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Math IA Topic Help: mandelbrot set??

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So I'm helping problems with my math IA topic that's due next week (only the topic, not the entire IA)... I've come up with some ideas (listed below), but I can't seem to focus/personalize them and find an actual aim for the investigation

  • Fractal Geometry and Chaos:The Math  behind the Mandelbrot Set (problems: math either too simple or too time-consuming, no known real-life applications)
  • Fractal Geometry as found in nature/ the universe ( too broad, and possibly too scientific)
  • Chaos Theory (Non-linear dynamics) as applied to the detection of epileptic seizures (again, possibly too scientific, and there are problems with resource availability as patient records are not usuallly published... plus, any academic papers on this I found where from the 90s)
  • the Fibonacci sequence  ( in nature, or, simply looking at patterns & their proofs... too experimental, no definite aim)
  • strong & weak induction (comparing the two, looking at why weak induction is preferred over strong induction... too trivial for HL?? too little for 6-12 pages??)
  • chess games (specifically, the knight's tour... looking at the number of possible solutions, geometrical representation and patterns etc... too simple? aim of investigation?)
  • florence nightingale (this was my first option as I had previously done a presentation on her and thought it was very interesting, but when i looked at published sample IAs I found one that was similar to what I had planned, and I'm worried this would end up being a problem)

I'd appreciate any advice you could give me... :):)

also, what are you planning on doing/ are you doing/ did you do for your math IA??

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So first of all, I want to say some things about the math IA in general:

  • as long as the math is commensurate with the level of the course (so in the HL syllabus or a bit beyond), you're more than fine. You don't have to go into really complicated, time-consuming ideas. And even if you use an SL topic, you can get 3/6 points in Criterion E (mathematics), which would mean you could still get a 17/20. So don't worry too much about the complexity of the maths. 
  • It's better to do a simpler topic, and explain it well, so that you lose some points in criterion E but gain all the other points (communication, persona engagement, reflection, and mathematical presentation), than to do a topic so complicated that you don't understand it/ can't explain it. 
  • make sure you connect you show your persona engagement (this is harder with some topics than with others, but it's doable); this does not necessarily mean that the topic is directly connected to your life (although the IB loves that): you can also show engagement by taking your own data, by finding real life applications of your topic, writing a piece of code (if you can write a program based on mathematical concepts in order to prove/show your investigation, this is a valid strategy), basically anything that explains why you should CARE about the investigation and shows that indeed, you do care. 
  • make sure you show reflection too; think about what you're doing, why you're doing it, and what the math means when applied to the particular situation/case you're exploring

You seem to have quite a number of ideas, so I'm sure at least one of them will work. 

I don't know anything about fractal geometry and very little of the Mandelbrot Set, so I can't help much there, or with the Chaos theory (I don't know what that is). 

The Fibonacci sequence could work! you could make it less experimental by explaining the sequence, talking about the golden ratio, and then trying to show its existence in some places (Renaissance paintings, the shell of a snail, pinecones, lots of things really). 

The chess one is really interesting! One of my classmates did something with chess and it turned out really well. You would need to narrow it down (your aim can't be "explain chess"); this does not look too simple at all :)

I would recommend against Florence Nightingale because she was used as one of the samples; 

For my own math IA, I looked at group theory and how it's connected to music theory, and measured the frequencies of the different musical notes and looked at the ratios between the frequencies in the notes in a particular chord to see if they related to the chord's dissonance. 

I hope this helped; if you have any other questions, feel free to PM me

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