Number theory challenges students to understand the properties of integers. Key topics include:
One of the most highly recommended resources for bridging the gap between school curriculum and competition math is the book by Xu Jiagu. You’ve mastered the basics of algebra, you know
: Each concept is followed by multiple worked examples, ranging from introductory applications to actual past Olympiad questions. You’ve mastered the basics of algebra
Many universities publish their training materials online for free. you know your geometry theorems
Owning the book or finding a PDF copy is only the first step. To truly benefit from Xu Jiagu’s lectures, follow this study roadmap:
Every serious mathematical olympiad competitor reaches a point where simple textbooks no longer cut it. You’ve mastered the basics of algebra, you know your geometry theorems, and you can handle a calculus problem. But when you look at a problem from the IMO Shortlist or a National Olympiad, the path forward vanishes.