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**zetafunc.****Guest**

Their solution identifies a pattern then uses the standard sum for n^2 to get to that formula. I tried a GF approach and it is too messy, I don't think it is a good approach for this part of the problem...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

I can generate a gf but I can not get the zeroth coefficient from 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**

I have the same problem too, it might be quicker to use the 'normal' method (the problem is aimed at students who have never encountered GFs).

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

Okay, I will have a look at that paper. Thanks for the link.

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

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**zetafunc.****Guest**

I found out that she leaves only a couple of minutes before I do. She has early lessons on Tuesday and Wednesday, so I can meet her on the way to school on those days.

She doesn't seem to be that interested in maths though... I just need to show her something nice, but I don't know what she is interested in. She just said she likes 'pure maths', but she only says that because she has never really done any applied maths. To be truthful, she doesn't even tend to do well in maths... but I'll see if I can find out why she likes it.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

Probably some reason that will be difficult to understand.

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

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**zetafunc.****Guest**

Her Dad has a PhD in physics, maybe he was pushy...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

Yeccchh! Ever heard of the teakettle principle?

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

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**zetafunc.****Guest**

Isn't that when you simplify a problem to one you how to solve? I remember reading something about a joke, don't know what it is though...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

A physicist and a mathematician are given an empty teakettle, a fire and a water supply and are asked to boil water. They both fill the teakettle, place it on the fire and boil the water. Now they are both given a teakettle already filled with water. The physicist after much thought shouts "Eureka" and places the teakettle on top of the fire and boils the water. The mathematician immediately empties his teakettle, the physicist asks why did you empty it? The mathematician says, "because I already know how to solve the empty teakettle problem."

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

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**zetafunc.****Guest**

Haha, that is good. I'll remember that one.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

Vilenkin, the Russian combinatoricist is the source.

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

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**zetafunc.****Guest**

Never heard of him...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

Neither did I until I came across his book. The Soviet authors did not get a lot of exposure over here.

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

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**zetafunc.****Guest**

It's the same here. We are never taught the history of any maths, or where things came from.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

That is what I have found. It is a shame, the history is fascinating.

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

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**zetafunc.****Guest**

It is a shame indeed. I was asking a maths teacher about Leibniz and do you know what he said?

"Oh, Leibniz! Those cost about £1.99 just across the street."

Turns out he wasn't joking, he thought Leibniz was a chocolate biscuit, not a man.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

I had a similar experience. I tried to compliment a supposedly pretty good math type with a phrase from Newton and one of the Bernoulli's. He had never heard of it.

Remember we were talking about cf's and Pell equations? There is an example, Pell had nothing to do with that equation. It was Fermat's! A historical error names them Pell equations.

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

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**zetafunc.****Guest**

Oh I see -- I've seen them called 'Pell-Fermat equations'... I do not really know what else Pell is famous for doing though. Pell equations are all I can associate with him.

Argand diagrams are a historical error too, aren't they? I don't think someone called Argand discovered them.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

I do not know about that one, I will have to look it up.

The Binet formula for the Fibonacci numbers, that was discovered by De Moivre, not Binet.

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

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**zetafunc.****Guest**

I did not know that, and we never do question these things when we learn about them. I just accepted it...

Venn diagrams were actually first used by Euler I think...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

I heard that. It is strange that in some cases they did not even get the name of the discoverer right. Makes you wonder what other mistakes there are.

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

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**zetafunc.****Guest**

Hopefully the errors are only historical ones...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,235

That is what we hope. I do not agree with cutting it out of the educational process. They should teach a little bit of the background of these men.

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

Combinatorics is Algebra and Algebra is Combinatorics.

**Online**

**zetafunc.****Guest**

Even fellow mathematicians care little for history or even for the beauty of maths itself. Not that those are necessary pre-requisites to study it, though.