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

Hi;

I'd better not ask what a polynomial is, then!

Those are polynomials.

coefficients encode information about a sequence of numbers;

- indexed by the natural numbers

Hahahahahahhahahahhahahha! That is what I am talking about! Get the motor oil, I spot a pure mathematician! What a pretentious definition of a polynomial.

**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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

I'll have to leave it there, Bobby: bed beckonszzzz...

Catcha later.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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

Hi;

Okay, rest well, we will talk again.

**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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hahahahahahhahahahhahahha! That is what I am talking about! Get the motor oil, I spot a pure mathematician! What a pretentious definition of a polynomial.

'Mathspeak' *noun* : Math jargonese employed by self-opinionated pure mathematicians in an unintelligible, highfalutin manner for the purpose of self-aggrandizement.

My eyes glazed over when I saw what that pm wrote, and I didn't try to read through the smoke.

A couple of non-mathspeak examples of such obfuscation (loosely on topic):

- Where there are visible vapors having their province in ignited carbonaceous material there is conflagration.

- The person with the ultimate cachinnation possesses, thereby, the optimal cachinnation.

*Last edited by phrontister (2011-11-17 14:58:14)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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

Hi;

Wikipedia is loaded with such guys. I once wrote a little piece for Wikipedia. Know what they did with it? They deleted 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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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi Bobby,

Maybe you didn't use enough sesquipedalian words!

Did you crack the two "non-mathspeak examples" in my previous post?

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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

Hi;

Yes, I did!

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Excellent!! And...?!

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

After having been accused by the meanest woman I have ever known of being sesquipedalian, I found that page awhile back.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

What is the number of solutions to

a + b + c + d + e + f = 50 with a,b,c,d,e,f being positive integers and

a>b>c>d>e>f ?

A says) No solutions!

B says) 1057

C says) That is correct!

D says) No is isn't. The answer is 1058 by direct count.

E says) How did you get that B?

What is the correct answer?

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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

Hi gAr;

Good to see you.

Both of those gf's are correct. Very good. Your second one is an improvement over mine, so I am stealing it!

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

Thank you!

Yes, gladly! I was the first to steal, your g.f gave the idea.

How did you come up with that solution? You too thought of partitioning?

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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

Hi gAr;

Actually, I was not thinking along those lines. I have in my notes the solution to various diophantine equations such as

I use them in the same way as I would use the quadratic formula. I never really thought about them.

Your idea is the first time I have seen any explanation of them.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

Okay.

I had tried the problem a while back, but was stuck with it. I'm happy that now we have a solution!

It's amazing the way the g.f's can be manipulated, wonderful!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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

Hi gAr;

They are truly amazing!

When I started learning combinatorics, I started with gf's first. So they are what I am used to and like. You know that I do not digest much theory. I learn by doing a problem and then trying to do a slightly more difficult problem of the same type. I know this is considered idiotic by the mathematical community and I take much ridicule on other forums. Unfortunately it is the only way I can learn.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Yes, that's the way I learn it too!

I read an example first to know whether it interests me.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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

Hi;

As you also know math types do not like to do an example. You can go through whole books where the guy never does a problem. These are the most difficult for me.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

Yes, I have seen such books. Some books where titles sound cool, but inside there will be no examples!

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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

Hi;

Some mathematicians think doing a problem where you get a number is beneath them. They think that it is inferior in some way. Most according to Zeilberger still will not use a CAS. They think they are just toys.

Had a guy tell me that any integral or sum that a CAS could do, he could! So of what use are they? Of course I was laughing too hard to answer him.

They still teach gf's as if they are advanced mathematics, only for graduate students.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

Yes, I agree!

I need to go out, see you later...

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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

Hi;

Okay, have a good night!

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

Combinatorics is Algebra and Algebra is Combinatorics.

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

**New problem**

**In the drawing below each little circle has a circumference of pi units. They also meet at only 1 point with each of the two other smaller circles. The center of each small circle is on the circumference of the red circle.What is the radius of the red circle?**

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi Bobby,

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

Hi phrontister;

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi Bobby,

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