules in the algebra )

i guess i will not perfect calculus before i start learning complex analysis and vector analysis

>>5869237
What is your actual credentials atm? How boring was/is undergrad for you?

>>5871558
>Implying it's not funny to see all the high-school grads thinking they done actual Integration post.

integrate (dx)^2 please

what's the integral from 0 to 2pi of cosx*cos4x dx?

>>5870706
how do you pirate text books? and..y-yeah k-kind of

>>5871988

get a program to let you DL torrents, then find a torrent and profit

>>5871670
0, as d^2 = 0

>>5871988
You should buy the texts. It is illegal to pirate them.

>>5872036
>what is a metric tensor

>>5868483
Unfortunately in our highschool, Calc is only offered in grade 12.

>>5869237
Mathematical Logic comes way before most of those things you listed in my experience

>>5869237
Can you tutor me in math?

>>5875697
Same. I couldn't take it till grade 12.
Got a 100 on my trig final....

>>5875925
Do you live in a third world country?

>>5876215

most public schools in smaller towns (population less than 40,000) don't offer many college classes if at all. Calc I and II were the only things I could take as post secondary at my school, and I live in Minnesota, one of the best states for primary education in the country

>>5876215
Ontario, Canada actually

What does OP mean by "integral calculus'?

>>5869114

I'm a grad student and path integrals still annoy me.

>>5870276

You mean Legendre's?

>>5871491
12x

>>5871683

It's zero. Got any non-trivial ones?

Well, I can look at an integral as a sum equal to 1 for PDFs; I can look at a integral as a sum of products like in MACs and Convolution; and I can look at integrals as transforms, and not get too fucked up by the dummy variables. I can even do Labesgue integrals of weird functions, but I still get stuck on most integral problems in even elementary text books because the algebra or the trig fucks me up. So no, I still am not proficient in integration.

>tfw getting a final mark of 50 in your grade 12 calculus class

>>5877709
How am I supposed to know what that means? Not everyone goes to your school and not everyone is familiar with your grading system.

>>5871491
What's the domain of integration?

>>5871988
http://gen.lib.rus.ec/search.php

Here you go mate, fuck the police

>>5876220
"Calc I and II" are not "college classes".

>>5877708
> I can even do Labesgue integrals of weird functions

What is the mathematical definition of a "weird function"?

>>5879990
Do not post that here. It is illegal.

ITT: high schoolers think the fundamental theorem of calculus is all there is to know about integral calculus

>>5882738
>>5882738
>>5882738
>>5882738
>>5882738
>>5882738

>>5880665
It depends on the degree. If you're going to art school they would be high up there. If you're going to school to math you should be starting in calc 2, depending on your high schools highest level of math.

> At what age you perfected in integral calculus?

You obviously haven't perfected basic English.

>>5870740
Triple integrals.

>>5884822
Was that the topic of your PhD thesis?

>>5886188
No. I am not intelligent enough to understand those.

>>5870740
I don't know, but this thing looks pretty difficult.

>>5887331
What does that symbol mean?

>>5888697
Triple contour integral

Someone has been keeping at least 35 threads alive
by bumping them twice a day. Compare the post times of
>>5873749 >>5875337 >>5876215 >>5877651 >>5878836 >>5879980
>>5880665 >>5882082 >>5882738 >>5884149 >>5884822 >>5886188
>>5887318 >>5888697
to the post times in other threads.
It's clear most of these are the same person.
The threads being bumped:
>>5858447 >>5861383 >>5862983 >>5863249 >>5865823 >>5866853
>>5867452 >>5867640 >>5868097 >>5868460 >>5868538 >>5869504
>>5869595 >>5869759 >>5869946 >>5872951 >>5873166 >>5873829
>>5874378 >>5874727 >>5875025 >>5876410 >>5876819 >>5878449
>>5878607 >>5878684 >>5878722 >>5880041 >>5880453 >>5880775
>>5881738 >>5883998 >>5884116 >>5884625 >>5885545
Write to moot@4chan.org if you want it to stop.

>>5884162
The moderation team appears to not have agreed with you.

>>5888707
Where do you need triple contour integrals?

>>5888707
How do you solve them?

>>5891308
It requires higher math only known to PhDs.

>>5889296
>/aspie as fuck

get bent, no1 cares.
if you've been paying attention that hard, you seriously need to get a fucking life.

>>5892970
says shitposter no. 2

>>5892971
The only shitposter ITT is the mentally defective poster she is replying to.

Where can I learn more about integral calculus?

>>5893780
that poster is using common sense and hating people like you who bump threads with nothing valuable to add to the discussion

>>5894904
Why would he hate people who want to discuss math on a science and math board?

Nobody has ever perfected in integral calculus.

>>5894896
What kind of integral calculus?

>>5897790
Skorokhod integrals

18 years old, just graduated HS in USA, and just took AP Calculus AB which was the first time I ever took calculus

>>5899241
>AP Calculus AB
What is that about?

>>5899834
It's about locally ringed spaces.

>>5869307
>all that shit
Why? What for? What use can one find for it on a practical/professional level?

>>5901101
>practical/professional level
What do you mean by that?

