9 Year Old Calculus & Algebra Kid - Indefinite Integration, Polynomial

[bazzsofly]

How to fold pizza boxes brought me here.. learning calc from a pre teen tool is why I leave

[setnoset]

very good =), doing calculus at this age

[BorealNeal]

his dad probly taught him all that hahah big deal even i can memorize useless facts

[xTIxLyricz]

I'm 16 and I don't even understand pre cal

[paulmccartneyloverrr]

damn I'm 15 and I've never seen anything like that o.o

[DeusGamesForPC]

Neerd

[tonychet2s]

differentiation i think i coulda done that at 12 if i was taught it too tho lol

[r3vmixman]

Smart kid. I wish I knew how to do this at your age. The only downside I see with you learning too quickly is you will grow up with a sense of "feeling older than your peers". That can be damaging to your social skills, which are very much important in your future. Good luck to you though. I subscribed in hopes to see how you progress.

[thatscientificgeek]

Please I would love to talk to you. (I'm the same age as you).

[LegendaryxEyes]

Cut him some slack, HE IS NINE YEARS OLD.

[birdwiser1]

Can the camera man/woman learn to hold the camera still and at the right zoom pleeeeease

[falloist]

yeah right. after this kid one equals 0,5 wtf.and this is not algebra

[enthusiastmathkid]

@falloist, I do have other videos. Check them out and you see some algebra. Besides, if one is doing calculus such as differentiation, then he/she simultaneously, doing algebra, because it is impossible to do calculus without solving for solutions (which is algebra). Eg, find the stationary points in the following function:

y = x*exp(-x)

dy/dx = (1 - x)*exp(-x)

Use algebra to solve for value/s of x where  dy/dx = 0 :

dy/dx = 0, when x=1

therefore stationary point is: (1,1/e)

[JumboStevo]

@falloist

one of the hardest parts in calculus is the algebra involved in the problems

[ElleonTheNerd]

After reading through some of the comments, I'd like to point out something odd I've noticed. I'm in a high school calculus class for college credit and we've learned the product rule, chain rule, etc. for derivatives, but we have not even spoken about integrals.

I also find it very upsetting that your principal won't get you on an accelerated course. You seem like a very bright kid. Good luck. (:

[GTPR3]

@ElleonTheNerd A little kid does not have to be a genius to solve that. I am very sure that any average child who knows something about Maths can learn it by simply looking into a book on how those mathematical formulas work step by step, how to deal with all the numbers and the symbols in each step and where each symbol fits. That this topic is from Grade 12 and he was in Grade 4 doesn't mean he isn't mentally capable of understanding it. The only difference is that he is not from Grade 12.

[luckeycatX]

@GTPR3 Even though I took calculus in grade 12, and again in college, I still have a bit of a struggle understanding it. Some of the concepts can be very overwhelming.

[Unknown831143]

good luck kidd and keep it up. u have talent

[fallllenangel]

damn i better dont write a comment.. you all seem to be math pros

[ViperNeck]

ummm.. 1+1=2 ! HAH! I'm SMART TOO!

[MucusFelidae]

@ViperNeck "1+1=2 ! HAH! I'm SMART TOO!"

No, you probably copied that line from your kid's schoolbook.

[Talant97]

He knows what integration is but the difference between a parenthesis (),and a bracket [ ] is foreign to him

[Marsc0met]

Can you derive the product rule, chain rule, quotient rule using first principals?

[enthusiastmathkid]

@Marsc0met , I know how to use first principle:

df(x)/dx = lim, h-> 0 : [ f(x+h) - f(x) ]/h

but I don't know how to start from first principle and ended up with chain, product and quotient rules. The current curriculum level that I'm learning calculus at the moment (CIE - Cambridge International Exam) don't include the derivation of chain, product and quotient rules starting from first principles. To my understanding on what I've been told, that it is a first year University level topic.

[Marsc0met]

@enthusiastmathkid At your age, it's quite impressive that you know this much! But you should really learn how it is derived because memorizing the product rule formula and just plugging in the numbers will not help. Anyhow, good job for doing this at the age of 9!

[xatzin2004]

@enthusiastmathkid try Spivak's "Calculus"

[fermionsbosons]

@Marsc0met, derivation of chain, product and quotient is an advanced level. It is not done at high school. Even at its advanced level it is a proof only and not a derivation. Google : "Proving Derivatives from First Principles" and you can see that it is only a proof (axiom) and no attempt to derive it from first principle. They do not need to know about it @ high school. Also they all know "Pythagorean Theorem" however its proof is not introduced until 1st year University or higher.

