18 100B Real Analysis Spring 2025

Do you want to move beyond computational calculus and understand the fundamental principles that underpin mathematical analysis? This course provides a rigorous foundation for grasping the deep theoretical underpinnings of calculus. By engaging with this course, you will not only master core concepts of real analysis but also cultivate the precision and logical reasoning required to construct and critique mathematical proofs, preparing you for more advanced theoretical work in mathematics or related quantitative fields. What you'll learn: * Understand the axiomatic foundations of real numbers and sequences. * Master concepts of limits, convergence, and continuity in rigorous detail. * Apply formal definitions to prove theorems related to differentiation and integration. * Develop robust proof-writing techniques for mathematical statements. * Explore the properties of metric spaces as a generalization of real analysis. * Grasp the foundational theory behind infinite series and their convergence. The course begins with the basic structure of the real number system and progresses through sequences, limits, and continuity. It then delves into differentiation, integration, and the generalization to metric spaces, all with a strong emphasis on formal proof construction and understanding. This course is designed for absolute beginners in real analysis and mathematical proof, requiring no prior experience with formal proofs. It is ideal for anyone seeking a deep, foundational understanding of calculus principles. Begin your journey into the elegant world of mathematical analysis and rigorous proof today.