: The material is derived from over 15 years of Olympiad training notes used in top Singaporean schools like Hwa Chong Institution and Victoria Junior College Amazon.com Two-Tiered Question Sets : Each lecture ends with practice problems divided into (foundational practice) and (challenging questions from actual worldwide competitions) WordPress.com Self-Contained Modules

This volume covers advanced algebra and geometry through 15 specific lectures, each featuring core theories, worked examples, and two parts of practice questions:

The material is inspired by the successful Singapore Math training model.

This book is often compared to Arthur Engel's Problem-Solving Strategies due to its problem-centric approach, but Xu Jiagu's work has a unique focus.

The exercise sets at the end of each chapter are where the real growth happens. Categorize your progress: : You have mastered the concept. Solved after a struggle : You are building stamina.

When a theorem is introduced, cover the proof and try to recreate it yourself. Understanding the mechanism behind a tool is crucial for tweaking it during an exam.

Number theory challenges students to understand the properties of integers. Key topics include:

: Understanding modular arithmetic, which serves as the language of number theory.

For rigorous mathematics, working out of a physical paperback is often highly recommended to reduce screen fatigue and allow for easy margin-notetaking.

If you have ever peered into the world of competitive mathematics—beyond the school curriculum, beyond the standard textbooks—you have likely encountered a wall. The problems from the IMO (International Mathematical Olympiad), the Asian Pacific, or the USAMO don’t just test knowledge; they test ingenuity .

Unlike school geometry, which relies heavily on coordinate computation, Olympiad geometry focuses on synthetic proofs and structural properties:

Using translations, rotations, reflections, and homothety to simplify complex configurations.

Originally published by World Scientific, this book is part of a celebrated series by mathematician . Unlike a typical textbook that moves from definition to example to drill problem, this volume is structured like a live course .

: Do not just read the proofs; recreate them on paper without looking at the book.

The text introduces structural properties of integers, including:

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