[Dial911Please]

Oh my god. You are a little genius, kid.

[AudioJustG]

We're just learning this in the 12th class. Dayum this kid is good :o

[TheHouseMusicForever]

is this the reincarnation of Albert Einstein ?! :D

[smokje]

dham im 32 and i dont have an clue whta this is can you explane how this works

[mshafaqoj]

How on earth did I end up here...?? I was watching something about Negus and dom dom or something...in Bee Spelling...!

[jigabotz]

Kia Ora bro, keep it up ay!

Do you go to school to learn or teach haha?.

[enthusiastmathkid]

@jigabotz, Kia Ora too and thanks for dropping by. I'm a year 6 @ primary school & I'm there to learn. In fact my parents requested at the beginning of this year (2011) to the school principal that I should be exempted from my daily math class at school so I can do my own study in preparation for my 2 CIE (Cambridge International Exam) year 13 calculus (pure maths P1 and P2 papers) at the end of this year (1st 1 started last week) but she declined. I still sit there and learn how to do 42+38

[jigabotz]

@enthusiastmathkid Aww really bro? That's gotta suck, i mean calculus is part of the year 13 curriculum. I'm currently at Uni doing engineering and trust me i've seen old-er kids struggle with advanced calculus (it's not that advanced lol). Umm have your parents tried having a chat with the ministry of education to see if they can sort you out a separate accelerated pathway?

What school do you currently attend? I think Auckland and Roskill grammar allow the accelerated pathway programme.

[awesomeirlable]

@enthusiastmathkid You must be bored out of your wits having to do those simple math equations in your regular class schedule

...I pity you :(

[enthusiastmathkid]

@awesomeirlable , that's true, i'm quite bored at my regular math class, since what 's being taught there is baby's stuff to me. I believe that school principal at my school had no idea of accelerated math learning. She told my parents that some University math professors don't agree with my accelerated math learning, since I need to know other basic stuff first before I start learning advanced math topics, which is what I'm currently doing. She thinks that the way I learn is damaging to me.

[awesomeirlable]

@enthusiastmathkid Well...there is some truth to what she says I guess, considering that some courses of accelerated learning tend to bombard you with work rather than taking a focus to learning the actual concepts (well at least that's how my school courses are like....I'm guessing it's just the teachers) but at the same time, she needs to acknowledge that you've ALREADY come to understanding those concepts -_____-, and that remaining in that class would merely render them as being trivial

[marklvrd]

@enthusiastmathkid it is damaging to you, you have to build a tool kit of math rules starting from algebra all the way up to cal, then you take this knowledge and try to solve problems that we face in the real world depending on what you want to do. But then you could also say i am not going to be in that kind of field, well then i say whats the point in doing this then, after that you say because i can, finally i say...touche!

[enthusiastmathkid]

@marklvrd , I think that what I'm learning now in the CIE (Cambridge International Exam) curriculum is pretty much what I need to know or learn. All the math rules that one needs to know are all there if one wants further advanced study in math. Lookup on Amazon the "table of contents" and topics of 2 CIE math textbooks I use:

- "Pure Mathematics 1 (Cambridge International Examinations)"

- "Pure Mathematics 2 and 3 (Cambridge International Examinations) "

What else am I missing? Any idea?

[marklvrd]

@enthusiastmathkid yes those are fine, i replied with the intention that you were skipping lower level math.

[enthusiastmathkid]

@marklvrd, my last CIE Math test was on Friday, 28th October (2011), last week. I sat 2 pure math CIE papers this year. In 2012, I'll be taking more pure maths, statistics & physics/mechanics. I've just received my 2 CIE textbooks for mechanics I ordered online. I'll start going thru them.

- "Mechanics 1 (CIE)"

- "Mechanics 2 (CIE)"

In "Mechanics 2" there's lots of integration, eg: object center of mass, energy/work done on an object: integrate F(x)*dx, where F(x) is force, dx is displacement

[mrssupercheese]

Like I'm gonna understand that no way !

[Matthew2400]

That's amazing! I thought I was good when I could do calculus at aged 15... Keep it up and you could become a famous mathematician!!!

