Discovering potential
Many people often don't know what their brain is capable of when it tries. Competitions provide a safe environment to test this, and for many are the beginning of their future journey for career and personal growth.
Competition Math Guide
List of competitions and various useful links related to competition math, written from a Czech-Slovak perspective. The plan is to continuously update these sections with the best content.
1Why math competitions?
Math competitions are not just about competition and math 🙂.
Developing logical thinking
Math competitions develop the ability to analyze problems and find creative solutions. These skills are then transferable to all spheres of life, as problems need to be solved everywhere.
Community and friendship
The environment of competitions and camps is very community-oriented and without it many would not even exist. Many people have found friends and partners for life in these communities.
Great career opportunities
People from the math competition environment are the most sought after for various positions requiring solving difficult problems, e.g. in AI, algorithmic trading etc. Thanks to acquired skills and contacts from the community they then easily obtain them.
2List of competitions
The most important competition is the Mathematical Olympiad (MO). However, there are plenty of other competitions and activities that are good as training for MO or even on their own 😇.
2.1Mathematical Olympiad
A competition in solving interesting mathematical problems for elementary and high schools, which starts with a home round and culminates in the most prestigious international mathematical olympiad IMO.
Czechia and Slovakia have shared problems but separate organizations
The Mathematical Olympiad is divided into two main parts: elementary school and high school category, each with its own grade levels and rounds.
Elementary categories
- Z5 – Z9 by elementary school grades (and corresponding grades of eight-year gymnasiums)
- Home and district rounds in each category
- In category Z9, also regional round and in Czechia national round
High school categories
- C for 1st, B for 2nd, A for 3rd and 4th year (and corresponding grades of eight-year gymnasiums)
- Home, school, and regional rounds in each category
- In category A, also national round, from which progression to selection camp is possible
- From the selection camp, you can advance to international competitions
- Fun multi-day events where math is only part of the program
- Rotating host countries, trips to new places guaranteed
IMO
(International Mathematical Olympiad)
The most prestigious international olympiad
- 6 best solvers from each country
- 100+ countries
- 2 competition days, each with 3 problems over 4.5 hours
MEMO
(Middle European Mathematical Olympiad)
Competition for the best future potential IMO participants
- 6 best solvers not going to IMO, who may go next year
- 11+ countries
- Individual and team parts
In addition, there are other events:
EGMO
(European Girls' Mathematical Olympiad)
Competition aimed at encouraging girls' participation in math competitions
- 6 best female solvers from each country
- Qualification through special selection camp
- Invitation based on results of regional round category A
- 55+ countries (including non-European)
- Same format as IMO
CAPS
(Czech Austrian Polish Slovak Match)
Preparatory competition for IMO teams of participating countries
- Same format as IMO
- Recently usually held at ISTA in Austria
CPSJ
(Czech-Polish-Slovak Junior Match)
Competition for the six best first-year high school students (and younger) from participating countries
- Qualification through special selection camp
- In Czechia selection based on category A results, in Slovakia category C
- Individual and team parts
- Three-member teams (1 member from each country) randomly drawn
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Tip
Don't be afraid to try solving higher categories, problems often don't require more complex knowledge and categories overlap. The best of the best often solved higher categories too.
2.2Correspondence seminars
Correspondence seminars are an integral part of Czech-Slovak mathematical culture, which is reflected in their number.
- Solving problems at home and sending solutions by mail (hence the name), although now mostly online
- Several series of problems during the year
- Camps packed with fun and math as an essential part of seminars
ES2.2.1Elementary school seminars
There are really quite a few elementary school seminars. Most of them are generally for upper elementary, but they have scaled problems for everyone.
Slovak
Riešky
riesky.skPikomat
pikomat.skSezam
www.sezam.skFor grades 7-9 of elementary school
Sezamko
www.sezam.sk/sezamkoFor grades 4-6 of elementary school
Matik
strom.sk/matikFor grades 7-9 of elementary school
Malynár
strom.sk/malynarFor grades 4-6 of elementary school
Czech
Pikomat
pikomat.mff.cuni.czKomár
komar.math.muni.czKoKoS
kokos.gmk.czFor grades 6-9 of elementary school
HS2.2.2High school seminars
Two Slovak, two Czech, and one Czech-Slovak. In addition, many Czech-Slovak students also participate in MBL. There's really no shortage of fun.
Slovak
KMS
kms.skStrom
strom.sk/stromCzech
PraSe
prase.czBRKOS
brkos.math.muni.czInternational
iKS
iksko.orgCzech-Slovak seminar for solvers with ambition to succeed at international rounds
Originally Polish, now international seminar with one round and one long camp
💡
Tip
Many people solve multiple seminars at the same time, both at elementary and high school level. It's also common for Slovaks to solve Czech seminars and vice versa. It's no coincidence that there's a big overlap between the best MO and seminar solvers 😉
2.3Other competitions
Besides the olympiad and seminars, there are many other competitions with various formats, mostly one-day fun events that you typically don't train for, but there's less pressure because of that 😌
2.3.1Team competitions
Team competitions are a great opportunity to have fun with friends. It's no surprise that they're popular and there are so many of them.
