Foundations of Sets, Relations, and Functions

Understanding how data and numbers group, connect, and transform is the cornerstone of modern mathematics and computer science. This course clarifies the fundamental concepts of sets, relations, and functions through clear, step-by-step written explanations. You will transition from basic mathematical definitions to solving complex problems involving mappings, domain and range, and equivalence relations. By practicing with structured text-based exercises, you will build the analytical thinking required for advanced algebra, calculus, and logical programming. What you'll learn: Understand the core terminology of set theory, including subsets, power sets, and universal sets; Perform essential set operations such as union, intersection, difference, and complement; Define Cartesian products and construct various types of mathematical relations; Identify and analyze equivalence relations, reflexivity, symmetry, and transitivity; Master functions by calculating domain, codomain, range, and classifying injective, surjective, and bijective mappings; Apply these mathematical principles to logical thinking and modern database relational models. The course begins with foundational definitions and notation before moving systematically into the algebraic properties of relations and the behavior of mathematical functions. You will progress through structured text-based lessons and written practice problems designed to reinforce your conceptual understanding. This course is designed for beginners, students preparing for advanced math, and self-taught programmers looking to strengthen their discrete math foundations. No prior advanced mathematical knowledge is required. Start reading today to build a rock-solid mathematical foundation.