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How much mathematics should an extended essay involve?

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I was thinking to do my extended essay on maths and I found the topic golden ratio pretty interesting and I thought about linking it to Fibonacci sequence. The question that I have is that, what level is expected from us? and is this a good topic to research on?

Edited by Robert142

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Guest michaelwm

I've uploaded the Extended Essay Guide for Mathematics - unless you've read the entire thing, don't choose a topic just yet. Read the guide first, and try finding some examples online. Read through them entirely (they're long reads), and ask yourself:

Did I fully understand the mathematics grounding this essay?

From the 8 examples I found and read, after my first read through for each - I didn't fully understand any of the 8 examples. The maths was very confusing and it took me a few read throughs to fully understand them. That is what my IB Coordinator says to look for. A good mathematics extended essay should have maths that wouldn't be immediately understood by anyone taking HL Math on their first read through. They are research papers after all - if the paper was grounded entirely in prior knowledge there wouldn't be any research going into them - right?

The essay is graded out of 36 possible marks. 20 of those marks are for how you have written your research paper (research question, introduction, investigation, conclusion, etc...) and the 16 remaining marks are for how you have met your subject specific criteria (refer to the guide I've uploaded). That's a good start for what level is expected from us.

For example, my favorite read was an example essay about the 3n + 1 conjecture - it read really well and I enjoyed the format the student chose, and his / her way of tackling the question. I chose to do something similar, and write my extended essay on the Riemann Hypothesis, in similar fashion. I'll be talking on the hypothesis' origin, it's specifics, the function and how it was derived, creating my own method to derive the function (if possible), introduce it's "family" of functions, attempt to solve the hypothesis (obviously not going to happen, but that's not the point) through inductive and computational attempts, and briefly touch on the applications of the hypothesis.

Ultimately - read the guide, read some examples, and write up a long list of topics. Not 1 or 2 - 4 or 5 at least. For each one, think or write about how you would write on the topic, and if you handed it to a friend in your maths class, would they be able to understand your paper on a first read through. Then, pick a topic, stick with it, and get going!

EE Guide - Mathematics.pdf

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