Foundational Mathematics: Relations and Functions

Relations and Functions are the bedrock of higher mathematics, computer science, and engineering, but the concepts can often seem abstract. This course demystifies these essential topics, providing a clear, step-by-step written guide to understanding mappings, domains, codomains, and inverse operations. By mastering the core principles, you will gain the mathematical fluency needed to tackle complex problems in calculus and discrete mathematics. What you'll learn: * Understand the rigorous definition of a relation, domain, codomain, and range using set theory notation. * Analyze and classify relations based on key properties: reflexivity, symmetry, transitivity, and equivalence. * Master the definitions of different function types, including injection (one-to-one), surjection (onto), and bijection. * Apply the concepts of function composition and determine the inverse of a given bijective function. * Practice solving problems involving binary operations and understanding their associativity and commutativity. The material begins with fundamental set theory concepts and progresses through the classification of relations before diving deeply into the types and composition of functions. The course emphasizes written practice to solidify conceptual understanding. This course is for absolute beginners, including high school students and those starting college-level mathematics or computer science. No prior knowledge of advanced math is required. Start building your essential mathematical foundation today.