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**zetafunc.****Guest**

If only I knew this before I did this problem! These things really do simplify combinatorics problems...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Probability problems too:

This is probability generating polynomial for throwing a die 5 times.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**zetafunc.****Guest**

Yes, I have seen those ones. Unfortunately with the probability questions they ask, I can never seem to find the right GF so I have to use other methods.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

That can be tough finding the right one sometimes you have to construct it.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**zetafunc.****Guest**

If only every problem had a GF...

...does every problem have a GF?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

I asked that question to a bunch of mathematicians, I got no answer.

I would say it is very easy to see that there is a generating polynomial but will there always be a generating function?

Look at this series:

It is unlikely that there is a gf for those coefficients.

But would that come up in a combinatorics problem? Probably not. So the question,"does every combinatoric problem have a gf?" I can not answer definitely but I think yes!

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**zetafunc.****Guest**

We almost got to do some combinatorics in chemistry today (he was explaining entropy). Unfortunately we never did any maths, just listed some possibilities.

Greatest part was when he asked how many ways there were to arrange 4 objects, nobody knew. The teacher listed them all and concluded from his list that the answer must be 22.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Technically, that is not combinatorics what he did. Someone described combinatorics as the art of counting without actually counting.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

I read that somewhere too. It would be nice if they knew about it though, then he wouldn't have to count. There is a module we have to do called 'combinatorial chemistry'. Containing no combinatorics...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

With me it was just the opposite.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

What do you mean?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

When they started getting into some math for chemistry I freaked out. It destroyed my future.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

What, why?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi;

Sorry, a bunch of morons are calling me about a census. I have been ducking them but not any longer. I will have to answer their question. See you after I am done.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Okay, see you later.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Sorry, they wanted to know about grocery shopping in my area.

The first time I saw a real math problem I was unable to understand it. I had to drop chemistry which was what I wanted to do for life.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

What maths problem?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

They were K ionization, K equilibrium and Constant solubility products. They were not the problem, the numbers were!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Interesting, I am studying those right now...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

It was the first time I saw scientific notation. Thanks to my math classes I thought all numbers were like 1,2,3,4, 1/2, 1/4, √2, π. When I saw

I could not deal with it or understand it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

They didn't have calculators in your day?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Nope, I taught myself how to use a slide rule. The shock of seeing numbers like that and having to work with equations that had them was too much. The chem teachers tried to teach us but those stupid math classes never prepared us to work with numbers, real numbers.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

Chem teachers could do arithmetic in those days? The modern chem teacher says that 1/0 = 1, pi is approximately 3, and that you are a genius if you can do 4*3*2*1 without a calculator.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Back then my chem teachers could calculate much better than a math teacher could. This was not unusual, the greatest living numerical analyst is Forman S. Acton and he is a chemist.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**zetafunc.****Guest**

I haven't heard of him, I was surprised he was born in 1920, that is quite old...