Real Analysis I

A rigorous introduction to real analysis, this course treats topics in point set topology, function spaces, differentiability of functions on Euclidean spaces, and Fourier series. Among the many topics and theorems we investigate in detail will be connectedness and compactness, the Arzela-Ascoli theorem, the inverse and implicit function theorems, and L^2 and pointwise convergence of Fourier series. It is recommended that a student take MATH 1010 before attempting MATH 1630 .