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!

REVIEW: The Body: A Guide for Occupants by Bill Bryson

Rating: 8/10

The Body: A Guide for Occupants is a whistle-stop tour of the human body.  Topics covered range from the main systems of the human body, including circulatory, respiratory, digestive and immune  to sleep, pain and diseases. Bryson often approaches topics from an evolutionary perspective, not just explaining functions but also theorising how and why the human body reached its current form.

The Body is generally fast-paced and succinct. Bryson deftly covers a vast array of topics. He doesn’t dwell too long on any particular aspect, keeping the reader’s interest piqued. In school biology is too often taught in a dull way, with an emphasis on rote learning for exams, so this is a refreshing take on the basics of human biology. 

Continue reading REVIEW: The Body: A Guide for Occupants by Bill Bryson

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Aileen Wynne is a mainframe systems programmer in AIB. In college she hated the idea of working with computers, but now considers her job to be ‘the best job in the whole universe’!

Many people have never heard of mainframes but they are used by many major companies across the world, including banks, insurance companies and many more. If you’re thinking about pursuing a career in computers, it is worth considering mainframes.

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Interview with Dr Mary Hanley: Science Teacher to Maths Researcher

In this interview, Dr Mary Hanley tells us about her fascinating and varied career, from studying chemistry in the sixties and becoming a science teacher before returning to university to become a mathematician. She gives us an insight into working as a mathematician.

Continue reading Interview with Dr Mary Hanley: Science Teacher to Maths Researcher

Interview with Kieran Cooney: Part 2: Mathematical Olympiads and Self-directed learning

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Continue reading Interview with Kieran Cooney: Part 2: Mathematical Olympiads and Self-directed learning

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In this instalment of our People in STEM series we talk to Kieran Cooney, a data scientist working in Optum. Kieran represented Ireland twice at the International Mathematical Olympiad.

Part one covers working in data science, while part two will delve deeper into Olympiad maths and self-driven learning.

Continue reading Interview with Kieran Cooney: Part 1: Working as a Data Scientist

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Welcome to the People in STEM Interview Series! Our first interview is with Dr Anca Mustata and Dr Andrei Mustata, lecturers and reasearchers in the field of algebraic geometry in University College Cork.

We discuss algebraic geometry, working as a mathematician and their experience taking part in maths Olympiads in Romania. Algebraic geometry is a fascinating branch of mathematics looking at the geometric properties of solutions to polynomials.

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Interview Series Launch

When I started to take part in Olympiads most thrilling thing for me was to connect with mathematicians in real life. I remember how I followed my leader and deputy leaders around just like how a five-year-old follows their teenage sibling. I asked about all sorts of things, their research subject, their time in college, their love story with maths… I soaked up this information faster than Spongebob.

At that time I was still unsure about what to study in the future, I swayed from studying theoretical physics to theatre stage design in the span of one day. In the end it was these encounters that finally helped me make up my mind, and I think it was one of the most valuable take aways from the Olympiad journey.

We think that many secondary school students are probably facing the same dilemma of choosing their dream course, and we thought it would be great if we could post a series of interviews with people in the STEM field so that people can see their experiences. Hopefully these would prove to be entertaining as well as helpful, and would help students make up their minds about the future.

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Here’s some of my favourite books, both fiction and non-fiction, to give you some inspiration for your next read. Let me know your thoughts on the books in the comments!

Alex’s Adventures in Numberland by Alex Bellos

This book is a journey through the world of maths, from the vastly different counting systems of the world to the concept of infinity. Bellos’ lively writing style ensures it is an engaging and informative read – full review here.

Continue reading My Favourite Books: Book Recommendations to Banish Boredom

Cork Intergenerational Climate Conference, 13 November 2019

This post has been almost finished for a long time, but here it is, better late than never!

On Wednesday the 13 of November the Intergenerational Climate Conference took place in Cork City Hall. With Michael D. Higgins, the Irish President, as the key speaker it was a fantastic event. Half of the audience were second level students, as well as a number of students speaking at the conference.

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