[musicmuscle123]

It's inspiring to see kids be interested in mathematics at such a young age. You just can't forget one thing, if you really want to be successful in math or science you always need to step back and look at the big picture. Really think about why you are learning it, and why it is useful. Also, don't do math to win prizes or to become famous, do it because its what you love and what you're interested in. and I hope one day I'll be seeing you at math seminars sitting at a table by me! good luck!

[CalebZed]

@musicmuscle123 I blame the parents

[dudeurugly23]

i think he was bio engineered by ancient aliens O.0

[PolitcalIslam]

You know the power rule… I am so impressed. When I was 10, I taught myself what is considered Calculus I (single-variable calculus) and Calculus II (infinite series and the likes) at most American universities. @milanpomothy55 I could too. I dropped out of a SUNY school when I was 11. I hate my life.

[snmart2]

We need more kids like you and less "smart critics" about the use of words or the relevance of theoretic or induced knowdlge . What your video tells me is that you are interested in learning and knowing and that is 100% more important than being a genius. We( human kind) are in great need of more people who care and work their brains from an early age. Keep it rolling kid!

[obanr]

learning the numerical process is extremely easy... it's as easy, if not easier, as algebra.

if he were to show that he has an actual deep understanding of what an integral is, then i'd be impressed.

on another level, yeah it's pretty impressive that he was able to retain that kind of math, though.

[enthusiastmathkid]

@obanr , thanks for dropping by. As you might have noted, the video above was from last year (2010). I have moved on from simple polynomial/rational function integration shown above to more advance calculus topics. For instance, I know how to do integration of a polynomial fractions (ie, numerator/denominator), where the solutions will almost always a natural log of the denominator, eg : (1/2)ln(2*x + 1). I use partial fractions (resulting in 2 or more terms) then followed by integration .

[PmQable1]

@42duckyduckers you are truly ignorant. this kid is about 12 and hes doing stuff that many people dont understand until college, even if its only elementary calculus. and by the way, the indefinite integral is just the reverse of the power rule in differentiation, which is pretty straightforward.

[1moomoos]

KIWI !!!!!!!!!! <3

[qwerty14142]

I read the comments expecting to see discussions on the wonders of math and how even children can be influenced to understand things such as Calculus. But no, instead people are using vulgar language and making ridiculous statements. Rehearsed or not, this beats video games ANY day. By the way, being cute AND smart is a great combination. Keep up the smartness kid. =)

[enthusiastmathkid]

@qwerty14142 , Kia Ora, bro!

[42DuckyDuckers]

If you're watching a video on indefinite integration, I'd think that you'd know what it means to raise a expression to a negative power. I kind of doubt he even knows what the chain law is.

All that would really be necessary to get somebody this age to do that would be to teach them the required equation. It's a simple one.

What a genius can do would be to derive the indefinate integral. You don't go anywhere in mathematics if all you do it copy and paste. That's what computers are for.

[enthusiastmathkid]

@42DuckyDuckers, thanks for dropping by. I know how to do differentiation using chain rule, product rule, quotient rule. I also know the differentiation of trigonometry functions, logarithmic functions and exponential functions. I've just learnt those within the last 4 months or so. My video here doing integration was from last year (2010), so obviously you can pretty much work out that I have moved on from differentiation of polynomial and rational functions into more advanced topics.

[jougetsu]

@enthusiastmathkid good job, finally parents start working with their kids instead of ignoring them. hopefully schools will stop teaching useless things in the future. nah, wont happen anyway, too many morons around.

[CalebZed]

@42DuckyDuckers thats all thats required at any age, i'm not sure what you're trying to prove, all it really takes to learn and do any of these problems is learning the right equations and practicing to know when to use them. This really applies to anything and everything. Memorization in any class although unfortunate versus actual understanding is more than acceptable and if you memorize the right things will get you the perfect grades.

[TheShadowmin0]

@CalebZed unfortunately...

[Hippoman141]

cool story bro, tell it again

[TheMoleMan95]

@enthusiastmathkid Calculus is easy per se, the only difficulty is in knowing where and how to apply it. There are many things in math that are so much more difficult than calculus.

[Tsukasa171]

People these days use the word genius too lightly, and often use it interchangeable with knowledgeable. Any time a person sees someone smarter than him, they call him a genius. This in reality is actually quite different from genius. It just requires proper instructions and discipline; and anyone can learn calculus. I had a math teacher who taught his nephew who was in 4th grade calculus. so to reiterate my point, there is quite big difference between being a genius and knowledgeable.

