Introduction to Real Analysis
An investigation into the mathematical foundations of calculus. Through lectures and exercises, visit fundamental concepts of mathematical analysis including logic, basic set theory, functions, number systems, order completeness of the real numbers and its consequences, sequences and series, topology of R^n, continuous functions, uniform convergence, compactness, and theory of differentiation and integration. Expand mathematical proof and writing skills through ample practice with LaTex to communicate mathematics effectively and demonstrate rigorous math thinking in preparation for more advanced courses.
The course is an introductory course and is designed to be accessible to students that are seeing proofs for the first time. The only prerequisite is an understanding of the results from single-variable calculus. Successful completion of undergraduate Calculus or equivalent courses is required to take this course. Multivariable calculus is not a prerequisite. If you are not sure about the prerequisite material, please contact the instructor at the beginning of the course.