Combinatorics and Number Theory for Math Competitions

Excelling in mathematical competitions requires a deep grasp of logical reasoning and structured problem-solving methods rather than simple formula memorization. This course provides a thorough introduction to combinatorics and number theory, equipping you with the essential tools needed to tackle classic competition challenges. You will begin by exploring fundamental definitions, mathematical terminology, and basic set theory before advancing to structured problem-solving strategies. What you'll learn: • Learn foundational counting principles, permutations, combinations, and the inclusion-exclusion principle • Understand core number theory concepts including prime factorization, divisibility rules, and modular arithmetic • Apply systematic algorithms and invariant strategies to analyze complex competition problems • Practice constructing clear mathematical proofs and logical arguments through written exercises • Explore modern problem-solving perspectives, including basic graph concepts and algorithmic logic. The course guides you step-by-step through core theories, worked examples, and written practice problems. Designed for motivated beginners, students preparing for math contests, and logic enthusiasts, this course requires no prior advanced mathematics background. Start reading today to sharpen your analytical thinking and master competition mathematics.