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#9051 2013-03-11 09:15:36

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

That is okay, we are all busy at some point.

#9052 2013-03-11 09:29:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,904

Re: Linear Interpolation FP1 Formula

I still did not get the can opener though.

Any news?


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.

Online

#9053 2013-03-11 09:31:17

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

No news, this has been a pretty dry day.

#9054 2013-03-11 09:32:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,904

Re: Linear Interpolation FP1 Formula

Sometimes that is good. No news is much better than bad news.


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.

Online

#9055 2013-03-11 09:52:38

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Been talking to my male friends though, I am going to a Steven Weinberg lecture in two days' time. Hopefully there is not a mile-long queue like last time.

#9056 2013-03-11 09:54:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,904

Re: Linear Interpolation FP1 Formula

That is very good. What is he speaking about?


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.

Online

#9057 2013-03-11 10:16:59

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

The Higgs boson, I think.

#9058 2013-03-11 10:22:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,904

Re: Linear Interpolation FP1 Formula

He is a good lecturer, an interesting guy. Especially when he is talking about philosophy.


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.

Online

#9059 2013-03-11 11:24:27

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I have never heard him speak in person, I have only watched him on YouTube. You have seen him live?

#9060 2013-03-11 11:38:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,904

Re: Linear Interpolation FP1 Formula

No, I have never seen him in person either. I have seen him in documentaries.


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.

Online

#9061 2013-03-11 12:00:28

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Me too. I have heard him talk about the laws of nature most of the time though.

Having another hard time with a combinatorics problem, that I do not know how to set up the GF of... or even if there exists a GF.

#9062 2013-03-11 12:33:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,904

Re: Linear Interpolation FP1 Formula

Post the problem and who knows what will happen. Could be the end of the world or maybe just a solution of sorts.


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.

Online

#9063 2013-03-11 18:58:43

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

How many numbers from 10,000 to 100,000 (inclusive) contain only two different digits? (e.g. 32332, 11114, but not 10002)

I don't understand how to set up the GF for this problem...

#9064 2013-03-11 19:20:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,904

Re: Linear Interpolation FP1 Formula

Hi;

I am getting 1216 for 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.

Online

#9065 2013-03-11 19:23:29

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

That is correct... how did you get the GF for this? The thing I'm having trouble representing is the constraint that only 2 different numbers are allowed. I tried representing each possible digit of a 5-digit number with polynomials of degree x^9, but I didn't know what to do with it...

#9066 2013-03-11 19:26:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,904

Re: Linear Interpolation FP1 Formula

These type are always a little bit tricky. I will start to work on it as soon as I handle this spammer.


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.

Online

#9067 2013-03-11 19:32:54

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Okay, thank you.

So, you did this one by hand/with a more systematic approach?

#9068 2013-03-11 19:47:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,904

Re: Linear Interpolation FP1 Formula

There are other ways to get at it by standard combinatorics and experimental methods.

No luck with the gf though. with hand methods.

Quite easy using a CAS:

With n being the number of digits in the number.

Closed form:

Linear recurrence:

with

GF:

I am going to take a little break.

Last edited by bobbym (2013-03-11 21:50:46)


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.

Online

#9069 2013-03-12 06:17:36

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I keep staring at that and I haven't got a clue how you got that...

#9070 2013-03-12 10:12:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,904

Re: Linear Interpolation FP1 Formula

Hi;

Computational mathematics has solved the problem of getting those to a very high degree.

There does not appear to be any way by hand methods that I can discover.


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.

Online

#9071 2013-03-12 10:30:57

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Oh, okay... thank you, though. I guess the other problem is deciding when to use a GF and when not to... I downloaded a book called 'Generatingfunctionology', I will read it and see if I can understand how these things work a bit more. I've heard it is good.

Nothing from adriana, hmm. It has been 3 days. I did not expect such a sharp decline.

#9072 2013-03-12 10:43:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,904

Re: Linear Interpolation FP1 Formula

That is a good book. Herbert passed away a little while back, he was the best all around mathematician of today.


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.

Online

#9073 2013-03-12 10:46:20

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I had never heard of him previously, unfortunately... but it does look like a great read. It seems to cover everything I would need to know -- one thing I was curious about is why exponential generating functions are used for permutations, and ordinary generating functions are used for combinations. I just learned it without understanding how someone found out that we could use them.

#9074 2013-03-12 10:53:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,904

Re: Linear Interpolation FP1 Formula

Exponential gf's are made from the e^x series. Each term has a factorial. By themselves they do not count permutations. You need to multiply the correct power of x by the factorial of the power.

The first couple of chapters are a very good introduction after that it does stiffen up.


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.

Online

#9075 2013-03-12 11:02:00

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Oh, of course... that makes so much sense, so they just needed to find a series that combined an OGF with factorials in it.

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