I love mathematics. It's my favorite subject. In particular, Complex Analysis is interesting.
I'm a junior in high school. I take the IB program, and for it, I have to type an extended essay on a subject of my choice, but I'm sure that it has to bring something "new". Which brings me to my main point/problem.
Mathematics has come a loooooooooooooooooooooooooooooooooong ways away from the subjects I'm still covering, but I want to do something mathrelated. Is there any kind of subject or field in mathematics that I can try, or is it pretty much hopeless?
First Paper
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Re: First Paper
xepher wrote:I love mathematics. It's my favorite subject. In particular, Complex Analysis is interesting.
I'm a junior in high school. I take the IB program, and for it, I have to type an extended essay on a subject of my choice, but I'm sure that it has to bring something "new". Which brings me to my main point/problem.
Mathematics has come a loooooooooooooooooooooooooooooooooong ways away from the subjects I'm still covering, but I want to do something mathrelated. Is there any kind of subject or field in mathematics that I can try, or is it pretty much hopeless?
I doubt they expect origional research.
I will not attack your math, just your epistemology.
You think you have it bad, I teach Intro to Project Management to Undergrads.
You think you have it bad, I teach Intro to Project Management to Undergrads.

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Re: First Paper
Why not switch focus a bit and write something on the history of maths? That way there are lots of topics to choose from and it fits better into an essay format but you can still include a lot of maths. Plus it can be 'new' in the sense that any history work is 'new', as in you provide a fresh perspective on it.
Off the top of my head you could do hugely broad things like 'How has the idea of mathematical proof changed' or more modern things like 'How has the advent of computer technology affected mathematics' or on the flip side 'How has modern computer technology been shaped by the work of mathematicians' or, as you said you were interested in complex analysis, something like 'How has the invention of complex numbers affected modern daytoday life'.
The history of maths is a really interesting subject and gives you a good opportunity to mix in the maths with the people/institutions/societies that were behind the ideas.
Off the top of my head you could do hugely broad things like 'How has the idea of mathematical proof changed' or more modern things like 'How has the advent of computer technology affected mathematics' or on the flip side 'How has modern computer technology been shaped by the work of mathematicians' or, as you said you were interested in complex analysis, something like 'How has the invention of complex numbers affected modern daytoday life'.
The history of maths is a really interesting subject and gives you a good opportunity to mix in the maths with the people/institutions/societies that were behind the ideas.
Re: First Paper
I have a friend in 10th grade at my school who's doing a mathrelated Personal Project for IB. I believe he's going to write a summary of some sort about partitions of integers.
Maybe you could do something similar? You could probably pick a fairly broad field of math and discuss its origins and important results that were discovered. I remember seeing a list of topic ideas for the EE. One of the suggestions was to write about Pick's theorem I believe.
Maybe you could do something similar? You could probably pick a fairly broad field of math and discuss its origins and important results that were discovered. I remember seeing a list of topic ideas for the EE. One of the suggestions was to write about Pick's theorem I believe.
Re: First Paper
I can't imagine they want original research, just something communicating that you have explored some math beyond what they've taught, and understood something interesting. If you want something different from what you've tried before and approachable, I've found knot theory to be great for that. On the other hand, talk to your teacher  I bet he'll suggest ideas for papers in Complex Analysis that he would be happy to see you write.
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