jacob15728
Regular
Oops, I meant to say Gparker. My bad.
Math Question
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Sin-H
Veteran
true. because actually, there is no way that someone exspects a 13-14-15-year old to know something about power series...
Lord Voldemort
He-Who-Must-Not-Be-Named
Well, I'm doing Taylor's series as part of calculus next year and I'll be 15.
Maybe he's in a similar program?
Maybe he's in a similar program?
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jacob15728
Regular
That problem is most likely more advanced than one would expect in AP calculus. I'm 15 and I know what a Taylor series is, but I don't know what a power series is nor do I have any idea what that problem is even talking about. This would have to be an 8th grader in Calculus 3, which would mean he's 6 years ahead of his age peers. This is so unlikely that we might as well assume he is lying.
Lord Voldemort
He-Who-Must-Not-Be-Named
But what would be his motive?
I mean, all would mean is that he's trying to make his friend sound smarter than he is. Unless it's his own stuff, which I doubt. He posted a first set of Pre-Algebra questions that would be quite simple is he's learning about Power Series and stuff like that.
@ qqwref -
I'm sure I'm missing something, or else you wouldn't have posted the problem. Is it something to do with the fact that you know that there will be at least one item in each box, since you're randomly selecting an item's box number, not just any box number?
If you're computing the average items per box, isn't it just k/n?
I mean, all would mean is that he's trying to make his friend sound smarter than he is. Unless it's his own stuff, which I doubt. He posted a first set of Pre-Algebra questions that would be quite simple is he's learning about Power Series and stuff like that.
@ qqwref -
I'm sure I'm missing something, or else you wouldn't have posted the problem. Is it something to do with the fact that you know that there will be at least one item in each box, since you're randomly selecting an item's box number, not just any box number?
If you're computing the average items per box, isn't it just k/n?
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Sin-H
Veteran
hm oh well. I also acquired my knowledge of these series when I was 15, but that also was part of a special programme.
but my doubts are rather settled at the infinitesimal stuff. I think you need it to calculate taylor polynoms... and I have no idea how early you could learn this. It's not hard, but you still normally do it pretty late...
but my doubts are rather settled at the infinitesimal stuff. I think you need it to calculate taylor polynoms... and I have no idea how early you could learn this. It's not hard, but you still normally do it pretty late...
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Gparker
Veteran
Well, whatever. I know im not lieing. He just gave me that problem since he said it would be fun to try. None of us are his math teacher. It would make more sense as to why it was extra credit. They probably have talked about it for a couple of days since finals were over. I'm not sure if he knows anything about it or not. Maybe the math teacher never gave extra credit and decided to give it out now and no one be able to do it.
@voldemort. How am i making him sound smarter? He doesnt even know anyone on these forums as far as my knowledge. He doesnt need to prove that hes smart on here, or tell me or someone else to say hes smart. He just gave me the problem and said he got it for extra credit, so i decided to post it here. Since i didnt know it was hard or anything, since i barely know abot this stuff. I guess I need to think more about what im typing since yall are bashing on me.
@voldemort. How am i making him sound smarter? He doesnt even know anyone on these forums as far as my knowledge. He doesnt need to prove that hes smart on here, or tell me or someone else to say hes smart. He just gave me the problem and said he got it for extra credit, so i decided to post it here. Since i didnt know it was hard or anything, since i barely know abot this stuff. I guess I need to think more about what im typing since yall are bashing on me.
Sin-H
Veteran
ThatGuy
Veteran
@jacob15728 It's not entirely impossible. Not to brag but I was and 8th grader in Calc 3. But that's only because my dad teaches math at the college and wanted to teach me seperately for math. But yes, it is quite unlikely. But depending on where he lives in the US and where he goes to school, it could be possible. Some private school are crazy.
jacob15728
Regular
Now, I'm not saying that's impossible, but I must say I have trouble believing that. For an 8th grader to even be able to comprehend mathematics at that level, they would certainly need to have an IQ of above 175. I don't really like or agree with IQ testing, but I think that is a good estimation of what one would have to score to have that level of mathematical aptitude. If your IQ is this high, you wouldn't be in 8th grade at the standard age for 8th grade unless you were a mathematical savant. Were you in many other accelerated programs as well?
ThatGuy
Veteran
My IQ is certainly not >175. I think i'm ~145. (OK pulling a stereotype: I'm Chinese so that may have something to do with it.) I don't agree with IQ either. I enjoy math and I enjoy challenging myself. There is another person at my school who enjoys math and could've been the same level as me.
