Competitive mathematics covers a wide range of topics, from basic arithmetic to advanced number theory and combinatorics. Yet, the focus is not on the theory itself, but rather on the way you can apply them, sometimes very creatively, to solve problems.
This section is dedicated to sharing my experiences and strategies for tackling problems in competitive mathematics. Any good problem solver has so many tricks up their sleeves, but it can sometimes be hard to express them in words. Hence, I will attempt in my best efforts to verbalize the recurring strategies that I have encountered.
This post specifically should not be used as a guide, moreso as a table of contents for the folders within this section. Indeed, just reading words of advice will not stick in your mind; and even if it does, it will be utterly useless to you if you don’t know what to do with it. I have had the unfortunate experience of being stuck with this ideology for too long, which totally halts any progress. This is why there must be concrete examplse and explanations for each strategy. Learning is a gradual process that gets refined as you learn to apply it more and more effectively, both broadly and efficiently.
The ./meta-strategies folder covers the analysis of the thought process itself, a possibly beneficial mindset to generalize strategies beyond specific problems or topics. This includes ideas like how to attack a problem in a competition, what it means to “break the problem down”, time management, thinking from different perspectives to “unstuck” yourself, how to generalize strategies to a broader context, etc.
The ./math-patterns folder covers the analysis of recurring patterns in specific areas and types of problems in competitive mathematics, and how to apply them. For example, how to find restrictions in number theory and algebra to find a solution or prove its impossibility, how to spot symmetries in combinatorics to reduce casework, how to choose formulas to reduce required computations, etc.