Náboj & Náboj Junior
ESHS
The most popular team competition in our region with answer-only problems
DuoGeo
ESHS
A pairs competition in solving olympiad-style geometry
Maso
ES
A competition with problems like Náboj, where answers unlock moves in a game
Mathrace
HS
An online competition with Náboj-style problems where software and programming is allowed
Mathing
HS
An online competition with olympiad-style problems
Purple Comet
HS
An international Náboj-like competition with over 80 countries
2.3.2Individual competitions
Individual competitions with a different format than the Mathematical Olympiad. All listed below require only the answer, which is how they differ from it.
Math Kangaroo
ESHS
A multiple-choice competition
Pythagoreiad
ES
A competition where speed and accuracy of answers matter
Pangea
ES
A competition similar to Math Kangaroo with themed problems
Attomat
ESHS
An online competition with answer-only problems
Maks & Maksík
ES
A competition where problems are solved at home and answers uploaded online
Logic Olympiad
ESHS
A popular competition among mathematicians for obvious reasons
Brloh
ESHS
A competition in solving mathematical-logical problems
3Other links
A brief list of the most important study/community resources from the world of competitive mathematics that are definitely worth knowing.
3.1Websites and communities
AoPS
(Art of Problem Solving)
Probably the biggest and most important website about olympiad mathematics in the world. Forums, huge problem collections, articles, all in one place. A must know.
MODS
(Math Olympiad Discord Server)
A large international Discord server where you can discuss with people from all over the world. For over 2000 days, it has been running a problem of the day feature, with access to older problems by topic and difficulty rating.
Evan Chen
Personal website of a world-famous olympiad expert. Through his site, you can navigate to many of his materials and other resources and information.
3.2Programs and tools
GeoGebra
A fantastic tool for learning geometry or drawing graphs. A well-drawn diagram can make the difference in whether we see the solution or not, and GeoGebra can draw them precisely 📐.
WolframAlpha
A fast and reliable tool for solving equations, factoring numbers, calculating sums, or even differentiation, integration, etc.
Overleaf
Online environment for writing in LaTeX, which is the standard for mathematics. Contains tutorials for LaTeX beginners.
💡
Tip
We all see that AI is getting better at math. It can be a quick helper when learning new things. Just be careful, as it's not always right and can make things up 🙃
3.3YouTube channels
MindYourDecisions
Videos solving problems of all difficulties, from purely popularizing to interesting olympiad ones.
Michael Penn
Solutions to competition problems from competitions around the world, explained on a blackboard.
3Blue1Brown
Unique visual treatment of various topics from mathematics.
3.4Study texts
In this section, we'll summarize some study materials. The priority is to give beginners an overview of where they can turn.
Our materials
There aren't many publicly available materials for beginners with good explanations of ideas. Our materials on this site aim to fill this gap. The collection will grow over time.
KMS collection
Older but timeless material. Pleasant explanations and short introductions to all topics with many examples from the KMS seminar.
Sample solutions
The easiest problems from seminars, or lower MO categories, are a good source. In seminars, solutions are written more in the style of how to approach problems, while in olympiad more in the style of how to write them once someone has figured it out.
Guided problems for MO home rounds
It's worth solving older MO home rounds, because guided and supplementary problems are released with them (with solutions/links), which is a good way to absorb a topic.
PraSe library
A large collection of materials from the PraSe seminar. For self-study, the so-called series are very interesting - these are thematic texts.
Info
You might be asking why this or that isn't here. It's mainly because this guide is written primarily for beginners, and overwhelming with materials right at the start may not be productive. Links to further study will gradually be added inside the materials on the site, or later a page with advanced guidance may appear, with a larger database. Anyway, there's really a lot in the PraSe library 😜.
4How to start and continue
At the beginning, there are always many options on how to start. Then there are many options on how to progress. The following advice aims to help with this process.
Beginnings are great because you improve quickly
- Try correspondence seminars. They have problems suitable for beginners and provide feedback. Attend their camps where you'll learn, meet people, and have fun.
- Look for math clubs at school or nearby. Ask your math teacher if they know of any.
- Try solving problems with someone else, you can motivate and entertain each other.
- Also find study materials for systematic learning, recommendations are just above.
Principles of good training
- Math needs to be actively trained, muscles aren't gained by watching exercise videos either. It's always better to try solving a problem independently first. The process of thinking, trying, and even failing helps the mind learn.
- Only after some effort should you look at model solutions for problems you didn't solve. The brain learns more from them when it struggled beforehand.
- Definitely also look at model solutions for problems you did solve, often you'll learn different approaches, maybe even more efficient ones.
- Some prefer systematic materials and books, others prefer solving random problems. Ideally, combine things, experiment, and find what you enjoy most.
In conclusion
The key is to enjoy the process. The world of competitions and seminars attracts many people and not everyone can be the best, but that doesn't mean it can't change everyone's life for the better 😊