Lecture Notes On Mathematical Olympiad Courses For Senior Section Vol 1 Pdf May 2026

The "Lecture Notes on Mathematical Olympiad Courses for Senior Section, Volume 1" is a fundamental resource for students aspiring to compete at the highest levels of high school mathematics. Authored primarily by Xu Jiagu, this volume serves as a bridge between standard school curricula and the rigorous, creative demands of national and international competitions like the IMO. It is not merely a collection of problems but a structured pedagogical tool designed to cultivate advanced mathematical intuition.

• You have finished an A-level, AP Calculus, or equivalent high school math.
• You can solve basic AIME problems (or national level-2 olympiad problems) with some effort.
• You want a systematic course, not random problem collections.

Step 2: The 3-Pass Strategy for Each Chapter

• Pass 1 (Warm-up): Solve all the "Basic Exercises" (marked with one star *). These directly mimic the examples.
• Pass 2 (Core): Solve the competition-level problems (two stars **). These are from actual national olympiads.
• Pass 3 (Challenge): Look at the three-star *** problems. Even reading the solutions here teaches new tricks.

1. Advanced Algebra (Beyond the Quadratic)

This isn't about solving for $x$. This is about inequalities, functional equations, and complex numbers. The "Lecture Notes on Mathematical Olympiad Courses for

Fractional & Irrational Equations: Specialized techniques for solving complex radical and rational equations. You have finished an A-level, AP Calculus, or

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 Step 2: The 3-Pass Strategy for Each Chapter

Lecture 4: Extremal Problems

A Critical Warning for Self-Learners

Before you rush to download a PDF, consider this: This book is ruthlessly difficult for a beginner.

Detailed lectures on logarithmic and indicial functions, along with extreme values of functions. Trigonometry: