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Maths EE - What exactly am I expected to do?

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I've spent a lot of my summer working on my EE through research and such, but I can't help but feel utterly lost in terms of what I should write. I've got a good idea of the topic I'm planning on writing on, but the presentation itself has me stuck.

First off, I'm looking at solving cubic equations by substituting trigonometric and hyperbolic functions. The derivation of the method is possible to work out and explain, the reason the method was first improved is also clear. Initially, I was thinking of deriving the methods and discussing the limitations + improvements of it, possibly with a mention of the origins.

The problem is, while I've derived some of the methods myself and worked out the limitations, it's nothing original. The method has been studied by many before and it's fairly well-known, so I'm not too sure about what to do with it. I was initially thinking of writing it as an investigation of some sort (perhaps starting with the STEP question that I initially found the method from), but now I don't think that's actually sufficient.

I've considered taking a historic perspective and such, but I don't really have enough information nor sources to make that the larger focus. I've also thought of taking another method (Cardano's) and comparing how they differed, but I'm not sure if I would have enough content in that case to write the entire EE. Would I still be able to include the derivations and long explanations of the limitations, or should I just have a brief explanation of both methods followed by a long comparison?

The thing I'm really trying to ask it, how exactly am I supposed to structure and write the essay? Can the large part of the essay be based on the derivation of the method and if so, how could I structure it then? If not, should I search for an entirely new topic and work from there?

Edited by ctrls

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Guest Maitri Fischer


As you said, the derivation is nothing new and neither is the research into the limitations. I would suggest that you apply the method to an interesting yet simple problem.

In this case you can show the derivation (proof) and discuss the the usefulness of it and then apply it to a real world problem.

Another thought I had, or you could just add it onto your EE, is comparing the solution of the cubic equation by trigonometric substitution and an approximation method such as Newton-Raphson. You could then compare the error and apply it to a real world problem and discuss the implications of this.

good luck!

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I suppose extending it and comparing the method with others is going to be my best bet then. I've done a bit of research already with Cardano's method and I can see some ways of comparing it, so I'll see what I can do from there. Having started to type up the derivation however it turned out to be relatively short anyways, so I guess I'll include that in at the beginning when I describe the method then.

Thanks for the reply, I think I've got a clearer idea of what to do now.

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