Tricky Problems (***)

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Tricky Problems (***)

Post by Foxide on Fri Jan 22, 2010 11:17 am

Simplify the equation to its simplest form;





where is Riemann's zeta function, is the gamma function, is the del operator, denotes the inverse Laplace transform, is the nth Chebyshev polynomial of the first kind, is a simple closed curve bounding a region having as an interior point, is a simplex of an oriented simplicial complex and [σ^m, σ^(m - 1)] is an incidence number, is a compact, orientable, differentiable k-dimensional manifold with boundary in and is a -form in , defined, and at all points of , and is Dirichlet's eta function.

EDIT: The last bit of that equation is cut off (the integral involving Dirichlet's Eta function). To see it, go here; http://www.physicsforums.com/latex_images/25/2504352-2.png


Last edited by Foxide on Fri Jan 22, 2010 1:14 pm; edited 5 times in total

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Re: Tricky Problems (***)

Post by SovietPatriot on Fri Jan 22, 2010 11:22 am

Easy. The answer is 2

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Re: Tricky Problems (***)

Post by remenant on Fri Jan 22, 2010 11:37 am

problem with your image code there Shocked

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Re: Tricky Problems (***)

Post by Foxide on Fri Jan 22, 2010 11:44 am

Damn... the trouble with posting an image link to a LaTeX code that's been rendered is that sometimes they may contain the ] and [ brackets, which, if removed, can be crucial to the LaTeX coding. Going to have to find a way around it...

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Re: Tricky Problems (***)

Post by Foxide on Fri Jan 22, 2010 11:47 am

Okay, fixed. I uploaded the image somewhere else. Smile

For those who don't have that much time on their hands, here is an easier challenge (but still feels nice completing it);

Simplify the equation to its lowest form;



where p is prime.


Last edited by Foxide on Fri Jan 22, 2010 1:19 pm; edited 1 time in total

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Re: Tricky Problems (***)

Post by SovietPatriot on Fri Jan 22, 2010 11:50 am

^^ Fail?

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Re: Tricky Problems (***)

Post by Foxide on Fri Jan 22, 2010 11:55 am

Did you have a go at the bottom problem? I think GCSE students should be able to manage it... a lot of the stuff can be cancelled out from first glance, but it should be a nice test going through it. Smile

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Re: Tricky Problems (***)

Post by remenant on Fri Jan 22, 2010 12:25 pm

i don't think that website likes hotlinking o_O

i keep seeing physicsforum.com

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Re: Tricky Problems (***)

Post by Foxide on Fri Jan 22, 2010 12:27 pm

Are you sure? It looks fine to me... I edited the changes into the first post.

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Re: Tricky Problems (***)

Post by We love you Ric =D on Fri Jan 22, 2010 12:48 pm

can I show my workings out?
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Re: Tricky Problems (***)

Post by remenant on Fri Jan 22, 2010 12:50 pm

EDIT: Problem Fixed, nothing to see here


Last edited by remenant on Fri Jan 22, 2010 1:29 pm; edited 1 time in total

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Re: Tricky Problems (***)

Post by Foxide on Fri Jan 22, 2010 12:56 pm

That is rather strange... I see the images fine.

You can see the images here in their respective order;

http://www.physicsforums.com/latex_images/25/2504352-1.png
http://www.physicsforums.com/latex_images/25/2504352-2.png

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Re: Tricky Problems (***)

Post by We love you Ric =D on Fri Jan 22, 2010 12:57 pm

or the same image but that's just as good.
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Re: Tricky Problems (***)

Post by Foxide on Fri Jan 22, 2010 1:01 pm

We love you Ric =D wrote:or the same image but that's just as good.

? They're different images...

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Re: Tricky Problems (***)

Post by We love you Ric =D on Fri Jan 22, 2010 1:03 pm

maybe when ever I see a complex question I always cover it up with www.physicsforums.com
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Re: Tricky Problems (***)

Post by Foxide on Fri Jan 22, 2010 1:04 pm

I'll upload it on to imageshack... I hope their compression doesn't suck, though.

What about the easier challenge? Is it visible?

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Re: Tricky Problems (***)

Post by We love you Ric =D on Fri Jan 22, 2010 1:05 pm

yes tis
oooh modish
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Re: Tricky Problems (***)

Post by Foxide on Fri Jan 22, 2010 1:14 pm

Okay, it should be fixed now.

Enjoy. Smile

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Re: Tricky Problems (***)

Post by We love you Ric =D on Fri Jan 22, 2010 1:18 pm

OK carry the one, finished I'll wait for everyone else before I ruin it for them
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Re: Tricky Problems (***)

Post by Foxide on Fri Jan 22, 2010 1:18 pm

'Carrying the one' is actually a step in the process to determine a solution for the easier challenge. O_o

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Re: Tricky Problems (***)

Post by We love you Ric =D on Fri Jan 22, 2010 1:25 pm

now I'm confused I thought I was dividing shit in the first one you don't wanna know how wrong I was. Sad
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Re: Tricky Problems (***)

Post by Foxide on Fri Jan 22, 2010 1:26 pm

There is a lot of dividing in the first one... you will notice how easily some of the things cancel out.

Hint: The divergence of a curl is zero.

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Re: Tricky Problems (***)

Post by remenant on Fri Jan 22, 2010 1:30 pm

i'm guessing you teach further maths cause no way have i heard anything about this on the syllabus in single

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Re: Tricky Problems (***)

Post by Foxide on Fri Jan 22, 2010 1:34 pm

Well, the trickier challenge is mainly orientated towards those who have studied mathematics up to degree level, but some things you will have come across before - there is a surface integral in there, which is in the syllabus, and the gamma function is right at the start, which is essential in combinatorics.

Has anyone tried the easier challenge? Looking to see how the denominator is tackled on the LHS. Hint: Do we need to bother integrating e^(x^2)? Wink

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Re: Tricky Problems (***)

Post by We love you Ric =D on Fri Jan 22, 2010 1:41 pm

there's a lot of greek in this "maths" shiz they should try updating them equation's and what not instead of zeta our homme's should be puttin fallout 3 up in there faces know what I'm sayin
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