18 014 Calculus With Theory Fall 2010

Many students learn how to solve calculus problems mechanically without ever understanding why the formulas actually work. This text-based course bridges the gap between routine calculation and true mathematical reasoning by introducing you to the theoretical foundations of calculus. You will learn to move beyond memorization and begin thinking like a mathematician. Starting with essential mathematical logic, set theory, and foundational definitions, you will explore the rigorous proofs that support limits, derivatives, and integrals. What you'll learn: Understand the formal definitions of limits, continuity, and differentiability; Apply mathematical induction and proof techniques to calculus theorems; Prove key concepts including the Mean Value Theorem and the Fundamental Theorem of Calculus; Analyze the rigorous construction of the real number system; Explore modern mathematical notation and basic set theory. The course begins with foundational concepts and terminology before guiding you step-by-step through the classic proofs of single-variable calculus. This course is designed for motivated beginners, analytical thinkers, and aspiring science or math students who want a deeper conceptual framework without needing prior advanced proof-writing experience. Start reading today to build a rock-solid mathematical foundation.