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Recently I've started to study mathematics with an olympic approach, and I'm feeling a little lost. The thing is that I understand the concepts pretty well and am able to solve some of the problems, but when it gets to a harder level I simply get stuck and am unable to solve anything, and sometimes even after I see the solution or demonstration I would never know how to follow those exact steps, specially when it comes to inequalities. It is hard to find material on the specific strategies you need to solve certain types of problem, and it is really frustrating for me since I really love math.

Do you guys have any suggestion of books or something I could do to actually succeed on solving those problems? How should I study for subjects like these?

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    $\begingroup$ Have you already checked out artofproblemsolving.com? And books like The Art and Craft of Problem Solving by Zeits. They have a lot of books for you to read and practice with. Olympiad problems are super tough so don't get discouraged. $\endgroup$ – littleO Jan 17 '17 at 1:03
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    $\begingroup$ very related math.stackexchange.com/questions/555655/… $\endgroup$ – user190080 Jan 17 '17 at 1:10
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    $\begingroup$ As @littleO said, AoPS is a good place where you can improve your skills for math contests. Although it's a forum like this, i.e., you can ask about a math problem at any level, AoPS is mostly aimed for high school students who are interested in the fascinating world of math olympiads. $\endgroup$ – Xam Jan 17 '17 at 1:36
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You could have a look at some of the titles in the New Mathematical Library series (particularly nos. 1, 3, 15, 19, 20, 34) and see if any of them appeal to you.

Or consider reading The Mathematical Olympiad Handbook by A. Gardiner, which also has a good bibliography.

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