Polynomials are often underestimated, but this volume treats them as functional equations. Topics include:
Ideal reader:
Not ideal for:
You don’t read this book. You grind it. Each chapter begins with a concise theory recap, followed by worked examples, and ends with a “Scoring Exercise” set. The PDF format allows you to keep a digital window open for scratch work or printing specific problem sets.
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.
You don’t need more calculations; you need a shift in perspective.
For years, one specific title has circulated among top-tier competitors like a whispered secret. It isn't always flashy, but it is dense with high-level insight. Today, we are diving into "Lecture Notes on Mathematical Olympiad Courses for Senior Section Vol 1"—why it matters, what’s inside, and how it can transform your problem-solving skills.
A concise, well-structured set of lecture notes that effectively prepares motivated senior students for olympiad contests. Recommended as a core study supplement, provided readers supplement sparse proofs and diagrams with additional references when necessary.
For students and educators aiming for the pinnacle of high school mathematics, the "Lecture Notes on Mathematical Olympiad Courses for Senior Section Vol 1" is a cornerstone resource. Authored by Jiagu Xu, a former professor at Fudan University with extensive experience training Singapore's national teams, this volume offers a structured "system for advancing mathematical education" rather than just a list of tricks. Core Philosophy and Origin
The book is based on over 15 years of lecture notes from top-tier Singaporean institutions like Victoria Junior College, Hwa Chong Institution, and Nanyang Girls' High School. Its philosophy is that Olympiad math is about developing flexible, rigorous thinking and the ability to bridge the concrete and the abstract. Key Content and Curriculum
Volume 1 focuses heavily on Algebra, Trigonometry, and Geometry, providing a deep dive into topics that often go beyond the standard high school syllabus. Algebraic Foundations
Fractional and Polynomial Equations: Techniques for solving high-degree equations and expressions where unknowns appear in denominators. Polynomials are often underestimated, but this volume treats
Indicial and Logarithmic Functions: Mastery of indices and logs as they relate to complex problem-solving.
Extreme Values: Utilizing the Mean Inequality and other tools to find maxima and minima of functions. Trigonometric Mastery
Law of Sines and Cosines: Advanced applications in geometry.
Trigonometric Expressions: Manipulation and simplification of complex series and identities.
Trigonometric Extreme Values: Finding boundaries for trigonometric functions. Geometric Theorems
Circle Properties: In-depth study of lines, circles, and their relations.
Cyclic Polygons: Specialized theorems for polygons inscribed in circles.
The Five Centers: Analysis of the Incenter, Circumcenter, Orthocenter, Centroid, and Excenter of a triangle. Why This Book Stands Out
Unlike many competition books that only offer problems, these lecture notes emphasize the theories and methods as the core.
Problem Sets: Each lecture includes "List A" problems to practice specific techniques and "List B" problems to challenge originality and experience.
Global Scope: Problems are sourced from worldwide competitions, including those from China, Russia, the USA, and the International Mathematical Olympiad (IMO). Not ideal for: You don’t read this book
Self-Contained: Because the standard syllabus is often insufficient, this book is designed to be a comprehensive, self-study guide with detailed solutions for every question. Access and Availability
The book is part of the Mathematical Olympiad Series (Volume 8) published by World Scientific Publishing.
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.
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) , authored by and published by World Scientific Publishing
, is a core resource for high school students preparing for elite math competitions like the IMO. Amazon.com This volume is part of the Mathematical Olympiad Series This is where the "puzzle" aspect of math shines
(Volume 8) and is based on lecture notes the author developed over 15 years while training students in Singapore. World Scientific Publishing Core Content & Topics
The book focuses on deep conceptual understanding rather than just rote problem-solving techniques. It contains 15 detailed lectures covering advanced algebra and geometry: Amazon.com Algebraic Foundations
: Fractional, higher-degree polynomial, and irrational equations. : Indicial, logarithmic, and trigonometric functions. Trigonometry
: Laws of Sines/Cosines, manipulation of expressions, and extreme value problems.
: Properties of circles, cyclic polygons, power of a point, and the five centers of a triangle. Inequalities : Mean inequality and extreme values of functions. World Scientific Publishing Key Features Self-Contained Structure
: Each lecture starts with core concepts and theories, followed by illustrative examples and test questions. International Problems
: Includes competition questions from diverse countries, including China, Russia, the USA, and Singapore Detailed Solutions
: Unlike many textbooks, this volume provides comprehensive solutions to all practice and testing questions. Advanced Scope
: The material goes significantly beyond the standard high school syllabus, introducing modern mathematical methods. Book Specifications Jiagu Xu (Former Professor at Fudan University) Publication Date March 2012 Available in Paperback and eBook Page Count ~260 pages World Scientific Publishing Company Lecture Notes On Math Olympiad Senior Vol 1 | PDF - Scribd
This is where the "puzzle" aspect of math shines.
The book goes far beyond arithmetic and geometric progressions. It tackles: