/sci/ - Science & Math

Where are you posting from, China?

>>7410521
Series questions at such a young age. It's just memorizaiton at that point.

Yep. Hong Kong

>>7410535
Ok, this is pretty alright if your child knows the sum of series, is that included in the syllabus? Are they allowed to use standard sums of say n, n^2, n^3?

>>7410521

>>7410541
this is wrong

This is right.

Waiting on you OP, you can tell us how much your kid knows or is required to know, are they provided with/required to know the formulas for power summations?

>>7410541
>>7410543
sry, it's early.

My kid has just finished Primary School and is going to Secondary School in August. This is part of her Summer Holiday homework. There are 60+ pages, everything from shapes/space, measurements and number work. This (picture) I can't help with. It's beyond my British schooling.

Thanks to those that have posted so far.

>>7410521

>First one:

Write the series as:
<span class="math">
\sum_{k=1}^{50}(2k-1)^3 - (2k)^3
[/spoiler]

and use:
<span class="math"> a^3 - b^3 = (a - b)(a^2 + ab + b^2) [/spoiler]

>Second one:

Similarly, write the sum as:
<span class="math">
\sum_{k=1}^{50}\frac{(2k)^4 - (2k - 1)^4}{(2k) + (2k - 1)}
[/spoiler]

This can be factored using:
<span class="math"> \frac{a^4 - b^4}{a + b} = (a^2 + b^2)(a - b)[/spoiler].

I assume he knows:
<span class="math">\sum_{k=1}^{N} k [/spoiler]
<span class="math">\sum_{k=1}^{N} k^2 [/spoiler]

This is 9)

>>7410578
Should be 500 in the second one, my mistake. Anyway the limit of the sum dosen't matter really.

>>7410521
(n^4-(n-1)^4)/(n+(n-1)) is n^2+(n-1)^2, so this simplifies quite a bit, it's just a sum of squares. The answer is 1000*(1000+1)*(2*1000+1)/6 =
333833500

>>7410521
I mean I always thought the American education system was shit. But on the opposite end of things I feel like this is a little extreme for an 11 year old.

>>7410911
What? I'm American and went to a public school and that was the kind of stuff we did when we were 11, most kids will turn 11 in 5th grade. These problems are pretty easy, it's just factorization and summing series.

>>7410923
How do I factorize such a series?

>>7410923
Um..I went to a public school and in 5th grade we were learning pre algebra

>>7410521
Hello, not from Hong Kong but is TVB dead? Why are their recent series so shit?

>>7410923
>>7410946
Where the fuck did you guys go to school.
The "advanced" students were allowed to take pre-algebra in the 8th grade where I went.

I didn't factor shit till my sophomore year of high-school or even see a series till my first year of uni.

>>7410954
i second this.

>>7410954
my school isn't even good like I read. I believe pre-algebra is the most you can go in 5th grade. In 8th grade we somehow had kids in algebra 2( the sequence is prealg, alg1, geometry, alg2, precal, calculus)
which blows my mind. I made it to precalc junior year and didn't do ap calc (wish I did)

>>7410954
i went to school in NJ and we were learning algebra
with chess peices and cubes
the cubes were X and whatever number was in the cube was how many X and the pawns each meant 1
so we would have equations like
pawn pawn pawn + 4cube = pawn pawn + 2cube
which would be 3 +4x = 2 + 2x
just giving an example, dont try to solve the equation

>>7410964
this was in 4th grade btw and was not a GT class or anything

>>7410940
In the first one group every two terms and factor, so you'll get (99^2+99*98+98^2)+(97^2+97*96+96^2)+...+(1^2+1*0+0^2). The middle terms can be factored further, so the series is (99^2+99^2-99+98^2)+(97^2+97^2-97+96^2)+...+(1^2+1^2-1+0^2). So this is the sum of the squares to 99, plus the sum of the odd squares to 99, minus the sum of the odd integers to 99.
99(99+1)(2*99+1)/6+50(2*50-1)(2*50+1)/3-((99+1)/2)^2 = 492500.
In the second one if you factor each term you'll see that the series is just (1000^2+999^2)+(998^2+997^2)+...+(2^2+1^2) = 1000(1000+1)(2*1000+1)/6.
There's probably an easier way to do the first as it seemed much more convoluted, but the second felt like a countdown problem for mathcounts, which are supposed to take 15-30 seconds to solve.

