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I did a research about mathematical competitions and I came to a conclusion that in order to do well, one needs to master a set of particular techniques and shortcuts. I was struggling with math pretty much my entire life and I generally hated it. However, a few months ago, it was brought to my attention a different perspective about the subject and I decided to give myself a second shot with it. I dedicated 4 hours a day, 5 days a week for study and practice, and I went from Algebra I all the way to Calculus II in a matter of 6 months. I did all the exercises in the 3 textbook manuals I was working with, and generally, I was pretty satisfied with the outcome. As I was gaining more and more confidence, I was attempting more and more challenging problems and I was getting them right most of the time. At some point, I picked up several sample AMO problems and as I was attempting to work them out, I realized that I wasn't even able to understand the questions let alone to solve them. Although, they cover topics from basic Algebra and Geometry (which I thought I have mastered), out of 12 questions I managed to answer 3, needless to say, I was very disappointed at myself. And if it wasn't for the fact that I am able to solve most of the problems in regular high school math textbooks, I would probably have given up already. I googled my issue and I was suggested to buy a copy of The Art of Problem Solving Volume I and II which I did. But sadly, it did not help me at all. I am still incapable of tackling problems from Olympiads. I will greatly appreciate it if anyone out there can recommend techniques and approaches for solving such problems, and also, books and study materials which could eventually help me build up my skills. So basically, my question boils down to - how to prepare myself for such mathematical contest?

Thanks in advance!

Nzewi Ernest Kenechukwu
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Eddie Spasov
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  • I'm voting to close this question as off-topic because this whole thing is just a mess. Almost every single thing applies. – The Count Aug 04 '19 at 02:58

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I went from Algebra 1 all the way to Calculus II in a matter of 6 months

You probably realized that didn't help much by now. Competition math doesn't require much mathematical knowledge to understand the questions or answers, in the sense of high school or college courses.

In competitions, an entirely different skillset has the main focus: the ability to find proofs to completely unique problems. You'll need to learn about basic proof techniques, which the Art of Problem Solving book does a very good job of explaining. You should definitely give it another try.

A big part of solving a problem is experience: It's a lot easier to solve a problem if you can tell at first glance which methods are promising to approach that problem. The only way to gain experience is by working through a ton of problems, peeking at the solutions only if you're stuck. It helps if you do problems grouped by proof technique, so you can immediately apply the ideas you see.

I suggest that you start out by tackling problems of lower grades and/or early rounds of contests, until you're confident you can solve 99% of them, in order to build a strong foundation. Once you're at that point, you'll be accustomed to the necessary thought processes that allow you to have those brilliant ideas that are absolutely mandatory to solve the more difficult problems.

Magma
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  • Thank you, sir. Very helpful. I was wondering, in your answer you have mentioned that in order to do well in competition math one needs a different skill set, does that mean that it is matter of practice and not a pure mental strength alone? I am asking because I felt very frustrated as I was reading comments of people which were sort of "hmm, that was easy".I was struggling with math through high school but I felt inlove with it recently. So, can I improve or I just lack the math gene? – Eddie Spasov Aug 03 '19 at 18:16
  • As I said, experience is the key. Having more talent helps you make more out of experience, but you need the experience either way, and loving math will help you more in that regard than talent can. About all those "that was easy" commenters: First off, they probably already have the experience. Second, the beautiful thing about contest math is that the solution is in most cases easy to understand or write down. The hard part is coming up with it. That's what you need the experience for. – Magma Aug 03 '19 at 19:11
  • So one day you'll be on that level, find an awesome solution to a nice problem, and everyone is gonna say "oh shit, it was so obvious" and it will be a compliment, because they actually mean "oh shit, that's so elegant, why couldn't I think of that?" – Magma Aug 03 '19 at 19:11
  • I hope you are not just sugar-coating the truth out of courtesy. I appreciate the time you took to answer my questions and the tips you gave me are of much importance as well, I hope they going to guide me further in my studies. Thank you. – Eddie Spasov Aug 03 '19 at 23:25
  • I'm completely serious, and speaking from my own experience. – Magma Aug 03 '19 at 23:38
  • If you ever find yourself wondering whether or not you should pay a visit to Eastern Europe and for some weird reason you choose to do so, and for some even weirder reason you choose to visit Bulgaria(which is my homeland), give me a call. I will gladly welcome you as my guest. – Eddie Spasov Aug 04 '19 at 00:37