Foundations of Algebra: Sets, Relations, Functions, and Complex Numbers

To excel in advanced mathematics, engineering, or computer science, you must first build an unshakeable foundation in core algebraic concepts. This text-based course is designed to take you from basic mathematical definitions to a confident understanding of how sets, relations, and complex numbers govern modern mathematics. You will learn how to approach abstract mathematical thinking systematically, transforming how you analyze and solve complex problems. By working through clear, step-by-step written explanations and practical exercises, you will develop the logical reasoning skills needed for academic exams and real-world applications. What you'll learn: Understand the foundational terminology of set theory, operations, and Venn diagrams; Analyze relations and map functions with a clear grasp of domain, codomain, and range; Solve complex numbers by mastering imaginary units, conjugate properties, and polar representations; Apply the Principle of Mathematical Induction (PMI) to prove mathematical statements logically; Practice solving algebraic equations with structured, written examples. The course begins with the absolute basics of sets and notation, gradually building up to functions, complex numbers, and the formal proofs of mathematical induction. This course is designed specifically for beginners, high school students preparing for exams, and self-learners who want to build a strong mathematical foundation with no prior advanced knowledge required. Start reading today to unlock a deeper understanding of algebraic principles.