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I want to hone my problem solving skills. I have been working on the Putnam exam, but I have found that the easy problems are a bit too easy and the hard problems often require advanced number theory / calculus / linear algebra, and I have not mastered those fields.

I am looking for maths competitons with hard problems from more basic fields of mathematics. Any suggestions?

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  • $\begingroup$ How about the IMO? or the Shortlists? $\endgroup$ – karvens Sep 27 '14 at 20:46
  • $\begingroup$ Check out Brilliant, which contains a lot of similar problems to what you are looking for. $\endgroup$ – Calvin Lin Sep 28 '14 at 16:12
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STEP papers are excellent: rather than expect you to memorise a bunch of formulae and apply it to a situation, they walk you through a problem, and then ask you a much-more-difficult generalisation of the problem that uses similar methods.

They are very challenging (particularly STEP II and STEP III) and are based on:

  • Calculus
  • Probability & Statistics
  • Complex numbers
  • Mechanics
  • Coordinate Geometry

The great thing about STEP papers is that they require only very basic knowledge of the topic. The hard part is applying the problems they give you, to solve harder tasks.

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