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#176 2012-05-03 07:31:45
- bobbym
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Re: Generating Functions
Correct! So what is the problem?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#177 2012-05-03 07:35:30
- anonimnystefy
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Re: Generating Functions
Nothing. You asked me to post it. I asked you then if you can post a more complicated one.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#178 2012-05-03 07:36:30
- bobbym
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Re: Generating Functions
Nope! You know how to do it. They do not get more complicated than that in books.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#179 2012-05-03 07:39:27
- anonimnystefy
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Re: Generating Functions
Can't you think of one?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#180 2012-05-03 07:41:16
- bobbym
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Re: Generating Functions
That is the prototypical problem for that type that appears in books. It tests your ability to form the generating function. You can do it. There are two things left...
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#181 2012-05-03 07:44:40
- anonimnystefy
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Re: Generating Functions
Which two things?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#182 2012-05-03 07:45:28
- bobbym
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Re: Generating Functions
1) Getting the coefficient.
2) Knowing when and where to use the GF.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#183 2012-05-03 07:49:31
- anonimnystefy
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Re: Generating Functions
Okay. The coeff can be found in two ways:
1)Computers. Nothing more to say about that.
2)Partial fractons and expand the GFs you get. Read off the general term from the GF you get when you sum all of those GFs you have after partial fractions.
There is no exact rule for the second one. It is I think mostly intuition,though some problems just look made for GFs and some look exactly opposite of that.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#184 2012-05-03 07:51:09
- bobbym
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Re: Generating Functions
2) There are many other ways. gAr and I have discussed them.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#185 2012-05-03 07:52:38
- anonimnystefy
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Re: Generating Functions
I know. I am saying that it is mostly intuition (gained by experience of course) that determines wheter ir not GFs should be used.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#186 2012-05-03 07:55:20
- bobbym
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Re: Generating Functions
No one can say. A brilliant guy I know asked whether every combinatoric question could be put into the form of a generating function. He posted that question to the best of the best of the best. He got no reply.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#187 2012-05-03 07:58:18
- anonimnystefy
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Re: Generating Functions
If the answer is yes,then we should be able to find a GF for juan's matrix problem.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#188 2012-05-03 08:00:43
- bobbym
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Re: Generating Functions
Me Pappy wrote:
If is a big word.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#189 2012-05-03 08:03:58
- anonimnystefy
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Re: Generating Functions
How lucky would I have been to ever have met Pappym.
Mathematics is based on lots of assumptions. We use Euclid's geometry,even though we live on a sphere.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#190 2012-05-03 08:06:10
- bobbym
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Re: Generating Functions
He was the greatest m that ever lived.
As a person he was a lot like you.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#191 2012-05-03 08:08:54
- anonimnystefy
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Re: Generating Functions
Greater than Grandpappym?
How is he a lot like me as a person?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#192 2012-05-03 08:13:19
- bobbym
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Re: Generating Functions
GrandPappym was little more than a beast posing as a man. Tremendously strong and powerfully built. He used his strength to dominate people.
How is he a lot like me as a person?
He was also rebellious in his youth. Unfocused and impatient, sort of like Luke Skywalker.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#193 2012-05-03 08:16:19
- anonimnystefy
- Real Member
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Re: Generating Functions
Wow,that really does sound like me!
Btw,I think I have over 6000 posts now.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#194 2012-05-03 08:17:16
- bobbym
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Re: Generating Functions
Yes, you do. Congratulations.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#195 2012-05-03 08:19:21
- anonimnystefy
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Re: Generating Functions
Thank you,but it is not the number that counts.
Would you like to propose the next topic if you have nothing more to say about this one?
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#196 2012-05-03 08:23:13
- bobbym
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Re: Generating Functions
We had that discussion a long time ago.
Keep the thread open, New stuff will go in.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#197 2012-05-03 08:25:50
- anonimnystefy
- Real Member
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Re: Generating Functions
Yes. We had it twice. I do not remember the conclusions though.
Of course I will keep it open. I wouldn't close this one if (enter a reason here). I was just asking if you would like to post the next topic or should I.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#198 2012-05-03 08:27:18
- bobbym
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Re: Generating Functions
No the discussion I am talking about was before you were a member. I was the lightweight in the group and no one paid any attention to what I said.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#199 2012-05-03 08:29:27
- anonimnystefy
- Real Member
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Re: Generating Functions
Do you know where that discussion is.
And you still haven't told if you want to open the new topic or should I.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#200 2012-05-03 08:34:39
- bobbym
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Re: Generating Functions
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.