Realizing that there are several other threads with similar inquiries, I need help choosing an appropriate topic for my I.B. mathematics extended essay. The extended essay is written on a topic of the (high school) student's choice and must be between 2000 and 4000 words. For some background information on the assignment, I'll pull information directly from the I.B.O.(adsbygoogle = window.adsbygoogle || []).push({});

"An extended essay in mathematics provides students with an opportunity to demonstrate an appreciation of any aspect of the subject, whether it is:

~the applicability of mathematics to solve both real and abstract problems

~the beauty of mathematics as in, for instance, geometry or fractal theory

~the elegance of mathematics in the proving of theorems as in, for example, number theory

~the origin and subsequent development of a branch of mathematics over a period of time, measured in tens, hundreds or thousands of years

~the links between different branches of mathematics and the powerful structures that enable may seemingly different problems to be solved by a single theory

~the way that a branch of mathematics has been born, or has flourished as a result of technology.

"The extended essay may be written on any topic that has a mathematical focus and it need not be confined to the theory of mathematics itself . . ."

My thoughts: Since the essay doesn't need to be exceedingly rigorous, I figured should be able to write a reasonable essay detailing how non-standard analysis can be used to simplify things like the definition of continuity. Recently, I've also been reading about the cardinality and countability of certain sets and I think it would be interesting to try and write an essay on that as well (the elementary stuff doesn't seem too difficult). However, since I don't if either of these would ultimately lend themselves to writing the essay, I'm in need of advice. Any recommendations are greatly appreciated. Thanks!

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# I.B. Extended Essay

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