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

Unlike typical textbooks, which present polished, final solutions, this series originated from actual classroom lectures. The author, a seasoned coach from China (a dominant force in the IMO), structured the content to mirror a live course progression.

Key advantages of this series:

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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

(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

The Lecture Notes on Mathematical Olympiad Courses: For Senior Section (Volume 1) Kindly provide feedback on this report

is a foundational textbook authored by Xu Jiagu 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

The book is structured into 15 specific "lectures," each serving as a self-contained module that focuses on essential theories and unconventional solving techniques.

Algebraic Foundations: Lectures 1–4 cover Fractional, Higher Degree Polynomial, and Irrational Equations, as well as Indicial and Logarithmic Functions.

Trigonometry Focus: Lectures 5–9 delve into Trigonometric Functions, the Laws of Sines and Cosines, manipulations of trigonometric expressions, and extreme value problems.

Geometric Depth: Lectures 10–15 explore the Properties of Circles, Cyclic Polygons, Power of a Point, and the "Five Centers of a Triangle". Key Pedagogical Features

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

is an authoritative training guide written by Jiagu Xu and published by World Scientific. This book is based on lecture notes from Olympiad training courses conducted in Singaporean schools like Victoria Junior College and Hwa Chong Institution. Rather than being a mere collection of problem-solving techniques, it aims to provide a systematic mathematical education that bridges the gap between high school curricula and modern mathematics. Core Philosophy and Structure

The book is structured into 15 distinct "lectures," each acting as a focused chapter on a specific mathematical theme.

Theory-Driven Learning: Each lecture begins with a concise exposition of essential theories, definitions, and major theorems.

Graduated Practice: Following the theory, the author provides several worked examples with detailed solutions to illustrate the concepts.

Testing Tiers: Every lecture concludes with two sets of practice questions:

Part A: Targeted practice to reinforce the techniques discussed in the examples.

Part B: Challenging problems taken from real national and international competitions (like the IMO) to test original thinking and advanced application. Key Topics and Educational Benefits

Volume 1 focuses heavily on advanced algebra and geometry, providing a rigorous foundation for senior-level competitions through topics including polynomial and irrational equations, trigonometry, inequalities, and comprehensive circle geometry.

Global Problem Source: The competition questions are sourced from various countries, including China, Russia, the United States, and Singapore, offering students a diverse range of problem styles. World Scientific Publishing Core Content & Topics The

Focus on Mathematical Thinking: The author emphasizes flexibility, rigorous logic, and the ability to convert concrete problems into abstract mathematical models.

Self-Study Capability: Detailed solutions for all practice problems are provided at the end of the book, making it an excellent resource for independent learners and coaches.

Lecture Notes on Mathematical Olympiad Courses for Senior Section (Vol. 1)

, edited by Xu Jiagu, is a highly regarded resource designed for high school students preparing for elite math competitions like the IMO. Published by World Scientific, it bridges the gap between standard school curriculums and the creative, rigorous thinking required for modern competitive mathematics. Content and Structure

The book is organized into 15 "lectures". Each lecture typically follows a consistent pedagogical flow: Theory & Concepts

: A concise introduction to notations, basic theorems, and core mathematical methods. Worked Examples

: Carefully chosen problems that demonstrate how to apply theoretical concepts. These are designed to be accessible enough for motivated students to grasp the logic quickly. Practice Problem Sets

: Designed to reinforce the specific techniques introduced in the lecture.

: More challenging problems requiring originality and unconventional thinking, often sourced from actual international competitions (China, Russia, USA, and Singapore).

: Detailed solutions for all practice questions are included at the end of the book. Core Topics Covered

Volume 1 focuses heavily on foundational algebra, functions, and trigonometry. Notable chapters include:

Fractional, higher-degree polynomial, and irrational equations. Logarithmic and indicial functions.

Trigonometric functions, expressions, and the Law of Sines/Cosines. Mean inequalities and extreme value problems. Fundamental properties of circles. Pros and Cons Reviewer Consensus Organization

Highly focused and logical; topics are narrowly defined, which helps in mastering one skill at a time. Problem Quality

Excellent selection of diverse international problems, particularly from China, known for its rigorous Olympiad standards. Explanations followed by worked examples

Explanations are "frugal" (brief). It assumes a certain level of mathematical maturity and may not hold a beginner's hand. Self-Study

Very suitable for self-study due to its self-contained nature and the inclusion of full solutions. This volume is best suited for advanced high school students math coaches

. It is an efficient, targeted "workout" for the mathematical mind. If you find the explanations in other standard textbooks too wordy, you will appreciate Xu Jiagu's direct and problem-centric approach.

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

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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.