Getting Started with Olympiad Maths

This advice is specific to Ireland, but much of it is applicable to other countries too.

You may or may not have heard of the International Maths Olympiad, or IMO, maybe you’re here because you did well in round one of the Irish Maths Olympiad in School.

If you’re thinking about getting involved in olympiad maths, it can seem rather daunting. You might look at a few IMO questions and think to yourself ‘not a hope’. Nobody starts off able to solve IMO problems. They’re really, really hard.

What is the International Maths Olympiad?

The International Maths Olympiad, or IMO, is regarded as the most prestigious maths competition for second level students in the world. It was founded in 1959 and more than 100 countries take part each year. Each country sends a team of up to six students, chosen through a national selection test(or tests), who sit two 4.5 hour papers consisting of three difficult questions each, which they have to solve with proof(i.e. Giving the reason behind each step). The problems each day are in order of difficulty, 1 and 4 are the most approachable, 2 and 5 are harder, 3 and 6 are the hardest and solved by very few participants each year.

Ireland also sends a team of four girls to the European Girls Mathematical Olympiad, or EGMO, each year. Contestants qualify from a selection test in February. EGMO aims to decrease the gender gap in Olympiad Maths – each year about 90% of the contestants at IMO are male.

How do I get involved?

My first recommendation is to go to maths enrichment classes, if you aren’t already. There are weekly classes in UCC, NUIG, UL, Maynooth and UCD. Here you’ll learn some introductory theory and get experience solving problems. Even if you don’t want to compete, if you’re interested in maths I’d highly advise giving these classes a go. You will be challenged far beyond school and sharpen your problem solving skills. COVID-19 will likely affect these classes in 2020/21 so follow Science Angles for updates on what’s happening in each centre!

Should I take part? Am I ‘good enough’ to take part?

The only way to find this out is to give it a go! Worst case scenario: you discover that you don’t enjoy it, and you slightly improve your problem solving skills. Taking part doesn’t cost any money and there’s no commitment (unless you get on the team)  so you have nothing to lose! When you start, you’ll almost definitely feel like it’s too difficult, you can’t solve much and you’re way out of your depth. This is normal – if you’re not struggling, you’re not challenging yourself enough! 

The main things you need are creativity, logic and perseverance. Olympiad maths is really, really, really hard. Olympiad problems are designed so they can’t be solved straightaway, they usually require some creativity and outside the box thinking. Working on these kinds of problems greatly improves your general  creative problem solving skills – which is great as these are needed in so many different careers!

How does the Irish Maths Olympiad work?

The first round is taken in schools. If you score well in that your teacher will recommend that you go to your local maths enrichment classes. The round doesn’t really count for anything and you can go to maths enrichment classes without it. THe classes begin in January everywhere except UCC, which starts in November. In UCD there’s a selection test in February, after which the top 40 or so are invited back. The UCD selection test doubles as the EGMO selection test – the top four girls nationwide are selected to represent Ireland at the European Girls Mathematical Olympiad. The Irish Maths Olympiad takes place in May in all of the enrichment centres, and consists of two three hour papers, with five questions in each. The top six represent Ireland at the International Maths Olympiad.

In Ireland, the top 25 or so in the Irish Maths Olympiad are invited to attend training camps, usually one in June and one in August. These are a bit more advanced than the enrichment classes and are a really useful way to learn about different areas of maths. 

How do I get better at solving problems?

The only way to get better at solving maths problems is by trying to solve problems. It is a skill you’ll get better with over time. Some of the questions I found impossible at first now seem almost easy to me. Don’t just try a problem for a few minutes, then give up and look at the solution. Only look at the solution after you’ve spent ages on the problem, left it for a few days, then tried it again. Sometimes a hint (if available) or just looking at the start of a solution to get the main idea, before tackling the problem again, can be useful. Persistence is key!

In terms of solving problems, don’t start with ones from IMO. They’re rather hard, and if you have no familiarity with Olympiad maths they’re really not the best place to start. Past EGMO/UCD selection tests have a good selection of more accessible problems, and once you’re a bit more comfortable, the problems from the Irish Maths Olympiad are much more accessible than IMO ones, yet should still pose a challenge. EGMO Q1/Q4 and Q1/Q4 from older IMOs are easier than current IMO Q1s/4s. 

The most important thing is that you enjoy it. If you don’t, just don’t bother doing it. 

What about theory? Do I need to learn loads of stuff?

 Well, of course you need some level of knowledge. Trying to do number theory without familiarity with things like modular arithmetic, Fermat’s Little Theorem and Euclid’s Algorithm, or inequalities without AM-GM or Cauchy-Schwarz won’t go well. However, you don’t need to get too bogged down with theory. It doesn’t matter if you know loads of advanced theory if you can’t solve problems, so once you’ve got the basics down don’t worry too much about the rest.

Remember, it is not about getting on the IMO or EGMO team. Sure, those things are enjoyable, but they should not be your main motivation. You should be doing it because you love it, because you enjoy the challenge and beauty of the problems. Olympiad maths improves a range of skills, from problem solving to communicating complex ideas to persisting even when it’s hard, but it should also be fun! Good luck and enjoy!