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    Hey guys!

    I'm doing the IB and I'm planning on doing my EE, which is an extended research paper written on any topic of your choice. I decided to do mine on Maths, and I'm currently fretting over how and what on earth I'm supposed to write 4000 words of intensive research on.

    I'm very much interested in pure maths and would love to have a project to do in Real Analysis or some such other pure course. The material needs to be say, first-year undergrad.

    I wouldn't mind exhibiting a nice big juicy Mathematical problem, something along the line of this essay; but preferably avoiding nasty geometry and instead tasty proper pure maths.

    Something on Abstract Algebra wouldn't go amiss either, although my current knowledge hasn't yet met Rings and I'd be severely limited. I'm planning to expand my knowledge over the next two or three months to cover Rings and Fields though, so it wouldn't be completely impossible to do a paper on that.

    Thank you, feel free to flood me with a million ideas!
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    Just a suggestion - what about Julia Sets of the famous complex: z=z^{2}+c iteration function for different c.

    You could investigate the behaviour of the points in the plane with various "c", and the weird shape of some sets because of the behaviour of these points (how some are neutral - meaning they have no effect one way or the other on points around them, how some are "repelling" points - which repel nearby points, how some are attracting - again attracting nearby points, and how those around some points behave chaotically - hence what a Julia Set looks like - e.g: ("dragon" sets, and"rabbit" sets.

    (one tip might be investigate your own choice of "c")
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    (Original post by Hasufel)
    Just a suggestion - what about Julia Sets of the famous complex: z=z^{2}+c iteration function for different c.

    You could investigate the behaviour of the points in the plane with various "c", and the weird shape of some sets because of the behaviour of these points (how some are neutral - meaning they have no effect one way or the other on points around them, how some are "repelling" points - which repel nearby points, how some are attracting - again attracting nearby points, and how those around some points behave chaotically - hence what a Julia Set looks like - e.g: ("dragon" sets, and"rabbit" sets.

    (one tip might be investigate your own choice of "c")
    I think I've come across that one term before, never paid much attention to it, but now that you've elaborated on it a bit, it does sound rather nice. I particularly like chaotic aspect you've described as one of my areas I was interested in was Chaos Theory. I especially liked the idea of the Chaotic/Double pendulum. What do you think of it?

    Thank you so much!
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    now that i see it, it does look pretty cool! - question is, though, how would you relate it essay-wise?...
 
 
 
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Updated: January 22, 2015
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