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#9501 2013-03-24 11:11:22

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I will have to learn to adapt.

#9502 2013-03-24 11:13:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,046

Re: Linear Interpolation FP1 Formula

Once they begin to see you in one of the 9 or 10 forms that they can not do without, then you will do better.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#9503 2013-03-24 11:16:44

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Until then, it is a waiting game...

#9504 2013-03-24 11:23:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,046

Re: Linear Interpolation FP1 Formula

I suggest doing your math and forgetting about them. Not completely but putting them in the last and smallest compartment of your mind.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#9505 2013-03-25 00:54:37

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I find it difficult to forget about them...

I finally found a STEP question that was easily done with generating functions, getting the co-efficient was just a bit tedious.

#9506 2013-03-25 00:56:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,046

Re: Linear Interpolation FP1 Formula

The tough part of any generating function approach is getting the coefficient.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#9507 2013-03-25 01:00:28

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Yes, unfortunately no calc/CAS is allowed for STEP. Luckily all I had to do was get the coefficient of x[sup]24[/sup] in (1 + x + x[sup]2[/sup] + x[sup]3[/sup] + x[sup]4[/sup] + x[sup]5[/sup] + x[sup]6[/sup])[sup]5[/sup]. If it was an EGF that would have been more tedious.

#9508 2013-03-25 01:06:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,046

Re: Linear Interpolation FP1 Formula

Hi;

I was working on a paper for just that sort of problem. I will back soon from doing a chore.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#9509 2013-03-25 01:09:41

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

A paper?

Okay, see you later.

#9510 2013-03-25 01:23:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,046

Re: Linear Interpolation FP1 Formula

Only thing it did not have the constant term.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#9511 2013-03-25 03:44:06

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Sorry, I had to go to school, I am back now.

So you have a good way of getting the co-efficient?

My method was

and then just get the co-efficient of x^24 from that but then the arithmetic can become a bit long...

#9512 2013-03-25 03:45:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,046

Re: Linear Interpolation FP1 Formula

You can play spot the pattern.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#9513 2013-03-25 03:49:05

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Okay............

#9514 2013-03-25 03:55:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,046

Re: Linear Interpolation FP1 Formula

Supposing you needed the coefficient of x^5 in


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#9515 2013-03-25 03:59:56

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

By hand, I think I would just go back to sleep if someone asked me to do that

#9516 2013-03-25 04:07:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,046

Re: Linear Interpolation FP1 Formula

That could be difficult even by computer. That is when math becomes an art and ceases to be a science.

Anyway this is the answer:


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#9517 2013-03-25 04:08:00

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

How do you know that?

#9518 2013-03-25 04:19:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,046

Re: Linear Interpolation FP1 Formula

Sometimes in combinatorics we have a big problem. We can often solve it by looking at smaller problems that have the same flavor and then spotting the pattern. For instance it is not too difficult to expand these:

What do you notice about the coefficient of x^5 in each case?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#9519 2013-03-25 04:25:16

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

The co-efficients are constant for the first sequence, (n+1) for the second sequence, and the triangular numbers for the third.

#9520 2013-03-25 04:28:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,046

Re: Linear Interpolation FP1 Formula

You can put that into a more succinct combinatoric notation.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#9521 2013-03-25 04:33:23

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

(n+1) choose (k-1), where k is the power of the big bracket?

#9522 2013-03-25 04:38:19

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Hmm maybe (n + k - 1) choose (k - 1).

#9523 2013-03-25 04:39:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,046

Re: Linear Interpolation FP1 Formula

You can phrase wholly in terms of the power n:


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#9524 2013-03-25 04:46:32

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Oh I see. So in my example I could have just done

#9525 2013-03-25 04:49:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 89,046

Re: Linear Interpolation FP1 Formula

Yes, because of symmetry:


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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