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**zetafunc.****Guest**

Unlike adriana my performance in STEP won't affect whether or not I go to UCL, but realistically I think I will get at least S, 1 and 2 in STEP I, II and III. I would like to get 3 S-grades, but that will take some more work. It is very difficult to get an S in STEP III.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,431

66 days away you say? That is plenty of time.

**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.**

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**zetafunc.****Guest**

Yes -- although it is hard to complete a whole paper in one day...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,431

If I can help just post it.

**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.**

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**zetafunc.****Guest**

It is OK at the moment, for 2004-2012 they provided solutions -- although for 2003 and beyond they didn't include them.

adriana says she will aim to do 6-8 questions on the weekends, which is pretty good.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,431

That may be your opportunity. Do not volunteer, let her ask.

**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.**

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**zetafunc.****Guest**

Sometimes she asks for help, sometimes we do a question together. She needed help on a geometry question and I couldn't help her with it because it puzzled me too.

Some of these questions can be really annoying, requiring tedious amounts of algebra...

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,431

That is what a CAS is for.

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

It would be nice to use one, but not for this exam, it is not permitted. No calculators. In fact I heard they ban measuring instruments/compasses/etc. too. Pen and paper.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,431

I meant for checking right now.

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

They provide solutions thankfully, so no need to use them for STEP. I use them occasionally though but only for simple things like pattern-spotting, like when you got me to work out the co-efficient of x[sup]n[/sup] in the expansion of (1 + x + x[sup]2[/sup] + ... )[sup]k[/sup], which was (n + k - 1) C (k - 1). That one has been very useful.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,431

Yes, that was a good problem.

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

Also, if G(x) is some generating function, is it always true that

G'(1) = E(X), and that

G''(1) + G'(1) - (E(X))^2 = Var(X)?

So for instance, the PGF for a simple 6-sided, fair die:

would this kind of thing work?

**zetafunc.****Guest**

The last bit of LaTeX should be differentiating the GF, setting equal to 1, and getting 3.5, the correct answer.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,431

Yes, you can get all the moments from the generating function.

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

Do the moments have any meaning for non-probability GFs? Combinatorial problems for instance?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,431

I do not think so, A probability GF is different.

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

Oh, okay. STEP III has some generating function questions, I didn't know they came up in STEP.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,431

They are slowly working their way into every level of mathematics.

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

adriana doesn't seem to get them at all unfortunately... maybe it is the way I am explaining it.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,431

They can be a bit difficult to get at first but once you do...

**In mathematics, you don't understand things. You just get used to them.**

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**zetafunc.****Guest**

I found them difficult at first too, I still find them a bit tricky, they are very powerful though.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,431

They are a lot of fun too.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,790

Speaking og GFs, bobbym, have you been able to get through the 3rd chapter of GFology?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,431

Absolutely not, it is said Wilf could not get through it.

**In mathematics, you don't understand things. You just get used to them.**

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