A Basic Course in Real Analysis
Explore a comprehensive course on real analysis covering fundamental concepts and theorems. Delve into limit theorems, continuity of functions, and set theory, including finite, infinite, countable, and uncountable sets of real numbers. Examine metric spaces, open sets, and their properties. Study ordered sets, least upper bounds, and greatest lower bounds. Investigate compact sets, the Weierstrass Theorem, and the Heine-Borel Theorem. Learn about connected sets and explore sequences, including convergence, divergence, and Cauchy sequences. Analyze infinite series, convergence tests, and absolute convergence. Discover limits of functions, cluster points, and continuity concepts. Examine properties of continuous functions, including boundedness and max-min theorems. Investigate uniform and absolute continuity, types of discontinuities, and the relationship between continuity, compactness, and connectedness. Explore the equivalence of Dedekind and Cantor's theories, irrational numbers, and rational cuts. Gain a solid foundation in real analysis through lectures, tutorials, and exercises over the course of 1 day and 7 hours. Read more