The Art of Inequalities: From AM-GM to Cauchy-Schwarz for Olympiads

Stop Memorizing Tricks. Start Seeing the Hidden Structure of Algebra.

In the high-stakes world of mathematics competitions—from the AMC 10/12 to the AIME, USAMO, and the International Math Olympiad (IMO)—inequality problems are the "Gatekeepers." They are the questions that separate the casual participants from the medalists.

Most students struggle with inequalities because they seem arbitrary. They ask: "How did you know to split the term like that?" or "Why apply AM-GM here and not Cauchy-Schwarz?"

The Art of Inequalities removes the mystery. Written by Rohan Kumar Singh (IIT Madras Alumnus & International Olympiad Gold Medalist), this book treats inequalities not as a "bag of tricks," but as a disciplined art form governed by logic, geometry, and pattern recognition.

ROCKET YOUR SCORES: WHAT YOU WILL MASTER

• Decode the Basics: Master the visual and algebraic intuition behind the Trivial Inequality, AM-GM, and Weighted AM-GM.

• Wield the Scalpel: Use Cauchy-Schwarz and Titu’s Lemma to dismantle complex fractional inequalities with precision.

• Think Strategically: Learn high-level techniques like Homogenization, Symmetry Breaking, and Ravi Substitutions.

• Go Beyond High School: Dive into advanced research-level tools including Schur’s Inequality, Muirhead’s Theorem, and Jensen’s Inequality.

THE EDUGLOBAL METHOD

This is not just a textbook; it is a high-performance training manual. Based on the curriculum used at EduGlobal Institute to produce 230+ Olympiad rankers and 350+ AP 5/5 scores, this book follows a strict pedagogical cycle:

1. Diagnostics: Test your baseline before every chapter to identify gaps.

2. Concept Sprints: High-intensity theory modules that value your time.

3. Coach’s Insights: Specific "Speed Hacks" and strategy notes usually reserved for private coaching.

4. The Pitfalls: Red-boxed warnings highlighting common errors that cost students points.

5. The Gauntlet: A curated collection of real exam problems from AIME, USAMO, and RMO.

ABOUT THE AUTHOR

Rohan Kumar Singh is the Founder & Chief Mentor at EduGlobal Institute. An IIT Madras alumnus and International Olympiad Gold Medalist, Rohan blends rigorous academic research with competitive strategy.

• 1,200+ Students Mentored

• 230+ Olympiad Rankers

• 350+ AP 5/5 Scores

• 160+ Student Publications

Whether you are aiming for a spot in the AIME, preparing for the Putnam, or building a foundation for Research Mathematics, this book is your roadmap to algebraic mastery.

Master the art of inequalities today.