## M365C REAL ANALYSIS I

**Prerequisite and degree relevance:** Either consent of Mathematics Advisor, or two of M341, 328K, 325K (Philosophy 313K may be substituted for M325K), with a grade of at least C-. Students who receive a grade of C in M325K or M328K are advised to take M361K before attempting M365C. Students who have received a grade of C- or better in Mathematics 365C may not take Mathematics 361K.

**Course description:** This course is an introduction to Analysis. Analysis, together with Algebra and Topology, form the central core of modern mathematics. Beginning with the notion of limit from calculus and continuing with ideas about convergence and the concept of function that arose with the description of heat flow using Fourier series, analysis is primarily concerned with infinite processes, the study of spaces and their geometry where these processes act and the application of differential and integral to problems that arise in geometry, pde, physics and probability.

A rigorous treatment of the real number system, Euclidean spaces, metric spaces, continuity of functions in metric spaces, differentiation and Riemann integration of real-valued functions of one real variable, and uniform convergence of sequences and series of functions.