Foundations of Calculus: Sets, Inequalities, and Functions

Many students struggle with calculus not because of the calculus itself, but because their pre-calculus foundations are weak. Mastering the core concepts of sets, inequalities, and functions is the critical first step to unlocking advanced mathematical success. This text-based course guides you step-by-step through the essential mathematical machinery required for calculus. By reading clear, structured explanations and working through conceptual exercises, you will develop the analytical intuition needed to solve complex mathematical problems with ease. What you'll learn: - Understand the fundamental language of sets, relations, and coordinate systems. - Solve complex linear, quadratic, and rational inequalities step-by-step. - Analyze different types of functions, including their domains, ranges, and behaviors. - Apply algebraic transformations to manipulate and simplify mathematical expressions. - Identify how foundational algebra directly connects to limits, derivatives, and integrals. The course begins with the absolute basics of set theory and mathematical notation before progressing to inequalities and the deep study of various function types. You will build up your skills sequentially, preparing you fully for any standard calculus curriculum. This course is designed for beginners, high school students, and returning learners who want to build a flawless foundation before starting calculus. No prior calculus knowledge is required. Start reading today to bridge the gap between algebra and calculus.