Introduction

In this series we will guide you through preparing for your country’s Mathematical Olympiad, International Mathematical Olympiads and similar competitions. If your knowledge doesn’t exceed the program of highschool, don’t worry. A wonderful thing about such competitions is that they are based on basic concepts and ask you to process it on an abstract level. The only four fields of Math you need to know are Number Theory, Algebra, Geometry and Combinatorics. However, you need to know them very well. For every field we have prepared a separate article where we explain the most important topics you need to know, and include tasks related to them. Don’t get discouraged, if you get intimidated by the problems – you will be surprised how simple the solutions can turn out to be. If you get intimidated by geometry – we all do. Just use as many colors as possible for the drawings.

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What do the Mathematical Olympiad and similar competitions look like?

The competitions take place over 2 consecutive days. Each day 3 problems are given to the students to work on for 4.5 or 5 hours. The best participants in their country’s final stage of the Olympiad go on to participate in International Olympiads, such as the International Mathematical Olympiad. The easiest way to practice for the Olympiad is to do problems from the past editions of the contest; there are also books and papers on Olympic Mathematics.

More on how to practise

Solve problems. I can’t stress this point enough: solve problems. Theory is cool, but problem solving skills come mostly with practice. Check out your country’s national olympiads and wonderful Contest Collections of Art of Problem Solving: https://artofproblemsolving.com/community/c13_contests for olympiads from other countries. It’s important to try to solve problems on your own, preferably over a longer period of time. You may be used to solving problems quickly on maths exams, but remember that during the olympiad you’ll have around 90 minutes for one problem and it’s perfectly OK if after 30 minutes you still don’t have any great ideas. Don’t assume that you can’t solve a problem because it requires theory you don’t know yet - it may sometimes be the case, but usually you’ll need to apply relatively simple ideas in a tricky way. On the other hand if you haven’t figured out the solution after a few hours, don’t hesitate to look it up so you can learn something new and move to another problem.

When it comes to learning the theory, there is no universal advice because everybody needs different content. Check our materials, try asking more experienced olympians or olympic teachers about resources you need. Mathematical olympic literature is very wide so you’ll probably find something that suits your needs and experience. It is often the best idea to search specifically for olympic materials - while academic mathematics is wonderful on its own, for olympiad you’ll need a very strong problem-solving focus.

10 tips for doing your best:

1. Do tasks from previous years, preferably under competition conditions (under time pressure and without being distracted)
2. Read solutions to problems that you could not solve
3. Don't learn difficult theorems quickly just before the competition – it is much more effective to practice the effective application of basic techniques
4. Take a break the day before the Olympics
5. Take food with you
6. Make clear, large drawings - especially in geometry
7. Check the problem “empirically” for small numbers
8. If don’t know how to go about the problem, start by applying familiar techniques or theorems into it
9. In assignments, there are sometimes useful methods associated with other fields
10. Check whether your solutions meet the conditions specified in the task