Sets, Relations, and Functions for Competitive Mathematics

Succeeding in competitive mathematics exams requires a rock-solid grasp of core algebraic structures. This course provides a clear, text-based path to mastering the fundamental concepts of sets, relations, and functions, helping you build the logical reasoning needed to solve challenging exam problems. You will transition from basic definitions to analyzing complex mathematical maps and mapping behaviors. What you'll learn: Understand core set theory concepts, operations, and Venn diagram representations; Analyze types of relations including equivalence relations and partial orderings; Classify functions by examining injectivity, surjectivity, and bijectivity; Compute composite and inverse functions using step-by-step algebraic methods; Apply modern domain and range finding techniques to diverse function types; Practice solving exam-style algebraic problems with structured written explanations. The course begins with foundational definitions of sets and relations before progressing to advanced function properties and exam-focused problem-solving strategies. Designed specifically for beginners and aspiring engineering students, this course requires only a basic background in high school algebra. Start building your mathematical foundation today.