Abstract Algebra I: Foundations of Group and Ring Theory

Abstract algebra is the language of modern mathematics, unlocking deep patterns in symmetry, numbers, and geometry. This course provides a clear, step-by-step introduction to the core structures of algebra, designed to make abstract concepts intuitive and accessible. You will transition from basic computational arithmetic to structural mathematical thinking, learning how to define, analyze, and prove properties of abstract algebraic systems. What you'll learn: Understand foundational concepts of sets, relations, functions, and binary operations; Master the core properties of groups, subgroups, cyclic groups, and permutation groups; Apply Lagrange's theorem and analyze group homomorphisms and normal subgroups; Explore the basic structures of rings, integral domains, and fields; Practice constructing rigorous mathematical proofs using clear, step-by-step written examples. The course begins with essential definitions and foundational set theory before guiding you through the elegant theory of groups and introducing the basics of rings and fields. This course is designed for beginners, math enthusiasts, and undergraduate students looking for a solid, text-based foundation in abstract algebra, with no advanced mathematical prerequisites. Start exploring the beauty of abstract mathematical structures today.