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

The book goes far beyond arithmetic and geometric progressions. It tackles:

This is often the longest section. The PDF covers:

Lecture 1: The Substitution Method

Lecture 2: The Transformation Method

Lecture 3: Inequalities (Basic & Classic)

Lecture 4: Extremal Problems

Lecture 5: Polynomials

Lecture 6: Functional Equations

Finding the PDF is the easy part. Using it correctly is where the work begins. Here is a 3-step strategy to get the most out of this resource: The book goes far beyond arithmetic and geometric

1. The Cover-Up Method When you see an example problem in the notes, do not read the solution immediately. Cover the page and attempt the problem yourself. Even if you struggle for 30 minutes, that struggle builds the neural pathways needed for competition day.

2. The "Why" Margin Print the PDF out (or

The Lecture Notes on Mathematical Olympiad Courses for Senior Section, Volume 1

, written by Jiagu Xu, 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

Volume 1 contains 15 detailed lectures that primarily cover advanced algebra and circle geometry: Advanced Algebra & Equations: Lecture 1: Fractional Equations. Lecture 2: Higher Degree Polynomial Equations. Lecture 3: Irrational Equations.

Lecture 4: Indicial (Exponential) and Logarithmic Functions. Trigonometry:

Lectures 5–7: Trigonometric Functions, Laws of Sines and Cosines, and Manipulation of Trigonometric Expressions. Lecture 9: Extreme Value Problems in Trigonometry. Inequalities & Functions: Lecture 8: Extreme Values of Functions and Mean Inequality. Circle Geometry:

Lectures 10–11: Fundamental Properties of Circles and Relations between Lines and Circles. Lecture 12: Cyclic Polygons. Lecture 13: Power of a Point with Respect to a Circle. Lecture 2: The Transformation Method

Lectures 14–15: Important Theorems in Geometry and the Five Centers of a Triangle. Lecture Notes on Mathematical Olympiad Courses

Lecture Notes on Mathematical Olympiad Courses: For Senior Section (Volume 1)

by Jiagu Xu is a comprehensive resource based on Olympiad training courses conducted in Singapore. It is designed for advanced students preparing for high-level competitions like the IMO, focusing on deep conceptual understanding rather than just rote problem-solving. Core Content & Topics

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

Fractional & Irrational Equations: Specialized techniques for solving complex radical and rational equations.

Higher Degree Polynomial Equations: Methods beyond the standard high school curriculum.

Logarithmic & Indicial Functions: Deep dive into indices and log laws applied to competition-style problems. Trigonometry

Manipulations: Mastering identities and expression transformations. Lecture 3: Inequalities (Basic & Classic)

Laws & Geometric Application: Extensive use of the Law of Sines and Law of Cosines.

Extreme Values: Solving for maximum and minimum values specifically within trigonometric contexts. Geometry

Circles: Fundamental properties, power of a point, and cyclic polygons.

Advanced Theorems: Important theorems in geometry and the "Five Centers of a Triangle". Key Features for Students

Structured Lectures: Every chapter begins with theories and concepts, followed by examples that serve as "intentions" for their application.

Global Problem Set: Practice questions are sourced from competitions in China, Russia, USA, and Singapore.

Complete Solutions: Detailed solutions for all testing questions are provided at the end of the book, making it suitable for self-study.

Difficulty Scaling: Examples are kept relatively simple for initial understanding, while testing questions (divided into Parts A and B) increase in complexity. Availability

Digital Access: You can find previews and digital copies on platforms like Scribd and Academia.edu .

Purchasing: Physical and official eBooks are available through World Scientific Publishing and major retailers like Amazon . Lecture Notes On Math Olympiad Senior Vol 1 | PDF - Scribd