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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: 86,227

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

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

If I can help just post 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**

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: 86,227

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

**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**

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: 86,227

That is what a CAS is for.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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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: 86,227

I meant for checking right now.

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 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: 86,227

Yes, that was a good problem.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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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: 86,227

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

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

Combinatorics is Algebra and Algebra is Combinatorics.

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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: 86,227

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

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

Combinatorics is Algebra and Algebra is Combinatorics.

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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: 86,227

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

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

Combinatorics is Algebra and Algebra is Combinatorics.

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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: 86,227

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

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 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: 86,227

They are a lot of fun too.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

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

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

Combinatorics is Algebra and Algebra is Combinatorics.

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