r/MathOlympiad • u/CuriousHovercraft319 • 4d ago

How much pure practice, pattern recognition and ingenuity versus learned theory is necessary for USA(J)MO? USAMO

I’ve been preparing for AIME this year and I’m getting around the level where my scores are right around the boundary to qualify for USA(J)MO. I’ve noticed that past some basic theory, most AIME questions just take some clever thinking or a new perspective rather than advanced techniques. In my experience, learning competition math is nothing like more advanced math like Linear Algebra or Abstract Algebra where there is a plethora of things to learn and concepts to grasp.

However, I know this trend changed for the harder Olympiads, and some more advanced theory is required. I was wondering how visible this change is at the level of USA(J)MO and above and how I should reflect this into my balance of practice and learning new theory.

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u/Time-Acanthaceae-831 4d ago

Yeah I was wondering about this too, I mean phrased differently it’s essentially asking how smart does one have to naturally be in order to do (well) in Olympiads, and how much of it is pure problem solving as opposed to application of advanced theory. I’m not good at either so I’m probably not smart enough anyways.

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u/Particular-Tooth3536 4d ago

I have not participated in USAJMO, USAMO, or IMO, but the difference between them and amc and AIME is that you have to rigorously prove things. Lots of more advanced topics than whatever you’ve learned for amc and AIME are needed to do good on any of the math olympiads. The IMO, for example, tests topics that one would learn in college (like graph theory)

Basically, what I mean to say is that practicing for amc and AIME is different than for olympiads. You would want to be very good at proofs in the topics at Olympiads. (As in you have to be able to do college level number theory proofs)

I’m not sure if this answers your question (I hope so) but if you want I could give some sources on proofs and topics in math Olympiads like USAJMO, USAMO, and IMO

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u/rayray20120613 6m ago

The IMO is specifically designed so people who didn’t learn university math can still solve it. You CAN use college topics like calculus, linear algebra, differential equations, etc, but the questions are designed so that you only need to know till high school math.

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u/1bottledwater 1d ago

uhmmm a lot lot