The only thing was an elementary school that let you test out of 4th, 5th, 6th, and 7th grade. I skipped to 6th in 4th grade, but then when I was in 6th grade my parents didn't want to drive me to the middle school for 8th grade math so my dad kept me home and taught me every day for ~1 hour. I'm sure that if some people in my class had put in the same amount of time and effort as me, they would be the same level.
The only thing was an elementary school that let you test out of 4th, 5th, 6th, and 7th grade. I skipped to 6th in 4th grade, but then when I was in 6th grade my parents didn't want to drive me to the middle school for 8th grade math so my dad kept me home and taught me every day for ~1 hour. I'm sure that if some people in my class had put in the same amount of time and effort as me, they would be the same level.
Sin-H
Veteran
Well, for example, I am 16 and I am just about to finish school, so I have already learned the maths for 18-year-olds and I have also read quite a bit about higher maths. But that is sort of my hobby. I don't really doubt the level someone can have at maths, but I doubt the fact that a teacher would teach something like that to such a pupil, even if it's especially for him...
oh I am a bit jealous about you Americans being able to take these and that courses and so on. But I am also not sure if that system is that good either :/
oh I am a bit jealous about you Americans being able to take these and that courses and so on. But I am also not sure if that system is that good either :/
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jacob15728
Regular
Alright, that's certainly impressive but I see your point. I personally despise mathematical education so I don't have much experience to judge what one can do with a teacher putting more time and effort in. I managed to teach myself basic calculus with no help, maybe if I had help and put more time into it I could have learned advanced calculus as well. I suppose anyone could learn more than they would normally be taught with the right effort and motivation.
qqwref
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Ah, but it's a bit more complicated than that. In the 'easy' problem, a box is more likely to be chosen when it has more objects in it (so that it is not k/n but actually a little more than that), and in the 'hard' one, you are only considering the non-empty boxes (but choosing the non-empty ones with equal probability), so the expected value is again greater than k/n.
For example, in the first problem, suppose you have 4 objects and 2 boxes, and 3 objects go in the first box. You'd be 3 times as likely to choose the first box, so the expected value of the number of objects in the box you found would be 3/4 (3) + 1/4 (1) = 2.5.
If you have 4 objects and 3 boxes, furthermore, and the distribution is 3 1 and 0 objects per box, for the 'easy' problem the expected value would again be 2.5, and for the hard problem it would be 1/2 (3) + 1/2 (1) = 2. You can see that both of these are higher than 4/3. Note that the problem is asking for the expected value over all possible circumstances, though, so this isn't the answer (although it might help).
Counterexample, in 8th grade I was doing Precalc in school (it had elements of calculus in it, though, and I remember we DID cover power series and convergence). My IQ is not as high as 175 of course
Honestly I don't think it's all that difficult for an 8th grader to be able to understand that stuff, but they do have to be interested in math and willing to learn stuff on their own (unless they have teachers who are willing to teach them at any speed the student can handle). If it's an extra credit problem it might very well require some independent research, and even if an 8th grader doesn't know what a power series is, he probably will after Googling a tutorial on it
A motivated student who is talented in math should be able to understand this stuff with a bit of work.
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peterbat
Regular
Aren't you the guy who said angle C was 12, 24, and 3 degrees?
Sin-H
Veteran
Then I would honestly like to see a way to calculate the first 5 terms of the power series of e^don't know what it was without using derivatives... that's the bigger problem, the way to calculate them using means of 8th graders... I only know that way...Counterexample, in 8th grade I was doing Precalc in school (it had elements of calculus in it, though, and I remember we DID cover power series and convergence). My IQ is not as high as 175 of course
jacob15728
Regular
Then I would honestly like to see a way to calculate the first 5 terms of the power series of e^don't know what it was without using derivatives... that's the bigger problem, the way to calculate them using means of 8th graders... I only know that way...Counterexample, in 8th grade I was doing Precalc in school (it had elements of calculus in it, though, and I remember we DID cover power series and convergence). My IQ is not as high as 175 of course
I think most 8th graders could easily learn how to calculate derivatives. But applying them to advanced problems like that is definately more difficult.
Gparker
Veteran
I know it probably does. But i guess thats how virginia goes
When he gave me the problem, i had almost no idea what it was. I tried some stuff but failed.
ThatGuy
Veteran
I have no clue why i typed 3, it was supposed to be 8. But yeah, 12 was eyeballing, 24 was being lazy, and 8 was actually doing it.
qqwref
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The power series of e^x is 1 + x + x^2/2! + x^3/3! + ..., right? And you can plug anything in for x. So e^(2x^2) is 1 + (2x^2) + (2x^2)^2/2 + (2x^2)^3/3! + .... If you know the power series of f(x), you can computer a lot of related ones, and it's not hard to look up the power series for e^x, sin, cos, ln(x+1), and so on.
