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In practice, yeah, "an average person" wouldn't know where to begin. And a brilliant high schooler who hasn't studied maths beyond the high-school curriculum wo
by dmurray 6y ago
In practice, yeah, "an average person" wouldn't know where to begin. And a brilliant high schooler who hasn't studied maths beyond the high-school curriculum won't ace the test. Though he could get a medal, particularly if the geometry and combinatorics questions are friendly.
But the conceit of the IMO has always been that the problems are drawn from a very limited selection of fields, which are/were commonly taught in high schools around the world. No need for complex numbers, calculus, abstract algebra, or trigonometry (though any of these may end up used in an alternative solution).
- im3w1l 6y agoCan't say I've seen inequality-problems like IMO has anywhere else.
- singhrac 6y agoThey show up in a few other areas, like probabilistic analysis of algorithms or sketching (e.g. Chernoff bounds and definitely the Cauchy-Schwartz ineq.). But you're right, nothing heavyweight like Muirheads has many applications.
- dmurray 6y agoBut a surprising number of them can be solved with the insight only that x^2 >= 0. (Both Cauchy-Schwartz and AM/GM reduce to that if you squint hard enough). And that's accessible to any maths student.