This course explores topics in mathematical analysis of real numbers and functions of real variables. Topics covered in this course include: real numbers, metric spaces, topology of metric spaces, the contraction principle, continuity of functions on metric spaces, differentiability of real-valued functions, sequences and series of functions, continuity and differentiability of functions of several variables, and Riemann integration. Additional topics may include Euclidean spaces, normed spaces, functions of bounded variation, and Riemann-Stieltjes integrals.
Prerequisites
None