Monotonicity
4 handouts in this topic
- Part 4: Advanced Inequalities and Majorization advanced • Sun Feb 22 2026The full algebraic and analytic arsenal — majorization theory, Schur convexity, Muirhead's theorem, the SOS algorithm, Vasc's EV method, L^p integral bounds, and the Rearrangement inequality — deployed against the deadliest competition problems.
- Part 3: The Inequality Machinery advanced • Sun Feb 22 2026The decisive edge — transforming derivative information into competition-grade inequality proofs through the Mean Value Theorems, convexity hierarchies, and a systematic heuristic arsenal.
- Part 2: Differential Analysis & Critical Points advanced • Fri Feb 20 2026A deep dive into the Discrete Zero Theorem, Darboux's Theorem, recursive derivative methods, and the advanced sign-analysis techniques that separate the elite from the rest.
- Part 1: The Algebraic & Topological Foundations advanced • Sat Feb 14 2026A rigorous exploration of pointwise vs. interval monotonicity, Darboux's Theorem, Froda's Theorem, and the essential manipulation techniques that separate the elite from the rest.