[BorealNeal]

there goes ur childhood

[enthusiastmathkid]

@fcdog555 , Mr or Mrs, go and educate your mother and father of how to learn calculus. I'm sure that they will find it easy. If calculus is easy as you said, you would have completed a PhD by age 15 (as of today) if you started at age 9. The fact that you're learning calculus at college or highschool today meant that you went thru each level one after the other without jumping ahead years in advanced. You're basically learning what I'm learning, but I'm 10 this year while you're 20.

[fermionsbosons]

@fcdog555 , yes, you just stated the 2 dimensional SVD (singular value decomposition). What's is the SVD for 4D , 5D, 6D or nth-D? Have any idea. Asshole, look which primary school that you're enrolling at?

Why do you need to enroll at all in college to do math, when you can be self taught, if you think its easy? Have you taught your dad/mother calculus yet if you think it is easy? Go and teach your parents who may be in their late 40s or 50s to learn calculus if you think its easy.

[fermionsbosons]

@MrCarsandstuff ,  check out his other videos from his channel page.

[MrCarsandstuff]

And then I wouldn't be surprised because that's on the Internet too do you even know what a polynominal is oh wait that's on the net too

[MrCarsandstuff]

Applications for it

[fermionsbosons]

@MrCarsandstuff , calculus is vital in physics/engineering. The application of integral calculus (IC) in the real world is unlimited. Lookup on the internet on the topic of "Circuit Theory and Laplace Transform" and you can see (even,no clue) how IC is used by electrical/electronic engineers to design electronic circuit filters. The very reason that you're able to tune in to one radio station in a specific frequency but filtered out other stations (no interference) is electronic filters.

[musicmuscle123]

@fermionsbosons I wouldn't spend any time with the people on here who feel they need to defend their ego because a kid has surpassed them in academia. I myself perform research in pure mathematics, and I didn't learn calculus at age 9. I, in fact, promote this because it gives me hope for the future. As a sidenote, calculus not only has applications, but is an essential tool in math, science, economics, medicine, you name it.

[ImpIsPro]

I think if you are able to do calculus, you know what a reciprocal is did you really need to explain it?

[fermionsbosons]

@ImpIsPro , note his introduction. He said, "welcome all you kids out there and welcome to my math session". He is trying to perhaps inspire other kids , because there are lots of them (in his age group) who don't know or being introduced at school of what reciprocal is.

[ImpIsPro]

@fermionsbosons If they don't know what a reciprocal is they probably shouldn't be watching calculus videos.

[fermionsbosons]

@ImpIsPro, then why are you yourself is watching the video? Why do you need to watch it if you already know? Obviously, the kid doesn't target PhD people who already know the stuff to watch it. He is obviously looking to share with other kids (his friends from primary schools). May be he can inspire them to do the same like him. Why don't you go and teach your younger 9, 10 or 11 year old brothers/sisters (or perhaps your cousins) to do the same? I'm sure that you'll be proud.

[fcdog555]

Now only if he did an actual complicated calc problem:p

this kind of integration takes no skill but rather memory.

not impressed troll is not impressed

[fermionsbosons]

@fcdog555 , so you think that even a 9 year old can solve elementary calculus, then that makes you know tensor calculus, huh? Or may you think that if a 9 year old can do elementary calculus then 10, 11 or even 12 year old can do multivariate calculus? Jeez, if you think in that way, then I suppose that your 10, 11 or even 12 old daughter can understand multivariate vector calculus. Daft comment from you. Look idiot he is only 9 he has been introduced to multivariate vector calculus already.

[goldenboyben]

This kids is so amazing.  I didn't know you can mix numbers with letters ... okay, I'm just jealous that he has parents pushing him in the right the direction. Engineer.

[nguyenb224]

he's not Asian?!

[DoctorBrute]

I'm disappointed n the older people using such foul language on a video of a child that's showing people what the human brain is capable of at an early age no less, if we get them off of tv & video games full time.I'm sure this kid likes them 2 but somewhere down the road he learned something useful.It really doesn't matter if he's teaching, it should inspire @ the very least. Every time i c a young genius on youtube,there r nasty adults taking away frm it,as if it were the devils plan.GROW UP!!