: Trigonometric functions, laws of sines and cosines, manipulations of expressions, and extreme value problems in trigonometry.
Problems:
What truly distinguishes this textbook from a simple problem collection is its structured and deliberate pedagogical approach. The book's power lies in its three-part chapter format:
When encountering a sample problem or exercise, do not look at the solution immediately. Spend at least 30 minutes attempting to solve it independently. Even if you fail, the mental wrestling match makes your brain receptive to the logic of the correct solution. : Trigonometric functions, laws of sines and cosines,
Olympiad math relies on small "helper theorems" (lemmas). Keep a notebook of these specific tools as you encounter them in the text.
If you are looking to optimize your study plan, let me know:
Deep dives into the Euclidean algorithm and the properties of divisor functions. 4. Combinatorics and Graph Theory Intro Spend at least 30 minutes attempting to solve
The series, often published by World Scientific, is designed to bridge the gap between school-level mathematics and the rigorous demands of competitions like the IMO (International Mathematical Olympiad), AIME, or national-level competitions.
The book contains "Practice" problems (easy to medium) and "Problems" (hard). Do at least 80% of the first set and 50% of the second before moving to the next chapter.
Not your average AM-GM. The notes explore advanced techniques: Cauchy-Schwarz, Chebyshev, rearrangement, Jensen’s inequality, and Schur’s inequality. Each theorem is followed by carefully chosen problems from past IMO Shortlists. Keep a notebook of these specific tools as
| Feature | Benefit | |---------|---------| | | Instantly locate “Pigeonhole Principle” or any keyword. | | Portable | Read on a laptop, tablet, or e‑reader anywhere—perfect for on‑the‑go revision. | | Print‑Friendly | High‑resolution diagrams print clearly on A4/A5 paper. | | Hyper‑linked Table of Contents | Jump directly to the chapter you need during a study session. |
For any student aiming to transition from local competitions to the national stage, mastering the contents of Volume 1 is not just recommended—it is mandatory.