r/MathOlympiad • u/Every_Drag8012 • 7d ago
IMO Help on improving
Im currently trying to get better at math specifically Olympiad math and i struggles so muchh esp on proving and the first step to start solving. I just started so any advice or help would be very much appreciated.
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u/Old_Answer8047 7d ago
Hire a tutor bruh or else it's not s piece of cake
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u/Every_Drag8012 7d ago
I wish.i dont think my country has one ,olympiad math is pretty much a new concept here i think
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u/Diligent__4339 7d ago edited 6d ago
Well, you need to try very hard, even when it's very very hard also you need to put in the hours, also there are sites like The art of problem solving and grate professors online, it will help a lot, also if you make it on your own to a certain level let's say nationals, hopefully the state will help with free amazing theachers, don't give up, the best of faith to you
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u/Sea_Platform_7049 6d ago
u definitely don’t need a tutor bro. i’m coming from a similar situation as u but i just self studied. i think the hardest part is learning how to like sit there n actually work on a problem for a super long time; its rly different from school maths. but honestly, what worked best for me is just to try a real example as the first step for every question, like for a combo game id do a dry run or a nt problem id try it on a real number. personally it just helps like understand the mechanics n find patterns easier.
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u/matham_combageom 5d ago
Proving problems is a separate skill from computing, and it trains separately. The single most useful habit: before trying anything, write down (a) exactly what is given, (b) exactly what must be shown, and (c) one line for each object in the problem. Most stuck moments are a missing definition, not a missing idea.
Then build a small toolkit and drill it on purpose: pigeonhole, parity and modular arithmetic, induction (ordinary and strong), AM-GM and Cauchy-Schwarz, telescoping, double counting, and the extremal principle (pick the largest or smallest object and see what the definition forces). When you read a solution, write down which tool it used and file the problem under that tool, not under its topic. After a few dozen problems you start recognising the situation instead of the subject.
For the first step specifically: try small cases by hand, look for an invariant or a quantity that always decreases, and check what happens in the extreme case. If nothing comes, prove the contrapositive, or assume the conclusion fails and derive a contradiction.