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Ideas for the Math IA | Update

Ideas Math

We have done posts like this in the past, but considering how intimidating the math IA can be, it might be good with a new list of ideas. Some of you have just finished your math IAs (sorry I’m late!!), whilst others still have it ahead of you. If you do, I hope you can find some inspiration from these ideas. As always, do not copy these ideas 1:1; instead, use them as a springboard that guides you to an idea you want to write about. I have organised them roughly by topic. To be honest, though, most ideas incorporate many different topics, so don’t take these categories as set in stone. 

Ideas for 1. Numbers and Algebra 

  • Fractals and complex numbers—mandelbrot is an excellent place to start your research. We see fractals used in just about everything, antennas for example! You can take a theoretical approach or something more practical if you mix some physics in. 
  • Fermat’s Last Theorem is one of the most famous puzzles that took mathematicians literal ages to solve. HL students could look into the proof of it!
  • Euler’s golden ratio of natural beauty is a classic. Be careful if you do this not to do something overdone!
  • AA HL students could discuss the efficacy of different proofs (proof by deduction vs proof by exhaustion etc.)
  • Prove the binomial formula from your data booklet (or any other exciting formula that looks complex there!)

2. Functions

  • For those struggling with domain, range & asymptotes (and I know many people do), you could write an IA about that to become more comfortable. 
  • Can you prove why transformations work the way you were taught in this topic?
  • Trigonometric functions often model things like clocks and even temperature. How can you prove if a function is sinusoidal? 

3. Geometry and Trigonometry

  • Look into the role vectors play in video games. They draw almost everything using vectors. Try making your own object in GeoGebra! (AA HL)
  • Eigenvalues and Eigenvectors from AI HL have fascinating real-life applications. Look into those!
  • Can you plot the ellipses that the earth travels around the sun in?
  • How did we use Geometry and Trigonometry to make maps before satellites (SL)?

4. Statistics and Probability

This one is a go-to for AI SL students in particular. Great time to use all those tests you have learnt!

  • Use spearman’s rank correlation coefficient to investigate a correlation between something like depression and GDP in different countries. 
  • See if you can find a statistically significant correlation between variables x and y using your classmates as a sample. What kind of biases does something like that introduce?
  • Is there a correlation between tuition fees and grade boundaries for acceptance to universities in the US?
  • Using data you find online, you can calculate specific probabilities using the probability calculus you have covered in class. For example, what is the likelihood that a Dane is currently employed, given that he lies in the upper 60% of the tax bracket? You could find the probabilities for those events on publicly available databanks. 
  • Use the chi-squared test to investigate whether the number of students attending class depends on the weather. 

5. Calculus

  • AA HL students have worked a little with the Maclaurin series. You can look at the Taylor series, the parent category for the Maclaurin series.
  • Use calculus to optimise the volume of any shape you fancy. If you want to keep it simple, do a cuboid. 
  • An SL student could investigate the first principle, which lays the foundation for how differentiation works and is a part of the HL syllabus.

Ideas Outside the Syllabus

  • VPNs often advertise with “military-grade encryption.” Try investigating what that means and how math plays a role. A good place to start could be RSA encryption. Data safety is super important!
  • Try investigating the whispering gallery. You know how there are those places in movies where, if one person stands in an exact spot, a person far away can hear them clear as day as they speak due to the room geometry? That works because of the whispering gallery. Beware, this is probably something for HL students.
  • A fun thing to do is to pick a topic you’re passionate about and google “the maths behind INSERT TOPIC). For example, if you google “the maths behind golf”, you find some fun stuff you could write about!

And there, a bunch of fun math IA ideas. If you still didn’t find an idea that seems like the one for you, or you just don’t know how to start, you can check out our math IA tuition! Be paired with an expert tutor with plenty of IA experience. Remember that they cannot come up with an idea for you, and you still have to write it all yourself, but they can support you along the way!

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