Foundations of Mathematics: Permutations, Combinations, and Induction

Struggling to make sense of complex counting rules and mathematical proofs? Understanding how to systematically count possibilities and prove mathematical statements is a fundamental milestone for any aspiring mathematician, programmer, or data analyst. This text-based course guides you step-by-step through the core principles of combinatorics and mathematical induction. You will transition from memorizing formulas to deeply understanding the underlying logic of permutations, combinations, and logical proofs, preparing you for advanced studies in algebra, probability, and computer science. What you'll learn: Understand the fundamental counting principle and when to apply permutations versus combinations; Master factorial notation and solve algebraic equations involving combinations; Apply mathematical induction to prove algebraic identities, inequalities, and divisibility properties; Explore modern connections between combinatorics and basic computer science algorithms; Practice solving structured word problems with clear, step-by-step logical reasoning. The course begins with foundational definitions and key terminology of set theory and counting principles. You will then progress through detailed written explanations, step-by-step proof walkthroughs, and practical exercises designed to build your mathematical confidence. This course is designed for beginners, high school students, and anyone looking to refresh their foundational algebra skills with no prior advanced mathematics required. Start building your mathematical foundation today.