Sorry not to have answered you earlier, I have been absent for the first days in the final round of selection for my country’s IMO team, which after years of practice I am finally on. Feel free to PM me if you have more questions, though I can’t promise that I’ll know all the answers.
As far as practice vs learning new maths goes, the IMO has something of an unwritten syllabus of theorems you need to know. If you don’t know everything on it, then by far your best route is to learn the things on it. Once you’ve got that, learning more theorems is unlikely to help much, and you just need practice, practice and more practice. I have tried to solve at least one problem every day for the past year.
The one exception is that if you start to find that you simply lack the raw talent required in one ore more of the areas, then try learning unconventional techniques for doing it, you may be better at those.
If you’re not sure which stage you’re at yet, try some problems on Art Of Problem Solving, then look at the solutions of the ones you couldn’t do within a day or so. If you understand all the solutions then you probably have a sufficient knowledge base.
A trap to avoid falling into is only practising the areas you are good at, this is a very seductive mistake since inevitably those areas will feel more fun to do. Try the areas that seem hard and boring until they become fun, but if you start to find yourself disliking maths in general switch back to something you enjoy.
If possible try to find a mentor of some kind, someone you can meet in real life is best. This is especially essential if you’re still at the stage where you don’t know the whole unwritten syllabus yet.
This type of approach may not be the best if you actually wish to become a good mathematician, but the IMO is sufficiently competitive that if you are unlikely to get on with anything less (I only made it by the tiniest margin as it is).
Sorry not to have answered you earlier, I have been absent for the first days in the final round of selection for my country’s IMO team, which after years of practice I am finally on. Feel free to PM me if you have more questions, though I can’t promise that I’ll know all the answers.
As far as practice vs learning new maths goes, the IMO has something of an unwritten syllabus of theorems you need to know. If you don’t know everything on it, then by far your best route is to learn the things on it. Once you’ve got that, learning more theorems is unlikely to help much, and you just need practice, practice and more practice. I have tried to solve at least one problem every day for the past year.
The one exception is that if you start to find that you simply lack the raw talent required in one ore more of the areas, then try learning unconventional techniques for doing it, you may be better at those.
If you’re not sure which stage you’re at yet, try some problems on Art Of Problem Solving, then look at the solutions of the ones you couldn’t do within a day or so. If you understand all the solutions then you probably have a sufficient knowledge base.
A trap to avoid falling into is only practising the areas you are good at, this is a very seductive mistake since inevitably those areas will feel more fun to do. Try the areas that seem hard and boring until they become fun, but if you start to find yourself disliking maths in general switch back to something you enjoy.
If possible try to find a mentor of some kind, someone you can meet in real life is best. This is especially essential if you’re still at the stage where you don’t know the whole unwritten syllabus yet.
This type of approach may not be the best if you actually wish to become a good mathematician, but the IMO is sufficiently competitive that if you are unlikely to get on with anything less (I only made it by the tiniest margin as it is).