>>5868460
OP in English language please keep vocabulary and sentence structure as simple as possible.
In English to make complicated sentence seems pretentious, arrogant and stupid to more familiar users. Only very young or or simple minded people use big words in American English.

Never did. Never done learning anything, not math, not any specific branch of math, I'm a student from now until the day I die and will never consider any body of knowledge perfect. Hell just last week I learned of a new visual method of solving differential equations.

>>5868460

At 15

>>5901895
Where did OP use "big words"?

>>5901904
>Never done learning anything
Not even the elementary school English lessons?

17, when it was first introduced.

What do you mean by integral? I learned Riemann and Darboux integration in my freshman year of college, Riemann-Stieltjes (and double/triple integrals and all that shit) in my second year, and now (entering third year) I'm teaching myself about the Lebesgue measure.

>>5905186
You should have learned Lebesgue integral in your freshman year.

>>5905186
>and double/triple integrals and all that shit
You are lying. Those are contents of graduate level mathematics.

>>5906317
What is this 4chan belief? Have any of you gone to college? I had a motherfucking art degree in undergrad, and I tested into calc III freshman year, you do double/triple integrals, path and surface integrals, etc. Of course to do this for a general function you need higher tools from analysis, measure theory, etc., but same goes for even the most basic math. You can construct simple solvable triple integral problems that are standard in introductory math (and I'm not even talking math major math!)

>>5871491
(dx)^2 = 0.
That should help.

>>5906562
Except that's wrong, you retard.

>>5906531
>claims to have an arts degree
>brags about knowing PhD math

Fucking lol'd
10/10 if troll
7/10 if copypasta

>>5891308
It's just 3 line integrals in row.

>>5908016
literally nothing he talked about are things you'd learn about in a grad class

>>5908022
You are partially correct. Triple integrals are normally a topic first encountered on the postdoctoral level, but you must not forget that some really intelligent students may see them in graduate school.

I stopped caring about math when I was introduced to the concept of imaginary numbers. What a crock of shit. If your equation can only be solved by inventing numbers that can't exist, like some kind of math deity , then you are fucking wrong and the math is flawed. Same for algebra solutions that basically say "the correct answer is whatever the correct answer is". Thats what the math said transcribed to words but god forbid if i wrote in down in english instead of the ancient math runes the teacher word mark me wrong.

Math is logical and numbers never lie my ass. Math is just as flawed as any other human construct.

>>5868460
What level?
>PHD in triple integrals
>300k starting
>Any manifold I want

>>5910179
What is a manifold and why do we need it?

>>5910179
What manifold do you want?

>>5912869
a Hopf manifold

>>5914219
I want a G_2 manifold.

If your so smart, then what is

<span class="math">\int_0^{2\pi}\! \frac{(1+2\cos x)^n \cos (nx)}{3+2\cos x} \, \mathrm{d}x.[/spoiler]

>>5916049
It's an integral -_-

----


but since the result for n=1 is
<span class="math">\dfrac{-\left(492{\cdot}\sqrt{5}-1100\right){\cdot}{\pi}}{21{\cdot}{5}^{\frac{3}{2}}-235}[/spoiler]
I seriously doubt there exist a general formula...-_-'

So if you wanted to troll you could have given more simple functions which have no analytical primitives...

>>5916570
<span class="math">\dfrac{-\left(492{\cdot}\sqrt{5}-1100\right){\cdot}{\pi}}{21{\cdot}{5}^{\frac{3}{2}}-235}[/spoiler]

>>5916571
Roraoroo
Here :

\dfrac{-\left(492{\cdot}\sqrt{5}-1100\right){\cdot}{\pi}}{21{\cdot}{5}^{\frac{3}{2}}-235}

what's wrong with this latex parser ?

>>5916573
There's a Latex preview userscript for /sci/ somewhere. That might help.

>>5916581
Usually I use texify...
But yeah it could help, I'll look for it

>>5916570
>I seriously doubt there exist a general formula.

You are wrong. Evidently you didn't "perfect in integral calculus" yet.

>>5916581
I use www.codecogs.com/latex/eqneditor.php to both write and preview LaTex. It's very nice and easy to use.

>>5917560
That link looks like a virus.

>>5919143
The site is harmless.

>>5908663
Are all of you trolling or something?

I was using tripple integrals in upper division undergraduate mechanics and electrodynamics.

How is a triple integral even considered special? It's just a consequence of geometry.

Stuff like Green's or Stoke's theorem are more complicated and those are still undergrad level physics/math.

>>5920610
>tripple integrals
I have no idea what those are. Are you a genius?

Everyone picks it up at a different time.

>>5908783
forever retarded

at school we integrated only trivial functions, so only when i started university at 19, I learned integration by parts and substitution. But only during the third semester, after applying the residue-theorem and a fourier series i solved an integral which even Maple and Mathematica couldnt handle.
That was the point where i realized that i will not so easily be replaced by robots

I feel extra stupid now.

>>5921719
What is the mathmatical definition of a "trivial function"?

>>5916049

Residues? or maybe it's some obscure substitution no non-austistic person can come up with?

>>5922314
The function must not include long division.

>>5923174
What is the difference between long division and short division?

>At what age you perfected in integral calculus?

12