Introducing the Notes

Math olympiads are competitive proof-based events where students gather to showcase their mathematical and critical thinking skills. Some major events include International Mathematical Olympiad (IMO), European Girls’ Mathematical Olympiad (EGMO), Asian Pacific Mathematical Olympiad (APMO), and National Mathematical Olympiads. The contents in this collection of notes includes must know theorems, lemmas, tips, techniques, patterns, and their applications with problems from diverse sources.

I don’t know why (maybe it was due to my naiveness), but I thought I could solve an IMO problems after winning some competitions like AMC. Like I thought “How bad could it be?” One day passed, two days, and after about a week or so, I decided to look at the solution. Of course as a student who only studied AMC 8/10 style problems, it took me only minutes to fully understand their solutions. Just kidding, I took days and weeks trying to digest the official solutions, and it actually took me more time to understand the solutions than to attempt them. This is how I first became aware of what olympiads are and also a moment where I humble myself due to the vastness of math. It is really interesting because the more I learn about math, the more I realize that I know nothing about math, and I think that is one of the reasons why I do math everyday.

After that incident, I really wanted to study more for olympiads because the rewards that you get for yourself when you solve an IMO problem is incredible when you are just starting. This is also the moment when I realized how hard it is to study olympiads. Not only the concepts become very (really, extremely) difficult, it is also very difficult to start without an experienced mentor, whose classes are beyond expensiveness in South Korea. Also, the amount of time needed to dedicate in order to be competitive is incredible.

I initially quite gave up and just casually read one or two solutions a week just because I didn’t know where to start. I have been searching online for resources, doomscrolling through AOPS forums, and collecting the resources. It was around 8th to 9th grade when I wanted to do more of olympiads and started learning the very basics starting from how to write a proof for olympiads, how to type math, what are different types of proof, etc. Of course students who start at the age of 6 were way ahead of me. However, I just continued trying because it is just fun to solve problems that you don’t know and experience that AHA moment.

Despite my experience in competition math, the transition was honestly very difficult. Therefore I started writing these notes with the things that I already knew and what I think would be best way to start. Please keep in mind that I, to, am still a learning student and in no position to “teach” olympiads. However, I am constantly updating the notes with the contents that I learned and am learning. If you are also interested in math olympiads, or if you are unsure whether to start, I really hope my notes help.