Understanding vertices, edges, and connectivity to model network problems.
Write down the clever tricks you learn along the way. Finding a PDF Version Online
: Lectures 1–4 cover Fractional, Higher Degree Polynomial, and Irrational Equations, as well as Indicial and Logarithmic Functions.
Mastering modular arithmetic and its application to massive exponential problems. Mastering modular arithmetic and its application to massive
Introducing convexity and concavity as powerful tools for algebraic proofs. 3. Modern Euclidean Geometry
Utilizing the Fundamental Theorem of Arithmetic to solve integer equations.
Xu’s book fits nicely between AoPS Vol 2 and Engel—it is more systematic than AoPS but less dense than Engel. Higher Degree Polynomial
The text introduces structural properties of integers, including:
When tackling the exercise sets at the end of each lecture, time yourself. This builds the mental stamina required for grueling 4-to-5-hour official examinations. 📥 Finding the PDF and Supplemental Materials
Fractional, higher-degree polynomial, and irrational equations. Functions: and Irrational Equations
| Pros | Cons | | :--- | :--- | | (often freely shared by alumni) | Legality issues – many PDFs circulating are unauthorized scans. | | Searchable text (if OCR'd) for quick lemma lookup | Missing pages or poor formatting from low-quality scans. | | Portable – study on a tablet during commutes | No physical copy – flipping between chapters is harder. | | Immediate download | Ethical concern – authors and publishers rely on sales to produce more volumes. |
Techniques for solving high-degree equations and expressions where unknowns appear in denominators.
Olympiad geometry requires a transition from coordinate calculations to synthetic, proof-based reasoning. Volume 1 introduces:
Explanations are "frugal" (brief). It assumes a certain level of mathematical maturity and may not hold a beginner's hand. Self-Study