<div class="math">\sum_{n=1}^{99}n^3 (-1)^{n+1} = - f(-1)</div>
If we define <span class="math">f[/spoiler] as
<div class="math">f(x) = \sum_{n=1}^{99}n^3 x^n</div>
To calculate it just remember the geometric sum formula and some basic Calculus
<div class="math">f(x) = \sum_{n=1}^{99}n^3 x^n = \sum_{n=1}^{99} \left(x \frac{d}{dx} \right)^3 x^n = \left(x \frac{d}{dx} \right)^3 \sum_{n=1}^{99} x^n = \left(x \frac{d}{dx} \right)^3 \frac{x - x^{100}}{1-x} = \frac{x^3 + 4x^2 + x}{(1-x)^4} - \frac{-970299 x^{103} + 2940004 x^{102} - 2969699 x^{101} + 1000000 x^{100}}{(1-x)^4}</div>

so <span class="math">\sum_{n=1}^{99}n^3 (-1)^{n+1} = - f(-1) = 492500[/spoiler]

>>7411032
nicely done.

>>7410521
Are you kidding when I was his age I couldn't even count my 12 times tables what the fuck.

>>7411206
Haha; you were a special kind of student, weren't you?

>>7411206
>hurrdurr plug and chug
>no real understanding of the logic behind it

cool

f(N)=\sum_{n=0}^N (2n+1)^3 = (N+1)^2 (2N^2+4N+1)
g(N)=\sum_{n=0}^N (2n)^3 = 2N^2 (N+1)^2
F(N)=f(N)-g(N)=(N+1)^2 (4N+1)
F(49)=492500

So you can get this from \sum n, \sum n^2 and \sum n^3. Very difficult for an 11 year old.

>>7411241
Still a retard tbh

>>7411244
i had a fat ass faggot of a college professor who used "plug and chug" all the time
i hated that fucking asshole, he was way jealous of me cause i was fucking the girl i sat next to and he wanted her so bad
god i hated community college

>>7411283
This sounds like something out of a terrible college drama.

>>7411283
you sure are a retard
how was your shit tier school?

>>7411285
lol he was gonna tutor her and he was like "yea we'll discuss prices after class when no one is here" and she was complaining about prices and he was like "last year a girl i tutored didnt have enough money but i did it anyway cause she kissed me on the cheek"
i then proceeded to make kissy noises at him every class i think he finally caught on near the end of the semester

>>7411288
>you sure are a retard
why?
>shit-tier school
you mean the community college i went to for one year? it was okay.

you sure have a lot of anger inside you, bud, i dont even know you but you've insulted my mental ability and my uni.
But i know that says a lot more about you than it does about me.

>>7411246
F(n)=f(n)-g(n)
= \sum_{n=0}^N ( (2n+1)^3 - (2n)^3 )
= \sum_{n=0}^N ( 12 n^2+6n+1 )
= 12 (\sum_{n=0}^N n^2) + 6 (\sum_{n=0}^N n) + 1
= (N+1)^2 (4N+1)

So you don't need the \sum n^3 formula. Anon up the thread pointed this out.

My 9 year old's summer homework
>tfw Russia

>>7411388

Wow no wonder Russkies rule the world.

>>7410964
I did that in second grade in a gifted and talented program. It was a good basis for me.

>>7411388
take-home exam... aka test of Google prowess.

>>7411388
fuck what does this mean

y'all dumb as hell
just use a2-b2 = (a+b)(a-b)

>>7411506
It's spectral theory. Pretty beautiful if you ask me.

>Russian again outbeautying chinks in mathematics

Mind if I save this rare meme for myself, anon ?

related

>>7411639
kekd

>>7410528
11 isn't so young. That's 6th grade.

>>7411639
>those pixels
fucking khan and his terrible low quality classes

>>7411639
I don't get it? Is 9th grade too young for calc 1? I took in 10th grade and found it easy as fuck, could've handled it in 9th grade no question.

>>7410521
>big numbers to make it look hard
gooks everyone

>>7411639
That boy is cute

>>7411712
Since he's looking at fucking youtube videos he obviously hasn't been "taking calc 1" Also you "took it in 10th grade" not "for the test tomorrow"

>>7411616
The course is called 'Sheaf theory and homological algebra' when literaly translated from Russian. I'm not sure how it's tied to spectral theory, am a first-year undegrad still, and this stuff is studied at the end of second/start of third year.

