A foundational tool for proving formulas.
Factorization over different fields, remainder theorems, symmetric polynomials, and Vieta's formulas for higher-degree equations.
Explanations are "frugal" (brief). It assumes a certain level of mathematical maturity and may not hold a beginner's hand. Self-Study
Check World Scientific or major academic repositories like Google Books for official e-book editions.
Volume 1 covers 15 distinct lectures focused primarily on algebra, functions, and plane geometry: Fractional Equations Extreme Value Problems in Trigonometry Higher Degree Polynomial Equations Fundamental Properties of Circles Irrational Equations Relation of Line and Circle Indicial & Logarithmic Functions Cyclic Polygons Trigonometric Functions Power of a Point Law of Sines and Cosines Important Theorems in Geometry Trigonometric Expressions Five Centers of a Triangle Extreme Values & Mean Inequality Accessing the PDF A foundational tool for proving formulas
Perfect for students who need a systematic way to tackle diverse math topics rather than jumping between disorganized problems.
Try to solve the exercises on your own first. Do not look at the answers right away. Spend at least 30 minutes thinking before you give up.
is a foundational textbook authored by and published by World Scientific . This volume is part of the "Mathematical Olympiad Series" (Volume 8) and is designed to transition students from standard school curricula to the complex, creative problem-solving required for high-level competitions like the International Mathematical Olympiad (IMO). Core Content and Structure
By systematically working through Xu Jiagu's lectures, you will not only expand your mathematical toolkit but also develop the sharp, analytical mindset required to tackle the world's toughest high school math competitions. If you want to tailor your study plan further, tell me: What are you preparing for? It assumes a certain level of mathematical maturity
Often considered the most creative branch of Olympiad math, combinatorics deals with counting, arrangement, and configuration. The text covers:
, written by , is a comprehensive resource designed to bridge the gap between standard high school curricula and the rigorous demands of international mathematical competitions. Based on training courses conducted in Singapore, it focuses on modern mathematical concepts through a structured "lecture-and-practice" format. Core Lectures and Topics
: Laws of Sines/Cosines, manipulation of expressions, and extreme value problems.
Linear congruences, systems of congruences, and the Chinese Remainder Theorem. Try to solve the exercises on your own first
Using homothety (dilation), inversion, and rotation to simplify intricate geometric configurations. 4. Number Theory Foundations
Before reading the provided solution to an example problem, cover it up and spend at least 20 to 30 minutes trying to solve it yourself.
Geometry: Circle Inversion