Foundations of Olympiad Mathematics for INMO, ISI, and CMI

Preparing for elite mathematical competitions and entrance exams requires more than just memorizing formulas; it demands deep conceptual understanding and rigorous proof-writing skills. This text-based course helps you build a solid foundation in the core pillars of Olympiad-level mathematics. Through clear written explanations, step-by-step proof breakdowns, and structured practice problems, you will transition from solving standard high school algebra to tackling complex non-routine challenges. You will learn to think like a mathematician and structure your solutions to meet the demanding standards of examiners. What you'll learn: Understand foundational mathematical logic and formal proof-writing techniques; Apply fundamental principles of number theory, including divisibility, modular arithmetic, and Diophantine equations; Master combinatorial reasoning, counting principles, and graph theory basics; Solve complex algebraic problems involving polynomials, inequalities, and functional equations; Analyze Euclidean geometry challenges using synthetic methods and coordinate systems; Develop systematic problem-solving strategies to approach unfamiliar, non-routine exam questions. The course begins with foundational concepts in logic and notation before guiding you through dedicated modules on algebra, geometry, number theory, and combinatorics. Each topic is reinforced with fully explained written examples and practice problems designed to build your confidence. This course is designed for aspiring mathematicians and students preparing for competitive exams like INMO, ISI, and CMI. No prior experience with Olympiad-level math is required, as we start with essential definitions and build up to advanced problem-solving. Start your journey toward mastering competitive mathematics today.