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(Another) HL Math IA Thread - I need clarification on the very basis of the math IA


Cam.m.k.7

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Preface: I realize this wall of text is unatractive, so if anyone wants to answer without reading my gratuitous commentary, I've bolded and separated the main questions I'm hoping to have answered, and italicized what I felt was semi-important and clarifying.

 

I realize that these threads might be very common, however I've been having trouble finding what I need. I've looked over several materials for the mathematics internal assessment, official and unofficial, including the guide on this forum, but cannot figure it out for myself.

 

My first question is: What is the goal of the Internal Assessment in Mathematics?

 

At its most basic level, what is the goal? What am I trying to do with my IA? I've seen it called an investigation, but that doesn't do it for me. I'm having trouble trying to pick a topic, but I don't have any idea what I would even do with a topic once I choose one. "Explore" it? How so? Place out a bunch of mathematical calculations on a page and explain them?

 

My second question is: What is "commensurate" with the level of my course?

 

I've been told that I should be avoiding core altogether, and going for "out-of-syllabus" mathematics for a Higher Level IA, and frankly I would love to learn a new mathematical concept for this investigation, but I'm having a fair bit of trouble trying to figure out what topic I'll use, which brings me to my final question.

 

My final question is: How do I choose an IA topic?

 

For a couple of days now I've just been going around from forum to forum, website to website, looking at other people's questions requesting IA topics, trying to learn new mathematical concepts, but I haven't been able to follow through on any of them, perhaps because I don't yet know what I'll be doing with them. I've looked at things like:

  • Fourier's Series
  • Fast Fourier's Transforms
  • Non-Standard Analysis
  • Differential Geometry
  • C*-Algebras
  • Law of Large Numbers
  • Differential Equations
  • Special Relativity (not mathematical topic, but uses math)

Are any of these topics suitable for a Higher Level mathematical investgiation? With the exception of Special Relativity, my list consists of manily raw mathematical concepts that encompass a large amount of knowledge. What do I need to add to these in order to start working towards a research question/focus for my IA? How would I develop these topics into suitable IA focuses?

 

Thanks for any and all help!

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IB publishes a lot of sample internal assessments. Some of them are here: https://ibpublishing.ibo.org/live-exist/rest/app/tsm.xql?doc=d_5_matsl_tsm_1205_1_e&part=2&chapter=2
The exploration should be an academic (written, of course) presentation of a topic that have been analyzed by you. Unlike many other subjects, there are no specific format expected by IB. There are many variants that you could do
- Route 1. Use math to solve an everyday problem. This is most similar to your "page of calculations and explain them". These problems should be more complex and more realistic than the ones that appear in your homework or exams. For example, calculate volume of something, that is not a perfect function or perfect revolution. This would involve you trying to find some functions or relations that describe your object, instead of having the function provide to you. (Analogous to an economics commentary.)
- Route 2. Research a new topic outside of the syllabus and try your best to describe the applications and how they are applicable to you or how you have used them before. For example, the topic of prime numbers can be connected to security and coding. (This is your typical look-stuff-online-then-write paper.)
- Route 3. Appreciate the beauty (or drawbacks?) of math. For example you talk about the mathematical spirals, why they look the way they are, how do they represent the beauty/simplicity of math. (This is like a group 1 literature commentary except you are praising math not literature.)
- Route 4. Experimenting with what you know to derive new relationships. For example, maybe looking at functions with complex numbers as coefficients and possibly how their graphs look differently. How the calculus would work, etc. (Similar to your Group 4 labwork.)

There are many other possibilities in addition to these 4 routes I listed.

I based my IA on core HL contents only (although in retrospect it is an introduction to a lot of my Option topics, which I didn't learn at the time). If you are doing my routes 2 or 3 from above, it's best recommended to look for math beyond IB or extensions of what you already know.

For your IA topic, it should be just about something that gives you enjoyment, fascinates you. For example, if you are a photographer, you can learn about the math used in a camera or in photo-editting softwares. 

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