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Math EE

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I am currently in the DP-1 and my school has introduced the EE part of my Diploma. I chose to do the extended essay on math because it is the subject I am most comfortable with (I have taken Math HL). With some research I landed on the topic Fourier Series and Transform. It has many applications in various fields and the concepts are relatively easy to understand. The problem I am having is in which aspect or application I frame my research question? Are there any limitations that can be explored in 4000 words?

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While I'm not familiar with Fourier series, I can offer some guidance on writing a math EE.

Criterion C (Investigation, including data collection) is likely the toughest criterion to score for a math paper of this nature. I think the EE should be centred around getting a good research question (as you have addressed) and at least get some personal (though doesn't have to be original) ways to experiment with the series and look for limitations (and strengths?) as you have said. You should definitely either narrow down on the field, or on a specific characteristics of the series (ie the accuracy of approximation, the number of terms needed, errors/problems/implications when the series approximation is applied in real life).

It will be tremendously helpful for you to also talk to your teachers and Year 2 candidates on learning the Calc option (Option 9 in 2014+ HL Math syllabus), especially the sections on Taylor series approximations, radius of convergence, interval of convergence, and finding truncation error. Although it is strongly recommended that you learn this after learning integration (and derivatives). Depending on when the EE is due for you, this may or may not be feasible.

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