The lecture notes for senior section Vol 1 cover
Lecture 7: Divisibility and Primes
Lecture 8: Greatest Common Divisor (GCD) & Least Common Multiple (LCM)
Lecture 9: Congruence
Lecture 10: Diophantine Equations
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 (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 The lecture notes for senior section Vol 1
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
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. Lecture 8: Greatest Common Divisor (GCD) & Least
Because you have a PDF (searchable), do not print the whole book. Instead:
Absolutely, but only if you commit to active learning.
The Lecture Notes on Mathematical Olympiad Courses for Senior Section Vol 1 PDF is not a casual read. It is a workout plan for your mathematical mind. The PDF format makes it portable, searchable, and perfect for a tablet-based study session. Pair it with a notebook and a timer, and work through each sequence problem until the method becomes second nature.
For the student who is serious about reaching the IMO or simply understanding the beauty of advanced algebra and combinatorics, this volume is a rite of passage. Download it, open the first chapter on sequences, and begin your journey toward mathematical mastery.
Have you used Xu Jiagu’s notes in your training? Share your experience and study tips in the comments below (or in your math study group). And remember: the PDF is a tool—your persistence is the engine.
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