>>7412407
Disregard this, I am an idiot. The picture is of MSc's course.

>>7411388
Doubt it
>timestamp

>>7411733
It's really not hard. It's literally one formula. I finished Calculus III in 11th grade.

>>7411702
> 11 isn't so young
/sci/ confirmed for pedos

>>7412435
>I finished Calculus III in 11th grade
who the fuck are you mystical people?
louisiana here

>>7412713
For me, in 5th grade we had a couple students from the university who would teach more advanced math to 4-5 kids separate from the rest of the class. 6th and 7th grade I did math classes at the high school, and from 8th grade on I took math classes at the university. I ended up with about 40 credits by the time I finished high school. Most students didn't do any of that, but the option was there for the few of us that wanted to.

>>7410578
I finished high school this year and I only know that E symbol is a summation, idk how it works though, how fuck'd am I?

>>7410521
>Asian brags about their seemingly difficult education
>the US and Europe utterly dominate science

my 3 year olds homework you guys.

>>7413414
>mfw international students

>>7410528
Does Germany seriously only have 1 fields?

>>7410528
Does Germany seriously only have 1 fields?

If the French weren't in there I would be ranting about Anglo bias right now.

>>7411639
>>7411712
We also start baby calc in 10th grade, differentiation and integration mostly.

-South African.

>>7413083
I'm in a similar situation - finished AP calc freshman year now taking classes at a uni. Any advice about what classes to take advantage of or how to keep the credits towards a degree?

>>7413388
lol hadn't realised it looks like an E to plebs
It's a greek S.

>>7413517
Math education and University system in Germany is shit-tier. Even worse than in the US. They literally ONLY look at your average highschool grades.
For example:
>Person1 has a C- in math and an A in literature
>Person2 has an A+ in math and a D in literature
Person1 would have better chances to study math than Person2, because his average is higher, even though his math grades are shit.
We don't even have things like proper interviews, personal statements etc.

>>7411712
>>7413526
here in canada we don't do calc at all until grade 12

>>7413388
http://www.coolmath.com/algebra/19-sequences-series/03-series-sigma-notation-01
:^)

>>7413837
That's absolutely not true.
1. Most universities don't have a numerus clausus in mathematics, because it's so hard.
2. There are several other factors than the average when applying, they will thoroughly inspect your grades, extra, etc.

>>7414034
>don't have a numerus clausus
>because it's so hard
I don't see how the first follows from the second. Why should the entry requirements be lower for hard subjects? Shouldn't it be the other way around?

>>7414034
>Most universities don't have a numerus clausus in mathematics, because it's so hard.
No, they don't have one because their capacity for students is higher than the number of applicants.
"Numerus clausus" means "limited number". If less people apply than places they can offer, everybody gets in.

>>7414034
>http://www3.uni-bonn.de/studium/vor-dem-studium/bewerbung-zulassung/zulassungsverfahren#nc-erklaerung
> "Zusammen mit der Abiturbestenquote werden daher 80% der Studienplätze nach der Abiturnote und 20% nach der Wartezeit vergeben."
As an example. There are no other factors besides average and Wartesemester. If you have an average just below the NC, you won't get in even if you're better qualified.

>>7413632
Look at the degree requirements and prerequisites for what you want to go into, and base it off that. I ended up getting a math minor plus filling a lot of prerequisites for CS courses. Definitely made the workload easier when I actually went to college. I can't see any reason why they wouldn't keep any of your credits, my transcript shows all the classes I took and all credits counted as normal.

>>7411709
can't tell if this is bait or just really fucking stupid
>tip, look at the youtube title

>>7413905
:^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^) :^)

it seems pretty simple, it's just order of operations. summer is plenty of time for that.

but tell him not to scribble on his homework like that

>>7413083
Again where in the balls do you live.

>>7413855
Canadians are idiots to be honest. I've never met an intelligent Canadian.

>>7414034
Maybe that's because the best German students would rather study math in the US/UK than shit-tier German universities, not to mention how your terrible "engineering" programmes are closer to our technologist diplomas than real professional engineering.

Honestly I don't see why anyone in their right mind would choose to study in Germany.

>>7415363
You must not have met me then.

>>7410521

BE GLAD THAT YOU ARE NOT FROM USA

>homework threads are not allowed

>>7410528
https://www.youtube.com/watch?v=NK0Y9j_CGgM

>>7415402
should i move to another country

>>7415402

>>7415398 says you are a nigger....