Hi there,
I’m starting my junior year in September and want to start my own research as soon as possible, in applied mathematics - an area I’m genuinely interested in. Doing research is required for the extended essay in IB Diploma (which I’m taking) and hopefully it’ll boost the admission chance at the top universities.
My school environment is generally not competitive and most probably I can’t take courses or work with professors at the local colleges since I don’t speak the local language very well.
Applied maths is a difficult direction and you’ll need massive professional knowledge so at the moment I’m reading some textbooks, to get an idea on the topic at least.
What should I do to start a research like this, any tips or opinions? Thank you! 
How much math and statististics have you already had?
Have you seen past essays? Some international schools have examples.
You may need guidance from your IB advisor to supplement your work with resources or advisors in your native language.
I saw on another website, consider problems from
International Mathematical Olympiad in algebra, geometry, or combinatorics.
I have already self-studied all the contents of IB maths AA HL and now I’m doing basic college maths like calculus for example.
As for past essays no I haven’t, choosing maths for the extended essay topic is rare in my school. The teacher is supportive and she told me I needed to come up with a topic by this October, and I hope to make my essay not only good for EE in IB but also for academic research, which is vital for college application.
Is this directed at US college admissions? I don’t recall any of my students having had to complete any academic research to apply for admission at a US college or university.
When our eldest was in high school, she was required to seek out a work experience for her biotech course setting, whereby the facility would involve biotech lab equipment. So, she ended up at our local UC, running tests. It was a tiny mention in her activities.
I am assuming that your “research” is for your regional university? Research takes a lot of time and requires intense scrutiny of approval forms for the research and its test subject.
I will admit that I have been wondering what counts as “research”.
One daughter is involved in something that clearly counts as research. However, bringing it to completion would require millions of dollars (perhaps more like hundreds of millions) and perhaps ten years. Even how to do something similar as a PhD thesis seems hard to me.
There may however be things that a high school student could do to apply math to the real world. I have been trying to think of some (I was a math major).
I have done such simple things as use the Pythagorean Theorem to lay out a 90 degree angle in my vegetable garden (actually to create the outline of the garden in the first place). On the job I have used math for a variety of tasks, but it is hard to think of something that would be useful for a high school student. I suppose that there are things like statistics to determine whether a political poll is valid or not. Probability and statistics is however relatively advanced math, and is not something that I would have studied in high school.
One could compute how much CO2 is taken out of the atmosphere in a year by a small stand of trees, and try to plant enough trees to offset your yearly release of CO2. Figuring out how much CO2 is needed to create your food might not be easy, but what your home and your family’s cars release directly might be easier to figure out. Similarly you could compute how much CO2 is needed to mine the materials to build the batteries for a Tesla (plus the copper wire for the engine), find out how electricity is produced where you live, find out how much CO2 is released in the production of electricity versus burning of fossil fuels to run a car, and figure out how long it would take given the actual sources of electricity current used in your location to offset the CO2 released in producing the electric car and make it come out as less polluting compared to for example just driving whatever cars you actually have in your family.
Could you use calculus to compute the trajectory of a stone thrown by a catapult, build the catapult, and see how it compares? You would need some way to figure out what the direction and velocity of the stone would be at the point when it leaves the catapult. You might expect that friction (which is very difficult to take into account) would result in a shorter trajectory compared to what is computed, then try to figure out whether this is what occurred.
I do not know if any of these count as “research”. They might be applications of mathematics.
Another thing that comes to mind is trying to find an internship at a local company. This might be tough for a high school student interested in mathematics.
And learning a programming language and programming a robot to run around your house also comes to mind as a possibility.
One thing I noticed…
Does this mean that you are not in the USA? I am not sure that this matters in terms of anything that I wrote above. However, it might impact your chances of admissions to top schools in the USA.
This school in TX has info on the IB Extended Essay in mathematics, which I thought the OP is pursuing.
There are IB schools all over the world with sample essays or rubrics.
My impression is, a topic of applied math as you described may suffice for the OP and IB requirement. Much research may be first a survey o the body of knowledge and then eventually narrowing down to a topic of investigation, following the scientific method.
https://mwschool.libguides.com/diploma/extended-essay/math-guide
But, the above does not seem to be the same as assisting with college level mathematics research, which the OP thinks they need for college admissions…
I at least got accepted to two very good universities to study mathematics without doing any research at all in high school. My ECs were on the level of “high school chess club”.
However, I do not know anything about OP’s situation.
I have a child that did research in math in high school, under the direction of university professors. The prep for doing so required 6 months of initial coaching in learning how to read and understand existing research papers in the field.
Now this was pure math, not applied math. But I am a still puzzled as to how a high student can be expected to do this on their own without guidance.
Me too!
thank you for all the amazing ideas mentioned! I’m in east europe, international school offers IB, so don’t speak the language well. In my case research means:
(1) EE for IB (2) college application
EE and a formal research conducted at college are definitely different.
In my school EE on maths in pretty uncommon, after a bit of searching online I figured out that it’s mainly about applying maths in real life situation, examples include investigating the trajectory when playing football or working on prime numbers.
But college level maths research would be much more advanced. I was thinking maybe I could get to know about research through EE and then move to more advanced topics so that I have a better shot at the US college admissions.
now the college admission is much more competitive… especially since that I’m an international student, applying from an international school in east europe
besides I truly enjoy maths and want to do more 
Neither do I, it’s just my dream to start a research
What you need to do is identify a real problem within your school, neighborhood, town, or community. Survey friends, teachers, administration. If you can be bold, meet with public service associations or groups helping women, refugees, disadvantaged children, migrant teens… what REAL problem do they have? How can data help them solve it? Make Applied Math part of a collective toward a solution.
What language(s) do you speak beside English ? Why don’t you speak the language spoken where you live (for instance, are you at a United World College and thus come from another country than the one where thr UWC is located?)
Before you target US colleges and begin any research, you may want to research what the US colleges will cost you. If you will need financial aid, to attend a US college or university, it will be extremely difficult because there is not enough money and too many students asking for funds. There is some funding, but the competition for funding is fierce. Also, assume that you will be returning to your home country for work, after receiving a US diploma.
thank you for this advice 
As for UWC, no 
I’m from east asia and I’ve been studying in east europe for three years, so I’m applying to college next year from europe, as an international applicant (but for sure I’ll get sorted into the super competitive pool)
Since there are other options available (colleges in europe for instance), I’ll only apply to the top unis in the US (also the places I want to get into the most, especially because of their prestige in the maths major) and can full pay
For Math, you have Polytechnique in France; Oxbridge (exams may be during 11th grade though), Imperial, St andrews, LSE, Warwick in the UK; lots of possibilities in Eastern Europe.
In the US, the criteria will be different than in Europe but the way you can apply your Math skills to the common good will count.
Are you preparing the IB diploma or ALevels? IB I assume since you’re talking Math EE.
yeah full IB diploma with maths, physics, english lit, german b as HL, and chemistry, business SL