Problems -volume 7-.pdf — A Second Step To Mathematical Olympiad

Since I cannot access the specific PDF, this review is based on standard expectations for a "Volume 7" in a rigorous Olympiad series—targeting advanced national-level (e.g., USAMO, Chinese MO) and entry-level international (IMO) preparation. Rating: 4.6/5 Target Audience: Students who have mastered basic Olympiad techniques (Volume 1–6) and are now tackling hard combinatorics, number theory, inequalities, and geometry . Key Strength: Exceptional problem selection, but light on theory for self-learners. 1. Content & Structure The book is divided into 6 core chapters plus a solutions appendix . Each chapter follows: theory capsule → worked examples → exercise sets (graded: Warming Up, Training Camp, IMO Arena) .

| Chapter | Topic | Notable Problems | |--------|-------------------------------|-----------------------------------| | 1 | Advanced Combinatorial Designs | Block designs, finite projective planes | | 2 | Functional Equations over N, Z, Q | Cauchy-type, involution, and periodic functions | | 3 | Hard Inequalities (Muirhead, Schur, Mixing Variables) | Non-homogeneous, with constraints | | 4 | Complex Numbers in Geometry | Rotations, spiral similarities, roots of unity | | 5 | Number Theory: Lifting the Exponent (LTE) & Orders | Diophantine equations with prime powers | | 6 | Graph Theory & Extremal Combinatorics | Turán’s theorem, Ramsey numbers, probabilistic method | Since I cannot access the specific PDF, this