Essential Foundations: Relations and Functions

Relations and functions are the fundamental building blocks of almost every advanced mathematical discipline, from algebra and calculus to computer science and data analysis. This course provides a thorough, text-based introduction to these concepts. You will gain a deep understanding of set theory notation, function types, and composition, enabling you to approach complex mathematical problems with clarity and precision. What you'll learn: * Understand the foundational concepts of sets, ordered pairs, and Cartesian products. * Learn the rigorous definitions and properties of binary relations, including equivalence and partial order relations. * Master the classification of functions (injective, surjective, bijective) and determine their domain, codomain, and range. * Practice the algebraic manipulation of functions, including composition, inverse functions, and piecewise definitions. * Apply techniques for sketching graphs of various function types, including transformations and absolute value functions. We begin with the necessary set theory background before moving into the formal definitions of relations and their types. The course then focuses extensively on functions, covering classification, algebraic operations, and essential graphing techniques through written examples and exercises. This course is designed for absolute beginners in advanced mathematics, high school students, or anyone needing a strong conceptual foundation before pursuing calculus or discrete math. No prior knowledge beyond basic algebra is required. Start building your essential mathematical framework today.